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014597_file10 | #1750748) and Institutional review boards at each Family Cancer Clinic.
The WEHI study cohort comprised 82 CRC patients who were treated at the Royal Melbourne Hospital (Parkville, VIC, Australia) and Western Hospital Footscray (Footscray, VIC, Australia), between Jan 1, 1993, and Dec 31, 2009. Fresh-frozen tumour and matched normal tissue specimens were obtained at surgery and accessed via hospital tissue banks. All patients gave written informed consent, and the study was approved by human research ethics committees at both sites (HREC 12/19).
## Whole Exome Sequencing
For the ACCFR and ANGELS study participants, formalin-fixed paraffin embedded (FFPE) tissues from CRCs were macrodissected and DNA extracted using the QIAamp DNA FFPE Tissue kit (Qiagen, Hilden, Germany) using standard protocols. Peripheral blood-derived DNAs were extracted using DNeasy blood and tissue kit (Qiagen) and sequenced as germline references. Capture of the whole exome was performed using Agilent Clinical Research Exome V2 (Agilent, Santa Clara, CA) with sequencing performed on an Illumina NovaSeq 6000 (San Diego, CA) comprising 150bp paired-end reads at the Australian Genome Research Facility. Mean on-target coverage was \(280.5\pm 192.0\) (mean \(\pm\) SD) for FFPE tumour DNA samples and \(164.4\pm 79.0\) for blood-derived DNA samples. For the WEHI CRCs, exome-enrichment was performed using the TruSeq Exome Enrichment Kit (Illumina) and 100 bp paired-end read sequencing performed on an Illumina HiSeq 2000 at the Australian Genome Research Facility.
## Bioinformatics Pipeline and Analysis
WES data from each of the studies were processed using the same pipeline and analysis. Adapter sequences were trimmed from the raw FASTQ files using trimmomatic 0.38, then aligned to the GRCh37 human reference genome using BWA 0.7.12. Somatic single-nucleotide variants (SNVs) and short insertions and deletions (indels) were called with Strelka 2.9.2 using Illumina's recommended workflow. Tumour mutational signatures (TMS) were calculated using the pre-defined set of 67 SBS, 11 doublet, and 17 ID signatures published on the COSMIC website as version 3. Doublet variant counts were too low to reliably reconstruct doublet signatures, so were not analysed further in this study. MSI status was assessed using the method described by MSIseq.
The impact and suitability of experimental settings was explored by filtering somatic SNVs and indel variants based on depth of coverage (DP) in the tumour (calculated by the GATK tool AnnotateVcfWithBamDepth) and the somatic variant allele fraction (VAF). TMS were calculated for each sample at each filter setting. We quantitatively evaluated the ability of TMS to separate classes of samples at different filtering settings, for each relevant TMS. We calculated three measures of separation, which were then used to select the best TMS or combination of TMS. We calculated: 1) Fisher's linear discriminant (LD), which measures the ratio of "between-group" variability and "within-group" variability to find filtering settings that produce tightly clustered groups that are well-separated (described in detail below); 2) the difference between the means of the two groups; and 3) p-values were calculated using a one-sided t-test.
### P-value calculations
When determining the discriminatory utility of TMS (**Table 1, Supplementary Table 5**), p-values were calculated using one-sided t-tests. The test is one-sided given that we were only interested in identifying TMS showing presence of a signal (higher than average), rather than absence of a signal.
We reported adjusted p-values with Bonferroni correction applied. We performed 1095 individual tests for significance; consequently, a raw p-value must be below 4.6 x 10-5 to be considered significant. **Supplementary Table 5** indicates all TMS observed to have significant unadjusted p-values, with significant adjusted p-values highlighted.
AUC confidence intervals were calculated using the method described by Hanley and McNeil, unless the AUC was measured as 1.0, in which case this method does not provide a confidence interval. For these instances, the confidence interval was estimated using the method suggested by Obuchowski and Lieber.
### Distribution of samples in a group
To determine 5th and 95th percentiles shown on the discrimination graphs (**Figures 5c, 5d, 5c, 5f, 6a, 6b, 6c, 6d, 6e, 6f, 7a, 7b, 7c, 7d**), the calculated TMS from each CRC in the group were fitted to a beta distribution. The beta distribution is a continuous probability distribution defined on the interval from zero to one. Given that TMS values are normalized to a percentage, the possible range of TMS values is bounded, suggesting the beta distribution as an appropriate distribution.
### Determining confidence levels
The discrimination graphs report 5% and 95% confidence levels, indicating that if we observed a tumour with the specified combined SBS18 and SBS36 or combined ID2 and ID7 TMS percentage, based on our cohort of samples, the tumour would be 5% or 95% likely to belong to the biallelic _MUTYH_ or Lynch syndrome hereditary group of CRCs, respectively.
An equivalent question is, given a measured TMS \(x\) in a sample of CRCs, how likely is that TMS value to have been generated by each of the two possible source distributions: the distribution of TMS from CRCs _with_ the syndrome of interest, or the distribution of TMS from CRCs _without_ the syndrome of interest? Here, we label the distribution of values with the syndrome and those without the syndrome _D1_ and _D2_ respectively. We assume that both _D1_ and _D2_ follow a beta distribution as discussed previously: _D1_ _- Beta(a1, b12)_ and _D2_ _- Beta(a2, b22)_.
Given the two overlapping possible distributions from which the point may have originated, we aim to calculate the conditional probability _P(D=D1|X=x)_. Given that the probability of observing an exact value is zero, we instead calculate the probability of observing \(x\) within a range, that is _P(X=x+d|D=D1)_, which can be calculated as the difference in the cumulative distribution function (cdf) at _x+d_ and _x-d_. i.e. _P(X=x+d|D=D1)=cdf(x+d, D1)_ - cdf(x-d, D1)_.
The application of Bayes' theorem enables the calculation of _P(X=x+d|D=D1)_ in terms of the cdf of each distribution:
\[P(D_{1}|X=x\pm\delta) =\frac{P(X=x\pm\delta|D_{1})P(D_{1})}{P(X=x\pm\delta)}\] \[=\frac{cdf(X=x\pm\delta,D_{1})P(D_{1})}{P(X=x\pm\delta|D_{1})P(D_{ 1})+P(X=x\pm\delta|D_{2})P(X=x\pm\delta|D_{2})}\]\[=\frac{cdf(X=x\pm\delta,D_{1})P(D_{1})}{cdf(X=x\pm\delta,D_{1})P(D_{1})+cdf(X=x\pm \delta,D_{2})P(D_{2})}\]
This approach requires prior probabilities to be assigned indicating the likelihood of a tumour belonging to each of the two distributions, given no prior information. For this analysis we assume an unbiased prior probability of \(P(D_{1})=P(D_{2})=0.5\).
We then calculated the confidence levels of interest by considering the probability at TMS values of \(x\) across each possible TMS value.
#### Fisher's Linear Discriminant
## Table 1
i.e. given groups A and B with means \(\mu_{\text{A}}\) and \(\mu_{\text{B}}\) and standard deviations \(\sigma_{\text{A}}\) and \(\sigma_{\text{B}}\), LD is given by:
\[LD=\frac{\mu_{A}+\mu_{B}}{\frac{1}{2}(\sigma_{A}+\sigma_{B})}\]
#### Selection of the best combination of TMS
We applied a greedy algorithm based on stepwise forward selection to find the best combination of TMS to identify the hereditary CRC group of interest while reducing the likelihood of overfitting.
Starting with each individual COSMIC V3 TMS (excluding artefact signatures), we select the TMS with the highest AUC that also has a minimum difference in means between the groups of at least 10%. We then iterate by assessing the AUC when each possible TMS is added to the current best combination of TMS, provided this new combination improves the AUC by at least 10%, and the absolute difference in means between the groups also improves by at least 10%. If the AUC has reached the maximum possible value (100%), then instead the margin between the groups must improve by at least 10%. These requirements ensure that only TMS with a strong additive benefit with the hereditary group are selected. Although it is possible that TMS with legitimate but weaker associations are excluded with this method, this stringency reduces the likelihood of spurious TMS arising due to overfitting.
As an additional verification of the selection algorithm, we employed logistic regression with L1 penalty to select TMS, an approach that favours simple and interpretable models. This algorithm selected the same set of TMS that were selected by forward selection; that is, SBS18 and SBS36 were selected to best differentiate biallelic _MUTYH_ carrier CRCs, and ID2 and ID7 were selected to best differentiate both Lynch syndrome-related CRCs from MMRp CRCs, and MMRd from MMRp CRCs. This algorithm did not select any TMS when attempting to classify Lynch syndrome from MMRd CRCs in the discovery set, which is concordant with the findings from the forward selection method.
### Comparison with The Cancer Genome Atlas (TCGA)
The non-hereditary ("sporadic") control groups from the ACCFR included in the study were younger than the mean age of diagnosis in the general population. To compare our hereditary CRC results with CRCs that are more reflective of the age at diagnosis of CRC in the general population we included TCGA colon adenocarcinomas (COAD) and rectal adenocarcinoma (READ) tumours and stratified them as MMR-proficient (MMRp) and MMR-deficient (MMRd).
### Determining MMR status from the TCGA COAD dataset
MSI status was determined for 399 COAD tumours and 137 READ tumours using MSIseq, with thresholds determined using published MSI results. Overall, 446 tumours (318 COAD, 128 READ) were classified as MSS or MSI-L with MSIseq values \(<\)0.18, which formed the group of TCGA MMRp controls, and 74 tumours (70 COAD, 4 READ) were classified as MSI-H with MSIseq values \(>\)1.9.
For the 74 MSI-H tumours, we determined which of these resulted from hypermethylation of the _MLH1_ gene promoter using either TCGA Infinium HM450k methylation data, or Infinium HM27k methylation data. We considered a tumour to be _MLH1_ hypermethylated if it met _both_ of the following conditions:
1. For HM450k data, the mean value of the _MLH1_ probes cg23658326, cg11600697, cg21490561 was greater than 0.2. For HM27k data, the value of the _MLH1_ probe cg00893636 was greater than 0.2; and
2. At least three of the genes _CACNA1G, RUNX3, SOCS1, NEUROG1_ and _IGF2_ exhibited mean methylation levels above 0.2, thus indicating high levels of CIMP (CpG Island Methylator Phenotype).
This method identified 52 MMRd tumours that showed _MLH1_ hypermethylation and high levels of CIMP and were thus classified as TCGA MMRd controls for this study.
The mean age of diagnosis of the TCGA MMRp and MMRd groups is 65.7\(\pm\)12.4 years and 74.6\(\pm\)10.7 years, respectively (**Supplementary Table 2**).
#### Variant Calling
Somatic SNVs and indels for the TCGA dataset were generated using Mutect2, then filtered with our established thresholds of minimum depth 50 and minimum variant allele fraction 0.1, to match the filtering strategy employed for the other CRCs in the study. We then generated TMS for each tumour as previously described.
#### Validation of hereditary CRC mutational signatures using TCGA tumours
To further validate our hereditary CRC TMS findings, we tested the effect of the later-onset and predominantly fresh-frozen tumours from TCGA controls. We repeated our analysis, replacing the MMRp cohort (n=160) with the TCGA MMRp cohort (n=446), and the MMRd cohort (n=25) with the TCGA MMRd cohort (n=52).
All statistical analyses were performed using Python 3.6.1. We utilised the NumPy scientific programming package v1.16.2 for numerical processing, SciPy v1.1.0 for performing the statistical analyses, as well as scikit-learn v0.20.2 for machine learning and classification algorithms.
AUC was calculated using the Python software package scikit-learn, specifically, the method _sklearn.metrics.roc_auc_score_, which accepts as arguments the calculated TMS values for the hereditary CRCs, and the calculated TMS values for the control CRCs, to generate an AUC value based on the trapezoid method.
## Supplementary Table 1.
Metadata and clinical observations associated with each CRC included in this study from the ACCFR, OCCFR, ANGELS and WEHI cohorts.
## Supplementary Table 2.** Clinical data obtained from TCGA for the colon adenocarcinoma (COAD) and rectal adenocarcinomas (READ) tumours included in this study. MMR status (proficient or deficient) was determined from published MSI status generated by MSIseq. MMRd CRCs were all determined to result from hypermethylation of the _MLH1_ gene promoter as described in the **Supplementary Methods.
## Supplementary Table 2.** Clinical data obtained from TCGA for the colon adenocarcinoma (COAD) and rectal adenocarcinomas (READ) tumours included in this study. MMR status (proficient or deficient) was determined from published MSI status generated by MSIseq. MMRd CRCs were all determined to result from hypermethylation of the _MLH1_ gene promoter as described in the **Supplementary Methods.
\begin{tabular}{l|c|c|c|c|c|c|c|c} \hline TCGA-A6-5664 & Proficient & 80 & T4a & Cecum & MALE & Colon Adenocarcinoma & C18.2 & 0.00 \\ \hline TCGA-A6-5666 & Proficient & 78 & T4b & Sigmoid Colon & MALE & Colon Adenocarcinoma & C18.9 & 0.09 \\ \hline TCGA-A6-5667 & Proficient & 40 & T3 & Sigmoid Colon & FEMALE & Colon Adenocarcinoma & C18.7 & 0.09 \\ \hline TCGA-A6-6137 & Proficient & 55 & T3 & Hepatic Flexure & MALE & Colon Adenocarcinoma & C18.2 & 0.07 \\ \hline TCGA-A6-6138 & Proficient & 61 & T2 & Cecum & MALE & Colon Adenocarcinoma & C18.0 & 0.04 \\ \hline TCGA-A6-6142 & Proficient & 56 & T3 & Sigmoid Colon & FEMALE & Colon Adenocarcinoma & C18.7 & 0.02 \\ \hline TCGA-A6-6648 & Proficient & 56 & T3 & NA & MALE & Colon Adenocarcinoma & C18.6 & 0.00 \\ \hline TCGA-A6-6649 & Proficient & 66 & T3 & NA & MALE & Colon Adenocarcinoma & C18.2 & 0.02 \\ \hline TCGA-A6-6650 & Proficient & 69 & T3 & NA & FEMALE & Colon Adenocarcinoma & C18.2 & 0.09 \\ \hline TCGA-A6-6651 & Proficient & 55 & T3 & Transverse Colon & FEMALE & Colon Adenocarcinoma & C18.9 & 0.04 \\ \hline TCGA-A6-6652 & Proficient & 59 & T3 & Sigmoid Colon & MALE & Colon Adenocarcinoma & C18.7 & 0.07 \\ \hline TCGA-A6-6654 & Proficient & 65 & T3 & Descending Colon & FEMALE & Colon Adenocarcinoma & C18.9 & 0.04 \\ \hline TCGA-A6-6782 & Proficient & 82 & T4a & NA & MALE & Colon Adenocarcinoma & C18.2 & 0.02 \\ \hline TCGA-A6-A566 & Proficient & 55 & T4 & Descending Colon & FEMALE & Colon Mucinous Adenocarcinoma & C18.6 & 0.07 \\ \hline TCGA-A6-A567 & Proficient & 56 & T3 & Sigmoid Colon & MALE & Colon Adenocarcinoma & C18.7 & 0.02 \\ \hline TCGA-A6-A56B & Proficient & 57 & T3 & Sigmoid Colon & MALE & Colon Adenocarcinoma & C18.7 & 0.04 \\ \hline TCGA-A3-4388 & Proficient & 58 & T3 & Sigmoid Colon & MALE & Colon Adenocarcinoma & C19 & 0.02 \\ \hline TCGA-A4-3489 & Proficient & 75 & T3 & Sigmoid Colon & MALE & Colon Adenocarcinoma & C18.9 & 0.04 \\ \hline TCGA-A4-3495 & Proficient & 79 & T2 & Hepatic Flexure & MALE & Colon Adenocarcinoma & C18.2 & 0.02 \\ \hline TCGA-A4-3496 & Proficient & 83 & T3 & Ascending Colon & FEMALE & Colon Adenocarcinoma & C18.2 & 0.13 \\ \hline TCGA-A4-3502 & Proficient & 73 & T2 & Transverse Colon & MALE & Colon Adenocarcinoma & C18.9 & 0.09 \\ \hline TCGA-A4-3506 & Proficient & 77 & T2 & Hepatic Flexure & MALE & Colon Adenocarcinoma & C18.9 & 0.13 \\ \hline TCGA-A4-3509 & Proficient & 54 & T3 & Sigmoid Colon & FEMALE & Colon Adenocarcinoma & C18.7 & 0.04 \\ \hline TCGA-A4-3510 & Proficient & 70 & T3 & Transverse Colon & MALE & Colon Adenocarcinoma & C18.2 & 0.11 \\ \hline TCGA-A4-3511 & Proficient & 64 & T4 & Sigmoid Colon & MALE & Colon Adenocarcinoma & C18.9 & 0.02 \\ \hline TCGA-A4-3530 & Proficient & 80 & T2 & Cecum & MALE & Colon Adenocarcinoma & C18.2 & 0.07 \\ \hline TCGA-A4-3655 & Proficient & 68 & T3 & Sigmoid Colon & MALE & Colon Adenocarcinoma & C18.7 & 0.02 \\ \hline TCGA-A4-3660 & Proficient & 51 & T3 & Sigmoid Colon & FEMALE & Colon Adenocarcinoma & C18.9 & 0.09 \\ \hline TCGA-A4-3662 & Proficient & 80 & T4 & Sigmoid Colon & FEMALE & Colon Adenocarcinoma & C18.9 & 0.02 \\ \hline TCGA-A4-3664 & Proficient & 74 & T3 & Cecum & FEMALE & Colon Adenocarcinoma & C18.2 & 0.04 \\ \hline TCGA-A4-3666 & Proficient & 68 & T3 & Cecum & MALE & Colon Adenocarcinoma & C18.9 & 0.00 \\ \hline TCGA-A4-3667 & Proficient & 36 & T2 & Sigmoid Colon & FEMALE & Colon Adenocarcinoma & C18.9 & 0.02 \\ \hline TCGA-A4-3673 & Proficient & 53 & T3 & Transverse Colon & FEMALE & Colon Adenocarcinoma & C18.4 & 0.09 \\ \hline TCGA-A4-3675 & Proficient & 84 & T3 & Hepatic Flexure & MALE & Colon Adenocarcinoma & C18.2 & 0.09 \\ \hline TCGA-A4-3678 & Proficient & 60 & T2 & Sigmoid Colon & FEMALE & Colon Adenocarcinoma & C18.7 & 0.04 \\ \hline \end{tabular}
\begin{tabular}{l|c|c|c|c|c|c|c|c} \hline TCGA-AA-3679 & Proficient & 59 & T3 & Descending Colon & MALE & Colon Adenocarcinoma & C18.9 & 0.00 \\ \hline TCGA-AA-3680 & Proficient & 67 & T4 & Cecum & FEMALE & Colon Adenocarcinoma & C18.0 & 0.02 \\ \hline TCGA-AA-3681 & Proficient & 77 & T3 & Cecum & FEMALE & Colon Adenocarcinoma & C18.0 & 0.09 \\ \hline TCGA-AA-3684 & Proficient & 65 & T4 & Cecum & FEMALE & Colon Adenocarcinoma & C18.0 & 0.02 \\ \hline TCGA-AA-3685 & Proficient & 69 & T3 & Sigmoid Colon & MALE & Colon Adenocarcinoma & C18.9 & 0.02 \\ \hline TCGA-AA-3688 & Proficient & 80 & T3 & Sigmoid Colon & MALE & Colon Adenocarcinoma & C18.9 & 0.02 \\ \hline TCGA-AA-3692 & Proficient & 47 & T3 & Splenic Flexure & FEMALE & Colon Mucinous Adenocarcinoma & C18.9 & 0.02 \\ \hline TCGA-AA-3693 & Proficient & 77 & T4 & Sigmoid Colon & FEMALE & Colon Adenocarcinoma & C18.7 & 0.00 \\ \hline TCGA-AA-3695 & Proficient & 63 & T3 & Cecum & FEMALE & Colon Adenocarcinoma & C18.0 & 0.09 \\ \hline TCGA-AA-3696 & Proficient & 75 & T3 & Sigmoid Colon & FEMALE & Colon Adenocarcinoma & C18.7 & 0.07 \\ \hline TCGA-AA-3697 & Proficient & 77 & T3 & Sigmoid Colon & MALE & Colon Adenocarcinoma & C18.9 & 0.13 \\ \hline TCGA-AA-3712 & Proficient & 65 & T3 & Descending Colon & MALE & Colon Adenocarcinoma & C18.6 & 0.07 \\ \hline TCGA-AA-3812 & Proficient & 82 & T3 & Sigmoid Colon & FEMALE & Colon Adenocarcinoma & C18.7 & 0.04 \\ \hline TCGA-AA-3814 & Proficient & 85 & T3 & Ascending Colon & FEMALE & Colon Adenocarcinoma & C18.9 & 0.02 \\ \hline TCGA-AA-3818 & Proficient & 78 & T3 & Hepatic Flexure & FEMALE & Colon Adenocarcinoma & C18.9 & 0.11 \\ \hline TCGA-AA-3819 & Proficient & 41 & T3 & Sigmoid Colon & FEMALE & Colon Adenocarcinoma & C18.9 & 0.02 \\ \hline TCGA-AA-3831 & Proficient & 66 & T3 & Sigmoid Colon & MALE & Colon Adenocarcinoma & C18.9 & 0.00 \\ \hline TCGA-AA-3837 & Proficient & 67 & T3 & Hepatic Flexure & MALE & Colon Mucinous Adenocarcinoma & C18.9 & 0.13 \\ \hline TCGA-AA-3841 & Proficient & 66 & T3 & Sigmoid Colon & MALE & Colon Adenocarcinoma & C18.9 & 0.04 \\ \hline TCGA-AA-3842 & Proficient & 51 & T2 & Sigmoid Colon & MALE & Colon Adenocarcinoma & C18.9 & 0.04 \\ \hline TCGA-AA-3844 & Proficient & 78 & T3 & Sigmoid Colon & FEMALE & Colon Adenocarcinoma & C18.9 & 0.00 \\ \hline TCGA-AA-3846 & Proficient & 74 & T3 & Sigmoid Colon & FEMALE & Colon Adenocarcinoma & C18.7 & 0.04 \\ \hline TCGA-AA-3848 & Proficient & 82 & T3 & Sigmoid Colon & FEMALE & Colon Adenocarcinoma & C18.7 & 0.02 \\ \hline TCGA-AA-3850 & Proficient & 74 & T2 & Transverse Colon & MALE & Colon Adenocarcinoma & C18.4 & 0.02 \\ \hline TCGA-AA-3851 & Proficient & 74 & T3 & Ascending Colon & MALE & Colon Adenocarcinoma & C18.9 & 0.18 \\ \hline TCGA-AA-3852 & Proficient & 88 & T3 & Transverse Colon & MALE & Colon Mucinous Adenocarcinoma & C18.9 & 0.11 \\ \hline TCGA-AA-3854 & Proficient & 71 & T2 & Sigmoid Colon & FEMALE & Colon Mucinous Adenocarcinoma & C18.9 & 0.02 \\ \hline TCGA-AA-3855 & Proficient & 72 & T2 & Sigmoid Colon & MALE & Colon Adenocarcinoma & C18.9 & 0.02 \\ \hline TCGA-AA-3856 & Proficient & 59 & T3 & Sigmoid Colon & MALE & Colon Adenocarcinoma & C18.9 & 0.02 \\ \hline TCGA-AA-3858 & Proficient & 67 & T2 & Sigmoid Colon & MALE & Colon Adenocarcinoma & C18.9 & 0.02 \\ \hline TCGA-AA-3860 & Proficient & 53 & T3 & Sigmoid Colon & FEMALE & Colon Adenocarcinoma & C18.7 & 0.02 \\ \hline TCGA-AA-3861 & Proficient & 72 & T3 & Cecum & MALE & Colon Adenocarcinoma & C18.0 & 0.11 \\ \hline TCGA-AA-3862 & Proficient & 82 & T3 & Transverse Colon & MALE & Colon Adenocarcinoma & C18.2 & 0.00 \\ \hline TCGA-AA-3866 & Proficient & 78 & T2 & Cecum & FEMALE & Colon Adenocarcinoma & C18.9 & 0.02 \\ \hline TCGA-AA-3867 & Proficient & 74 & T3 & Sigmoid Colon & MALE & Colon Adenocarcinoma & C18.7 & 0.02 \\ \hline TCGA-AA-3869 & Proficient & 76 & T4 & Cecum & MALE & Colon Adenocarcinoma & C18.0 & 0.04 \\ \hline \end{tabular}
\begin{tabular}{l|c|c|c|c|c|c|c|c} \hline TCGA-AA-3870 & Proficient & 71 & T3 & Ascending Colon & FEMALE & Colon Adenocarcinoma & C18.2 & 0.04 \\ \hline TCGA-AA-3872 & Proficient & 45 & T4 & Sigmoid Colon & MALE & Colon Adenocarcinoma & C18.9 & 0.07 \\ \hline TCGA-AA-3875 & Proficient & 78 & T1 & Ascending Colon & FEMALE & Colon Adenocarcinoma & C18.2 & 0.02 \\ \hline TCGA-AA-3930 & Proficient & 66 & T3 & Ascending Colon & MALE & Colon Adenocarcinoma & C18.2 & 0.09 \\ \hline TCGA-AA-3939 & Proficient & 83 & T3 & Ascending Colon & MALE & Colon Adenocarcinoma & C18.9 & 0.07 \\ \hline TCGA-AA-3941 & Proficient & 84 & T4 & Ascending Colon & FEMALE & Colon Adenocarcinoma & C18.9 & 0.11 \\ \hline TCGA-AA-3952 & Proficient & 68 & T3 & Desending Colon & MALE & Colon Adenocarcinoma & C18.6 & 0.02 \\ \hline TCGA-AA-3955 & Proficient & 38 & T2 & Desending Colon & MALE & Colon Adenocarcinoma & C18.9 & 0.02 \\ \hline TCGA-AA-3956 & Proficient & 65 & T3 & Cecum & MALE & Colon Adenocarcinoma & C18.9 & 0.02 \\ \hline TCGA-AA-3967 & Proficient & 77 & T3 & Sigmoid Colon & MALE & Colon Adenocarcinoma & C18.9 & 0.02 \\ \hline TCGA-AA-3968 & Proficient & 55 & T2 & Sigmoid Colon & FEMALE & Colon Adenocarcinoma & C18.7 & 0.07 \\ \hline TCGA-AA-3971 & Proficient & 58 & T3 & Sigmoid Colon & MALE & Colon Adenocarcinoma & C18.9 & 0.00 \\ \hline TCGA-AA-3972 & Proficient & 72 & T3 & Sigmoid Colon & MALE & Colon Adenocarcinoma & C18.7 & 0.09 \\ \hline TCGA-AA-3973 & Proficient & 69 & T4 & Sigmoid Colon & MALE & Colon Adenocarcinoma & C18.9 & 0.07 \\ \hline TCGA-AA-3975 & Proficient & 80 & T2 & Sigmoid Colon & MALE & Colon Adenocarcinoma & C18.9 & 0.02 \\ \hline TCGA-AA-3976 & Proficient & 70 & T2 & Sigmoid Colon & MALE & Colon Adenocarcinoma & C19 & 0.02 \\ \hline TCGA-AA-3979 & Proficient & 84 & T3 & Sigmoid Colon & MALE & Colon Adenocarcinoma & C18.7 & 0.02 \\ \hline TCGA-AA-3980 & Proficient & 89 & T2 & Sigmoid Colon & FEMALE & Colon Adenocarcinoma & C18.9 & 0.04 \\ \hline TCGA-AA-3982 & Proficient & 75 & T3 & Sigmoid Colon & MALE & Colon Adenocarcinoma & C18.9 & 0.02 \\ \hline TCGA-AA-3986 & Proficient & 73 & T2 & Transverse Colon & MALE & Colon Adenocarcinoma & C18.9 & 0.04 \\ \hline TCGA-AA-3989 & Proficient & 84 & T3 & Transverse Colon & MALE & Colon Adenocarcinoma & C18.9 & 0.00 \\ \hline TCGA-AA-3994 & Proficient & 69 & T3 & Transverse Colon & MALE & Colon Mucinous Adenocarcinoma & C18.9 & 0.07 \\ \hline TCGA-AA-A004 & Proficient & 76 & T3 & Sigmoid Colon & MALE & Colon Adenocarcinoma & C18.7 & 0.00 \\ \hline TCGA-AA-AA01C & Proficient & 57 & T3 & Sigmoid Colon & FEMALE & Colon Adenocarcinoma & C18.2 & 0.00 \\ \hline TCGA-AA-AA01I & Proficient & 76 & T2 & Sigmoid Colon & MALE & Colon Adenocarcinoma & C18.7 & 0.02 \\ \hline TCGA-AA-A01S & Proficient & 47 & T3 & Sigmoid Colon & FEMALE & Colon Adenocarcinoma & C18.7 & 0.04 \\ \hline TCGA-AA-A01T & Proficient & 63 & T3 & Sigmoid Colon & FEMALE & Colon Adenocarcinoma & C18.7 & 0.02 \\ \hline TCGA-AA-A01V & Proficient & 59 & T2 & Cecum & MALE & Colon Adenocarcinoma & C18.0 & 0.02 \\ \hline TCGA-AA-AA-01X & Proficient & 80 & T2 & Sigmoid Colon & FEMALE & Colon Adenocarcinoma & C18.7 & 0.00 \\ \hline TCGA-AA-AA01Z & Proficient & 68 & T3 & Ascending Colon & MALE & Colon Adenocarcinoma & C18.2 & 0.02 \\ \hline TCGA-AA-A024 & Proficient & 81 & T3 & Desending Colon & MALE & Colon Mucinous Adenocarcinoma & C18.6 & 0.00 \\ \hline TCGA-AA-AA-02E & Proficient & 82 & T3 & Cecum & FEMALE & Colon Adenocarcinoma & C18.0 & 0.07 \\ \hline TCGA-AA-AA-02F & Proficient & 68 & T3 & Sigmoid Colon & FEMALE & Colon Adenocarcinoma & C18.7 & 0.02 \\ \hline TCGA-AA-AA02H & Proficient & 74 & T3 & Sigmoid Colon & FEMALE & Colon Adenocarcinoma & C18.7 & 0.00 \\ \hline TCGA-AA-AA-02K & Proficient & 50 & T4 & Ascending Colon & MALE & Colon Adenocarcinoma & C18.2 & 0.11 \\ \hline \end{tabular}
\begin{tabular}{l|c|c|c|c|c|c|c|c} \hline TCGA-AA-A02O & Proficient & 82 & T3 & Transverse Colon & MALE & Colon Adenocarcinoma & C18.4 & 0.00 \\ \hline TCGA-AA-A02W & Proficient & 73 & T2 & Sigmoid Colon & FEMALE & Colon Adenocarcinoma & C18.7 & 0.00 \\ \hline TCGA-AA-A02Y & Proficient & 73 & T2 & Cecum & MALE & Colon Adenocarcinoma & C18.0 & 0.02 \\ \hline TCGA-AA-A03F & Proficient & 90 & T3 & Cecum & FEMALE & Colon Mucinous Adenocarcinoma & C18.0 & 0.00 \\ \hline TCGA-AA-A03J & Proficient & 65 & T2 & Sigmoid Colon & FEMALE & Colon Adenocarcinoma & C18.7 & 0.02 \\ \hline TCGA-AD-6548 & Proficient & 81 & T2 & Splenic Flexure & FEMALE & Colon Adenocarcinoma & C18.5 & 0.02 \\ \hline TCGA-AD-6888 & Proficient & 73 & T3 & Hepatic Flexure & MALE & Colon Adenocarcinoma & C18.2 & 0.04 \\ \hline TCGA-AD-6890 & Proficient & 65 & T1 & Ascending Colon & MALE & Colon Adenocarcinoma & C18.2 & 0.11 \\ \hline TCGA-AD-6990 & Proficient & 84 & T4a & Cecum & MALE & Colon Mucinous Adenocarcinoma & C18.9 & 0.02 \\ \hline TCGA-AD-6961 & Proficient & 78 & T3 & Cecum & MALE & Colon Adenocarcinoma & C18.0 & 0.04 \\ \hline TCGA-AD-6963 & Proficient & 58 & T3 & Ascending Colon & MALE & Colon Adenocarcinoma & C18.2 & 0.02 \\ \hline TCGA-AD-6965 & Proficient & 62 & T4a & Cecum & MALE & Colon Adenocarcinoma & C18.0 & 0.07 \\ \hline TCGA-AD-ASEK & Proficient & 51 & T2 & Ascending Colon & MALE & Colon Adenocarcinoma & C18.2 & 0.02 \\ \hline TCGA-AU-3779 & Proficient & 80 & T3 & Rectosigmoid Junction & FEMALE & Colon Adenocarcinoma & C18.7 & 0.00 \\ \hline TCGA-AY-4070 & Proficient & 50 & T3 & Cecum & FEMALE & Colon Adenocarcinoma & C18.2 & 0.02 \\ \hline TCGA-AY-4071 & Proficient & 63 & T1 & [Not Available] & FEMALE & INet Available] & C18.7 & 0.00 \\ \hline TCGA-AY-5543 & Proficient & 65 & T3 & Ascending Colon & FEMALE & Colon Adenocarcinoma & C18.2 & 0.07 \\ \hline TCGA-AY-6196 & Proficient & 47 & T3 & Cecum & MALE & Colon Mucinous Adenocarcinoma & C18.2 & 0.09 \\ \hline TCGA-AY-6386 & Proficient & 66 & T3 & Cecum & FEMALE & Colon Adenocarcinoma & C18.0 & 0.16 \\ \hline TCGA-AY-A54L & Proficient & 74 & T2 & Transverse Colon & FEMALE & Colon Adenocarcinoma & C18.3 & 0.11 \\ \hline TCGA-AY-A69D & Proficient & 55 & T3 & Transverse Colon & FEMALE & Colon Adenocarcinoma & C18.4 & 0.07 \\ \hline TCGA-AY-A71X & Proficient & 54 & T2 & Cecum & FEMALE & Colon Adenocarcinoma & C18.0 & 0.09 \\ \hline TCGA-AY-A8Y & Proficient & 44 & T3 & Sigmoid Colon & MALE & Colon Adenocarcinoma & C18.7 & 0.00 \\ \hline TCGA-AZ-4308 & Proficient & 47 & T3 & Sigmoid Colon & FEMALE & Colon Adenocarcinoma & C18.7 & 0.00 \\ \hline TCGA-AZ-4323 & Proficient & 37 & T4 & Cecum & MALE & Colon Adenocarcinoma & C18.0 & 0.02 \\ \hline TCGA-AZ-4614 & Proficient & 71 & T4a & [Not Available] & FEMALE & Colon Adenocarcinoma & C18.0 & 0.07 \\ \hline TCGA-AZ-4616 & Proficient & 82 & T3 & Cecum & FEMALE & Colon Adenocarcinoma & C18.0 & 0.04 \\ \hline TCGA-AZ-4681 & Proficient & 79 & T3 & Ascending Colon & FEMALE & Colon Adenocarcinoma & C18.2 & 0.04 \\ \hline TCGA-AZ-4682 & Proficient & 61 & T3 & Sigmoid Colon & FEMALE & Colon Adenocarcinoma & C19 & 0.02 \\ \hline TCGA-AZ-4684 & Proficient & 49 & T3 & [Not Available] & MALE & Colon Adenocarcinoma & C19 & 0.00 \\ \hline TCGA-AZ-5403 & Proficient & 43 & T3 & Sigmoid Colon & MALE & Colon Adenocarcinoma & C18.6 & 0.00 \\ \hline TCGA-AZ-5407 & Proficient & 51 & T1 & Cecum & FEMALE & Colon Adenocarcinoma & C18.0 & 0.00 \\ \hline TCGA-AZ-6599 & Proficient & 72 & T2 & Cecum & MALE & Colon Adenocarcinoma & C18.0 & 0.04 \\ \hline TCGA-AZ-6600 & Proficient & 64 & T4 & Hepatic Flexure & MALE & Colon Adenocarcinoma & C18.2 & 0.13 \\ \hline TCGA-AZ-6603 & Proficient & 77 & T2 & Sigmoid Colon & FEMALE & Colon Adenocarcinoma & C18.7 & 0.09 \\ \hline TCGA-AZ-6605 & Proficient & 77 & T4 & Ascending Colon & MALE & Colon Adenocarcinoma & C18.2 & 0.13 \\ \hline \end{tabular}
\begin{tabular}{l|c|c|c|c|c|c|c|c} \hline TCGA-AZ-6606 & Proficient & 81 & T4 & Cecum & MALE & Colon Adenocarcinoma & C18.0 & 0.00 \\ \hline TCGA-AZ-6607 & Proficient & 69 & T4 & Sigmoid Colon & MALE & Colon Adenocarcinoma & C18.7 & 0.04 \\ \hline TCGA-AZ-6608 & Proficient & 55 & T2 & Sigmoid Colon & FEMALE & Colon Adenocarcinoma & C18.7 & 0.11 \\ \hline TCGA-CA-5254 & Proficient & 42 & T3 & Transverse Colon & FEMALE & Colon Adenocarcinoma & C18.9 & 0.07 \\ \hline TCGA-CA-5255 & Proficient & 45 & T3 & Ascending Colon & MALE & Colon Adenocarcinoma & C18.9 & 0.00 \\ \hline TCGA-CA-5256 & Proficient & 54 & T3 & Hepatic Flexure & FEMALE & Colon Adenocarcinoma & C18.9 & 0.07 \\ \hline TCGA-CA-5796 & Proficient & 52 & T3 & Ascending Colon & FEMALE & Colon Mucinous Adenocarcinoma & C18.2 & 0.09 \\ \hline TCGA-CA-5797 & Proficient & 56 & T3 & Sigmoid Colon & MALE & Colon Adenocarcinoma & C18.9 & 0.04 \\ \hline TCGA-CA-6715 & Proficient & 63 & T3 & Sigmoid Colon & MALE & Colon Adenocarcinoma & C18.7 & 0.04 \\ \hline TCGA-CA-6716 & Proficient & 65 & T3 & Ascending Colon & MALE & Colon Adenocarcinoma & C18.2 & 0.16 \\ \hline TCGA-CA-6719 & Proficient & 77 & T3 & Desending Colon & MALE & Colon Adenocarcinoma & C18.6 & 0.07 \\ \hline TCGA-CK-4947 & Proficient & 46 & T4 & Sigmoid Colon & FEMALE & Colon Adenocarcinoma & C18.7 & 0.07 \\ \hline TCGA-CK-4948 & Proficient & 45 & T3 & Sigmoid Colon & FEMALE & Colon Adenocarcinoma & C18.7 & 0.04 \\ \hline TCGA-CK-4950 & Proficient & 68 & T3 & Cecum & FEMALE & Colon Mucinous Adenocarcinoma & C18.0 & 0.13 \\ \hline TCGA-CK-4952 & Proficient & 48 & T4 & Ascending Colon & FEMALE & Colon Mucinous Adenocarcinoma & C18.2 & 0.09 \\ \hline TCGA-CK-5912 & Proficient & 81 & T2 & Cecum & MALE & Colon Adenocarcinoma & C18.2 & 0.02 \\ \hline TCGA-CK-5914 & Proficient & 81 & T3 & Sigmoid Colon & MALE & Colon Adenocarcinoma & C18.7 & 0.07 \\ \hline TCGA-CK-5915 & Proficient & 63 & T2 & Sigmoid Colon & MALE & Colon Adenocarcinoma & C18.7 & 0.07 \\ \hline TCGA-CK-6748 & Proficient & 45 & T3 & Sigmoid Colon & FEMALE & Colon Mucinous Adenocarcinoma & C18.7 & 0.04 \\ \hline TCGA-CK-6751 & Proficient & 88 & T2 & Ascending Colon & FEMALE & Colon Mucinous Adenocarcinoma & C18.2 & 0.07 \\ \hline TCGA-CM-4744 & Proficient & 69 & T2 & Cecum & MALE & Colon Adenocarcinoma & C18.0 & 0.16 \\ \hline TCGA-CM-4747 & Proficient & 47 & T4a & Cecum & MALE & Colon Adenocarcinoma & C18.0 & 0.02 \\ \hline TCGA-CM-4748 & Proficient & 53 & T4a & Transverse Colon & MALE & Colon Mucinous Adenocarcinoma & C18.4 & 0.02 \\ \hline TCGA-CM-4750 & Proficient & 34 & T1 & [Not Available] & FEMALE & Colon Adenocarcinoma & C19 & 0.09 \\ \hline TCGA-CM-4751 & Proficient & 62 & T3 & Cecum & MALE & Colon Adenocarcinoma & C18.0 & 0.00 \\ \hline TCGA-CM-4752 & Proficient & 58 & T3 & Ascending Colon & MALE & Colon Adenocarcinoma & C18.2 & 0.04 \\ \hline TCGA-CM-5341 & Proficient & 82 & T2 & Sigmoid Colon & FEMALE & Colon Adenocarcinoma & C18.7 & 0.04 \\ \hline TCGA-CM-5344 & Proficient & 39 & T3 & Sigmoid Colon & FEMALE & Colon Adenocarcinoma & C18.7 & 0.04 \\ \hline TCGA-CM-5348 & Proficient & 72 & T3 & Cecum & MALE & Colon Adenocarcinoma & C18.0 & 0.00 \\ \hline TCGA-CM-5349 & Proficient & 68 & T3 & Cecum & FEMALE & Colon Adenocarcinoma & C18.0 & 0.04 \\ \hline TCGA-CM-5860 & Proficient & 44 & T3 & Ascending Colon & MALE & Colon Adenocarcinoma & C18.2 & 0.00 \\ \hline TCGA-CM-5862 & Proficient & 80 & T3 & Ascending Colon & MALE & Colon Adenocarcinoma & C18.2 & 0.11 \\ \hline TCGA-CM-5863 & Proficient & 60 & T3 & Ascending Colon & FEMALE & Colon Mucinous Adenocarcinoma & C18.2 & 0.02 \\ \hline TCGA-CM-5864 & Proficient & 60 & T2 & Cecum & MALE & Colon Adenocarcinoma & C18.0 & 0.09 \\ \hline TCGA-CM-5868 & Proficient & 59 & T4a & Sigmoid Colon & FEMALE & Colon Adenocarcinoma & C18.7 & 0.13 \\ \hline TCGA-CM-6161 & Proficient & 36 & T2 & Sigmoid Colon & FEMALE & Colon Adenocarcinoma & C18.7 & 0.07 \\ \hline \end{tabular}
\begin{tabular}{l|c|c|c|c|c|c|c|c} \hline TCGA-CM-6163 & Proficient & 74 & T1 & Sigmoid Colon & MALE & Colon Adenocarcinoma & C18.7 & 0.02 \\ \hline TCGA-CM-6164 & Proficient & 46 & T3 & Sigmoid Colon & FEMALE & Colon Adenocarcinoma & C18.7 & 0.09 \\ \hline TCGA-CM-6165 & Proficient & 74 & T3 & Sigmoid Colon & MALE & Colon Adenocarcinoma & C18.7 & 0.00 \\ \hline TCGA-CM-6166 & Proficient & 48 & T2 & Ascending Colon & FEMALE & Colon Adenocarcinoma & C18.2 & 0.00 \\ \hline TCGA-CM-6167 & Proficient & 57 & T3 & Cecum & FEMALE & Colon Adenocarcinoma & C18.0 & 0.09 \\ \hline TCGA-CM-6169 & Proficient & 67 & T3 & Cecum & MALE & Colon Adenocarcinoma & C18.0 & 0.02 \\ \hline TCGA-CM-6170 & Proficient & 73 & T2 & Descending Colon & FEMALE & Colon Adenocarcinoma & C18.6 & 0.07 \\ \hline TCGA-CM-6172 & Proficient & 70 & T3 & Sigmoid Colon & FEMALE & Colon Adenocarcinoma & C18.7 & 0.00 \\ \hline TCGA-CM-6675 & Proficient & 35 & T3 & Cecum & MALE & Colon Adenocarcinoma & C18.0 & 0.02 \\ \hline TCGA-CM-6676 & Proficient & 82 & T2 & Sigmoid Colon & MALE & Colon Adenocarcinoma & C18.7 & 0.04 \\ \hline TCGA-CM-6677 & Proficient & 75 & T3 & Hepatic Flexure & FEMALE & Colon Adenocarcinoma & C18.3 & 0.09 \\ \hline TCGA-CM-6678 & Proficient & 63 & T4a & Sigmoid Colon & FEMALE & Colon Adenocarcinoma & C18.7 & 0.02 \\ \hline TCGA-CM-6679 & Proficient & 58 & T3 & Sigmoid Colon & MALE & Colon Adenocarcinoma & C18.7 & 0.02 \\ \hline TCGA-CM-6680 & Proficient & 78 & T3 & Cecum & FEMALE & Colon Adenocarcinoma & C18.0 & 0.04 \\ \hline TCGA-DC5-5537 & Proficient & 83 & T3 & Ascending Colon & MALE & Colon Adenocarcinoma & C18.9 & 0.09 \\ \hline TCGA-DC5-5538 & Proficient & 60 & T3 & Cecum & FEMALE & Colon Adenocarcinoma & C18.0 & 0.11 \\ \hline TCGA-DC5-5539 & Proficient & 60 & T3 & Ascending Colon & MALE & Colon Mucinous Adenocarcinoma & C18.2 & 0.04 \\ \hline TCGA-DC5-5540 & Proficient & 73 & T3 & Cecum & MALE & Colon Adenocarcinoma & C18.0 & 0.00 \\ \hline TCGA-DC5-5541 & Proficient & 63 & T3 & Sigmoid Colon & MALE & Colon Adenocarcinoma & C18.7 & 0.02 \\ \hline TCGA-DC5-6529 & Proficient & 69 & T3 & NA & MALE & Colon Adenocarcinoma & C18.9 & 0.00 \\ \hline TCGA-DC5-6531 & Proficient & 75 & T3 & Hepatic Flexure & MALE & Colon Adenocarcinoma & C18.3 & 0.07 \\ \hline TCGA-DC5-6532 & Proficient & 61 & T3 & Sigmoid Colon & MALE & Colon Adenocarcinoma & C18.7 & 0.04 \\ \hline TCGA-DC5-6533 & Proficient & 68 & T4b & Transverse Colon & FEMALE & Colon Adenocarcinoma & C18.4 & 0.09 \\ \hline TCGA-DC5-6534 & Proficient & 62 & T3 & Ascending Colon & FEMALE & Colon Mucinous Adenocarcinoma & C18.9 & 0.02 \\ \hline TCGA-DC5-6535 & Proficient & 80 & T3 & Ascending Colon & FEMALE & Colon Adenocarcinoma & C18.9 & 0.02 \\ \hline TCGA-DC5-6536 & Proficient & 73 & T3 & Sigmoid Colon & MALE & Colon Adenocarcinoma & C18.9 & 0.00 \\ \hline TCGA-DC5-6537 & Proficient & 64 & T3 & Transverse Colon & MALE & Colon Adenocarcinoma & C18.4 & 0.02 \\ \hline TCGA-DC5-6538 & Proficient & 79 & T3 & Hepatic Flexure & FEMALE & Colon Adenocarcinoma & C18.3 & 0.13 \\ \hline TCGA-DC5-6539 & Proficient & 45 & T3 & Transverse Colon & FEMALE & Colon Adenocarcinoma & C18.4 & 0.02 \\ \hline TCGA-DC5-6541 & Proficient & 49 & T3 & Splenic Flexure & MALE & Colon Adenocarcinoma & C18.5 & 0.11 \\ \hline TCGA-DC5-6898 & Proficient & 51 & T2 & Sigmoid Colon & FEMALE & Colon Adenocarcinoma & C18.9 & 0.02 \\ \hline TCGA-DC5-6920 & Proficient & 77 & T3 & Sigmoid Colon & FEMALE & Colon Adenocarcinoma & C18.7 & 0.07 \\ \hline TCGA-DC5-6922 & Proficient & 76 & T3 & Sigmoid Colon & MALE & Colon Adenocarcinoma & C18.7 & 0.02 \\ \hline TCGA-DC5-6924 & Proficient & 68 & T3 & Sigmoid Colon & MALE & Colon Adenocarcinoma & C18.7 & 0.02 \\ \hline TCGA-DC5-6926 & Proficient & 65 & T4a & Sigmoid Colon & MALE & Colon Adenocarcinoma & C18.7 & 0.07 \\ \hline TCGA-DC5-6929 & Proficient & 49 & T3 & Sigmoid Colon & FEMALE & Colon Adenocarcinoma & C18.9 & 0.04 \\ \hline \end{tabular}
\begin{tabular}{l|c|c|c|c|c|c|c|c} \hline TCGA-D5-6931 & Proficient & 77 & T4b & Transverse Colon & MALE & Colon Adenocarcinoma & C18.9 & 0.07 \\ \hline TGA-D5-6932 & Proficient & 69 & T3 & Transverse Colon & MALE & Colon Adenocarcinoma & C18.9 & 0.02 \\ \hline TGA-D5-7000 & Proficient & 79 & T2 & Cecum & FEMALE & Colon Mucinous Adenocarcinoma & C18.0 & 0.04 \\ \hline TGA-DM-AX03 & Proficient & 71 & T3 & NA & FEMALE & Colon Adenocarcinoma & C18.2 & 0.16 \\ \hline TGA-DM-AXD & Proficient & 65 & T3 & NA & MALE & Colon Adenocarcinoma & C18.0 & 0.07 \\ \hline TGA-DM-A0XF & Proficient & 68 & T3 & NA & FEMALE & NA & C18.7 & 0.02 \\ \hline TGA-DM-A1D0 & Proficient & 79 & T3 & Sigmoid Colon & FEMALE & Colon Adenocarcinoma & C18.7 & 0.04 \\ \hline TGA-DM-A1D4 & Proficient & 80 & T3 & Cecum & MALE & Colon Adenocarcinoma & C18.0 & 0.11 \\ \hline TGA-DM-A1D6 & Proficient & 88 & T3 & Splicatic Flexture & MALE & Colon Mucinous Adenocarcinoma & C18.5 & 0.02 \\ \hline TGA-DM-A1D7 & Proficient & 82 & T3 & Sigmoid Colon & MALE & NA & 0.18 & 0.04 \\ \hline TGA-DM-A1D8 & Proficient & 50 & T3 & Ascending Colon & FEMALE & Colon Adenocarcinoma & C18.2 & 0.09 \\ \hline TGA-DM-A1D9 & Proficient & 67 & T3 & Cecum & FEMALE & Colon Adenocarcinoma & C18.0 & 0.04 \\ \hline TGA-DM-A1DA & Proficient & 71 & T3 & Cecum & FEMALE & Colon Adenocarcinoma & C18.0 & 0.00 \\ \hline TGA-DM-A1DB & Proficient & 68 & T3 & Sigmoid Colon & MALE & Colon Adenocarcinoma & C18.7 & 0.07 \\ \hline TGA-DM-A1HA & Proficient & 82 & T3 & Ascending Colon & MALE & Colon Adenocarcinoma & C18.2 & 0.07 \\ \hline TGA-DM-A280 & Proficient & 70 & T3 & Ascending Colon & FEMALE & Colon Mucinous Adenocarcinoma & C18.2 & 0.13 \\ \hline TGA-DM-A282 & Proficient & 60 & T3 & Hepatic Flexure & FEMALE & Colon Adenocarcinoma & C18.3 & 0.07 \\ \hline TGA-DM-A285 & Proficient & 71 & T3 & Ascending Colon & FEMALE & Colon Mucinous Adenocarcinoma & C18.2 & 0.02 \\ \hline TGA-DM-A288 & Proficient & 68 & T3 & Cecum & MALE & Colon Mucinous Adenocarcinoma & C18.0 & 0.00 \\ \hline TGA-DM-A28A & Proficient & 78 & T3 & Cecum & MALE & Colon Adenocarcinoma & C18.0 & 0.07 \\ \hline TGA-DM-A28C & Proficient & 74 & T3 & Sigmoid Colon & MALE & Colon Adenocarcinoma & C18.7 & 0.04 \\ \hline TGA-DM-A28E & Proficient & 72 & T3 & Sigmoid Colon & FEMALE & Colon Adenocarcinoma & C18.7 & 0.02 \\ \hline TGA-DM-A28F & Proficient & 73 & T3 & Sigmoid Colon & MALE & Colon Adenocarcinoma & C18.7 & 0.07 \\ \hline TGA-DM-A28G & Proficient & 75 & T3 & Ascending Colon & MALE & Colon Adenocarcinoma & C18.2 & 0.02 \\ \hline TGA-DM-A28H & Proficient & 50 & T3 & Cecum & MALE & Colon Adenocarcinoma & C18.0 & 0.02 \\ \hline TGA-DM-A28K & Proficient & 75 & T3 & Hepatic Flexure & MALE & Colon Mucinous Adenocarcinoma & C18.3 & 0.11 \\ \hline TGA-DM-A28M & Proficient & 63 & T3 & Descending Colon & MALE & Colon Adenocarcinoma & C18.6 & 0.04 \\ \hline TGA-FA-6459 & Proficient & 61 & T3 & Sigmoid Colon & FEMALE & Colon Adenocarcinoma & C18.7 & 0.09 \\ \hline TGA-FA-6460 & Proficient & 51 & T3 & Sigmoid Colon & FEMALE & Colon Adenocarcinoma & C18.7 & 0.07 \\ \hline TGA-FA-6461 & Proficient & 41 & T4b & Hepatic Flexure & FEMALE & Colon Adenocarcinoma & C18.9 & 0.04 \\ \hline TCGA-FA-6463 & Proficient & 51 & T3 & Transverse Colon & MALE & Colon Mucinous Adenocarcinoma & C18.4 & 0.02 \\ \hline TGA-FA-6569 & Proficient & 60 & T2 & Transverse Colon & MALE & Colon Adenocarcinoma & C18.9 & 0.02 \\ \hline TGA-FA-6704 & Proficient & 60 & T3 & Sigmoid Colon & MALE & Colon Mucinous Adenocarcinoma & C18.7 & 0.00 \\ \hline TGA-FA-6805 & Proficient & 58 & T3 & Descending Colon & FEMALE & Colon Adenocarcinoma & C18.9 & 0.00 \\ \hline TGA-FA-6806 & Proficient & 59 & T2 & Sigmoid Colon & FEMALE & Colon Adenocarcinoma & C18.7 & 0.07 \\ \hline TGA-FA-6807 & Proficient & 51 & T3 & Hepatic Flexure & FEMALE & Colon Adenocarcinoma & C18.9 & 0.02 \\ \hline \end{tabular}
\begin{tabular}{l|c|c|c|c|c|c|c|c} \hline TCGA-F4-6808 & Proficient & 54 & T1 & Sigmoid Colon & FEMALE & Colon Adenocarcinoma & C18.7 & 0.02 \\ \hline TGA-F4-6809 & Proficient & 52 & T3 & Sigmoid Colon & FEMALE & Colon Adenocarcinoma & C18.7 & 0.09 \\ \hline TGA-F4-6854 & Proficient & 77 & T3 & Sigmoid Colon & FEMALE & Colon Adenocarcinoma & C18.7 & 0.02 \\ \hline TGA-F4-6855 & Proficient & 70 & T3 & Sigmoid Colon & FEMALE & Colon Adenocarcinoma & C18.7 & 0.02 \\ \hline TGA-G4-6293 & Proficient & 49 & T3 & Transverse Colon & FEMALE & Colon Adenocarcinoma & C18.4 & 0.04 \\ \hline TCGA-G4-6294 & Proficient & 75 & T3 & Cecum & MALE & Colon Adenocarcinoma & C18.0 & 0.02 \\ \hline TCGA-G4-6295 & Proficient & 70 & T3 & Cecum & FEMALE & Colon Adenocarcinoma & C18.0 & 0.07 \\ \hline TGA-G4-6297 & Proficient & 55 & T3 & Cecum & FEMALE & Colon Adenocarcinoma & C18.0 & 0.11 \\ \hline TGA-G4-6298 & Proficient & 90 & T4a & Cecum & MALE & Colon Adenocarcinoma & C18.0 & 0.00 \\ \hline TGA-G4-6299 & Proficient & 69 & T3 & Descending Colon & MALE & Colon Adenocarcinoma & C18.6 & 0.04 \\ \hline TGA-G4-6303 & Proficient & 54 & T3 & Sigmoid Colon & FEMALE & Colon Adenocarcinoma & C18.7 & 0.13 \\ \hline TCGA-G4-6306 & Proficient & 71 & T2 & Ascending Colon & MALE & Colon Adenocarcinoma & C18.2 & 0.04 \\ \hline TCGA-G4-6307 & Proficient & 37 & T3 & Sigmoid Colon & FEMALE & Colon Adenocarcinoma & C18.7 & 0.00 \\ \hline TCGA-G4-6310 & Proficient & 69 & T3 & Cecum & MALE & Colon Adenocarcinoma & C18.9 & 0.04 \\ \hline TGA-G4-6311 & Proficient & 80 & T3 & Ascending Colon & MALE & Colon Adenocarcinoma & C18.2 & 0.04 \\ \hline TGA-G4-6314 & Proficient & 76 & T3 & Cecum & FEMALE & Colon Adenocarcinoma & C18.0 & 0.02 \\ \hline TGA-G4-6315 & Proficient & 66 & T3 & Descending Colon & MALE & Colon Adenocarcinoma & C18.6 & 0.16 \\ \hline TGA-G4-6317 & Proficient & 51 & T3 & Sigmoid Colon & FEMALE & Colon Adenocarcinoma & C18.7 & 0.04 \\ \hline TGA-G4-6321 & Proficient & 60 & T2 & Cecum & FEMALE & Colon Adenocarcinoma & C18.0 & 0.09 \\ \hline TGA-G4-6322 & Proficient & 65 & T3 & Descending Colon & MALE & Colon Mucinous Adenocarcinoma & C18.6 & 0.02 \\ \hline TGA-G4-6323 & Proficient & 50 & Tis & Cecum & MALE & Colon Adenocarcinoma & C18.0 & 0.00 \\ \hline TGA-G4-6625 & Proficient & 77 & T3 & Sigmoid Colon & FEMALE & Colon Adenocarcinoma & C18.7 & 0.07 \\ \hline TGA-G4-6626 & Proficient & 90 & T3 & Ascending Colon & MALE & Colon Adenocarcinoma & C18.2 & 0.04 \\ \hline TGA-G4-6627 & Proficient & 84 & T3 & Ascending Colon & MALE & Colon Adenocarcinoma & C18.2 & 0.00 \\ \hline TGA-NH-A50T & Proficient & 68 & T3 & Splenic Flexure & FEMALE & Colon Adenocarcinoma & C18.5 & 0.04 \\ \hline TGA-NH-A50U & Proficient & 42 & T4a & Cecum & MALE & Colon Mucinous Adenocarcinoma & C18.0 & 0.02 \\ \hline TGA-NH-A50V & Proficient & 69 & T3 & Cecum & MALE & Colon Adenocarcinoma & C18.0 & 0.11 \\ \hline TGA-NH-A66A & Proficient & 58 & T4a & Ascending Colon & MALE & Colon Adenocarcinoma & C18.2 & 0.02 \\ \hline TGA-NH-A66B & Proficient & 71 & T3 & Transverse Colon & FEMALE & Colon Adenocarcinoma & C18.4 & 0.04 \\ \hline TGA-NH-A6GC & Proficient & 66 & T4b & Descending Colon & FEMALE & Colon Mucinous Adenocarcinoma & C18.6 & 0.18 \\ \hline TCGA-NH-A8F7 & Proficient & 53 & T3 & Sigmoid Colon & FEMALE & Colon Adenocarcinoma & C18.7 & 0.02 \\ \hline TGA-NH-A8F8 & Proficient & 79 & T4a & Ascending Colon & MALE & Colon Adenocarcinoma & C18.2 & 0.00 \\ \hline TGA-QG-A5YV & Proficient & 64 & T4b & Sigmoid Colon & FEMALE & Colon Adenocarcinoma & C18.7 & 0.09 \\ \hline TGA-QG-A5YW & Proficient & 55 & T3 & Cecum & FEMALE & Colon Mucinous Adenocarcinoma & C18.0 & 0.07 \\ \hline TGA-QG-A5YX & Proficient & 61 & T3 & Sigmoid Colon & FEMALE & Colon Adenocarcinoma & C18.7 & 0.09 \\ \hline TGA-QG-A5Z1 & Proficient & 71 & T3 & Sigmoid Colon & MALE & Colon Adenocarcinoma & C19 & 0.02 \\ \hline \end{tabular}
\begin{tabular}{l|c|c|c|c|c|c|c|c} \hline TCGA-QL-A97D & Proficient & 84 & T2 & Cecum & FEMALE & Colon Adenocarcinoma & C18.2 & 0.07 \\ \hline TCGA-RL-ASFL & Proficient & 51 & T3 & Cecum & MALE & Colon Adenocarcinoma & C18.0 & 0.00 \\ \hline TCGA-SS-ATHO & Proficient & 44 & T4a & Cecum & FEMALE & Colon Adenocarcinoma & C18.0 & 0.09 \\ \hline TCGA-IF-A92H & Proficient & 82 & T3 & Sigmoid Colon & MALE & Colon Adenocarcinoma & C18.7 & 0.07 \\ \hline TCGA-AF-2687 & Proficient & 57 & T3 & Rectum & MALE & Rectal Adenocarcinoma & C19 & 0.02 \\ \hline TCGA-AF-2690 & Proficient & 76 & T3 & Rectum & FEMALE & Rectal Adenocarcinoma & C20 & 0.00 \\ \hline TCGA-AF-2693 & Proficient & 75 & T2 & Sigmoid Colon & MALE & [Not Available] & C19 & 0.00 \\ \hline TCGA-AF-3911 & Proficient & 48 & T3 & Rectum & MALE & Rectal Adenocarcinoma & C20 & 0.04 \\ \hline TCGA-AF-3914 & Proficient & 60 & T3 & Rectosigmoid Junction & MALE & Rectal Adenocarcinoma & C19 & 0.04 \\ \hline TCGA-AF-4110 & Proficient & 77 & T4a & Rectosigmoid Junction & MALE & [Not Available] & C20 & 0.00 \\ \hline TCGA-AF-5654 & Proficient & 73 & T2 & Rectosigmoid Junction & FEMALE & Rectal Adenocarcinoma & C19 & 0.00 \\ \hline TCGA-AF-6136 & Proficient & 72 & T3 & Rectosigmoid Junction & FEMALE & Rectal Adenocarcinoma & C19 & 0.02 \\ \hline TCGA-AF-6655 & Proficient & 66 & T2 & Rectum & MALE & Rectal Adenocarcinoma & C19 & 0.02 \\ \hline TCGA-AF-6672 & Proficient & 43 & T4a & Rectosigmoid Junction & MALE & Rectal Adenocarcinoma & C19 & 0.02 \\ \hline TCGA-AF-456K & Proficient & 56 & T3 & Sigmoid Colon & MALE & Rectal Adenocarcinoma & C19 & 0.09 \\ \hline TCGA-AF-A56L & Proficient & 48 & T3 & Sigmoid Colon & FEMALE & Rectal Adenocarcinoma & C19 & 0.04 \\ \hline TCGA-AF-A56N & Proficient & 47 & T3 & Rectum & FEMALE & Rectal Adenocarcinoma & C19 & 0.02 \\ \hline TCGA-AG-3591 & Proficient & 66 & T3 & Rectum & FEMALE & Rectal Adenocarcinoma & C19 & 0.11 \\ \hline TCGA-AG-3592 & Proficient & 68 & T3 & Rectum & MALE & Rectal Adenocarcinoma & C19 & 0.09 \\ \hline TCGA-AG-3725 & Proficient & 90 & T3 & Rectum & FEMALE & Rectal Adenocarcinoma & C19 & 0.00 \\ \hline TCGA-AG-3726 & Proficient & 63 & T2 & Rectum & FEMALE & Rectal Adenocarcinoma & C20 & 0.09 \\ \hline TCGA-AG-3727 & Proficient & 78 & T3 & Rectum & FEMALE & Rectal Adenocarcinoma & C19 & 0.09 \\ \hline TCGA-AG-3728 & Proficient & 73 & T3 & Rectum & MALE & Rectal Adenocarcinoma & C20 & 0.00 \\ \hline TCGA-AG-3731 & Proficient & 65 & T3 & Rectum & MALE & Rectal Adenocarcinoma & C20 & 0.04 \\ \hline TCGA-AG-3732 & Proficient & 78 & T2 & Rectum & FEMALE & Rectal Adenocarcinoma & C19 & 0.02 \\ \hline TCGA-AG-3742 & Proficient & 85 & T1 & Rectum & FEMALE & Rectal Adenocarcinoma & C18.9 & 0.04 \\ \hline TCGA-AG-3878 & Proficient & 64 & T2 & Rectum & MALE & Rectal Adenocarcinoma & C20 & 0.09 \\ \hline TCGA-AG-3881 & Proficient & 83 & T3 & Rectum & FEMALE & Rectal Arableble & C80.1 & 0.00 \\ \hline TCGA-AG-3882 & Proficient & 66 & T2 & Rectum & FEMALE & Rectal Adenocarcinoma & C18.9 & 0.04 \\ \hline TCGA-AG-3883 & Proficient & 69 & T2 & Rectum & MALE & Rectal Adenocarcinoma & C20 & 0.02 \\ \hline TCGA-AG-3885 & Proficient & 71 & T3 & Rectum & FEMALE & Rectal Adenocarcinoma & C20 & 0.00 \\ \hline TCGA-AG-3887 & Proficient & 68 & T3 & Rectum & MALE & Rectal Mucinous Adenocarcinoma & C20 & 0.04 \\ \hline TCGA-AG-3890 & Proficient & 62 & T2 & Rectum & MALE & Rectal Adenocarcinoma & C20 & 0.04 \\ \hline TCGA-AG-3893 & Proficient & 74 & T3 & Rectum & MALE & Rectal Adenocarcinoma & C19 & 0.02 \\ \hline TCGA-AG-3894 & Proficient & 65 & T3 & Rectum & MALE & Rectal Adenocarcinoma & C20 & 0.02 \\ \hline \end{tabular}
\begin{tabular}{l|c|c|c|c|c|c|c|c} \hline TCGA-AG-3896 & Proficient & 85 & T2 & Rectum & FEMALE & Rectal Adenocarcinoma & C20 & 0.00 \\ \hline TCGA-AG-3898 & Proficient & 61 & T3 & Rectum & MALE & Rectal Adenocarcinoma & C20 & 0.07 \\ \hline TCGA-AG-3901 & Proficient & 67 & T3 & Rectum & FEMALE & Rectal Mucinous Adenocarcinoma & C19 & 0.00 \\ \hline TCGA-AG-3902 & Proficient & 61 & T3 & Rectum & MALE & Rectal Adenocarcinoma & C19 & 0.07 \\ \hline TCGA-AG-3909 & Proficient & 69 & T3 & Rectum & FEMALE & Rectal Adenocarcinoma & C19 & 0.04 \\ \hline TCGA-AG-4001 & Proficient & 74 & T3 & Rectum & FEMALE & Rectal Adenocarcinoma & C19 & 0.02 \\ \hline TCGA-AG-4008 & Proficient & 63 & T3 & Rectum & MALE & Rectal Adenocarcinoma & C18.9 & 0.02 \\ \hline TCGA-AG-4009 & Proficient & 83 & T2 & Rectum & MALE & Rectal Adenocarcinoma & C20 & 0.07 \\ \hline TCGA-AG-4015 & Proficient & 85 & T3 & Rectum & FEMALE & Rectal Adenocarcinoma & C18.9 & 0.02 \\ \hline TCGA-AG-4021 & Proficient & 84 & T3 & Rectum & FEMALE & Rectal Adenocarcinoma & C20 & 0.04 \\ \hline TCGA-AG-4022 & Proficient & 59 & T3 & Rectum & FEMALE & Rectal Adenocarcinoma & C20 & 0.02 \\ \hline TCGA-AG-A008 & Proficient & 50 & T2 & Rectum & FEMALE & Rectal Mucinous Adenocarcinoma & C20 & 0.02 \\ \hline TCGA-AG-A00C & Proficient & 49 & T3 & Rectum & FEMALE & Rectal Adenocarcinoma & C20 & 0.07 \\ \hline TCGA-AG-A00Y & Proficient & 68 & T3 & Rectum & MALE & Rectal Adenocarcinoma & C20 & 0.04 \\ \hline TCGA-AG-A011 & Proficient & 80 & T3 & Rectum & MALE & Rectal Adenocarcinoma & C20 & 0.04 \\ \hline TCGA-AG-A014 & Proficient & 86 & T2 & Rectum & MALE & Rectal Adenocarcinoma & C20 & 0.04 \\ \hline TCGA-AG-A015 & Proficient & 64 & T1 & Rectum & FEMALE & Rectal Adenocarcinoma & C20 & 0.02 \\ \hline TCGA-AG-A016 & Proficient & 55 & T3 & Rectum & MALE & Rectal Adenocarcinoma & C20 & 0.00 \\ \hline TCGA-AG-A01J & Proficient & 59 & T3 & Rectum & FEMALE & Rectal Adenocarcinoma & C20 & 0.02 \\ \hline TCGA-AG-A01L & Proficient & 58 & T3 & Rectum & MALE & Rectal Adenocarcinoma & C20 & 0.00 \\ \hline TCGA-AG-A01N & Proficient & 68 & T2 & Rectum & FEMALE & Rectal Adenocarcinoma & C20 & 0.04 \\ \hline TCGA-AG-A01W & Proficient & 67 & T3 & Rectum & FEMALE & Rectal Adenocarcinoma & C20 & 0.00 \\ \hline TCGA-AG-A01V & Proficient & 49 & T3 & Rectum & FEMALE & Rectal Adenocarcinoma & C20 & 0.04 \\ \hline TCGA-AG-A020 & Proficient & 57 & T3 & Rectum & FEMALE & Rectal Mucinous Adenocarcinoma & C20 & 0.02 \\ \hline TCGA-AG-A023 & Proficient & 62 & T4 & Rectum & FEMALE & Rectal Adenocarcinoma & C20 & 0.04 \\ \hline TCGA-AG-A026 & Proficient & 66 & T4 & Rectum & MALE & Rectal Adenocarcinoma & C20 & 0.04 \\ \hline TCGA-AG-A02X & Proficient & 77 & T2 & Rectum & MALE & Rectal Adenocarcinoma & C20 & 0.07 \\ \hline TCGA-AG-A032 & Proficient & 68 & T3 & Rectum & MALE & Rectal Adenocarcinoma & C20 & 0.00 \\ \hline TCGA-AG-A036 & Proficient & 71 & T3 & Rectum & MALE & Rectal Adenocarcinoma & C20 & 0.04 \\ \hline TCGA-AH-6544 & Proficient & 60 & T3 & Rectosigmoid Junction & MALE & Rectal Adenocarcinoma & C19 & 0.04 \\ \hline TCGA-AH-6547 & Proficient & 79 & T3 & Rectosigmoid Junction & FEMALE & Rectal Adenocarcinoma & C19 & 0.00 \\ \hline TCGA-AH-6549 & Proficient & 66 & T3 & Rectum & MALE & Rectal Adenocarcinoma & C20 & 0.02 \\ \hline TCGA-AH-6643 & Proficient & 50 & T3 & Rectosigmoid Junction & MALE & Rectal Adenocarcinoma & C19 & 0.04 \\ \hline TCGA-AH-6644 & Proficient & 73 & T3 & Rectosigmoid Junction & MALE & Rectal Adenocarcinoma & C19 & 0.07 \\ \hline TCGA-AH-6897 & Proficient & 48 & T2 & Rectosigmoid Junction & MALE & Rectal Adenocarcinoma & C19 & 0.04 \\ \hline TCGA-AH-6903 & Proficient & 46 & T3 & Rectosigmoid Junction & MALE & Rectal Mucinous Adenocarcinoma & C19 & 0.00 \\ \hline \end{tabular}
\begin{tabular}{l|c|c|c|c|c|c|c|c} \hline TCGA-BM-6198 & Proficient & 73 & T3 & Rectum & MALE & Rectal Adenocarcinoma & C20 & 0.02 \\ \hline TCGA-C1-6619 & Proficient & 41 & T3 & Rectum & MALE & Rectal Adenocarcinoma & C20 & 0.11 \\ \hline TCGA-C1-6620 & Proficient & 41 & T3 & Rectum & FEMALE & Rectal Adenocarcinoma & C20 & 0.11 \\ \hline TCGA-C1-6621 & Proficient & 63 & T3 & Rectum & MALE & Rectal Adenocarcinoma & C20 & 0.00 \\ \hline TCGA-C1-6622 & Proficient & 74 & T4 & Rectum & MALE & Rectal Adenocarcinoma & C20 & 0.02 \\ \hline TCGA-C1-6623 & Proficient & 44 & T1 & Rectum & MALE & Rectal Adenocarcinoma & C20 & 0.09 \\ \hline TCGA-C1-6624 & Proficient & 53 & T2 & Rectosigmoid Junction & FEMALE & Rectal Adenocarcinoma & C20 & 0.07 \\ \hline TCGA-C1-4957 & Proficient & 79 & T3 & [Not Available] & FEMALE & Rectal Adenocarcinoma & C20 & 0.02 \\ \hline TCGA-C1-5917 & Proficient & 71 & T3 & Rectosigmoid Junction & FEMALE & Rectal Adenocarcinoma & C19 & 0.02 \\ \hline TCGA-C1-5918 & Proficient & 90 & T3 & Rectosigmoid Junction & FEMALE & Rectal Adenocarcinoma & C20 & 0.07 \\ \hline TCGA-DC-4745 & Proficient & 49 & T3 & Rectosigmoid Junction & FEMALE & Rectal Adenocarcinoma & C19 & 0.02 \\ \hline TCGA-DC-4749 & Proficient & 57 & T2 & Rectosigmoid Junction & MALE & Rectal Adenocarcinoma & C19 & 0.00 \\ \hline TCGA-DC-5337 & Proficient & 69 & T1 & Rectosigmoid Junction & MALE & Rectal Adenocarcinoma & C19 & 0.02 \\ \hline TCGA-DC-5869 & Proficient & 62 & T3 & Rectum & FEMALE & Rectal Adenocarcinoma & C20 & 0.02 \\ \hline TCGA-DC-6154 & Proficient & 57 & T4a & Rectosigmoid Junction & FEMALE & Rectal Adenocarcinoma & C19 & 0.00 \\ \hline TCGA-DC-6155 & Proficient & 31 & T2 & Rectosigmoid Junction & FEMALE & Rectal Adenocarcinoma & C19 & 0.00 \\ \hline TCGA-DC-6157 & Proficient & 48 & T2 & Rectosigmoid Junction & MALE & Rectal Adenocarcinoma & C19 & 0.04 \\ \hline TCGA-DC-6158 & Proficient & 70 & T2 & Rectum & MALE & Rectal Adenocarcinoma & C20 & 0.00 \\ \hline TCGA-DC-6160 & Proficient & 68 & T2 & Rectosigmoid Junction & MALE & Rectal Adenocarcinoma & C19 & 0.13 \\ \hline TCGA-DC-6681 & Proficient & 70 & T3 & Rectosigmoid Junction & FEMALE & Rectal Adenocarcinoma & C19 & 0.02 \\ \hline TCGA-DC-6682 & Proficient & 57 & T3 & Rectosigmoid Junction & MALE & Rectal Adenocarcinoma & C19 & 0.13 \\ \hline TCGA-DC-6683 & Proficient & 43 & T3 & Rectosigmoid Junction & MALE & Rectal Adenocarcinoma & C19 & 0.00 \\ \hline TCGA-DC-5265 & Proficient & 51 & T3 & Rectum & MALE & Rectal Adenocarcinoma & C20 & 0.02 \\ \hline TCGA-DY-A0XA & Proficient & 57 & T3 & Rectosigmoid Junction & FEMALE & Rectal Adenocarcinoma & C19 & 0.09 \\ \hline TCGA-DY-A1DC & Proficient & 72 & T3 & Rectosigmoid Junction & FEMALE & Rectal Adenocarcinoma & C19 & 0.04 \\ \hline TCGA-DY-A1DD & Proficient & 77 & T3 & Rectosigmoid Junction & FEMALE & Rectal Adenocarcinoma & C19 & 0.04 \\ \hline TCGA-DY-A1DG & Proficient & 75 & T3 & Rectum & MALE & Rectal Adenocarcinoma & C20 & 0.02 \\ \hline TCGA-DY-A1H8 & Proficient & 77 & T2 & Rectum & FEMALE & Rectal Adenocarcinoma & C20 & 0.04 \\ \hline TCGA-EF-5830 & Proficient & 54 & T4a & Rectum & MALE & Rectal Adenocarcinoma & C20 & 0.04 \\ \hline TCGA-EF-5831 & Proficient & 72 & T3 & Rectum & MALE & Rectal Adenocarcinoma & C20 & 0.04 \\ \hline TCGA-EI-6506 & Proficient & 78 & T3 & Rectosigmoid Junction & FEMALE & Rectal Adenocarcinoma & C20 & 0.04 \\ \hline TCGA-EI-6508 & Proficient & 48 & T3 & Rectosigmoid Junction & FEMALE & Rectal Adenocarcinoma & C20 & 0.07 \\ \hline TCGA-EI-6509 & Proficient & 53 & T3 & Rectosigmoid Junction & MALE & Rectal Adenocarcinoma & C20 & 0.02 \\ \hline TCGA-EI-6510 & Proficient & 77 & T2 & Rectosigmoid Junction & FEMALE & Rectal Adenocarcinoma & C20 & 0.02 \\ \hline TCGA-EI-6511 & Proficient & 52 & T3 & Rectum & MALE & Rectal Adenocarcinoma & C20 & 0.07 \\ \hline \end{tabular}
\begin{tabular}{l|c|c|c|c|c|c|c|c} \hline TCGA-El-6512 & Proficient & 64 & T3 & Rectoisigmoid Junction & FEMALE & Rectal Adenocarcinoma & C20 & 0.11 \\ \hline TCGA-El-6513 & Proficient & 59 & T3 & Rectosigmoid Junction & MALE & Rectal Adenocarcinoma & C20 & 0.07 \\ \hline TCGA-El-6514 & Proficient & 59 & T3 & Sigmoid Colon & FEMALE & Rectal Adenocarcinoma & C20 & 0.02 \\ \hline TCGA-El-6881 & Proficient & 60 & T3 & Rectoisigmoid Junction & MALE & Rectal Adenocarcinoma & C20 & 0.02 \\ \hline TCGA-El-6883 & Proficient & 63 & T3 & Rectoisigmoid Junction & MALE & Rectal Adenocarcinoma & C20 & 0.11 \\ \hline TCGA-El-6884 & Proficient & 71 & T3 & Rectoisigmoid Junction & MALE & Rectal Adenocarcinoma & C20 & 0.07 \\ \hline TCGA-El-6885 & Proficient & 57 & T3 & Rectoisigmoid Junction & FEMALE & Rectal Adenocarcinoma & C20 & 0.04 \\ \hline TCGA-El-7002 & Proficient & 58 & T3 & Rectum & MALE & Rectal Adenocarcinoma & C20 & 0.00 \\ \hline TCGA-El-7004 & Proficient & 37 & T4a & Rectoisigmoid Junction & FEMALE & Rectal Mucinous Adenocarcinoma & C19 & 0.04 \\ \hline TCGA-F5-6464 & Proficient & 77 & T4b & Rectum & FEMALE & Rectal Adenocarcinoma & C19 & 0.02 \\ \hline TCGA-F5-6465 & Proficient & 64 & T3 & Rectoisigmoid Junction & FEMALE & Rectal Adenocarcinoma & C19 & 0.00 \\ \hline TCGA-F5-6571 & Proficient & 62 & T3 & Rectum & FEMALE & Rectal Adenocarcinoma & C20 & 0.04 \\ \hline TCGA-F5-6702 & Proficient & 71 & T3 & Rectosigmoid Junction & MALE & Rectal Adenocarcinoma & C19 & 0.00 \\ \hline TCGA-F5-6810 & Proficient & 71 & NA & NA & MALE & Rectal Adenocarcinoma & NA & 0.02 \\ \hline TCGA-F5-6811 & Proficient & 72 & T3 & Rectoisigmoid Junction & FEMALE & Rectal Adenocarcinoma & C19 & 0.04 \\ \hline TCGA-F5-6812 & Proficient & 67 & T3 & Rectum & MALE & Rectal Adenocarcinoma & C49.4 & 0.04 \\ \hline TCGA-F5-6813 & Proficient & 70 & T4a & Rectum & MALE & Rectal Adenocarcinoma & C49.4 & 0.02 \\ \hline TCGA-F5-6861 & Proficient & 60 & T3 & Rectum & FEMALE & Rectal Adenocarcinoma & C20 & 0.00 \\ \hline TCGA-F5-6863 & Proficient & 71 & T4a & Rectum & FEMALE & Rectal Adenocarcinoma & C20 & 0.02 \\ \hline TCGA-F5-6864 & Proficient & 74 & T3 & Rectum & FEMALE & Rectal Adenocarcinoma & C20 & 0.11 \\ \hline TCGA-G5-6233 & Proficient & 74 & T3 & Sigmoid Colon & MALE & Rectal Adenocarcinoma & C20 & 0.07 \\ \hline TCGA-G5-6235 & Proficient & 72 & T3 & Rectoisigmoid Junction & MALE & Rectal Adenocarcinoma & C19 & 0.04 \\ \hline & & & & & & & \\ \hline TCGA-G5-6572 & Proficient & 56 & Available & Rectoisigmoid Junction & MALE & Rectal Adenocarcinoma & C19 & 0.04 \\ \hline TCGA-G5-6641 & Proficient & 67 & T1 & Rectosigmoid Junction & MALE & Rectal Mucinous Adenocarcinoma & C19 & 0.11 \\ \hline TCGA-A6-2672 & Deficient & 82 & T3 & NA & FEMALE & Colon Adenocarcinoma & C18.2 & 4.01 \\ \hline TCGA-A6-2686 & Deficient & 81 & T3 & Cecum & FEMALE & Colon Adenocarcinoma & C18.9 & 11.77 \\ \hline TCGA-A6-3809 & Deficient & 71 & T4 & Transverse Colon & FEMALE & Colon Mucinous Adenocarcinoma & C18.9 & 8.20 \\ \hline TCGA-A6-5661 & Deficient & 80 & T3 & Ascending Colon & FEMALE & Colon Adenocarcinoma & C18.2 & 6.70 \\ \hline TCGA-A6-5665 & Deficient & 84 & T3 & Ascending Colon & FEMALE & Colon Adenocarcinoma & C18.2 & 11.35 \\ \hline TCGA-A6-6653 & Deficient & 82 & T2 & Ascending Colon & MALE & Colon Adenocarcinoma & C18.9 & 6.72 \\ \hline TCGA-A-A-3492 & Deficient & 90 & T3 & Ascending Colon & FEMALE & Colon Adenocarcinoma & C18.2 & 10.31 \\ \hline TCGA-A-3663 & Deficient & 42 & T3 & Cecum & MALE & Colon Adenocarcinoma & C18.0 & 11.73 \\ \hline TCGA-A-3672 & Deficient & 90 & T3 & Transverse Colon & FEMALE & Colon Adenocarcinoma & C18.4 & 11.91 \\ \hline TCGA-A-3713 & Deficient & 68 & T3 & Ascending Colon & MALE & Colon Adenocarcinoma & C18.9 & 7.21 \\ \hline TCGA-A-3715 & Deficient & 77 & T3 & Ascending Colon & MALE & Colon Adenocarcinoma & C18.2 & 11.86 \\ \hline \end{tabular}
\begin{tabular}{l|c|c|c|c|c|c|c|c} \hline TCGA-AA-3811 & Deficient & 84 & T3 & Hepatic Flexure & FEMALE & Colon Adenocarcinoma & C18.0 & 5.88 \\ \hline TCGA-AA-3815 & Deficient & 65 & T3 & Cecum & FEMALE & Colon Adenocarcinoma & C18.0 & 4.46 \\ \hline TCGA-AA-3821 & Deficient & 81 & T2 & Hepatic Flexure & FEMALE & Colon Mucinous Adenocarcinoma & C18.2 & 4.57 \\ \hline TCGA-AA-3833 & Deficient & 63 & T3 & Ascending Colon & FEMALE & Colon Adenocarcinoma & C18.9 & 3.15 \\ \hline TCGA-AA-3845 & Deficient & 86 & T3 & Ascending Colon & FEMALE & Colon Adenocarcinoma & C18.2 & 4.35 \\ \hline TCGA-AA-3877 & Deficient & 83 & T1 & Transverse Colon & FEMALE & Colon Mucinous Adenocarcinoma & C18.4 & 5.32 \\ \hline TCGA-AA-3947 & Deficient & 60 & T4 & Ascending Colon & FEMALE & Colon Mucinous Adenocarcinoma & C18.9 & 11.64 \\ \hline TCGA-AA-3949 & Deficient & 87 & T3 & Ascending Colon & FEMALE & Colon Mucinous Adenocarcinoma & C18.2 & 4.57 \\ \hline TCGA-AA-3950 & Deficient & 79 & T3 & Ascending Colon & FEMALE & Colon Mucinous Adenocarcinoma & C18.2 & 4.97 \\ \hline TCGA-AA-3966 & Deficient & 89 & T3 & Hepatic Flexure & FEMALE & Colon Mucinous Adenocarcinoma & C18.9 & 5.65 \\ \hline TCGA-AA-A01P & Deficient & 80 & T3 & Ascending Colon & FEMALE & Colon Adenocarcinoma & C18.2 & 4.66 \\ \hline TCGA-AA-A022 & Deficient & 88 & T4 & Cecum & FEMALE & Colon Adenocarcinoma & C18.0 & 8.91 \\ \hline TCGA-AA-A02R & Deficient & 84 & T3 & Cecum & FEMALE & Colon Adenocarcinoma & C18.0 & 8.25 \\ \hline TCGA-AD-5900 & Deficient & 67 & T2 & Ascending Colon & MALE & Colon Mucinous Adenocarcinoma & C18.2 & 8.38 \\ \hline TCGA-AD-6889 & Deficient & 76 & T3 & Ascending Colon & MALE & Colon Adenocarcinoma & C18.2 & 11.84 \\ \hline TCGA-AD-6895 & Deficient & 84 & T3 & Cecum & MALE & Colon Adenocarcinoma & C18.0 & 5.88 \\ \hline TCGA-AD-ASEJ & Deficient & 74 & T3 & Cecum & FEMALE & Colon Adenocarcinoma & C18.0 & 8.78 \\ \hline TCGA-AM-5821 & Deficient & 68 & T3 & Sigmoid Colon & FEMALE & Colon Adenocarcinoma & C18.7 & 5.34 \\ \hline TCGA-AU-6004 & Deficient & 69 & T2 & Cecum & FEMALE & Colon Adenocarcinoma & C18.0 & 6.87 \\ \hline TCGA-AY-6197 & Deficient & 60 & T3 & Cecum & MALE & Colon Adenocarcinoma & C18.2 & 6.39 \\ \hline TCGA-AZ-4615 & Deficient & 84 & T3 & [Not Available] & MALE & Colon Adenocarcinoma & C18.0 & 5.88 \\ \hline TCGA-AZ-6598 & Deficient & 77 & T3 & NA & FEMALE & Colon Adenocarcinoma & C18.2 & 16.34 \\ \hline TCGA-AZ-4951 & Deficient & 79 & T3 & Ascending Colon & FEMALE & Colon Mucinous Adenocarcinoma & C18.0 & 6.32 \\ \hline TCGA-C-5913 & Deficient & 58 & T3 & Cecum & FEMALE & Colon Adenocarcinoma & C18.2 & 5.50 \\ \hline TCGA-CK-5916 & Deficient & 71 & T1 & Cecum & FEMALE & Colon Adenocarcinoma & C18.2 & 9.38 \\ \hline TCGA-CK-6746 & Deficient & 84 & T4b & Cecum & FEMALE & Colon Adenocarcinoma & C18.0 & 8.18 \\ \hline TCGA-CM-AT4743 & Deficient & 69 & T3 & Hepatic Flexure & MALE & Colon Adenocarcinoma & C18.2 & 6.96 \\ \hline TCGA-CM-5861 & Deficient & 63 & T3 & Cecum & FEMALE & Colon Adenocarcinoma & C18.0 & 7.45 \\ \hline TCGA-Cd-6471 & Deficient & 77 & T2 & Ascending Colon & FEMALE & Colon Adenocarcinoma & C18.2 & 7.16 \\ \hline TCGA-D5-6540 & Deficient & 66 & T2 & Cecum & MALE & Colon Mucinous Adenocarcinoma & C18.0 & 8.12 \\ \hline TCGA-D5-6928 & Deficient & 80 & T3 & Ascending Colon & MALE & Colon Mucinous Adenocarcinoma & C18.3 & 7.10 \\ \hline TCGA-D5-6930 & Deficient & 67 & T3 & Ascending Colon & MALE & Colon Mucinous Adenocarcinoma & C18.0 & 6.59 \\ \hline TCGA-DM-A1HB & Deficient & 75 & T3 & Transverse Colon & MALE & NA & C18.4 & 6.30 \\ \hline TCGA-F4-6570 & Deficient & 78 & T3 & Transverse Colon & FEMALE & Colon Adenocarcinoma & C18.9 & 8.29 \\ \hline TCGA-G4-6302 & Deficient & 90 & T3 & Cecum & FEMALE & Colon Mucinous Adenocarcinoma & C18.0 & 5.52 \\ \hline TCGA-G4-6304 & Deficient & 66 & T4 & Transverse Colon & FEMALE & Colon Adenocarcinoma & C18.4 & 4.99 \\ \hline \end{tabular}
\begin{tabular}{l|c|c|c|c|c|c|c|c} \hline TCGA-G4-6586 & Deficient & 73 & T3 & Ascending Colon & FEMALE & Colon Adenocarcinoma & C18.2 & 6.74 \\ \hline TCGA-G4-6588 & Deficient & 58 & T3 & Cecum & FEMALE & Colon Adenocarcinoma & C18.0 & **11.11** \\ \hline TCGA-G4-6628 & Deficient & 78 & T2 & Cecum & MALE & Colon Adenocarcinoma & C18.0 & 9.51 \\ \hline TCGA-QG-A5Z2 & Deficient & 61 & T2 & Cecum & MALE & Colon Adenocarcinoma & C18.0 & 5.46 \\ \hline TCGA-WS-AB45 & Deficient & 52 & T3 & Cecum & FEMALE & Colon Mucinous Adenocarcinoma & C18.0 & **13.17** \\ \hline \end{tabular}
## Supplementary Table 3.
Summary of the hereditary CRC and polyposis syndromes investigated in this study, including their underlying gene defect, previously reported mutational signature associations and the number of individuals and CRCs tested by WES for each group. In addition to CRCs from the ACCFR, OCCFR, and WEHI studies, non-hereditary CRCs from the TCGA COAD and READ studies were included as a separate group of controls for validation.
\begin{tabular}{p{142.3pt} p{142.3pt} p{142.3pt} p{142.3pt} p{142.3pt} p{142.3pt} p{142.3pt}} \hline
## Hereditary CRCs** & **Defective gene/s** & **DNA repair mechanism** & **Associated Signatures** & **Study Group** & **Individuals** & **CRCs** & **CRC Study IDs
\\ \hline
## Hereditary CRCs
& & & & & & & \\ \hline MUTYH-associated polyposis (MAP) & & Biallelic _MUTYH_ & Base excision repair & SBS18, SBS36 & & Biallelic _MUTYH_ & 8 & 12 & M01-M12 \\ & & & & & & & \\ & & & & & & & \\ & & & & & & & \\ & & & & & & & \\ & & & & & & & \\ & & & & & & & \\ \hline
## Non-hereditary CRCs
& & & & & & & & \\ \hline Sporadic MMR-deficient CRC & \(\frac{M\_HJ}{\text{tumour}}\) & & & & & & & \\ & & & & & & & \\ & & & & & & & \\ & & & & & & & \\ & & & & & & & \\ & & & & & & & \\ & & & & & & & \\ \hline
## TOTAL
& & & & & & & & \\ \hline
## TCGA Non-hereditary CRCs
& & & & & & & \\ \hline Sporadic MMR-deficient CRC & \(\frac{M\_HJ}{\text{tumour}}\) & & & & & & & \\ & & & & & & & \\ & & & & & & & \\ & & & & & & & \\ & & & & & & & \\ & & & & & & & \\ \hline
## Non-hereditary CRCs
& & & & & & & \\ \hline Sporadic MMR-deficient CRC & \(\frac{M\_HJ}{\text{tumour}}\) & & & & & & & \\ & & & & & & & \\ & & & & & & & \\ & & & & & & & \\ & & & & & & & \\ & & & & & & \\ \hline
## TOTAL
& & & & & & & & \\ \hline \hline \end{tabular}
## Supplementary Table 4.
The accuracy (acc), sensitivity (sens), specificity (spec), positive predictive value (PPV), and negative predictive value (NPV) for each comparison in the study, across the discovery, validation and combined datasets, for a range of possible TMS thresholds.
## Supplementary Table 4.
The accuracy (acc), sensitivity (sens), specificity (spec), positive predictive value (PPV), and negative predictive value (NPV) for each comparison in the study, across the discovery, validation and combined datasets, for a range of possible TMS thresholds.
\begin{tabular}{|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline
35\% & 76.7\% & 100.0\% & 71.9\% & 42.3\% & 100.0\% & 76.5\% & 100.0\% & 72.4\% & 38.6\% & 100.0\% & 76.9\% & 100.0\% & 71.0\% & 47.1\% & 100.0\% \\ \hline
40\% & 79.8\% & 100.0\% & 75.6\% & 45.8\% & 100.0\% & 80.9\% & 100.0\% & 77.6\% & 43.6\% & 100.0\% & 78.2\% & 100.0\% & 72.6\% & 48.5\% & 100.0\% \\ \hline
45\% & 87.6\% & 100.0\% & 85.0\% & 57.9\% & 100.0\% & 89.6\% & 100.0\% & 87.8\% & 58.6\% & 100.0\% & 84.6\% & 100.0\% & 80.6\% & 57.1\% & 100.0\% \\ \hline
50\% & 91.7\% & 100.0\% & 90.0\% & 67.3\% & 100.0\% & 93.9\% & 100.0\% & 92.9\% & 70.8\% & 100.0\% & 88.5\% & 100.0\% & 85.5\% & 64.0\% & 100.0\% \\ \hline
55\% & 94.3\% & 100.0\% & 93.1\% & 75.0\% & 100.0\% & 96.5\% & 100.0\% & 95.9\% & 81.0\% & 100.0\% & 91.0\% & 100.0\% & 88.7\% & 69.6\% & 100.0\% \\ \hline
60\% & 96.9\% & 100.0\% & 96.3\% & 84.6\% & 100.0\% & 97.4\% & 100.0\% & 96.9\% & 85.0\% & 100.0\% & 96.2\% & 100.0\% & 95.2\% & 84.2\% & 100.0\% \\ \hline
65\% & 97.9\% & 100.0\% & 97.5\% & 89.2\% & 100.0\% & 98.3\% & 100.0\% & 98.0\% & 89.5\% & 100.0\% & 97.4\% & 100.0\% & 96.8\% & 88.9\% & 100.0\% \\ \hline
70\% & 99.0\% & 100.0\% & 98.9\% & 94.3\% & 100.0\% & 99.1\% & 100.0\% & 99.0\% & 94.4\% & 100.0\% & 98.7\% & 100.0\% & 98.4\% & 94.1\% & 100.0\% \\ \hline
## 75\%** & **99.5\%** & **100.0\%** & **99.4\%** & **97.1\%** & **100.0\%** & **100.0\%** & **100.0\%** & **100.0\%** & **100.0\%** & **100.0\%** & **100.0\%** & **98.7\%** & **100.0\%** & **98.4\%** & **94.1\%** & **100.0\%
\\ \hline
80\% & 99.0\% & 97.0\% & 99.4\% & 97.0\% & 99.4\% & 100.0\% & 100.0\% & 100.0\% & 100.0\% & 100.0\% & 97.4\% & 93.8\% & 98.4\% & 93.8\% & 98.4\% \\ \hline
85\% & 90.7\% & 48.5\% & 99.4\% & 94.1\% & 90.3\% & 90.4\% & 35.3\% & 100.0\% & 100.0\% & 89.9\% & 91.0\% & 62.5\% & 98.4\% & 90.9\% & 91.0\% \\ \hline
90\% & 85.0\% & 15.2\% & 99.4\% & 83.3\% & 85.0\% & 86.1\% & 5.9\% & 100.0\% & 100.0\% & 86.0\% & 83.3\% & 25.0\% & 98.4\% & 80.0\% & 83.6\% \\ \hline
95\% & 82.4\% & 0.0\% & 99.4\% & 0.0\% & 82.8\% & 85.2\% & 0.0\% & 100.0\% & 0.0\% & 85.2\% & 78.2\% & 0.0\% & 98.4\% & 0.0\% & 79.2\% \\ \hline \end{tabular}
\begin{tabular}{|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline
## Threshold** & \multicolumn{4}{c|}{**MMRd v MMRp**} & \multicolumn{4}{c|}{**Discovery**} & \multicolumn{4}{c|}{**Validation
\\
## I02+ID2+ID7** & \multicolumn{1}{c|}{**Acc**} & \multicolumn{1}{c|}{**Sens**} & \multicolumn{1}{c|}{**Spec**} & \multicolumn{1}{c|}{**PPV**} & \multicolumn{1}{c|}{**NPV**} & \multicolumn{1}{c|}{**Acc**} & \multicolumn{1}{c|}{**Sens**} & \multicolumn{1}{c|}{**Spec**} & \multicolumn{1}{c|}{**PPV**} & \multicolumn{1}{c|}{**NPV**} & \multicolumn{1}{c|}{**Acc**} & \multicolumn{1}{c|}{**Sens**} & \multicolumn{1}{c|}{**Spec**} & \multicolumn{1}{c|}{**PPV**} & \multicolumn{1}{c|}{**NPV**} & \multicolumn{1}{c|}{**Acc**} & \multicolumn{1}{c|}{**Sens**} & \multicolumn{1}{c|}{**Spec**} & \multicolumn{1}{c|}{**PPV**} & \multicolumn{1}{c|}{**NPV
\\ \hline
5\% & 34.9\% & 100.0\% & 11.3\% & 29.0\% & 100.0\% & 27.3\% & 100.0\% & 5.1\% & 24.4\% & 100.0\% & 45.6\% & 100.0\% & 21.0\% & 36.4\% & 100.0\% \\
10\% & 42.2\% & 100.0\% & 21.2\% & 31.5\% & 1
## Figures
## Supplementary
The tumour mutational signature (TMS) profiles based on the COSMIC v3 signature set for each of the 97 CRCs tested by whole exome sequencing and included in the validation group: (a) Single base substitution (SBS)-derived TMS and (b) insertion and deletion (ID)-derived TMS profiles. CRCs were grouped by subtype: (i) biallelic _MUTYH_ pathogenic variant carriers, (ii) monoallelic _MUTYH_ pathogenic variant carriers, (iii) mismatch repair (MMR) gene pathogenic variant carriers (Lynch syndrome), (iv) MMR-deficient (MMRd) controls related to _MLH1_ gene promoter hypermethylation and (v) MMR-proficient (MMRp) controls. Individual SBS or ID TMS with proportional values below 5% across all the CRC samples were excluded.
## Supplementary Figure 2.** Assessment of somatic loss of heterozygosity (LOH) across _MUTYH_ in monoallelic samples W01 (monoallelic _MUTYH_ germline pathogenic variant carrier), C20 (POLE somatic pathogenic variant) and L01 (_MSH2_ germline pathogenic variant carrier) **(a-c)** as well as monoallelic _MUTYH_ sample W07 which exhibited a combined SBS18 and SBS36 signature profile indicative of biallelic _MUTYH_ inactivation **(d).
Each dot indicates a variant seen at a given allele fraction in the tumour, with "+" indicating the equivalent germline allele fraction. LOH is unlikely in regions containing heterozygous variants (red), while somatic homozygous variants seen as heterozygous in the germline sequence are indicative of LOH (green). Samples W01, C20 and L01 did not exhibit LOH, nor any somatic pathogenic variant in _MUTYH_, while W07 exhibits LOH across the entire _MUTYH_ gene. This suggests that LOH causes loss of the wildtype allele and accounts for the high SBS18 and SBS36 signature profile observe for this germline monoallelic _MUTYH_ CRC.
|
016576_file02 | ###### Contents
* 15 S1 Overview
* 26 S2 Generalisation of Nomenclature
* 2.1 Model Diagram
* 2.2 Population Heterogeneity
* 2.3 Exposure, Protection, Infection, and Recruitment
* 2.4 Recruitment-Related Parameters
* 2.5 Summary Recruitment Categories
* 2.6 Expanded TND Intervention Effectiveness Estimator
* 33 Effectiveness Estimator Bias
* 3.1 Test-Positive Odds
* 3.2 Test-Negative Odds
* 3.3 Relaxing Assumption that Prevented Infections Remain Secondary Recruits
* 34 Total Estimator Bias & Limiting Scenarios
* 3.1 True efficacy, \(E\), limits
* 3.2 Targeted fraction, \(p_{\text{in}}\), limits
* 3.3 Secondary Case Recruitment, \(p_{t}\), limits
* 3.4 Lower Limit on Secondary Relative Recruiting, \(\rho\)
* 35 Hybrid Study Design
* 3.5.1 Hybrid Estimator
* 36 Translation of Limits to Recruitment Constraints for Conventional TND
* 3.6.1 Attempting to Limit Recruitment to Targeted Population Only
* 3.6.2 Attempting to Limit to Primary Recruitment Only
* 37 Calculation of Coverage, \(L\), and Targeted Fraction, \(p_{\text{in}}\)
* 3.7.1 Measures During Intervention Distribution
* 38 Alternative Scenario Translation
Overview
A Test-Negative Design (TND) study has been proposed to evaluate a new Ebola Virus Disease (EVD) vaccine during the then-ongoing epidemic in Eastern Democratic Republic of Congo (DRC). The main text discussed a model of such a study: we described a population of individuals i) who heterogeneously receive a study vaccine, ii) some of whom subsequently exhibit symptoms of EVD or have contact with a known EVD case, and thus iii) are identified by either self-reporting and contact-tracing processes as part of an outbreak response, and finally iv) are tested for EVD, making them recruitable for a TND study of that vaccine. Particularly, we explored the potential for bias due to route of recruitment into the study, and due to heterogeneity in vaccine distribution. As we noted in the discussion, TND studies could be used to evaluate other kinds interventions.
To support application of the model to other contexts, we use more general terms in this Supplement (Section S2). Using those terms, we provide derivations of equations quoted in the main text (Sections S3-S6), additional results (Section S7), and translate the model to another example (Section S8).
## S2 Generalisation of Nomenclature
We consider a generic _study intervention_. The study intervention is in addition to any other outbreak control measures that might be ongoing. As in the main text, this study intervention is heterogeneously distributed at an individual level, which we represent with targeted status and intervention coverage. The TND study goal is to estimate the intervention efficacy; this observational estimate is often called the _effectiveness_.
The main text discusses self-reporting and contact-tracing as particular recruiting routes for EVD, which more generally are a random _primary_ process and a reactive _secondary_ process, respectively; we also use these qualifiers to distinguish the associated exposure processes to the pathogen of interest. For both routes, we still assume a highly sensitive and specific test for identifying infections with the target pathogen. For EVD, recruitment is symptom-related, but it does not have to be for all pathogens, so here we discuss intervention efficacy in terms of infection rather than disease.
The key assumptions in this model are:
* exposure to the target pathogen is identical for all individuals
* if infected by exposure, the probability of detection by the primary process is identical for all individuals
* the rate of exposure to any other pathogens that could result in testing (and therefore recruitment) is the same for all individuals
* all secondary recruits associated with an initial primary case have the same targeted status as that primary case
* the secondary transmission and recruitment process is identical for all individuals
### S2.1 Model Diagram
### Population Heterogeneity
There are two groups within the recruitable population: _non-targeted_ and _targeted_. Individuals in the non-targeted group do not receive the study intervention. Targeted individuals randomly receive the intervention with some probability. Aside from targeted and intervention status, individuals are identical: they have the same exposure risk for the target pathogen, same primary testing rate given exposure and non-exposure, and same secondary distribution and probability of exposing those individuals.
In the equations that follow, we label counts of individuals corresponding to their targeted and intervention status. The totals of these categories determine the population heterogeneity characteristics.
* \(U\)**,**: the number of targeted individuals that did not receive the intervention
* \(C\)**,**: of the recruitable population, those that are targeted; \(C=V+U\)
* \(N\)**,**: individuals that were not targeted
* \(T\)**,**: total potentially recruitable study population; \(T=C+N\)
* \(p_{\text{in}}\)**,**: the targeted fraction for the study, \(p_{\text{in}}=\frac{C}{T}\); used as targeted probability for individuals
* \(L\)**,**: the intervention coverage in the targeted population, \(L=\frac{V}{C}\); used as the probability targeted individuals have the intervention
### Exposure, Protection, Infection, and Recruitment
During the outbreak, individuals \(\{V,U,N\}\) are potentially exposed and tested, and thus recruited in the study, via two routes: i) the primary route, where individuals are exposed and tested randomly, independent of any association with an identified case; ii) the secondary route, where individuals are exposed by and tested because of connection with an identified case.
Test-positive individuals found by the primary process and those they associate with as detect by the secondary process have the same targeted status in the model. Therefore primary test-positives from the targeted population only interact via the secondary process with other targeted individuals, and likewise for non-targeted primary test-positives.
Relative to transmission of the target pathogen, all infections discovered by secondary route are assumed to result from exposures due to the associated primary case. Primary cases are assumed to result from a random exposure process (_i.e._ exposing individuals of the different types according to the relative proportions in the population).
All exposures result in infections, unless protected by the study intervention; potential infections prevented by other outbreak response measures (which benefit all individuals in the study population equally) are assumed to not be exposures in the context of the model. For both primary and secondary exposures, an individual that has received the intervention may avoid infection with probability corresponding to the study intervention efficacy. Exposed individuals who have not received the intervention become infected.
The intervention is also assumed to have no impact on infections that are not by the target pathogen, even where those infections could lead to a test.
We will refer to these as the test-positive odds and the test-negative odds.
## S3 Effectiveness Estimator Bias
To determine the potential bias of \(\hat{E}\) for a TND study in an outbreak setting, we need to translate Eq. S1 from being in terms of total individual counts, into the expected totals, given the study target intervention and outbreak conditions. We will examine each of the two odds terms in turn, then combine the results.
### Test-Positive Odds
Starting with the test-positive odds term, we first factorise (by \(C^{\prime}_{+}\), or \(N^{\prime}_{+}\)), such that most terms are expressed as proportions:
\[\frac{V^{\prime}_{+}+V^{\prime\prime}_{+}}{N^{\prime}_{+}+N^{ \prime\prime}_{+}+U^{\prime}_{+}+U^{\prime\prime}_{+}} = \frac{C^{\prime}_{+}\left(\frac{V^{\prime}_{+}}{C^{\prime}_{+}}+ \frac{V^{\prime\prime}_{+}}{C^{\prime}_{+}}\right)}{N^{\prime}_{+}\left(1+ \frac{N^{\prime\prime}_{+}}{N^{\prime}_{+}}\right)+C^{\prime}_{+}\left(\frac{U ^{\prime}_{+}}{C^{\prime}_{+}}+\frac{U^{\prime\prime}_{+}}{C^{\prime}_{+}} \right)}\] (S2)
Recall we defined \(R^{\prime\prime}\) as the expected number of cases that would be found via the secondary route among individuals that had not received the study intervention (_i.e._, non-targeted individuals or individuals outside of the recruitable population). The proportion \(\frac{N^{\prime\prime}_{+}}{N^{\prime}_{+}}\) is total number of secondary cases over the total number of primary cases (among non-targeted individuals), which is also the average number of secondary cases per primary case, so we can substitute \(R^{\prime\prime}=\frac{N^{\prime\prime}_{+}}{N^{\prime}_{+}}\). Since we have restricted the study to a scenario where only a single primary case exposes secondary cases, there is neither indirect protection or force of infection from multiple sources. Thus, amongst targeted individuals (_i.e._ those in \(C\)), \(R^{\prime\prime}\) will be reduced on average by the probability that exposed individuals are intervention recipients and protected. This probability is equal to coverage, \(L\), multiplied by the true efficacy, \(E\). Therefore, \(\frac{C^{\prime}_{+}}{C^{\prime}_{+}}=R^{\prime\prime}(1-LE)\) in the targeted population.
Using these substitutions and introducing some identity multipliers, \(1=\frac{C^{\prime\prime}_{+}}{C^{\prime\prime}_{+}}\), we can rewrite Eq. S2 as:
\[\frac{C^{\prime}_{+}\left(\frac{V^{\prime}_{+}}{C^{\prime}_{+}}+ \frac{C^{\prime\prime}_{+}}{C^{\prime\prime}_{+}}\frac{V^{\prime\prime}_{+}}{ C^{\prime}_{+}}\right)}{N^{\prime}_{+}\left(1+\frac{N^{\prime\prime}_{+}}{N^{ \prime}_{+}}\right)+C^{\prime}_{+}\left(\frac{U^{\prime}_{+}}{C^{\prime}_{+}} +\frac{C^{\prime\prime}_{+}}{C^{\prime\prime}_{+}}\frac{U^{\prime\prime}_{+}} {C^{\prime\prime}_{+}}\right)} = \frac{C^{\prime}_{+}\left(\frac{V^{\prime}_{+}}{C^{\prime}_{+}}+ \frac{V^{\prime\prime}_{+}}{C^{\prime\prime}_{+}}R^{\prime\prime}(1-LE)\right) }{N^{\prime}_{+}\left(1+R^{\prime\prime}\right)+C^{\prime}_{+}\left(\frac{U^{ \prime}_{+}}{C^{\prime}_{+}}+\frac{U^{\prime\prime}_{+}}{C^{\prime\prime}_{+} }R^{\prime\prime}(1-LE)\right)}\] (S3)
Next, we show how the proportions between the counts of the targeted individuals can be substituted to express the odds in terms of model parameters. Starting with \(\frac{V^{\prime}_{+}}{C^{\prime}_{+}}\): this is the probability of an individual receiving the intervention, conditional on there being an initial infection in the targeted population. Though the exposure probabilities are the same between targeted and non-targeted populations, if \(LE>0\), the probability that an exposure results in an infection is lower. Given an exposure event:
\[\frac{V^{\prime}_{+}}{C^{\prime}_{+}} =P(\text{received intervention }|\text{ is infected \& targeted})=P(i\in V|+,i\in C)\] \[=\frac{P(+|i\in V)\times P(i\in V|i\in C)}{P(+|i\in C)}=\frac{(1 -E)\times L}{(1-L)+L(1-E)}=\frac{(1-E)L}{1-LE}\]We can use the same logic for the secondary exposures: conditional on a secondary exposure that could result in infection, the same relationship applies. To solve for \(\frac{U_{\ast}^{\prime}}{C_{\ast}^{\prime}}\), we take the complements. Therefore, these four ratios are:
\[\frac{V_{\ast}^{\prime}}{C_{\ast}^{\prime}}=\frac{V_{\ast}^{\prime \prime}}{C_{\ast}^{\prime\prime}}= \frac{(1-E)L}{1-LE}\] \[\frac{U_{\ast}^{\prime}}{C_{\ast}^{\prime}}=\frac{U_{\ast}^{ \prime\prime}}{C_{\ast}^{\prime\prime}}= \frac{1-L}{1-LE}\] (S4)
S3:
\[\frac{C_{\ast}^{\prime}\left(\frac{V_{\ast}^{\prime}}{C_{\ast}^{ \prime}}+\frac{V_{\ast}^{\prime\prime}}{C_{\ast}^{\prime\prime}}R^{\prime\prime }(1-LE)\right)}{N_{\ast}^{\prime}\left(1+R^{\prime\prime}\right)+C_{\ast}^{ \prime}\left(\frac{U_{\ast}^{\prime}}{C_{\ast}^{\prime}}+\frac{U_{\ast}^{\prime \prime}}{C_{\ast}^{\prime\prime}}R^{\prime\prime}(1-LE)\right)} =\frac{C_{\ast}^{\prime}\frac{V_{\ast}^{\prime}}{C_{\ast}^{ \prime}}(1+R^{\prime\prime}(1-LE))}{N_{\ast}^{\prime}\left(1+R^{\prime\prime} \right)+C_{\ast}^{\prime}\frac{U_{\ast}^{\prime}}{C_{\ast}^{\prime}}(1+R^{ \prime\prime}(1-LE))}\] \[=\frac{C_{\ast}^{\prime}\frac{(1-E)L}{1-LE}\left(1+R^{\prime \prime}(1-LE)\right)}{N_{\ast}^{\prime}\left(1+R^{\prime\prime}\right)+C_{\ast }^{\prime}\frac{1-L}{1-LE}\left(1+R^{\prime\prime}(1-LE)\right)}\] \[=\frac{\frac{C_{\ast}^{\prime}}{C_{\ast}^{\prime}}\frac{(1-E)L}{ 1-LE}}{\frac{N_{\ast}^{\prime}}{T_{\ast}^{\prime}}\frac{(1+R^{\prime\prime})}{ 1+R^{\prime\prime}(1-LE)}+\frac{C_{\ast}^{\prime}}{T_{\ast}^{\prime}}\frac{1- L}{1-LE}}\] (S5)
Like for determining the fraction of infections in targeted individuals that did or did not receive the intervention (Eq. S3.1), we can also use Bayes Theorem to find the relative fractions of infections that occurred in individuals that were or were not targeted, \(\frac{C_{\ast}^{\prime}}{T_{\ast}^{\prime}}\) and \(\frac{N_{\ast}^{\prime}}{T_{\ast}^{\prime}}\):
\[\frac{C_{\ast}^{\prime}}{T_{\ast}^{\prime}}=P(i\in C|+)=\frac{P( +|i\in C)P(i\in C)}{P(+)}=\frac{(1-LE)p_{\mathrm{in}}}{(1-p_{\mathrm{in}})+(1- LE)p_{\mathrm{in}}} = \frac{(1-LE)p_{\mathrm{in}}}{1-LEp_{\mathrm{in}}}\] \[\frac{N_{\ast}^{\prime}}{T_{\ast}^{\prime}}=P(i\in N|+)=1-P(i\in C |+) = \frac{1-p_{\mathrm{in}}}{1-LEp_{\mathrm{in}}}\] (S6)
which means that,
\[\frac{\frac{C_{\ast}^{\prime}}{T_{\ast}^{\prime}}\frac{(1-E)L}{ 1-LE}}{\frac{N_{\ast}^{\prime}}{T_{\ast}^{\prime}}\frac{(1+R^{\prime\prime})}{ 1+R^{\prime\prime}(1-LE)}+\frac{C_{\ast}^{\prime}}{T_{\ast}^{\prime}}\frac{1- L}{1-LE}} =\frac{1-LEp_{\mathrm{in}}}{1-LEp_{\mathrm{in}}}\frac{(1-LE)p_{ \mathrm{in}}\frac{(1-E)L}{1-LE}}{(1-p_{\mathrm{in}})\frac{(1+R^{\prime\prime}) }{1+R^{\prime\prime}(1-LE)}+(1-LE)p_{\mathrm{in}}\frac{1-L}{1-LE}}\] \[=\frac{p_{\mathrm{in}}(1-E)L}{(1-p_{\mathrm{in}})\frac{(1+R^{ \prime\prime})}{1+R^{\prime\prime}(1-LE)}+p_{\mathrm{in}}(1-L)}\] (S7)
and therefore,
\[\frac{V_{\ast}^{\prime}+V_{\ast}}{N_{\ast}^{\prime}+N_{\ast}+U_ {\ast}^{\prime}+U_{\ast}} = \frac{p_{\mathrm{in}}(1-E)L}{(1-p_{\mathrm{in}})\frac{(1+R^{ \prime\prime})}{1+R^{\prime\prime}(1-LE)}+p_{\mathrm{in}}(1-L)}\] (S8)
In conventional TND studies there is no secondary recruitment. If secondary recruitment were eliminated under outbreak circumstances, that would imply that \(\lambda\to 0\), which also means that \(R^{\prime\prime}\to 0\). During outbreaks, the secondary process would still occur as part of the response (_i.e._ there would both testing and case-finding), but the people identified would not be recruited. Under that limit:\[\lim_{R^{\prime\prime}\to 0}\frac{1+R^{\prime\prime}}{1+R^{\prime\prime}(1-LE)} =1\] \[\lim_{R^{\prime\prime}\to 0}\frac{Lp_{\text{in}}(1-E)}{(1-p_{\text{in}}) \frac{1+R^{\prime\prime}}{1+R^{\prime\prime}(1-LE)}+p_{\text{in}}-Lp_{\text{in}}} =\frac{Lp_{\text{in}}(1-E)}{1-Lp_{\text{in}}}\] (S9)
which suggests a useful re-arrangement of the final form of the test-positive odds, so it has a clear separation of the terms which appear in the unbiased estimator (_i.e._ primary recruiting only) and the remaining factors:
\[\frac{Lp_{\text{in}}(1-E)}{(1-p_{\text{in}})\frac{1+R^{\prime\prime }}{1+R^{\prime\prime}(1-LE)}+p_{\text{in}}(1-L)} =\frac{Lp_{\text{in}}(1-E)}{(1-p_{\text{in}})\frac{1+R^{\prime \prime}}{1+R^{\prime\prime}(1-LE)}+p_{\text{in}}-Lp_{\text{in}}+1-1}\] \[\text{obtain }1-Lp_{\text{in}}\text{ term to factor out}... =\frac{Lp_{\text{in}}(1-E)}{(1-p_{\text{in}})\frac{1+R^{\prime \prime}}{1+R^{\prime\prime}(1-LE)}-(1-p_{\text{in}})+(1-Lp_{\text{in}})}\] \[\text{factor other term}... =\frac{Lp_{\text{in}}(1-E)}{(1-Lp_{\text{in}})+(1-p_{\text{in}}) \left(\frac{1+R^{\prime\prime}}{1+R^{\prime\prime}(1-LE)}-1\right)}\] \[\text{simplify other term}... =\frac{Lp_{\text{in}}(1-E)}{(1-Lp_{\text{in}})+(1-p_{\text{in}}) \left(\frac{LER^{\prime\prime}}{1+R^{\prime\prime}(1-LE)}\right)}\] \[\text{factor out target terms}... =\frac{Lp_{\text{in}}(1-E)}{1-Lp_{\text{in}}}\left[1+\frac{ER^{ \prime\prime}}{1+R^{\prime\prime}(1-LE)}\frac{L(1-p_{\text{in}})}{1-Lp_{\text {in}}}\right]^{-1}\] (S10)
In Eq. S10, we now have only terms that describe the intervention (targeted and coverage probabilities, \(p_{\text{in}}\) and \(L\), and efficacy \(E\)) and epidemiology (\(R^{\prime\prime}\)).
### Test-Negative Odds
We assume that the testing criteria for the secondary process is not affected by the presence of the intervention. For example, a contact-tracing-related criteria might be principally about high-risk interactions rather than particular symptoms, or the symptom threshold might be sufficiently relaxed that almost all contacts meet it. Similarly, a purely geographical criteria would be unaffected by presence or absence of the intervention. Thus, in our model all the prevented secondary infections (via true intervention efficacy \(E\)) are still recruited by the secondary process as test-negatives. This is a bounding assumption; see the end of this section for relaxing this assumption.
Turning to the test-negative odds, we first replace the primary test-negatives by the contribution from \(B\), the average number of test-negatives per test-positive via the primary route. Given that definition, the total number of primary test-negatives is \(T^{\prime}_{-}=BT^{\prime}_{+}\). Because the intervention has no effect on the causes that lead to testing negative via the primary route, the representation of individuals follows their proportions in the population:
\[\frac{N^{\prime}_{-}+U^{\prime}_{-}+N^{\prime\prime}_{-}+U^{\prime\prime}_{-}} {V^{\prime}_{-}+V^{\prime\prime}_{-}} =\frac{BT^{\prime}_{+}(1-Lp_{\text{in}})+N^{\prime\prime}_{-}+U^{\prime \prime}_{-}}{BT^{\prime}_{+}Lp_{\text{in}}+V^{\prime\prime}_{-}}\] (S11)
As with the test-positives odds, we can factorise and introduce identity multiples to re-arrange into terms that we can then use Bayes Theorem to replace with model parameters:\[\frac{BT_{+}^{\prime}(1-Lp_{\rm in})+N_{-}^{\prime\prime}+U_{-}^{ \prime\prime}}{BT_{+}^{\prime}Lp_{\rm in}+V_{-}^{\prime\prime}} = \frac{B(1-Lp_{\rm in})+\frac{1}{T_{+}^{\prime}}\left(N_{-}^{\prime \prime}+U_{-}^{\prime\prime}\right)}{BLp_{\rm in}+\frac{V_{-}^{\prime\prime}}{T _{+}^{\prime\prime}}}\] (S12) \[= \frac{B(1-Lp_{\rm in})+\left(\frac{N_{-}^{\prime}}{T_{+}^{\prime} }\frac{N_{-}^{\prime\prime}}{N_{+}^{\prime\prime}}+\frac{C_{+}^{\prime}}{T_{+} ^{\prime}}\frac{U_{-}^{\prime\prime}}{C_{+}^{\prime}}\right)}{BLp_{\rm in}+\frac {C_{+}}{T_{+}^{\prime}}\frac{V_{-}^{\prime\prime}}{C_{+}^{\prime\prime}}}\]
We can use the targeted and non-targeted fractions of primary test-positives, \(\frac{C_{+}^{\prime}}{T_{+}^{\prime}}\) and \(\frac{N_{+}^{\prime}}{T_{+}^{\prime}}\), from refactoring the test-positive odds (Eq. S6).
Amongst non-targeted individuals, on average \(\lambda-R^{\prime\prime}\) of recruits from the secondary route will be test-negative. This means that \(\frac{N_{-}^{\prime\prime}}{N_{+}^{\prime}}=\lambda-R^{\prime\prime}\).
This definition also implies that the exposed proportion is \(p_{t}=\frac{R^{\prime\prime}}{\lambda}\) because \(R^{\prime\prime}\) individuals are infected per \(\lambda\) secondary individuals. The complementary non-exposed proportion is therefore \(1-p_{t}=\frac{\lambda-R^{\prime\prime}}{\lambda}\). This value is like a transmission probability, though that interpretation should be used with caution: the denominator is determined by the secondary observation process, and thus the proportion may not clearly translate to the biological process probability.
Also by definition, amongst targeted individuals, only \(1-LE\) of the exposed individuals are infected, therefore:
\[\frac{C_{-}^{\prime\prime}}{C_{+}^{\prime}}=(1-p_{t}(1-LE))\lambda=\lambda-R^ {\prime\prime}(1-LE)\]
We again use Bayes Theorem to translate these ratios into model parameter expressions.
\[\frac{U_{-}^{\prime\prime}}{C_{-}^{\prime\prime}} = P(\text{is unvaccinated }|\text{ is not infected \& targeted})=P(i\in U|-,i\in C)=\frac{P(-|i\in U)P(i\in U|i\in C)}{P(-|i\in C)}\] \[=\frac{\frac{\lambda-R^{\prime\prime}}{\lambda}(1-L)}{\frac{ \lambda-R^{\prime\prime}}{\lambda}(1-L)+L\left(\frac{\lambda-R^{\prime\prime} }{\lambda}+\frac{R^{\prime\prime}}{\lambda}E\right)}=\frac{(\lambda-R^{\prime \prime})(1-L)}{\lambda-R^{\prime\prime}(1-LE)}\] \[\frac{V_{-}^{\prime\prime}}{C_{-}^{\prime\prime}} = 1-P(i\in U|-,i\in C)=\frac{(\lambda-(1-E)R^{\prime\prime})L}{ \lambda-(1-LE)R^{\prime\prime}}\] \[\frac{U_{-}^{\prime\prime}}{C_{+}^{\prime}} = \frac{U_{-}^{\prime\prime}}{C_{-}^{\prime\prime}}\frac{C_{-}^{ \prime\prime}}{C_{+}^{\prime}}=(\lambda-R^{\prime\prime})(1-L)\] \[\frac{V_{-}^{\prime\prime}}{C_{+}^{\prime}} = (\lambda-(1-E)R^{\prime\prime})L\] (S13)
Substituting these into the for the appropriate ratios, we obtain:
\[\frac{B(1-Lp_{\rm in})+\left(\frac{N_{-}^{\prime}}{T_{+}^{\prime}}\frac{N_{-} }{N_{+}^{\prime}}+\frac{C_{-}^{\prime}}{T_{+}^{\prime}}\frac{U_{-}^{\prime}}{C _{+}^{\prime}}\right)}{BLp_{\rm in}+\frac{C_{+}^{\prime}}{T_{+}^{\prime}}\frac{V _{-}^{\prime}}{C_{+}^{\prime}}} = \frac{B(1-Lp_{\rm in})+\left(\frac{1-p_{\rm in}}{1-LEp_{\rm in}}( \lambda-R^{\prime\prime})+\frac{(1-LE)p_{\rm in}}{1-LEp_{\rm in}}(\lambda-R^{ \prime\prime})(1-L)\right)}{BLp_{\rm in}+\frac{(1-LE)p_{\rm in}}{1-LEp_{\rm in}} (\lambda-(1-E)R^{\prime\prime})L}\] \[\frac{N_{-}^{\prime}+U_{-}^{\prime}+N_{-}+U_{-}}{V_{-}^{\prime}+V _{-}} = \frac{B(1-Lp_{\rm in})+\left(1-Lp_{\rm in}\frac{1-LE}{1-LEp_{\rm in }}\right)(\lambda-R^{\prime\prime})}{BLp_{\rm in}+Lp_{\rm in}\frac{1-LE}{1-LEp_{ \rm in}}(\lambda-R^{\prime\prime}+ER^{\prime\prime})}\] (S14)
As in Section S3.1, for the conventional TND assumptions, \(\lambda\to 0\) and \(R^{\prime\prime}\to 0\). Again, it is not that the secondary process ceases, but just that recruitment via that route is disallowed. Enforcing those constraints:\[\lim_{\lambda\to 0}\frac{B(1-Lp_{\text{in}})+\left(1-Lp_{\text{in}} \frac{1-LE}{1-LEp_{\text{in}}}\right)(\lambda-R^{\prime\prime})}{BLp_{\text{in}} +Lp_{\text{in}}\frac{1-LE}{1-LEp_{\text{in}}}(\lambda-R^{\prime\prime}+ER^{ \prime\prime})} =\frac{B(1-Lp_{\text{in}})+\left(1-Lp_{\text{in}}\frac{1-LE}{1- LEp_{\text{in}}}\right)0}{BLp_{\text{in}}+Lp_{\text{in}}\frac{1-LE}{1-LEp_{\text{in}}}0}\] \[=\frac{1-Lp_{\text{in}}}{Lp_{\text{in}}}\] (S15)
As with test-positives odds, we can refactor in terms of the conventional TND limit:
\[\frac{B(1-Lp_{\text{in}})+\left(1-Lp_{\text{in}}\frac{1-LE}{1-LEp _{\text{in}}}\right)(\lambda-R^{\prime\prime})}{BLp_{\text{in}}+Lp_{\text{in}} \frac{1-LE}{1-LEp_{\text{in}}}(\lambda-R^{\prime\prime}+ER^{\prime\prime})} =\frac{1-Lp_{\text{in}}}{Lp_{\text{in}}}\frac{B+\frac{1-Lp_{\text {in}}\frac{1-LE}{1-LEp_{\text{in}}}}{1-LEp_{\text{in}}}(\lambda-R^{\prime\prime }+ER^{\prime\prime})}{B+\frac{1-LE}{1-LEp_{\text{in}}}(\lambda-R^{\prime\prime }+ER^{\prime\prime})}\] \[=\frac{1-Lp_{\text{in}}}{Lp_{\text{in}}}\frac{B+\frac{1-LEp_{\text {in}}-Lp_{\text{in}}(1-LE)}{(1-Lp_{\text{in}})(1-LEp_{\text{in}})}(\lambda-R^{ \prime\prime})}{B+\frac{1-LE}{1-LEp_{\text{in}}}(\lambda-R^{\prime\prime}+ER^{ \prime\prime})}\] \[=\frac{1-Lp_{\text{in}}}{Lp_{\text{in}}}\frac{B+\frac{1-Lp_{\text {in}}-LEp_{\text{in}}+L^{2}Ep_{\text{in}}}{1-Lp_{\text{in}}-LEp_{\text{in}}+L^ {2}Ep_{\text{in}}^{2}}(\lambda-R^{\prime\prime})}{B+\frac{1-LE}{1-LEp_{\text{ in}}}(\lambda-R^{\prime\prime}+ER^{\prime\prime})}\] (S16)
In Eq. S16, we now have only terms that describe the intervention (\(p_{\text{in}}\), \(L\), and \(E\)) and epidemiology (\(R^{\prime\prime}\), \(\lambda\), and \(B\)). Note that this term includes more of the model parameters than the test-positive odds (Eq. S10).
### Relaxing Assumption that Prevented Infections Remain Secondary Recruits
Earlier, we assumed that the secondary recruitment process was unperturbed by the study intervention. For a secondary process that is, for example, purely geographical because it concerns a pathogen that is highly asymptomatic (_e.g._, neighbor-household testing for dengue), this assumption is consistent. Where it becomes less clearly acceptable as a simplification, is if there remains some disease- or symptom-based component to secondary recruitment.
In the main text, we focus on a vaccine study for EVD, where the primary process was self-reporting with multiple EVD-like symptoms leading to testing. The secondary process is nominally contact-tracing combined with a fever. We assumed that subjective fever would almost always be present for the contacts that avoided EVD infection because of the vaccine. In reality there would be some attack rate less than 100%.
If we define the proportion of people meeting a symptom-based component of the secondary process as \(\alpha\) and ignore the zero-bias term (Eq. S15) as a coefficient, then Eq. S16 becomes:
\[\text{test-negative odds}\propto\frac{B+\frac{1-Lp_{\text{in}}-LEp_{\text{in}} +L^{2}Ep_{\text{in}}}{1-Lp_{\text{in}}-LEp_{\text{in}}+L^{2}Ep_{\text{in}}^{2} }(\lambda-R^{\prime\prime})}{B+\frac{1-LE}{1-LEp_{\text{in}}}(\lambda-R^{\prime \prime}+E\alpha R^{\prime\prime})}\] (S17)
That is, of all the potential secondary recruits that could be added to test-negatives due to prevention of infection, only some exhibit the additional criteria. Note that there is no impact of relaxing this assumption on the test-positive odds.
If \(\alpha\to 1\), _i.e._ everyone meets this extra criteria, we get Eq. S16. As \(\alpha\to 0\), the denominator decreases, increasing the test-negative odds overall, and in turn reducing the estimated effectiveness. When \(\alpha=0\):\[\text{test-negative~odds}\propto\frac{B+\frac{1-Lp_{\text{in}}-LEp_{\text{in}}+L^{2}Ep_ {\text{in}}}{1-Lp_{\text{in}}-LEp_{\text{in}}+L^{2}Ep_{\text{in}}^{2}}\left( \lambda-R^{\prime\prime}\right)}{B+\frac{1-LE}{1-LEp_{\text{in}}}(\lambda-R^{ \prime\prime})}\] (S18)
In the case of \(p_{\text{in}}=1\), this reduces to unity.
\[Lp_{\text{in}}\leq L \implies 1-Lp_{\text{in}}\geq 1-L\implies\frac{1-L}{1-Lp_{\text{in}}} \leq 1\] \[\implies 1\geq p_{\text{in}}\frac{1-L}{1-Lp_{\text{in}}}\implies LE \geq LEp_{\text{in}}\frac{1-L}{1-Lp_{\text{in}}}\] \[\implies 1-LE\leq 1-LEp_{\text{in}}\frac{1-L}{1-Lp_{\text{in}}} \implies 1-LE\leq\frac{1-Lp_{\text{in}}-LEp_{\text{in}}-L^{2}Ep_{\text{in}}}{1-Lp_{ \text{in}}}\] \[\implies \frac{1-LE}{1-LEp_{\text{in}}}\leq\frac{1-Lp_{\text{in}}-LEp_{ \text{in}}-L^{2}Ep_{\text{in}}}{(1-LEp_{\text{in}})(1-Lp_{\text{in}})}\] \[\implies B+\frac{1-LE}{1-LEp_{\text{in}}}(\lambda-R^{\prime\prime}) \leq B+\frac{1-Lp_{\text{in}}-LEp_{\text{in}}-L^{2}Ep_{\text{in}}}{(1-LEp_{ \text{in}})(1-Lp_{\text{in}})}(\lambda-R^{\prime\prime})\] \[\implies 1\leq\frac{B+\frac{1-Lp_{\text{in}}-LEp_{\text{in}}-L^{2}Ep_{ \text{in}}}{(1-LEp_{\text{in}})(1-Lp_{\text{in}})}(\lambda-R^{\prime\prime})}{ B+\frac{1-LE}{1-LEp_{\text{in}}}(\lambda-R^{\prime\prime})}\] (S19)
This means that without any contribution from \(\alpha\), test-negative odds biases increasingly towards underestimation as targeted fraction decreases. As \(\alpha\to 1\), this effect is counteracted, but can in turn lead to overestimation of effectiveness.
## S4 Total Estimator Bias & Limiting Scenarios
Combining the test-positives odds and test-negatives odds:
\[\hat{E} =1-\frac{V_{+}^{\prime}+V_{+}^{\prime\prime}}{N_{+}^{\prime}+N_{ \prime\prime}^{\prime}+U_{+}^{\prime}+U_{+}^{\prime\prime}}\frac{N_{-}^{\prime }+U_{-}^{\prime}+N_{-}^{\prime\prime}+U_{-}^{\prime\prime}}{V_{-}^{\prime}+V_{ -}^{\prime\prime}}\] \[=1-\frac{Lp_{\text{in}}(1-E)}{1-Lp_{\text{in}}}\left[1+\frac{ER^ {\prime\prime}}{1+R^{\prime\prime}(1-LE)}\frac{L(1-p_{\text{in}})}{1-Lp_{\text {in}}}\right]^{-1}\frac{1-Lp_{\text{in}}}{Lp_{\text{in}}}\frac{B+\frac{1-Lp_{ \text{in}}-LEp_{\text{in}}+L^{2}Ep_{\text{in}}}{1-Lp_{\text{in}}-LEp_{\text{in} }+L^{2}Ep_{\text{in}}^{2}}\left(\lambda-R^{\prime\prime}\right)}{B+\frac{1-LE} {1-LEp_{\text{in}}}(\lambda-R^{\prime\prime}+ER^{\prime\prime})}\] \[=1-(1-E)\left[1+\frac{ER^{\prime\prime}}{1+R^{\prime\prime}(1-LE )}\frac{L(1-p_{\text{in}})}{1-Lp_{\text{in}}}\right]^{-1}\frac{B+\frac{1-Lp_{ \text{in}}-LEp_{\text{in}}+L^{2}Ep_{\text{in}}}{1-Lp_{\text{in}}-LEp_{\text{in} }+L^{2}Ep_{\text{in}}^{2}}\left(\lambda-R^{\prime\prime}\right)}{B+\frac{1-LE} {1-LEp_{\text{in}}}(\lambda-R^{\prime\prime}+ER^{\prime\prime})}\] (S20)
This suggests a different factorization:
\[\hat{E}=1-(1-E)\left[1+\frac{E\frac{R^{\prime\prime}}{\lambda} \frac{\lambda}{B+1}(B+1)}{1+\frac{R^{\prime\prime}}{\lambda}\frac{\lambda}{B+ 1}(B+1)(1-LE)}\frac{L(1-p_{\text{in}})}{1-Lp_{\text{in}}}\right]^{-1}\frac{1+ \frac{1-Lp_{\text{in}}-LEp_{\text{in}}+L^{2}Ep_{\text{in}}}{1-Lp_{\text{in}}- LEp_{\text{in}}+L^{2}Ep_{\text{in}}^{2}}\frac{\lambda}{B+1}\frac{B+1}{B} \left(1-\frac{R^{\prime\prime}}{\lambda}\right)}{1+\frac{1-LE}{1-LEp_{\text{in} }}\frac{\lambda}{B+1}\frac{B+1}{B}(1-\frac{R^{\prime\prime}}{\lambda}+E\frac{R^ {\prime\prime}}{\lambda})}\] (S21)
We can define secondary test-positive fraction, \(p_{t}=\frac{R^{\prime\prime}}{\lambda}\), the negative proportion of primary alerts, \(f_{-}=\frac{B}{B+1}\), and relative rate of secondary recruitment to primary recruitment, \(\rho=\frac{\lambda}{B+1}\). Noting that \(B+1=(1-f_{-})^{-1}\) This yields:\[\hat{E}=1-(1-E)\left[1+\frac{E\frac{p_{t}\rho}{1-f_{-}}}{1+\frac{p_{t}\rho}{1-f_{-} }(1-LE)}\frac{L(1-p_{\text{in}})}{1-Lp_{\text{in}}}\right]^{-1}\frac{1+\frac{1- Lp_{\text{in}}-LEp_{\text{in}}+L^{2}Ep_{\text{in}}}{1-Lp_{\text{in}}-LEp_{\text{in}}+L^{2}Ep_{ \text{in}}^{2}}\frac{\rho}{f_{-}}\left(1-p_{t}\right)}{1+\frac{1-LEp_{\text{in} }}{1-LEp_{\text{in}}}\frac{\rho}{f_{-}}(1-p_{t}(1-E))}\] (S22)
We use this framing for all the main text results. This formulation highlights the important relative values within the model, while still maintaining terms that can be reasoned about and potentially measured. In this framing \(\hat{E}\) is still a function of six variables, _i.e._\(\{E,L,p_{\text{in}},R^{\prime\prime},\lambda,B\}\)_versus_\(\{E,L,p_{\text{in}},p_{t},\rho,f_{-}\}\).
In the following subsections, we show limiting conditions for the estimator with respect to the assorted parameters.
### True efficacy, \(E\), limits
As the intervention tends toward either doing nothing (\(E\to 0\)) or perfect protection (\(E\to 1\)), the estimator bias tends to vanish.
\[\lim_{E\to 0}\hat{E} =1-^{-1}\,\frac{1+\frac{1-Lp_{\text{in}}}{1-Lp_{\text{in}}} \frac{\rho}{f_{-}}\left(1-p_{t}\right)}{1+\frac{\rho}{f_{-}}(1-p_{t})}=1-1=0\] \[\lim_{E\to 1}\hat{E} =1-0\left(\cdots\right)=1\] (S23)
### Targeted fraction, \(p_{\text{in}}\), limits
\[\lim_{p_{\text{in}}\to 0}\hat{E} =1-(1-E)\left[1+\frac{LE\frac{p_{t}\rho}{1-f_{-}}}{1+\frac{p_{t} \rho}{1-f_{-}}(1-LE)}\right]^{-1}\frac{1+\frac{1}{1}\frac{\rho}{f_{-}}\left(1- p_{t}\right)}{1+\frac{1-LE}{1}\frac{\rho}{f_{-}}(1-p_{t}(1-E))}\] \[=1-(1-E)\left[\frac{1+\frac{p_{t}\rho}{1-f_{-}}}{1+\frac{p_{t} \rho}{1-f_{-}}(1-LE)}\right]^{-1}\frac{1+\frac{\rho}{f_{-}}\left(1-p_{t}\right) }{1+(1-LE)\frac{\rho}{f_{-}}(1-p_{t}(1-E))}\] \[=1-(1-E)\left[\frac{1+\frac{p_{t}\rho}{1-f_{-}}}{1+\frac{p_{t} \rho}{1-f_{-}}(1-LE)}\right]^{-1}\frac{1+\frac{\rho}{f_{-}}\left(1-p_{t}\right) }{1+(1-LE)\frac{\rho}{f_{-}}(1-p_{t}(1-E))}\] \[=1-(1-E)\frac{1+\frac{p_{t}\rho}{1-f_{-}}(1-LE)}{1+\frac{p_{t} \rho}{1-f_{-}}}\frac{1+\frac{\rho}{f_{-}}\left(1-p_{t}\right)}{1+(1-LE)\frac{ \rho}{f_{-}}(1-p_{t}(1-E))}\] (S24)\[\lim_{p_{in}\to 1}\hat{E} = 1-(1-E)\left[1\right]^{-1}\frac{B+\left[1+\frac{L}{1-L}D\right]( \lambda-R^{\prime\prime})}{B+(\lambda-R^{\prime\prime}+ER^{\prime\prime})}\] (S25) \[= 1-(1-E)\left[1+0\frac{E\frac{p_{t}p_{t}}{1-f_{-}}}{1+\frac{p_{t} p}{1-f_{-}}(1-LE)}\right]^{-1}\frac{1+\frac{1-L-LE+L^{2}E}{1-L-LE+L^{2}E}\frac{ \rho}{f_{-}}\left(1-p_{t}\right)}{1+\frac{1-LE}{1-LE}\frac{\rho}{f_{-}}\left(1- p_{t}(1-E)\right)}\] \[= 1-(1-E)\frac{1+\frac{\rho}{f_{-}}\left(1-p_{t}\right)}{1+\frac{ \rho}{f_{-}}(1-p_{t}(1-E))}\] \[= 1-(1-E)\frac{B+\lambda-R^{\prime\prime}}{B+\lambda-R^{\prime \prime}+ER^{\prime\prime}}\] \[= 1-(1-E)\frac{1-\frac{R^{\prime\prime}}{B+\lambda}}{1-\frac{R^{ \prime\prime}}{B+\lambda}(1-E)}\]
The final factorization in Eq. S25 shows that, in the limit of perfect alignment of targeting and recruitment, the intervention coverage, \(L\), is removed, and the bias depends only on the true efficacy, \(E\), and a combination of epidemiological parameters: \(\frac{R^{\prime\prime}}{B+\lambda}\). This relationship can be inverted; which allows us to determine the true efficacy in terms of the estimator value and other parameters:
\[1-\hat{E} = (1-E)\frac{1-\frac{R^{\prime\prime}}{B+\lambda}}{1-\frac{R^{\prime \prime}}{B+\lambda}(1-E)}\] \[\left(1-\hat{E}\right)\left(1-\frac{R^{\prime\prime}}{B+\lambda}( 1-E)\right) = (1-E)\left(1-\frac{R^{\prime\prime}}{B+\lambda}\right)\] \[\left(1-\hat{E}\right) = (1-E)\left[1-\frac{R^{\prime\prime}}{B+\lambda}+\left(1-\hat{E} \right)\frac{R^{\prime\prime}}{B+\lambda}\right]\] \[(1-E) = (1-\hat{E})\left[1-\hat{E}\frac{R^{\prime\prime}}{B+\lambda} \right]^{-1}\] \[E = 1-\left(1-\hat{E}\right)\left[1-\hat{E}\frac{R^{\prime\prime}}{B +\lambda}\right]^{-1}\] \[E-\hat{E} = (1-\hat{E})\left(1-\left[1-\hat{E}\frac{R^{\prime\prime}}{B+ \lambda}\right]^{-1}\right)\] \[E-\hat{E} = -(1-\hat{E})\left(\frac{\hat{E}\frac{R^{\prime\prime}}{B+\lambda }}{1-\hat{E}\frac{R^{\prime\prime}}{B+\lambda}}\right)\] (S26)
\(\frac{R^{\prime\prime}}{B+\lambda}\) corresponds to a potentially measurable quantity; recall that in the model, \(R^{\prime\prime}\) is the expected number of additional test-positives that are identified via the secondary process in a group without the intervention, and \(B+\lambda\) is all the other tests (primary negatives and all secondary tests) per primary test-positive. Thus, \(\frac{R^{\prime\prime}}{B+\lambda}\) is the fraction of secondary test-positives out of all non-index case-finding tests, when measuring in a non-intervention group. This value could be estimated from a comparable population without the intervention, or an upper limit could be estimated from data within the study population itself: the expected number of secondary cases in the intervention population is \(R^{\prime\prime}(1-LE)\), so the measured non-primary test-positive fraction would be reduced maximally by a factor \((1-L)\) when the efficacy is perfect. Note that because this factor only has \(B+\lambda\), we do not need to distinguish primary versus secondary test-negatives. If a test-negative from \(\lambda\) was mistakenly assigned to \(B\) (or _vice versa_), that would not change this factor.
Thus, if a study were able to achieve \(p_{\text{in}}\approx 1\), it only need to be able to distinguish between primary and secondary test-positives to correctly bound the estimator.
### Secondary Case Recruitment, \(p_{t}\), limits
If we consider secondary _case_ limits, that is what proportion of secondary recruiting is test-positive, then we obtain:
\[\lim_{p_{t}\to 0}\hat{E} =1-(1-E)\left[1+\frac{0}{1+0}\frac{L(1-p_{\text{in}})}{1-Lp_{\text {in}}}\right]^{-1}\frac{1+\frac{1-Lp_{\text{in}}-LEp_{\text{in}}+L^{2}Ep_{\text {in}}}{1-Lp_{\text{in}}-LEp_{\text{in}}+L^{2}Ep_{\text{in}}^{2}}\frac{\rho}{f_{ -}}}{1+\frac{1-LE}{1-LEp_{\text{in}}}\frac{\rho}{f_{-}}}\] \[=1-(1-E)\frac{1+\frac{1-Lp_{\text{in}}-LEp_{\text{in}}+L^{2}Ep_{ \text{in}}}{1-Lp_{\text{in}}-LEp_{\text{in}}+L^{2}Ep_{\text{in}}^{2}}\frac{ \rho}{f_{-}}}{1+\frac{1-LE}{1-LEp_{\text{in}}}\frac{\rho}{f_{-}}}\] \[\lim_{p_{t}\to 1}\hat{E} =1-(1-E)\left[1+\frac{E\frac{\rho}{1-f_{-}}}{1+\frac{\rho}{1-f_{ -}}(1-LE)}\frac{L(1-p_{\text{in}})}{1-Lp_{\text{in}}}\right]^{-1}\frac{1+\frac{ 1-LEp_{\text{in}}-LEp_{\text{in}}+L^{2}Ep_{\text{in}}}{1-Lp_{\text{in}}-LEp_{ \text{in}}+L^{2}Ep_{\text{in}}^{2}}\frac{\rho}{f_{-}}0}{1+\frac{1-LE}{1-LEp_{ \text{in}}}\frac{\rho}{f_{-}}E}\] \[=1-(1-E)\left[1+\frac{E\frac{\rho}{1-f_{-}}}{1+\frac{\rho}{1-f_{ -}}(1-LE)}\frac{L(1-p_{\text{in}})}{1-Lp_{\text{in}}}\right]^{-1}\frac{1}{1+ \frac{1-LE}{1-LEp_{\text{in}}}\frac{\rho}{f_{-}}E}\] (S27)
One way to interpret \(p_{t}\to 1\) is that transmission probability (conditional on high risk contact) is going up. Another way to think about it is \(\lambda\) coming down to meet \(R^{\prime\prime}\); _i.e._, the decision about whether to test a contact or not becoming more accurately linked to whether they were infected.
### Lower Limit on Secondary Relative Recruiting, \(\rho\)
As primary recruiting increasingly outweighs secondary recruiting (including both increasing primary recruitment and disallowing secondary recruitment), \(\rho\to 0\). In this limit:
\[\lim_{\rho\to 0}\hat{E} =1-(1-E)\left[1+\frac{0}{1+0}\frac{L(1-p_{\text{in}})}{1-Lp_{ \text{in}}}\right]^{-1}\frac{1+\frac{1-Lp_{\text{in}}-LEp_{\text{in}}+L^{2}Ep_ {\text{in}}}{1-Lp_{\text{in}}-LEp_{\text{in}}+L^{2}Ep_{\text{in}}^{2}}\frac{0} {f_{-}}\left(1-p_{t}\right)}{1+\frac{1-LE}{1-LEp_{\text{in}}}\frac{0}{f_{-}} \left(1-p_{t}(1-E)\right)}\] \[=1-(1-E)\left[1\right]^{-1}\frac{1}{1}=E\] (S28)
Thus, for sufficiently high rate of primary recruitment leading to test-negatives, the bias goes to 0.
## S5 Hybrid Study Design
Given that the bias in conventional design arises from aggregating the primary and secondary recruitment routes, we might expect that treating the recruitment routes as separate could limit this bias. If we consider the secondary recruitment population as a cohort study, then the conventional cohort design estimator is:
\[\frac{\text{estimated}}{\text{effectiveness}}=1-\frac{\text{attack rate in individuals receiving study intervention}}{\text{attack rate in remaining individuals}}\] \[\hat{E}=1-\frac{V_{+}^{\prime\prime}}{V^{\prime\prime}}\times \frac{N^{\prime\prime}+U^{\prime\prime}}{N_{+}^{\prime\prime}+U_{+}^{\prime \prime}}=1-\frac{V_{+}^{\prime\prime}}{N_{+}^{\prime\prime}+U_{+}^{\prime \prime}}\times\frac{N^{\prime\prime}+U^{\prime\prime}}{V^{\prime\prime}}\] (S29)We make a simpler argument in the main text, but we can also use previously identified relationships to show this is unbiased. Recall Eq. S4 and additional definitions:
\[\frac{V^{\prime}_{+}}{C^{\prime}_{+}} =\frac{V^{\prime\prime}_{+}}{C^{\prime\prime}_{+}} = \frac{(1-E)L}{1-LE}\] \[\frac{U^{\prime}_{+}}{C^{\prime}_{+}} =\frac{U^{\prime\prime}_{+}}{C^{\prime\prime}_{+}} = \frac{1-L}{1-LE}\] \[\frac{N^{\prime\prime}}{N^{\prime}_{+}} =\lambda\] \[\frac{V^{\prime\prime}}{C^{\prime}_{+}} =L\lambda\] \[\frac{U^{\prime\prime}}{C^{\prime}_{+}} =(1-L)\lambda\] (S30)
Using a similar approach as that for the TND estimator, and re-using those ratios:
\[\hat{E} =1-\frac{\frac{C^{\prime}_{+}}{T^{\prime}_{+}}\frac{V^{\prime \prime}_{+}}{C^{\prime}_{+}}}{\frac{N^{\prime}_{+}}{T^{\prime}_{+}}\frac{C^{ \prime}_{+}}{T^{\prime}_{+}}\frac{N^{\prime\prime}_{+}}{C^{\prime}_{+}}}\frac{ \frac{N^{\prime}_{+}}{T^{\prime\prime}_{+}}+\frac{C^{\prime}_{+}}{T^{\prime}_ {+}}\frac{U^{\prime\prime}_{+}}{C^{\prime}_{+}}}{\frac{C^{\prime}_{+}}{C^{ \prime}_{+}}\frac{V^{\prime\prime}_{+}}{C^{\prime}_{+}}}\] \[=1-\frac{\frac{C^{\prime\prime}_{+}}{C^{\prime}_{+}}\frac{V^{ \prime\prime}_{+}}{C^{\prime\prime}_{+}}}{\frac{N^{\prime}_{+}}{T^{\prime}_{+} }\frac{N^{\prime\prime}_{+}}{T^{\prime}_{+}}\frac{N^{\prime\prime}_{+}}{C^{ \prime}_{+}}\frac{N^{\prime\prime}_{+}}{C^{\prime\prime}_{+}}}\frac{\frac{N^{ \prime}_{+}}{T^{\prime}_{+}}+\frac{C^{\prime}_{+}}{T^{\prime}_{+}}(1-L)\lambda} {L}\] \[=1-\frac{R^{\prime\prime}(1-LE)\frac{V^{\prime}_{+}}{C^{\prime}_{ +}}}{\frac{N^{\prime}_{+}}{T^{\prime}_{+}}R^{\prime\prime}+\frac{C^{\prime}_{+ }}{T^{\prime}_{+}}R^{\prime\prime}(1-LE)\frac{V^{\prime}_{+}}{C^{\prime}_{+}}} \times\frac{\frac{N^{\prime}_{+}}{T^{\prime}_{+}}+\frac{C^{\prime}_{+}}{T^{ \prime}_{+}}(1-L)}{L}\] (S31) \[=1-\frac{(1-E)L}{\frac{N^{\prime}_{+}}{T^{\prime}_{+}}+\frac{C^{ \prime}_{+}}{T^{\prime}_{+}}(1-L)}\times\frac{\frac{N^{\prime}_{+}}{T^{\prime }_{+}}+\frac{C^{\prime}_{+}}{T^{\prime}_{+}}(1-L)}{L}\] \[=1-(1-E)=E\] \[=1-(1-E)=E\]
Eq. S31 implies that if it were possible to observe secondary cases (out of secondary contacts) as a cohort, there would be no bias in such a study, regardless of heterogeneity in vaccine uptake. Another advantage of this study design is that there's no uncertainty about testing criteria (high risk contacts, regardless of symptoms), unlike the test-negative design (where symptoms may play a role in secondary recruitment).
### Hybrid Estimator
We can now consider combining the TND estimator and the cohort estimator:
\[\hat{E}=1-\frac{\omega_{\text{OR}}\text{OR}_{\text{TND}}+\omega_{\text{RR}} \text{RR}_{\text{CS}}}{\sum\omega}\] (S32)
In this combination, the limiting condition for the TND of no secondary testing applies (all those individuals go into the cohort term) and thus the TND estimator is unbiased (per Eq. S28). We have just shown that the cohort study using only secondary recruitment is also unbiased (under our other assumptions). Thus, any weighted average of the terms, like Eq. S32, is also unbiased. Therefore, selection of these weights can optimize for other study features, such as power.
Translation of Limits to Recruitment Constraints for Conventional TND
### Attempting to Limit Recruitment to Targeted Population Only
Figures S2-S10 show the general response of the estimator to varying factors in the model. Each plot shows \(p_{\text{in}}\in\{0.01,0.1,0.25,0.5,0.75,0.9,1\}\) (columns) and \(p_{t}\in\{0.01,0.1,0.25,0.5,0.75,0.9,1\}\) (rows). Each plot shows one of the combinations of \(\rho\in\{1/9,1/3,1\}\) and \(f_{-}\in\{0.5,0.75,0.9\}\); \(\rho\) is indicated at the top of each plot, \(f_{-}\) on the right side.
These plots show some trends under specific conditions. In general, increasing targeted fraction decreases bias range, though not absolutely (_e.g._, \(\rho=1/9,p_{t}=1/4,f_{-}=0.75\)). Increasing coverage can shift bias towards underestimation or overestimation, depending \(p_{t}\).
Figure S2: **General Bias Sensitivity, 1 of 9**: These series of plots show general sensitivity of the TND estimator to all of the model parameters. For each plot, the rightmost column corresponds to very high (99%) targeted fraction, which indicates the minimal bias surface when the study manages to maximize targeted fraction. Recall, \(\rho=\frac{\lambda}{B+1}\) is the expected ratio of secondary to primary recruits; \(p_{t}=R^{\prime\prime}/\lambda\) is the expected fraction of secondary recruits that test positive when no intervention is present; and \(f_{-}=\frac{B}{B+1}\) is the expect fraction of primary recruits that are test-negative. _In this panel, \(\rho=1/9\) and \(f_{-}=0.5\).
Figure S3: **General Bias Sensitivity. 2 of 9**: Recall, \(\rho=\frac{\lambda}{B+1}\) is the expected ratio of secondary to primary recruits; \(p_{t}=R^{\prime\prime}/\lambda\) is the expected fraction of secondary recruits that test positive when no intervention is present; and \(f_{-}=\frac{B}{B+1}\) is the expect fraction of primary recruits that are test-negative. _In this panel, \(\rho=1/9\) and \(f_{-}=0.75\).
Figure S4: **General Bias Sensitivity. 3 of 9**: Recall, \(\rho=\frac{\lambda}{B+1}\) is the expected ratio of secondary to primary recruits; \(p_{t}=R^{\prime\prime}/\lambda\) is the expected fraction of secondary recruits that test positive when no intervention is present; and \(f_{-}=\frac{B}{B+1}\) is the expect fraction of primary recruits that are test-negative. _In this panel, \(\rho=1/9\) and \(f_{-}=0.9\).
Figure S5: **General Bias Sensitivity. 4 of 9**: Recall, \(\rho=\frac{\lambda}{B+1}\) is the expected ratio of secondary to primary recruits; \(p_{t}=R^{\prime\prime}/\lambda\) is the expected fraction of secondary recruits that test positive when no intervention is present; and \(f_{-}=\frac{B}{B+1}\) is the expect fraction of primary recruits that are test-negative. _In this panel, \(\rho=1/3\) and \(f_{-}=0.5\).
Figure S7: **General Bias Sensitivity. 6 of 9**: Recall, \(\rho=\frac{\lambda}{B+1}\) is the expected ratio of secondary to primary recruits; \(p_{t}=R^{\prime\prime}/\lambda\) is the expected fraction of secondary recruits that test positive when no intervention is present; and \(f_{-}=\frac{B}{B+1}\) is the expect fraction of primary recruits that are test-negative. _In this panel, \(\rho=1/3\) and \(f_{-}=0.9\).
Attempting to Limit to Primary Recruitment Only
An alternative approach to controlling the bias is to restrict to primary recruitment only. If we assume that the study excludes secondary recruitment perfectly for test-positives (_e.g._ because they are extensively monitored) but incompletely excludes secondary recruitment for test-negatives (_e.g._ because data for them is incomplete) then the full estimator equation:
\[\hat{E}=1-(1-E)\left[1+\frac{E\frac{p_{t}\rho}{1-f_{-}}}{1+\frac{p_{t}\rho}{1- f_{-}}(1-LE)}\frac{L(1-p_{\text{in}})}{1-Lp_{\text{in}}}\right]^{-1}\frac{1+ \frac{1-Lp_{\text{in}}-LEp_{\text{in}}+L^{2}Ep_{\text{in}}}{1-Lp_{\text{in}}- LEp_{\text{in}}+L^{2}Ep_{\text{in}}^{2}}\frac{\rho}{f_{-}}\left(1-p_{t} \right)}{1+\frac{1-LE}{1-LEp_{\text{in}}}\frac{\rho}{f_{-}}\left(1-p_{t}(1-E) \right)}\]
will lose the test-positive bias contribution, because it goes to 1 (note that for any non-zero \(p_{t}\), this term is less than 1):
\[\left[1+\frac{E\frac{0\rho}{1-f_{-}}}{1+\frac{0\rho}{1-f_{-}}(1-LE)}\frac{L(1 -p_{\text{in}})}{1-Lp_{\text{in}}}\right]^{-1}=1\] (S33)
So the overall bias becomes:
\[\hat{E}=1-(1-E)\frac{1+\frac{1-Lp_{\text{in}}-LEp_{\text{in}}+L^{2}Ep_{\text{ in}}}{1-Lp_{\text{in}}-LEp_{\text{in}}+L^{2}Ep_{\text{in}}^{2}}\frac{\beta\rho}{f _{-}}\left(1-p_{t}\right)}{1+\frac{1-LE}{1-LEp_{\text{in}}}\frac{\beta\rho}{f _{-}}(1-p_{t}(1-E))}\] (S34)
Note that this factor is simply reducing \(\rho\) in the test-negative odds term. Thus, we can drop \(\beta\) and instead reduce the range we consider for \(\rho\). The error expression for this scenario is:
\[E-\hat{E} =E-1+(1-E)\frac{1+\frac{1-Lp_{\text{in}}-LEp_{\text{in}}+L^{2}Ep_{ \text{in}}}{1-Lp_{\text{in}}-LEp_{\text{in}}+L^{2}Ep_{\text{in}}^{2}}\frac{ \rho}{f_{-}}\left(1-p_{t}\right)}{1+\frac{1-LE}{1-LEp_{\text{in}}}\frac{\rho}{ f_{-}}(1-p_{t}(1-E))}\] \[=(1-E)\left[\frac{1+\frac{1-Lp_{\text{in}}-LEp_{\text{in}}+L^{2}Ep _{\text{in}}}{1-Lp_{\text{in}}-LEp_{\text{in}}+L^{2}Ep_{\text{in}}^{2}}\frac{ \rho}{f_{-}}\left(1-p_{t}\right)}{1+\frac{1-LE}{1-LEp_{\text{in}}}\frac{\rho}{ f_{-}}(1-p_{t}(1-E))}-1\right]\] (S35)
For an unbiased estimate, the first term in the square brackets would need to be 1, which would imply:\[1+\frac{1-Lp_{\rm in}-LEp_{\rm in}+L^{2}Ep_{\rm in}}{1-Lp_{\rm in}-LEp _{\rm in}+L^{2}Ep_{\rm in}^{2}}\frac{\rho}{f_{-}}\left(1-p_{t}\right) =1+\frac{1-LE}{1-LEp_{\rm in}}\frac{\rho}{f_{-}}(1-p_{t}(1-E))\] \[\frac{1-Lp_{\rm in}-LEp_{\rm in}+L^{2}Ep_{\rm in}}{1-Lp_{\rm in}- LEp_{\rm in}+L^{2}Ep_{\rm in}^{2}}\frac{\rho}{f_{-}}\left(1-p_{t}\right) =\frac{1-LE}{1-LEp_{\rm in}}\frac{\rho}{f_{-}}(1-p_{t}(1-E))\] \[\frac{1-Lp_{\rm in}-LEp_{\rm in}+L^{2}Ep_{\rm in}}{1-Lp_{\rm in}} \left(1-p_{t}\right) =(1-LE)(1-p_{t}(1-E))\] \[\left(1-Lp_{\rm in}-LEp_{\rm in}+L^{2}Ep_{\rm in}\right)(1-p_{t}) =(1-LE)(1-Lp_{\rm in})(1-p_{t}(1-E))\] \[\left(1-LEp_{\rm in}-Lp_{\rm in}(1-LE)\right)(1-p_{t}) =\ldots\] \[\left(1-LEp_{\rm in}+LE-LE-Lp_{\rm in}(1-LE)\right)(1-p_{t}) =\ldots\] \[\left((1-Lp_{\rm in})(1-LE)+LE(1-p_{\rm in})\right)(1-p_{t}) =\ldots\] \[\left(1-Lp_{\rm in}\right)(1-LE)\left(1-p_{t}\right)+LE(1-p_{\rm in })\left(1-p_{t}\right) =(1-LE)(1-Lp_{\rm in})(1-p_{t})+(1-LE)(1-Lp_{\rm in})Ep_{t}\] \[LE(1-p_{\rm in})\left(1-p_{t}\right) =(1-LE)(1-Lp_{\rm in})Ep_{t}\] \[L(1-p_{\rm in})(1-p_{t}) =(1-LE)(1-Lp_{\rm in})p_{t}\]
There is no further reduction to the final line of Eq. S36, thus this term is only equal to 1 for specific combinations of \(\{L,E,p_{\rm in},p_{t}\}\). Nor is there a strict direction of inequality. For example, at \(L\approx 0\), the left hand side is less than or equal to the right, while at \(L\approx 1\) the inequality can be either direction depending on the value of \(p_{t}\). The directions of this inequality determine whether the residual term in Eq. S36 is greater than 1 (_i.e._, the left hand side is greater than the right) or less than 1 (_vice versa_).
Defining this residual term as \(Y\) for the moment, and term corresponding to the test-positives as \(X\) (which recall is \(X\leq 1\)), we can consider the magnitude of the error excluding only the secondary test-positives versus keeping all the secondary recruiting by:
\[\frac{|E-\hat{E}|}{|E-\hat{E}^{*}|}=\frac{(1-E)|YX-1|}{(1-E)|Y-1|}=\frac{|YX-1 |}{|Y-1|}\] (S37)
For \(Y\leq 1\), we know \(XY\leq Y\leq 1\) and thus \(XY-1\leq Y-1\leq 0\). This implies reduced (or at least the same) error magnitude whenever \(Y\leq 1\) holds, _i.e._ the left hand side of Eq. S36 is less than or equal to the right. Decreasing \(E\) always increases the right hand side without effecting the left, making the constraint harder to satisfy and the least true efficacy we considered was \(E=0\). Increasing \(p_{t}\) always decreases the left hand side while increasing the right, so the smallest \(p_{t}\) is also the most restrictive condition to meet this criterion. In the main text, the smallest value we considered was \(p_{t}\approx 0.07\). Under these circumstances:
\[\frac{L(1-p_{\rm in})}{1-Lp_{\rm in}}\stackrel{{?}}{{\leq}}\frac{ p_{t}}{(1-p_{t})}\approx 0.07\] (S38)
This only true for low \(L\) and high \(p_{\rm in}\) combinations, outside what we considered in the main text.
For \(Y>1\), some reduction in \(XY\) due the \(X\leq 1\) term reduces bias magnitude, namely if
\[XY\geq 1-(Y-1)\implies X\geq\frac{2-Y}{Y}\] (S39)
Of course, \(X\) and \(Y\) share terms, so
\(\{0.01,0.1,0.25,0.5,0.75,0.9,1\}\) (rows). Each plot shows one of the combinations of \(\rho\in\{1/9,1/3,1\}\) and \(f_{-}\in\{0.5,0.75,0.9\}\); \(\rho\) is indicated at the top of each plot, \(f_{-}\) on the right side.
In general, these plots show the same trends as Figures S2-S10, with lower bias magnitude and tendency to shift towards underestimation.
Figure S11: **Bias Sensitivity Without Secondary Test-Positives, 1 of 9**: These series of plots show sensitivity of the TND estimator which excludes secondary test-positives to all of the model parameters. For each plot, the rightmost column corresponds to very high (99%) targeted fraction, which indicates the minimal bias surface when the study manages to maximize targeted fraction. Recall, \(\rho=\frac{\lambda}{B+1}\) is the expected ratio of secondary to primary recuits; \(p_{t}=R^{\prime\prime}/\lambda\) is the expected fraction of secondary recruits that test positive when no intervention is present; and \(f_{-}=\frac{B}{B+1}\) is the expect fraction of primary recruits that are test-negative. _In this panel, \(\rho=1/9\) and \(f_{-}=0.5\).
Figure S12: **Bias Sensitivity Without Secondary Test-Positives. 2 of 9**: Recall, \(\rho=\frac{\lambda}{B+1}\) is the expected ratio of secondary to primary recruits; \(p_{t}=R^{\prime\prime}/\lambda\) is the expected fraction of secondary recruits that test positive when no intervention is present; and \(f_{-}=\frac{B}{B+1}\) is the expect fraction of primary recruits that are test-negative. _In this panel, \(\rho=1/9\) and \(f_{-}=0.75\).
Figure S13: **Bias Sensitivity Without Secondary Test-Positives. 3 of 9**: Recall, \(\rho=\frac{\lambda}{B+1}\) is the expected ratio of secondary to primary recruits; \(p_{t}=R^{\prime\prime}/\lambda\) is the expected fraction of secondary recruits that test positive when no intervention is present; and \(f_{-}=\frac{B}{B+1}\) is the expect fraction of primary recruits that are test-negative. _In this panel, \(\rho=1/9\) and \(f_{-}=0.9\).
Figure S14: **Bias Sensitivity Without Secondary Test-Positives. 4 of 9**: Recall, \(\rho=\frac{\lambda}{B+1}\) is the expected ratio of secondary to primary recruits; \(p_{t}=R^{\prime\prime}/\lambda\) is the expected fraction of secondary recruits that test positive when no intervention is present; and \(f_{-}=\frac{B}{B+1}\) is the expect fraction of primary recruits that are test-negative. _In this panel, \(\rho=1/3\) and \(f_{-}=0.5\).
Figure S15: **Bias Sensitivity Without Secondary Test-Positives. 5 of 9**: Recall, \(\rho=\frac{\lambda}{B+1}\) is the expected ratio of secondary to primary recruits; \(p_{t}=R^{\prime\prime}/\lambda\) is the expected fraction of secondary recruits that test positive when no intervention is present; and \(f_{-}=\frac{B}{B+1}\) is the expect fraction of primary recruits that are test-negative. _In this panel, \(\rho=1/3\) and \(f_{-}=0.75\).
Figure S16: **Bias Sensitivity Without Secondary Test-Positives. 6 of 9**: Recall, \(\rho=\frac{\lambda}{B+1}\) is the expected ratio of secondary to primary recruits; \(p_{t}=R^{\prime\prime}/\lambda\) is the expected fraction of secondary recruits that test positive when no intervention is present; and \(f_{-}=\frac{B}{B+1}\) is the expect fraction of primary recruits that are test-negative. _In this panel, \(\rho=1/3\) and \(f_{-}=0.9\).
Figure S17: **Bias Sensitivity Without Secondary Test-Positives. 7 of 9**: Recall, \(\rho=\frac{\lambda}{B+1}\) is the expected ratio of secondary to primary recuits; \(p_{t}=R^{\prime\prime}/\lambda\) is the expected fraction of secondary recruits that test positive when no intervention is present; and \(f_{-}=\frac{B}{B+1}\) is the expect fraction of primary recruits that are test-negative. _In this panel, \(\rho=1\) and \(f_{-}=0.5\).
Figure S18: **Bias Sensitivity Without Secondary Test-Positives. 8 of 9**: Recall, \(\rho=\frac{\lambda}{B+1}\) is the expected ratio of secondary to primary recruits; \(p_{t}=R^{\prime\prime}/\lambda\) is the expected fraction of secondary recruits that test positive when no intervention is present; and \(f_{-}=\frac{B}{B+1}\) is the expect fraction of primary recruits that are test-negative. _In this panel, \(\rho=1\) and \(f_{-}=0.75\)._
Figure S19: **Bias Sensitivity Without Secondary Test-Positives.**: Recall, \(\rho=\frac{\lambda}{B+1}\) is the expected ratio of secondary to primary recuits; \(p_{t}=R^{\prime\prime}/\lambda\) is the expected fraction of secondary recruits that test positive when no intervention is present; and \(f_{-}=\frac{B}{B+1}\) is the expect fraction of primary recruits that are test-negative. _In this panel, \(\rho=1\) and \(f_{-}=0.9\).
Calculation of Coverage, \(L\), and Targeted Fraction, \(p_{\text{in}}\)
In addition to parameters associated with epidemiology and response activities (\(B\), \(\lambda\), and \(R^{\prime\prime}\)), the values of \(L\) and \(p_{\text{in}}\) are required to determine what level of bias may be present. Our model proposes a population where there are three groups, non-targeted, and targeted individuals that receive the intervention or not. If we have an estimate for the size of the total recruitable population, we can use measures taken during the intervention distribution to estimate these values. Alternatively, additional data could be collected when testing recruits to estimate these values. The estimates proposed hereafter are not definitive; in addition to assuming our model of heterogeneity is a sufficiently useful approximation, they make further strong assumptions about behaviour around intervention uptake. However, as estimates they are potentially informative about the limits of \(p_{\text{in}}\) and \(L\) within the model framework we have proposed.
### Measures During Intervention Distribution
During distribution of the intervention, one could count the number of people receiving the intervention (\(V\)) and the number ineligible (\(U*\)). From those values we can compute the crude minimum and maximum values of \(L\) and \(p_{\text{in}}\) (where \(\max(L)\) corresponds to \(\min(p_{\text{in}})\), and _vice versa_).
\[L\in\left(\frac{V}{T},\frac{V}{V+U*}\right)\] \[p_{\text{in}}\in\left(0,1-\frac{V+U*}{T}\right)\] (S43)
In the model, we make no assumptions of how non-intervention occurs in the targeted population, just that it occurs randomly within that group. Thus the ineligible count represents the minimum non-intervention amongst the targeted population (the upper limit of \(L\)); there may be other sources (_e.g._, targeted individuals are unavailable on the day offered). Potentially, when distributing the intervention, targeted individuals could be asked about members of their household, neighbors, _etc._ that wanted to get the intervention, but were unable to do so, but this number would also have many uncertainties (_e.g._ duplicate reporting, reporting individuals that do receive the intervention at a different time or place).
If the study intervention has multiple steps (_e.g._ a two-dose vaccine, repeat application of vector-control insecticides), then the decrease in coverage between steps could be informative about the targeted fraction, \(p_{\text{in}}\). If we assume not receiving the intervention is due to a mix of short-term (_e.g._ ill that day) and long-term (_e.g._ too young to be eligible) effects, then we can potentially further constrain \(L\) and \(p_{\text{in}}\). In the following we assume that: i) long-term ineligibles only present themselves at the first step (though they may also not), ii) short-term ineligibles present at the same rate in the subsequent steps, and iii) individuals that did not present at earlier steps will also not present later. If we apply these assumptions to a two-step intervention, and we call unobserved long-term ineligibles \(I_{0}\), the long-term ineligibles that appear initially are \(I_{1}\), and the intervention recipients (\(V\)) and short-term ineligibles that present (\(U^{*}\)) or not (\(U\)) at each stage (\(V_{1},V_{2},U*_{1},U*_{2},U_{1},U_{2}\)), then the following relations hold.
We have six observed pieces of information: the total population (\(T\)), the number given the intervention versus short term ineligible at both steps (\(V_{1},V_{2},U*_{1},U*_{2}\)), and the number of long-term ineligibles at the first step (\(I_{1}\)).
We know that at the second intervention step, we have only people that got vaccinated in the previous step, no new long term ineligibles, and the breakdown of short term ineligibles versus those that receive the second step.
In the main text, we described applying this model to evaluating a novel vaccine during an Ebola outbreak, but noted in the discussion that the approach could be generically applicable. The previous sections outline the model in generic terms. Here we provide an example translation of that generalisation to another case: a vector control intervention for dengue.
In this scenario, we consider an intervention like indoor residual spraying, applied to urban households on a block basis (_i.e._ set of contiguous households, determined by street intersections) ahead of the dengue season. Some blocks would get no coverage (_i.e._ be amongst the non-targeted population), while others would receive coverage at some level (with non-coverage corresponding to _e.g._ availability to let treatment teams into house on that day or presence of children under some age).
Later, during the dengue season, people in the study population would seek healthcare with symptoms that would lead to testing for dengue, corresponding to the primary process. However, because dengue is frequently asymptomatic, the secondary process would be to test individuals in the primary cases household and adjacent households. Instead of a contacts-based secondary route, there is geospatial secondary route.
Whether a TND study would be ideal for this scenario is certainly a topic for debate. However, it is possible to frame this scenario and other potential pathogen spread and surveillance processes in the same terms we have introduced in this analysis. |
018523_file02 | ## 4.72
& -0.21 & 1.90E-04 & 3 & _RP4-555D20.2_ & miRNA \\
## 4.65
& -1.60 & 9.13E-04 & 17 & _IGF2BP1_ & Novel interacting partner of p38 MAPK. RNA-binding protein, involved in tumour progression \\
## 4.50
& -0.31 & 9.13E-04 & 5 & _GDNF_ & Glial cell derived neurotrophic factor \\
## 3.66
& 1.57 & 9.92E-04 & 18 & _CCBE1_ & High levels contribute to aggressiveness and poor prognosis of Colon Cancer \\
## 3.57
& 3.41 & 7.26E-04 & 12 & _WNT5B_ & Activator of WNT signalling \\
## 3.45
& -2.82 & 9.13E-04 & 15 & _CTD-_ & Non-coding cDNA \\
## 2.033D15.2
& & & _2033D15.2_ & miRNA \\
## 3.33
& -3.95 & 9.91E-04 & 3 & _RP4-555D20.4_ & miRNA \\
## 2.89
& -3.88 & 7.18E-04 & X & _RP11-320G24.1_ & miRNA \\
## 2.66
& 1.29 & 7.26E-04 & 17 & _HS3ST3A1_ & Tumour regulator and prognostic marker in breast cancer. \\
## 2.27
& 5.55 & 2.10E-04 & 1 & _NAVI_ & Potentiates migration of breast cancer cells \\
## 2.25
& 3.73 & 7.26E-04 & 2 & _CHN1_ & Actin dynamics in cell migration \\
## 2.15
& 3.41 & 7.26E-04 & 15 & _GPR176_ & Orphan G-protein-coupled receptor that sets the pace of circadian behaviour \\
## 1.95
& 6.25 & 2.58E-04 & 4 & _SEPT11_ & \\
## 1.73
& 5.81 & 9.57E-04 & 6 & _TRAM2_ & Putative metastatic factor for oral cancer \\
## 1.50
& 3.88 & 9.57E-04 & 2 & _SERTAD2_ & Promotes oncogenesis in nude mice and is frequently overexpressed in multiple human tumours. \\ \hline \end{tabular}
Genes differentially upregulated in sarcomatoid and mixed histology compared to epithelioid. Transcripts with average expression \(\geq\) 1 are shown. \(P\) values are adjusted for multiple comparisons (false discovery rate!0.05).
\begin{tabular}{l c c c c c c c c c} \hline \hline NCMR n=35 & \multicolumn{2}{c}{_SUFU_} & \multicolumn{2}{c}{_PTCH2_} & \multicolumn{2}{c}{_PTCH1_} & \multicolumn{2}{c}{_CR1_} & \multicolumn{2}{c}{_KLRD1_} & \multicolumn{2}{c}{_PD-L1_} \\ \hline _PTCH12_ & -0.38 & _2.5E-02_ & & & & & & & \\ _PTCH11_ & -0.37 & _3.1E-02_ & 0.75 & _1.7E-07_ & & & & & & \\ _CR1_ & 0.50 & _2.2E-03_ & -0.59 & _1.8E-04_ & -0.41 & _1.4E-02_ & & & & \\ _KLRD1_ & 0.37 & _2.9E-02_ & -0.60 & _1.4E-04_ & -0.52 & _1.3E-03_ & 0.56 & _5.1E-04_ & & & \\ _PD-L1_ & 0.10 & _3.5E-01_ & -0.39 & _2.2E-02_ & -0.44 & _8.1E-03_ & 0.35 & _4.1E-02_ & 0.37 & _2.8E-02_ & & \\ _VISTA_ & 0.61 & _1.1E-04_ & -0.52 & _1.3E-03_ & -0.41 & _1.3E-02_ & 0.43 & _1.0E-02_ & 0.68 & _7.3E-06_ & 0.09 & _6.1E-01_ \\ \hline \multicolumn{10}{l}{TGC-Mos n=86} & & & & & & & & \\ _PTCH2_ & -0.08 & _4.6E-01_ & & & & & & & & \\ _PTCH1_ & 0.09 & _3.9E-01_ & 0.77 & _2.2E-16_ & & & & & & \\ _CR1_ & -0.04 & _7.1E-01_ & -0.09 & _4.1E-01_ & -0.11 & _3.4E-01_ & & & & \\ _KLRD1_ & -0.04 & _7.0E-01_ & -0.36 & _6.2E-04_ & -0.33 & _1.9E-03_ & 0.41 & _7.9E-05_ & & & \\ _PD-L1_ & -0.26 & _1.7E-02_ & -0.22 & _4.0E-02_ & -0.30 & _5.5E-03_ & 0.35 & _8.1E-04_ & 0.40 & _1.7E-04_ & & \\ _VISTA_ & 0.25 & _2.1E-02_ & -0.47 & _5.9E-06_ & -0.25 & _2.2E-02_ & -0.06 & _5.9E-01_ & 0.37 & _4.8E-04_ & -0.09 & _4.0E-01_ \\ \hline \multicolumn{10}{l}{Bueno _et al._ n=211} & & & & & & & & & \\ _PTCH12_ & -0.22 & _1.4E-03_ & & & & & & & & \\ _PTCH11_ & -0.16 & _1.8E-02_ & _0.71_ & _2.2E-16_ & & & & & & \\ _CR1_ & 0.30 & _0.6E-06_ & -0.20 & _2.9E-03_ & -0.23 & _7.9E-04_ & & & & \\ _KLRD1_ & 0.26 & _1.1E-04_ & -0.37 & _3.1E-08_ & -0.35 & _2.4E-07_ & 0.49 & _7.1E-14_ & & & \\ _PD-L1_ & -0.08 & _2.3E-01_ & -0.16 & _1.7E-02_ & -0.31 & _6.0E-06_ & 0.42 & _2.8E-10_ & 0.38 & _1.2E-08_ & & \\ _VISTA_ & 0.27 & _5.6E-05_ & -0.36 & _6.0E-08_ & -0.27 & _8.3E-05_ & 0.06 & _3.9E-01_ & 0.36 & _6.8E-08_ & -0.06 & _3.5E-01_ \\ \hline \multicolumn{10}{l}{Combined studies} & & & & & & & & \\ _PTCH12_ & -0.21 & _9.96E-05_ & & & & & & & & \\ _PTCH11_ & -0.14 & _1.20E-02_ & 0.73 & _<2.2E-16_ & & & & & & \\ _CR1_ & 0.16 & _5.33E-03_ & -0.17 & _2.23E-03_ & -0.15 & _6.8E-03_ & & & & \\ _KLRD1_ & 0.14 & _9.8E-03_ & -0.33 & _6.71E-10_ & -0.28 & _3.33E-07_ & 0.55 & _<2.2E-16_ & & & \\ _PD-L1_ & -0.09 & _8.96E-02_ & -0.18 & _7.87E-04_ & -0.28 & _3.31E-07_ & 0.42 & _1.78E-15_ & 0.42 & _1.33E-15_ & & \\ _VISTA_ & 0.33 & _6.9E-10_ & -0.42 & _2.00E-15_ & -0.32 & _3.81E-09_ & -0.06 & _2.66E-01_ & 0.22 & _5.59E-05_ & -0.11 & _5.50E-02_ \\ \hline \hline \end{tabular} Pearson correlations between abundances of Hedgehog pathway transcripts _SUFU_, _PTCH1_, _PTCH2_ and transcripts related to immune checkpoints. The official gene names for PD-L1 and VISTA are _CD274_ and _VISR_, respectively. Results are shown for the present study, two previous investigations and for all studies combined. Two sided-_P_ values are shown in italics throughout.
Supplementary_Analytical structure
## a) Summary of samples used in each analysis; b) Venn diagram showing overlapping of samples used in WES, SNP genotyping and targeted capture sequencing (please refer to Supplementary File 2- Table1 for further details); c) Sankey diagram on histological subtype and patients' gender; d) Kaplan-Meier survival curves on histological subtypes
Oncoplot from targeted sequencing panel
## a)** Summary of mutation spectrum observed for genes from targeted capture sequencing panel; **b-d)** Distribution of mutations in _BAP1_, _NF2_, and _TP53_; **e)** Mutational signature in 21 paired MPM analysed by WES; **f)** Mean percentage of contribution for COSMIC signatures: red bars indicate signatures associated with DNA damage; **g)** Mutational signature in 19 patient-derived MPM cell lines; **h)** Mean percentage COSMIC signatures in each cell line; **i)
Tumour mutation burden (TMB) derived from targeted capture sequencing of 57-gene panel and hence abbreviated as 'Surrogate TMB', in 77 paired samples. Briefly, all somatic SNVs or, InDels observed per sample, across the gene-panel are summed to derive surrogate TMB.
Supplementary_WES and RNA sequencing correlations for _RASSF7_, _RB1_ and _SUFU_ in primary and replication datasets
Copy-number profiles from SNP array (NCMR, n=30) (panels **a**, **c** and **e**) or WES (Bueno _et al._, n=98) (**b**, **d** and **f**). were correlated with gene expression from RNA-sequencing. Homozygous vs. heterozygous deletions of _RB1_ and _SUFU_ loci could be predicted from SNP array data, but we could not discriminate homozygous vs. heterozygous amplification of _RASSF7_. In the Bueno _et al._ WES data only presence of absence of CNAs could be called. Kruskal-Wallis tests were applied to compare expression differences between three classes, and two classes were compared by Mann-Whitney tests. In each case the Bueno _et al._ results confirm the presence of correlations between CNA status and transcript abundance.
Oncoplot showing alterations in mesothelioma in whole-genome sequenced primary cell lines (19 mesothelioma and one mesothelial primary cell).
## a** and **b**) IGV (Integrated Genome Viewer) snapshots of matching genomic positions in patient tumour and the paired germline whole-exome sequencing (WES) BAM files. Upper panel shows germline somatic mutational load ((somatic SNV + InDels), lower panel shows tumour mutational load. **a**) is from a patient with somatic MSH6 loss and **b**) is from a patient with germline BRACA2 loss. **c
Tumour somatic mutational in tumour undergoing WES: BRACA2 and MHS6 mutations are at the extreme of the load spectrum |
018929_file02 | ## Figure S4: Simulation results under various scenarios.** These Raincloud boxplots represent the distribution of parameter estimates from 50 different data generations under various conditions. For each generation, standard MR methods as well as our LHC-MR were used to estimate a causal effect. The true values of the parameters used in the data generations are represented by the blue dots/lines. **a** Estimation under standard settings (\(\pi_{x}=5\times 10^{-3},\pi_{y}=1\times 10^{-2},\pi_{u}=5\times 10^{-2},h_{x}^{2}=0. 25,h_{y}^{2}=0.2,h_{u}^{2}=0.3,t_{x}=0.16,t_{y}=0.11\)). **b** Addition of a reverse causal effect \(\alpha_{y\to x}=-0.2\). **c
Confounder with opposite causal effects on \(X\) and \(Y\) (\(t_{x}=0.16,\overset{\text{th}}{\text{th}}_{y}=-0.11\)).
## Figure S5: Simulation results showing varying sample sizes for the two exposure and outcome samples**. Raincloud boxplots representing the distribution of parameter estimates from 50 different data generations. For each generation, standard MR methods as well as our LHC-MR were used to estimate a causal effect. The true values of the parameters used in the data generations are represented by the blue dots/lines.
## Figure S6: Simulation results under various scenarios.** These Raincloud boxplots represent the distribution of parameter estimates from 50 different data generations under various conditions. For each generation, standard MR methods as well as our LHC-MR were used to estimate a causal effect. The true values of the parameters used in the data generations are represented by the blue dots/lines. **a** The data simulated had no causal effect in either direction. **b** The data simulated had no confounder effect with \(\pi_{u},t_{x}\), and \(t_{y}=0\). **c
This model had a small causal effect of \(\alpha_{x\to y}=0.1\).
## Figure S7: Simulation results under various scenarios.** These Raincloud boxplots represent the distribution of parameter estimates from 50 different data generations under various conditions. For each generation, standard MR methods as well as our LHC-MR were used to estimate a causal effect. The true values of the parameters used in the data generations are represented by the blue dots/lines. **a** The data simulated had no causal effect in either direction. **b** The data simulated had no confounder effect with \(\pi_{u},t_{x}\), and \(t_{y}=0\). **c
This model had a small causal effect of \(\alpha_{x\to y}=0.1\).
## Figure S8: Simulation results under various scenarios.** These Raincloud boxplots represent the distribution of parameter estimates from 50 different data generations under various conditions. For each generation, standard MR methods as well as our LHC-MR were used to estimate a causal effect. The true values of the parameters used in the data generations are represented by the blue dots/lines. **a** The data simulated shows the increased effect of \(U\) on \(X\) and \(Y\) through \(t_{x}=0.41,t_{y}=0.27\) instead of the standard setting \(t_{x}=0.16,t_{y}=0.11\). **b
This panel show the same thing but with a larger sample size of \(n_{x}=n_{y}=500,000\)
## Figure S9: Simulation results where there is an increased polygenicity for all traits.** Box-plots representing the distribution of parameter estimates from 100 different data generations. For each generation, standard MR methods as well as our LHC-MR were used to estimate a causal effect. The true values of the parameters used in the data generations are represented by the blue dots/lines. The proportion of effective SNPs that make up the spike-and-slab distributions of the \(\gamma\) vectors in this setting is \(10\%,15\%,and20\%\) for traits \(X,Y\) and \(U\) respectively. **a** Results for smaller sample size of \(n_{x}=n_{y}=50,000\). **b
Results for larger sample size of \(n_{x}=n_{y}=500,000\).
## Figure S10: Simulation results where the polygenicity of the confounder is reduced.** Boxplots representing the distribution of parameter estimates from 100 different data generations. For each generation, standard MR methods as well as our LHC-MR were used to estimate a causal effect. The true values of the parameters used in the data generations are represented by the blue dots/lines. In this figure, the polygenicity for \(U\) is decreased in the form of lower \(\pi_{u}=0.01\). **a** Results for smaller sample size of \(n_{x}=n_{y}=50,000\). **b
Results for larger sample size of \(n_{x}=n_{y}=500,000\).
## Figure S11: Simulation results where there are two underlying confounders, once with concordant and another with discordant effects on the exposure-outcome pair.** Boxplots representing the distribution of parameter estimates from 100 different data generations. For each generation, standard MR methods as well as our LHC-MR were used to estimate a causal effect. The true values of the parameters used in the data generations are represented by the blue dots/lines. **a** The underlying data generations have two concordant heritable confounders \(U_{1}\) and \(U_{2}\) with positive effects on traits \(X\) and \(Y\). **b
The data generations have two discordant heritable confounders with \(t_{x}^{}=0.16,t_{y}^{}=0.11\) shown as blue dots and \(t_{x}^{}=0.22,t_{y}^{}=-0.16\) shown as red dots.
## Figure S12: Simulation results where there are two underlying confounders, once with concordant and another with discordant effects on the exposure-outcome pair.** Boxplots representing the distribution of parameter estimates from 100 different data generations. For each generation, standard MR methods as well as our LHC-MR were used to estimate a causal effect. The true values of the parameters used in the data generations are represented by the blue dots/lines. **a** The underlying data generations have two concordant heritable confounders \(U_{1}\) and \(U_{2}\) with positive effects on traits \(X\) and \(Y\). **b
The data generations have two discordant heritable confounders with \(t_{x}^{}=0.16,t_{y}^{}=0.11\) shown as blue dots and \(t_{x}^{}=0.22,t_{y}^{}=-0.16\) shown as red dots.
## Figure S13: Simulation results under various scenarios.** These Raincloud boxplots represent the distribution of parameter estimates from 50 different data generations under various conditions. For each generation, standard MR methods as well as our LHC-MR were used to estimate a causal effect. The true values of the parameters used in the data generations are represented by the blue dots/lines. **a** The different coloured boxplots represent the underlying non-normal distribution used in the simulation of the three \(\gamma_{x},\gamma_{x},\gamma_{u}\) vectors associated to their respective traits. The Pearson distributions had the same 0 mean and skewness, however their kurtosis ranged between 2 and 10, including the kurtosis of 3, which corresponds to a normal distribution assumed by our model. The standard MR results reported had IVs selected with a p-value threshold of \(5\times 10^{-6}\). **b
Addition of a third component for exposure \(X\), while decreasing the strength of \(U\). True parameter values are in colour, blue and red for each component (\(\pi_{x1}=1\times 10^{-4},\pi_{x2}=1\times 10^{-2},h_{x1}^{2}=0.15,h_{x2}^{2}=0.1\)).
## Figure S14: Running CAUSE on LHC-MR simulated data under the standard settings
Boxplots of the parameter estimation of CAUSE on LHC-simulated data (\(n_{x}=n_{y}=50,000\)) under three different scenarios: presence of a shared factor only, presence of a causal effect only, presence of both. CAUSE returns two possible models with a respective p-value, the sharing and the causal model, where the causal mode is the significant of the two. When only an underlying shared factor was present in the simulated data, CAUSE had no significant causal estimates. With a true underlying causal effect, or when both an underlying causal effect and a shared factor was present, the causal model was significant only 4% of the simulations.
## Figure S15: Running CAUSE on LHC-MR simulated data under the standard settings
Boxplots of the parameter estimation of CAUSE on LHC-simulated data (\(n_{x}=n_{y}=500,000\)) under three different scenarios: presence of a shared factor only, presence of a causal effect only, presence of both. CAUSE returns two possible models with a respective p-value, the sharing and the causal model, where the causal mode is the significant of the two. When only an underlying shared factor was present in the simulated data, CAUSE had no significant causal estimates. With a true underlying causal effect, or when both an underlying causal effect and a shared factor was present, the causal model was significant 100% of the simulations.
## Figure S16: Running LHC-MR on CAUSE simulated data under various scenarios**. Rain-cloud boxplots representing the distribution of parameter estimates from LHC-MR of 50 different data generations using the CAUSE framework. For each generation, standard MR methods, CAUSE as well as our LHC-MR were used to estimate a causal effect. The true values of the parameters used in the data generations are represented by the blue dots/lines. **a** CAUSE data was generated with no causal effect but with a shared factor with an \(\eta\) value of \(\sim 0.22\). CAUSE chooses a sharing model 100% of the time with no estimate for a causal effect. **b** CAUSE is simulated with causal effect but with no shared factor. **c
CAUSE is simulated with both a causal effect and a shared factor.
## Figure S17: Running LHC-MR on CAUSE simulated data under various scenarios**. Rain-cloud boxplots representing the distribution of parameter estimates from LHC-MR of 50 different data generations using the CAUSE framework. For each generation, standard MR methods, CAUSE as well as our LHC-MR were used to estimate a causal effect. The true values of the parameters used in the data generations are represented by the blue dots/lines. **a** CAUSE data was generated with no causal effect but with a shared factor with an \(\eta\) value of \(\sim 0.22\). **b** CAUSE is simulated with causal effect but with no shared factor. **c
CAUSE is simulated with both a causal effect and a shared factor. LHC-MR seems to exhibit a bimodal effect at first glance, but the two peaks are not connected.
## Figure S19: A scatter plot of the causal effect estimates between LHC-MR and CAUSE.
To improve visibility, non-significant estimates by both methods are placed at the origin, while significant estimates by both methods appear on the diagonal with 95% CI error bars for LHC-MR estimates, and 95% credible interval error bars for CAUSE estimates. Labelled pairs are those with an estimate difference greater than 0.1.
## Supplementary Tables
## Table S7: Cross tables between LHC-MR and various standard MR methods comparing the significance and sign of each respective causal estimate**. **f
\begin{table}
\begin{tabular}{l|c c|c|c c}
## Pair** & \(\alpha_{x\to y}\) & **p-value** & \(\gamma\) & **IVW**\(\alpha_{x\to y}\) & **p-value
\\ \hline \hline BMI-Asthma & 0.1290 & 4.99E-14 & 0.02 (0.01, 0.02) & 0.0593 & 1.00E-08 \\ BMI-DM & 0.2958 & 1.07E-99 & 0.04 (0.03, 0.04) & 0.2447 & 2.25E-140 \\ BMI-SBP & 0.1878 & 5.55E-09 & 0.13 (0.11, 0.14) & 0.1547 & 1.11E-24 \\ BMI-SVstat & 0.1670 & 2.08E-91 & 0.03 (0.03, 0.03) & 0.1570 & 4.26E-63 \\ BMI-MI & 0.1396 & 1.67E-41 & 0.01 (0.01, 0.01) & 0.1027 & 9.16E-32 \\ BWeight-SHeight & 0.4748 & 9.60E-18 & 0.34 (0.29, 0.39) & 0.2959 & 8.01E-10 \\ SHeight-BWeight & 0.1806 & 1.93E-53 & 0.24 (0.22, 0.25) & 0.1803 & 7.21E-86 \\ SBP-DM & 0.1437 & 3.17E-07 & 0.02 (0.01, 0.02) & 0.0697 & 3.69E-07 \\ DM-SVstat & 0.3147 & 4.11E-12 & 0.39 (0.33, 0.46) & 0.2524 & 1.28E-16 \\ SHeight-Edu & 0.0715 & 8.42E-09 & 0.08 (0.07, 0.09) & 0.0643 & 2.28E-21 \\ SBP-SVstat & 0.2089 & 4.84E-26 & 0.04 (0.04, 0.05) & 0.1853 & 1.46E-52 \\ Edu-HDL & 0.4037 & 5.25E-12 & 0.22 (0.17, 0.27) & 0.2848 & 4.06E-08 \\ BMI-CAD & 0.2373 & 2.37E-64 & 0.28 (0.25, 0.32) & 0.1800 & 2.42E-53 \\ CAD-DM & 0.1920 & 5.92E-13 & 0.01 (0.01, 0.01) & 0.0659 & 0.00245431 \\ DM-CAD & 0.4283 & 5.60E-19 & 1.95 (1.26, 2.64) & 0.1796 & 4.15E-05 \\ SBP-CAD & 0.2807 & 2.86E-46 & 0.45 (0.39, 0.51) & 0.2500 & 9.77E-24 \\ CAD-SVstat & 0.2491 & 8.82E-44 & 0.03 (0.03, 0.04) & 0.3077 & 1.15E-25 \\ CAD-MI & 0.4634 & 0 & 0.02 (0.02, 0.02) & 0.4191 & 3.07E-285 \\ LDL-CAD & 0.3402 & 1.17E-45 & 0.31 (0.24, 0.38) & 0.2014 & 8.56E-27 \\ BMI-Edu & -0.2241 & 3.74E-14 & -0.12 (-0.14, -0.11) & -0.1892 & 6.15E-35 \\ SHeight-BMI & -0.1278 & 1.40E-22 & -0.13 (-0.14, -0.11) & -0.0854 & 9.01E-23 \\ SBP-BWeight & -0.2565 & 9.85E-08 & -0.13 (-0.16, -0.1) & -0.1646 & 1.20E-11 \\ SBP-SHeight & -0.3657 & 4.81E-08 & -0.12 (-0.15, -0.1) & -0.0967 & 0.004422636 \\ SHeight-SBP & -0.0759 & 5.74E-05 & -0.08 (-0.09, -0.07) & -0.0652 & 1.25E-15 \\ SHeight-SVstat & -0.0465 & 4.76E-09 & -0.01 (-0.02, -0.01) & -0.0328 & 6.78E-12 \\ BMI-HDL & -0.3760 & 3.54E-56 & -0.28 (-0.29, -0.26) & -0.3630 & 3.17E-111 \\ SHeight-LDL & -0.0716 & 4.26E-09 & -0.04 (-0.05, -0.02) & -0.0298 & 5.07E-06 \\ BWeight-CAD & -0.1745 & 2.05E-06 & -0.21 (-0.28, -0.14) & -0.0978 & 2.83E-05 \\ SHeight-CAD & -0.0802 & 3.72E-20 & -0.15 (-0.18, -0.12) & -0.0482 & 2.18E-12 \\ HDL-CAD & -0.1729 & 7.00E-31 & -0.26 (-0.3, -0.21) & -0.0778 & 5.45E-10 \\ \end{tabular}
\end{table}
Table S8: Table comparing the causal estimates of LHC-MR, CAUSE, and IVW for trait pairs that had a significant causal effect in LHC-MR and CAUSE. The column showing the gamma (causal effect) estimate of the CAUSE method also reports its 95% credible intervals. A complete table for all the studied pairs is found in the Supplementary Table S5. |
021691_file02 | # & risk factor & _MIP_ & \(\hat{\theta}_{\rm MACE}\) \\
1 & ApoB & 0.818 & 0.355 \\
2 & S.HDL.TG & 0.201 & 0.048 \\
3 & LDL.C & 0.105 & 0.022 \\
4 & XXL.VLDL.TG & 0.072 & 0.014 \\
5 & IDL.C & 0.064 & 0.012 \\
6 & Serum.C & 0.061 & 0.014 \\
7 & M.HDL.C & 0.057 & -0.007 \\
8 & Serum.TG & 0.051 & 0.008 \\
9 & HDL.C & 0.048 & -0.007 \\
10 & S.LDL.C & 0.048 & 0.003 \\ \hline \multicolumn{4}{l}{\(\sigma=0.5\)} \\ \# & risk factor & _MIP_ & \(\hat{\theta}_{\rm MACE}\) \\ \hline
1 & ApoB & 0.868 & 0.392 \\
2 & S.HDL.TG & 0.136 & 0.033 \\
3 & LDL.C & 0.075 & 0.015 \\
4 & XXL.VLDL.TG & 0.047 & 0.01 \\
5 & Serum.C & 0.045 & 0.011 \\
6 & IDL.C & 0.042 & 0.008 \\
7 & S.LDL.C & 0.04 & 0.001 \\
8 & M.HDL.C & 0.038 & -0.005 \\
9 & HDL.C & 0.036 & -0.006 \\
10 & Serum.TG & 0.035 & 0.006 \\ \hline \multicolumn{4}{l}{\(\sigma=0.7\)} \\ \# & risk factor & _MIP_ & \(\hat{\theta}_{\rm MACE}\) \\ \hline
1 & ApoB & 0.907 & 0.415 \\
2 & S.HDL.TG & 0.101 & 0.025 \\
3 & LDL.C & 0.055 & 0.011 \\
4 & XXL.VLDL.TG & 0.03 & 0.006 \\
5 & S.LDL.C & 0.029 & 0.006 \\
6 & Serum.C & 0.028 & 0.005 \\
8 & M.HDL.C & 0.026 & -0.003 \\
9 & Serum.TG & 0.023 & 0.004 \\
10 & HDL.C & 0.023 & -0.003 \\ \hline \end{tabular}
\end{table}
Table S10: Parameter check for the prior variance \(\sigma^{2}\), ranging from \(\sigma=0.1\) to \(\sigma=0.7\). The main analysis used \(\sigma=0.5\). Abbreviations: _MIP_=marginal inclusion probability, MACE=model-averaged causal effect.
\begin{table}
\begin{tabular}{l c c c} \(p=0.01\) & & & \\ \# & risk factor & _MIP_ & \(\hat{\theta}_{\text{MACE}}\) \\ \hline
1 & ApoB & 0.979 & 0.454 \\
2 & S.HDL.TG & 0.015 & 0.004 \\
3 & LDL.C & 0.009 & 0.002 \\
4 & S.VLDL.C & 0.007 & 0.002 \\
5 & S.LDL.C & 0.004 & 0 \\
6 & Serum.C & 0.004 & 0.001 \\
7 & XS.VLDL.TG & 0.004 & 0.001 \\
8 & IDL.C & 0.004 & 0.001 \\
9 & M.HDL.C & 0.004 & 0 \\
10 & XXL.VLDL.TG & 0.004 & 0.001 \\ \hline \hline \multicolumn{4}{l}{\(p=0.05\)} \\ \# & risk factor & _MIP_ & \(\hat{\theta}_{\text{MACE}}\) \\ \hline
1 & ApoB & 0.929 & 0.426 \\
2 & S.HDL.TG & 0.071 & 0.017 \\
3 & LDL.C & 0.039 & 0.008 \\
4 & Serum.C & 0.022 & 0.005 \\
5 & S.LDL.C & 0.02 & 0.001 \\
6 & XXL.VLDL.TG & 0.02 & 0.004 \\
7 & IDL.C & 0.02 & 0.004 \\
8 & M.HDL.C & 0.019 & -0.002 \\
9 & HDL.C & 0.017 & -0.003 \\
10 & S.VLDL.C & 0.016 & 0.001 \\ \hline \hline \multicolumn{4}{l}{\(p=0.1\)} \\ \# & risk factor & _MIP_ & \(\hat{\theta}_{\text{MACE}}\) \\ \hline
1 & ApoB & 0.868 & 0.392 \\
2 & S.HDL.TG & 0.136 & 0.033 \\
3 & LDL.C & 0.075 & 0.015 \\
4 & XXL.VLDL.TG & 0.047 & 0.01 \\
5 & Serum.C & 0.045 & 0.011 \\
6 & IDL.C & 0.042 & 0.008 \\
7 & S.LDL.C & 0.04 & 0.001 \\
8 & M.HDL.C & 0.038 & -0.005 \\
9 & HIDL.C & 0.036 & -0.006 \\
10 & Serum.TG & 0.035 & 0.006 \\ \hline \hline \multicolumn{4}{l}{\(p=0.2\)} \\ \# & risk factor & _MIP_ & \(\hat{\theta}_{\text{MACE}}\) \\ \hline
1 & ApoB & 0.791 & 0.347 \\
2 & S.HDL.TG & 0.238 & 0.059 \\
3 & LDL.C & 0.127 & 0.025 \\
4 & XXL.VLDL.TG & 0.099 & 0.022 \\
5 & Serum.C & 0.083 & 0.019 \\
6 & IDL.C & 0.076 & 0.013 \\
7 & Serum.TG & 0.071 & 0.014 \\
8 & S.LDL.C & 0.07 & 0.001 \\
9 & M.HDL.C & 0.068 & -0.008 \\
10 & HIDL.C & 0.068 & -0.01 \\ \hline \hline \multicolumn{4}{l}{\(p=0.3\)} \\ \# & risk factor & _MIP_ & \(\hat{\theta}_{\text{MACE}}\) \\ \hline
1 & ApoB & 0.744 & 0.318 \\
2 & S.HDL.TG & 0.32 & 0.081 \\
3 & XXL.VLDL.TG & 0.18 & 0.046 \\
4 & LDL.C & 0.164 & 0.032 \\
5 & Serum.TG & 0.117 & 0.025 \\
6 & Serum.C & 0.11 & 0.023 \\
7 & IDL.C & 0.106 & 0.018 \\
8 & S.VLDL.C & 0.103 & -0.014 \\
9 & M.HDL.C & 0.092 & -0.011 \\
10 & S.LDL.C & 0.092 & 0.001 \\ \hline \hline \end{tabular}
\end{table}
Table S11: Parameter check for the prior probability \(p\), ranging from \(p=0.01\) to \(p=0.3\). This reflects \(0.3\) to \(9\) expected causal risk factors. The main analysis used \(p=0.1\) reflecting an a priori expected number of \(3\) causal risk factors. Abbreviations: _MIP_=marginal inclusion probability, MACE=model-averaged causal effect.
## Supplementary FiguresFigure S2: Diagnostic plots with Cooks distance: Estimates of genetic associations with the outcome against predicted genetic associations with the outcome from the primary analysis based on \(n\) = 138 genetic variants after exclusion of outliers. Here we show the diagnostics for all four top models with posterior probability > 0.02 as given in Main Table 1.Colour code of points indicates influence, as measured by the variant's Cook’s distance.
Figure S3: Diagnostic plots with \(q\)-statistic: Estimates of genetic associations with the outcome against predicted genetic associations with the outcome from the primary analysis based on \(n\) = 138 genetic variants after exclusion of outliers. Here we show the diagnostics for all four top models with posterior probability > 0.02 as given in Main Table 1. Colour code of points indicates heterogeneity, as measured by the variant's \(q\)-statistic.
## Supplementary Methods
## Mendelian randomization using summarized data
A genetic variant can be used to make causal inferences about the effect of a risk factor on an outcome if it satisfies the three instrumental variable assumptions:
1. The variant is associated with the risk factor;
2. The variant is not confounded in its associations with the outcome;
3. The variant does not influence the outcome directly, only potentially indirectly via its association with the risk factor.
These assumptions imply that a genetic variant behaves analogously to random assignment to a treatment group in a randomized controlled trial, in that it divides the population into subgroups that differ only with respect to their average level of the risk factor. Any difference in the outcome between these groups implies a causal effect of the risk factor on the outcome, analogous to an intention-to-treat effect in a randomized trial.
We consider an extension of the Mendelian randomization paradigm known as multivariable Mendelian randomization, in which genetic variants are allowed to influence multiple risk factors, provided that any causal pathway from the genetic variants to the outcome passes via one or more of the measured risk factors. The assumptions for genetic variants to be valid instruments in multivariable Mendelian randomization are:
1. Each variant is associated with at least one of the risk factors;
2. Variants are not confounded in their associations with the outcome;
3. Variants are not associated with the outcome conditional on the risk factors and confounders.
In turn, the assumptions for a risk factor to be included in a multivariable Mendelian randomization model are:
1. No risk factor can be linearly explained by any other included risk factor or a combination of multiple risk factors.
2. Each risk factor is associated with at least one of the genetic variants.
Assumption RF1 is needed to distinguish between correlated risk factors. RF2 ensures that each risk factor is adequately predicted by the genetic variants selected as instrumental variables in the analysis.
For a particular set of risk factors, causal effects are estimated by weighted linear regression of the genetic associations with the outcome on the genetic associations with the risk factors
\[\beta_{Y}=\theta_{1}\beta_{X1}+\theta_{2}\beta_{X2}+\ldots+\theta_{d}\beta_{ Xd}+\varepsilon,\quad\varepsilon\sim N(0,\text{diag}(\text{se}(\beta_{Y})^{2})),\]
\(\beta_{X1},\beta_{X2},\ldots,\beta_{Xd}\) are the genetic associations with the \(d\) risk factors, and \(\theta_{1},\theta_{2},\ldots,\theta_{d}\) are the causal effects of the \(d\) risk factors on the outcome. If there are causal relationships between the risk factors, then these parameters represent the direct effects of the risk factors, i.e. the effect of changing the target risk factor keeping all other risk factors constant.
### Variable selection and Bayesian model averaging
The model averaging approach is implemented by considering different sets of risk factors in turn. For each risk factor set, MR-BMA fits the relevant multivariable Mendelian randomization model and assigns a score to the set of risk factors considered that captures the posterior probability that this particular model represents the true causal risk factors for the outcome given the observed genetic association data. As prior parameters MR-BMA requires to set an a priori probability for a risk factor to be causal, which is set to 0.1 reflecting an a priori epectation of three causal risk factors. Additionally, the prior variance is set to 0.25. Sensitivity analysis with respect to the prior parameters is important and we can show that ranking is not impacted by the choice of the prior. Results for a wide range of prior specifications are given in Supplementary Table S10 (prior variance) and Supplementary Table S11 (prior probability).
When considering many candidate risk factors, the model space (including all possible combinations of risk factors) may be prohibitively large to consider all possible combinations of risk factors. To alleviate this we have implemented a stochastic search algorithm to explore the relevant model space (all models with a non-negligible posterior probability) in an efficient way.
When the number of risk factors considered is large, the evidence for each particular model may be small. Hence, we average over the models visited and for each risk factor compute its marginal inclusion probability, which is the sum of the posterior probabilities for all models visited that include this particular risk factor. Further, we provide the model-averaged causal effect estimate, representing the average causal effect estimate for the given risk factor across models in which it is included. As is common for variable-selection methods, this is a conservative estimates of the true causal effect and underestimates its magnitude, but may be used for the interpretation of effect direction and for comparison among the risk factors.
### Resampling to compute empirical \(p-\)values
Empirical \(p\)-values for the marginal inclusion probability of each risk factor are obtained using a permutation procedure, where the risk factor association data are held constant and the outcome associations of the genetic variants are randomly perturbed. The empirical \(p\)-value for risk factor \(j\) quantifies how extreme the actual observed marginal inclusion probability is with respect to all permuted marginal inclusion probabilities for that particular risk factor. Formally, the empirical \(p\)-value is computed by the rank (\(r_{j}\)) of the actual observed marginal inclusion probability for risk factor \(j\) among all permuted marginal inclusion probabilities for risk factor \(j\) over the total number of permutations (\(n_{perm}\) = 1,000).
\[p_{j}=(r_{j}+1)/(n_{perm}+1).\]
Multiple testing adjustment is done using the Benjamini and Hochberg false discovery rate (FDR) procedure.
### Model diagnostics
Two approaches are considered for model diagnostics. Firstly, to identify influential variants for each visited model with a model posterior probability larger than \(0.02\), we calculated Cook's distance for each genetic variant and excluded all variants that have in any selected model a Cook's distance which exceeds the median of a central \(F\)-distribution with \(d\) and \(n-d\) degrees of freedom, where \(d\) is the number of risk factors and \(n\) the number of genetic variants used as instrumental variables.
Secondly, to identify outlying variants, we consider for each visited model with a model posterior probability larger than \(0.02\) a version of Cochran's Q statistic used to detect heterogeneity in meta-analysis
\[Q=\sum_{i=1}^{n}q_{i}=\sum_{i=1}^{n}\mathrm{se}(\beta_{Y_{i}})^{-2}(\beta_{Y_{ i}}-\hat{\beta}_{Y_{i}})^{2},\]
A genetic variant with a high value of \(q_{i}\) (compared to the \(0.05/n\)th upper tail of a \(\chi^{2}\) distribution with one degree of freedom representing Bonferroni multiple testing adjustment by the number of variants included) in any of the models visited (with a model posterior probability larger than \(0.02\)) was considered to be an outlying variant.
We then repeated the analyses excluding such variants. The reason for excluding outliers and influential variants is that a single genetic variant can have a strong impact on the models visited and subsequently on variable selection. However, in this case for both main and sensitivity analyses, excluding these variants did not change the headline results.
|
029660_file02 | ## ***************************************************************
// 6 a-priori subgroups
* Participants reporting short (6 months) vs. long (>6 months) apopphysitis symptom duration.
//short duration symptom
replace apo_duration_shortlong=0 if apo_duration<=3
//long duration symptom
replace apo_duration_shortlong=1 if apo_duration>=4 & apo_duration<8
// Note: the answers "ved ikke/kan ikke huske" + missing values are all excluded from the subgroup.
label variable apo_duration_shortlong "Apophysitis symptoms ranged by duration"
label define apo_duration_shortlong 0 "Short (<6 months)" 1 "Long (>6 months)"
label values apo_duration_shortlong apo_duration_shortlong
tab apo_duration_shortlong
* Participants reporting significant limitation to sport and physical activity during their apophysitis vs. those that were not significantly affected.
//Participants that were not significantly affected.
replace apo_limit_sport=0 if apo_limits<=3 //Participants reporting significant limitation to sport and physical activity
label variable apo_limit_sport "Limitations to sport during their apophysis"
label define apo_limit_sport 0 "Minimal or no limitation" 1 "Very or total limitation"
label values apo_limit_sport apo_limit_sport
tab apo_limit_sport
* Participants who currently have knee pain or symptoms from the same general area vs. those who currently do not.
//Participants who currently do not
replace kneepain_current=0 if kneepain_vas_week=0 //Participants who currently have knee pain
label variable kneepain_current "Current knee pain symptoms"
label define kneepain_current 0 "No pain" 1 "Pain"
label values kneepain_current kneepain_current
tab kneepain_current
* Participants who report having met WHO recommendations for physical activity in their adult life vs.
//Participants that report having been less physically active
replace pa_adult_rec=0 if pa_in_adulthood>=3 & pa_in_adulthood<=5
//Participants who report having met WHO recommendations for physical activity
replace pa_adult_rec=1 if pa_in_adulthood<=2
//Note: Missing values are all excluded from the subgroup.
label variable pa_adult_rec "WHO recommendations for physical activity"
label define pa_adult_rec 0 "Does not follow" 1 "Follows"
label values pa_adult_rec pa_adult_rec
tab pa_adult_rec
* Participants that report currently having a large bony prominence thought to originate from their apopphysitis (only Osgood Schlatter patients) vs.
//participants that report currently having a large bony prominence thought to originate from their apopphysitis (only Osgood Schlatter patients)
replace large_bony=1 if bony_deform==3 | bony_deform==4
//participants that do not
replace large_bony=0 if bony_deform==1 | bony_deform==2
//Note: the answers "ved ikke/kan ikke huske" + missing values are all excluded from the subgroup.
label variable large_bony "Bony prominence (Osgood Schlatter)"
label define large_bony 0 "No bony prominence" 1 "Small or large bony prominence"
label values large_bony large_bony
tab large_bony
* Participants that report severe symptoms during their apopphysitis vs. those who only report having experienced light or moderate symptoms (based on pain intensity and restriction in physical activity and sport).
replace apo_severity=1 if apo_limits==4 & pain_during_apo<=2 | apo_limits==5 & pain_during_apo<=2
// Note: the answers "ved ikke/kan ikke huske" + missing values are all excluded from the subgroup.
label variable apo_severity "Symptom severity during their apopphysitis"
label define apo_severity 0 "Light or moderate symptoms" 1 "Severe symptoms"
label values apo_severity apo_severity
tab apo_severity
## ****************************************************************************
* Test for normality continous variables *
## ****************************************************************************
* Demographic variables
//age total
hist age
qnorm age
//age in apophysitis diagnosis groups
hist age if apo_diagnose==1
hist age if apo_diagnose==2
hist age if apo_diagnose==3
hist age if apo_diagnose==4
qnorm age if apo_diagnose==1
qnorm age if apo_diagnose==2
qnorm age if apo_diagnose==3
qnorm age if apo_diagnose==4//height total
hist height
qnorm height
//height in apophysitis diagnosis groups
hist height if apo_diagnose==1
hist height if apo_diagnose==2
hist height if apo_diagnose==3
hist height if apo_diagnose==4
qnorm height if apo_diagnose==1
qnorm height if apo_diagnose==2
qnorm height if apo_diagnose==3
qnorm height if apo_diagnose==4
//weight total
hist weight
qnorm weight
//weight in apophysitis diagnosis groups
hist weight if apo_diagnose==1
hist weight if apo_diagnose==2
hist weight if apo_diagnose==3
hist weight if apo_diagnose==4
qnorm weight if apo_diagnose==1
qnorm weight if apo_diagnose==2
qnorm weight if apo_diagnose==3
qnorm weight if apo_diagnose==4
*Outcome variables
* SF-12//PCS-12 total
hist agg_phys
qnorm agg_phys
//PCS-12 in apopphysitis diagnosis groups
hist agg_phys if apo_diagnose==1
hist agg_phys if apo_diagnose==2
hist agg_phys if apo_diagnose==3
hist agg_phys if apo_diagnose==4
qnorm agg_phys if apo_diagnose==1
qnorm agg_phys if apo_diagnose==2
qnorm agg_phys if apo_diagnose==3
qnorm agg_phys if apo_diagnose==4
*KOOS
//KOOS-pain total
hist KOOS_pain
qnorm KOOS_pain
//KOOS-pain in apophysitis diagnosis groups
hist KOOS_pain if apo_diagnose==1
hist KOOS_pain if apo_diagnose==2
hist KOOS_pain if apo_diagnose==3
hist KOOS_pain if apo_diagnose==4
qnorm KOOS_pain if apo_diagnose==1
qnorm KOOS_pain if apo_diagnose==2
qnorm KOOS_pain if apo_diagnose==3
qnorm KOOS_pain if apo_diagnose==4
//KOOS-symptoms total hist KOOS_symp
qnorm KOOS_symp
//KOOS-symptoms in apophysisti diagnosis groups
hist KOOS_symp if apo_diagnose==1
hist KOOS_symp if apo_diagnose==2
hist KOOS_symp if apo_diagnose==3
hist KOOS_symp if apo_diagnose==4
qnorm KOOS_symp if apo_diagnose==1
qnorm KOOS_symp if apo_diagnose==2
qnorm KOOS_symp if apo_diagnose==3
qnorm KOOS_symp if apo_diagnose==4
//KOOS-sport/rec total
hist KOOS_sport
qnorm KOOS_sport
//KOOS-sport/rec in apophysisti diagnosis groups
hist KOOS_sport if apo_diagnose==1
hist KOOS_sport if apo_diagnose==2
hist KOOS_sport if apo_diagnose==3
hist KOOS_sport if apo_diagnose==4
qnorm KOOS_sport if apo_diagnose==1
qnorm KOOS_sport if apo_diagnose==2
qnorm KOOS_sport if apo_diagnose==3
qnorm KOOS_sport if apo_diagnose==4
## ***************************************************************
* Presentation of demographic variables *- table 1.
sum age
ci means age
tab gender
sum height
ci means height
sum weight
ci means weight
sum agg_phys
ci means agg_phys
sum KOOS_symp
ci means KOOS_symp
sum KOOS_pain
ci means KOOS_pain
sum KOOS_sport
ci means KOOS_sport
//Musculoskeletal conditions
ci means KOOS_pain if apo_diagnose==2 ci means KOOS_pain if apo_diagnose==3 ci means KOOS_pain if apo_diagnose==4 sum KOOS_sport if apo_diagnose==1 sum KOOS_sport if apo_diagnose==2 sum KOOS_sport if apo_diagnose==3 sum KOOS_sport if apo_diagnose==4 ci means KOOS_sport if apo_diagnose==1 ci means KOOS_sport if apo_diagnose==2 ci means KOOS_sport if apo_diagnose==3 ci means KOOS_sport if apo_diagnose==4 //Musculoskeletal conditions tab2 diseases_knee_heel_related 1 apo_diagnose, column tab2 diseases_knee_heel_related 2 apo_diagnose, column tab2 diseases_knee_heel_related 3 apo_diagnose, column tab2 diseases_knee_heel_related 4 apo_diagnose, column tab2 diseases_knee_heel_related 5 apo_diagnose, column tab2 diseases_knee_heel_related 6 apo_diagnose, column tab2 diseases_knee_heel_related 7 apo_diagnose, column tab2 diseases_knee_heel_related 8 apo_diagnose, column tab2 diseases_knee_heel_related 9 apo_diagnose, column tab2 diseases_knee_heel_r_v_1 apo_diagnose, column tab2 diseases_knee_heel_r_v_2 apo_diagnose, column tab2 diseases_knee_heel_r_v_3 apo_diagnose, column
## ***************************************************************
* Statistical tests of continous variables *
## ***************************************************************
* SF-12 statistics //PCS-12 in subgroups 1-6 with t-test and model checking + effect size estimation regress agg_phys apo_duration_shortlong
predict sdres, rstandard
predict fit
qnorm sdres
ttest agg_phys, by(apo_duration_shortlong)
esize twosample agg_phys, by(apo_duration_shortlong)
### //2
regress agg_phys apo_limit_sport
predict sdres, rstandard
predict fit
qnorm sdres
ttest agg_phys, by(apo_limit_sport)
esize twosample agg_phys, by(apo_limit_sport)
### //3
regress agg_phys kneepain_current
predict sdres, rstandard
predict fit
qnorm sdres
ttest agg_phys, by(kneepain_current)
esize twosample agg_phys, by(kneepain_current)
### //4
regress agg_phys pa_adult_rec
predict sdres, rstandardpredict fit qnorm sdres ttest agg_phys, by(pa_adult_rec)
esize twosample agg_phys, by(pa_adult_rec)
//5 regress agg_phys large_bony predict sdres, rstandard predict fit qnorm sdres ttest agg_phys, by(large_bony)
esize twosample agg_phys, by(large_bony)
//6 regress agg_phys apo_severity predict sdres, rstandard predict fit qnorm sdres ttest agg_phys, by(apo_severity)
esize twosample agg_phys, by(apo_severity)
* oneway ANOVA, assumptions (outlier, normal distribution and Levene's test) and post-hoc test(tukey's).
// SF-12 PCS-12 tw sc agg_phys apo_diagnose swilk agg_phys if apo_diagnose==1 swilk agg_phys if apo_diagnose==2swilk agg_phys if apo_diagnose==3
swilk agg_phys if apo_diagnose==4
robvar agg_phys, by(apo_diagnose)
oneway agg_phys apo_diagnose, tabulate
pwmean agg_phys, over(apo_diagnose) mcompare(tukey) effects
* KOOS statistics
//KOOS-symp in subgroups 1-6 t-test, model checking and effect size
//1
regress KOOS_symp apo_duration_shortlong
predict sdres, rstandard
predict fit
qnorm sdres
ttest KOOS_symp, by(apo_duration_shortlong)
esize twosample KOOS_symp, by(apo_duration_shortlong)
//2
regress KOOS_symp apo_limit_sport
predict sdres, rstandard
predict fit
qnorm sdres
ttest KOOS_symp, by(apo_limit_sport)
esize twosample KOOS_symp, by(apo_limit_sport)
//3
regress KOOS_symp kneepain_current
predict sdres, rstandardpredict fit
qnorm sdres
ttest KOOS_symp, by(kneepain_current)
esize twosample KOOS_symp, by(kneepain_current)
//4
regress KOOS_symp pa_adult_rec
predict sdres, rstandard
predict fit
qnorm sdres
ttest KOOS_symp, by(pa_adult_rec)
esize twosample KOOS_symp, by(pa_adult_rec)
//5
regress KOOS_symp large_bony
predict sdres, rstandard
predict fit
qnorm sdres
ttest KOOS_symp, by(large_bony)
esize twosample KOOS_symp, by(large_bony)
//6
regress KOOS_symp apo_severity
predict sdres, rstandard
predict fit
qnorm sdres
ttest KOOS_symp, by(apo_severity)esize twosample KOOS_symp, by(apo_severity)
* oneway ANOVA, assumptions (outlier, normal distribution and Levene's test) and post-hoc test(tukeys).
//KOOS symptoms
tw sc KOOS_symp apo_diagnose
swilk KOOS_symp if apo_diagnose==1
swilk KOOS_symp if apo_diagnose==2
swilk KOOS_symp if apo_diagnose==3
swilk KOOS_symp if apo_diagnose==4
robvar KOOS_symp, by(apo_diagnose)
oneway KOOS_symp apo_diagnose, tabulate
pwmean KOOS_symp, over(apo_diagnose) mcompare(tukey) effects
//KOOS-pain in subgroups 1-6 t-test, model checking and effect size
//1
regress KOOS_pain apo_duration_shortlong
predict sdres, rstandard
predict fit
qnorm sdres
ttest KOOS_pain, by(apo_duration_shortlong)
esize twosample KOOS_pain, by(apo_duration_shortlong)
//2
regress KOOS_pain apo_limit_sport
predict sdres, rstandard
predict fit qnorm sdres
ttest KOOS_pain, by(apo_limit_sport)
esize twosample KOOS_pain, by(apo_limit_sport)
#### 1/3
regress KOOS_pain kneepain_current
predict sdres, standard
predict fit
qnorm sdres
ttest KOOS_pain, by(kneepain_current)
#### 1/4
regress KOOS_pain pa_adult_rec
predict sdres, rstandard
predict fit
qnorm sdres
ttest KOOS_pain, by(pa_adult_rec)
esize twosample KOOS_pain, by(pa_adult_rec)
#### 1/5
regress KOOS_pain large_bony
predict sdres, rstandard
predict fit
qnorm sdres
ttest KOOS_pain, by(large_bony)esize twosample KOOS_pain, by(large_bony)
//6
regress KOOS_pain apo_severity
predict sdres, rstandard
predict fit
qnorm sdres
ttest KOOS_pain, by(apo_severity)
esize twosample KOOS_pain, by(apo_severity)
* oneway ANOVA, assumptions (outlier, normal distribution and Levene's test) and post-hoc test(tukey's).
//KOOS pain
tw sc KOOS_pain apo_diagnose
swilk KOOS_pain if apo_diagnose==1
swilk KOOS_pain if apo_diagnose==2
swilk KOOS_pain if apo_diagnose==3
swilk KOOS_pain if apo_diagnose==4
robvar KOOS_pain, by(apo_diagnose)
oneway KOOS_pain apo_diagnose, tabulate
pwmean KOOS_pain, over(apo_diagnose) mcompare(tukey) effects
//KOOS-sport/rec in subgroups 1-6 t-test, model checking and effect size
//1
regress KOOS_sport apo_duration_shortlong
predict sdres, rstandard
predict fit
qnorm sdresttest KOOS_sport, by(apo_duration_shortlong)
esize twosample KOOS_sport, by(apo_duration_shortlong)
#### //2
regress KOOS_sport apo_limit_sport
predict sdres, rstandard
predict fit
qnorm sdres
ttest KOOS_sport, by(apo_limit_sport)
esize twosample KOOS_sport, by(apo_limit_sport)
#### //3
regress KOOS_sport kneepain_current
predict sdres, rstandard
predict fit
qnorm sdres
ttest KOOS_sport, by(kneepain_current)
#### //4
regress KOOS_sport pa_adult_rec
predict sdres, rstandard
predict fit
qnorm sdres
ttest KOOS_sport, by(pa_adult_rec)
### //5
regress KOOS_sport large_bony
predict sdres, rstandard
predict fit
qnorm sdres
ttest KOOS_sport, by(large_bony)
esize twosample KOOS_sport, by(large_bony)
### //6
regress KOOS_sport apo_severity
predict sdres, rstandard
predict fit
qnorm sdres
ttest KOOS_sport, by(apo_severity)
esize twosample KOOS_sport, by(apo_severity)
* oneway ANOVA, assumptions (outlier, normal distribution and Levene's test) and post-hoc test(tukeys).
### //KOOS sport-req
tw sc KOOS_sport apo_diagnose
swilk KOOS_sport if apo_diagnose==1
swilk KOOS_sport if apo_diagnose==2
swilk KOOS_sport if apo_diagnose==3
swilk KOOS_sport if apo_diagnose==4
robvar KOOS_sport, by(apo_diagnose)
oneway KOOS_sport apo_diagnose, tabulatepwmean KOOS_sport, over(apo_diagnose) mcompare(tukey) effects
## *******************************************************************************************
* Statistical associations of disease variables in subgroups and apop
logistic diseases_knee_heel_r_v_3pa_adult_rec, baselevels
//Subgroup logistic diseases_knee_heel_related1large_bony, baselevels logistic diseases_knee_heel_related2large_bony, baselevels logistic diseases_knee_heel_related3large_bony, baselevels logistic diseases_knee_heel_related4large_bony, baselevels logistic diseases_knee_heel_related5large_bony, baselevels logistic diseases_knee_heel_related6large_bony, baselevels logistic diseases_knee_heel_related7large_bony, baselevels logistic diseases_knee_heel_related8large_bony, baselevels logistic diseases_knee_heel_related9large_bony, baselevels logistic diseases_knee_heel_r_v_1large_bony, baselevels logistic diseases_knee_heel_r_v_2large_bony, baselevels logistic diseases_knee_heel_r_v_3large_bony, baselevels
//Subgroup logistic diseases_knee_heel_related1apo_severityapo_severity, baselevels logistic diseases_knee_heel_related2apo_severityapo_severity, baselevels logistic diseases_knee_heel_related3apo_severityapo_severity, baselevels logistic diseases_knee_heel_related4apo_severityapo_severity, baselevels logistic diseases_knee_heel_related5apo_severityapo_severity, baselevels logistic diseases_knee_heel_related6apo_severityapo_severity, baselevels logistic diseases_knee_heel_related7apo_severityapo_severity, baselevels logistic diseases_knee_heel_related8apo_severityapo_severity, baselevels logistic diseases_knee_heel_related9apo_severityapo_severity, baselevels logistic diseases_knee_heel_r_v_1apo_severity, baselevels logistic diseases_knee_heel_r_v_2apo_severity, baselevels logistic diseases_knee_heel_r_v_3apo_severity, baselevels |
045237_file02 | ## parameter
& \\ \hline \(x\) and \(A(\tau)\) & rate coefficient for infection and expected infectiousness \(\tau\) days after infection, respectively \\ \(Q\) & relative infection rate by outside contact (travel) \\ \(\epsilon\) & ratio between infection rate of self-quarantined and non-quarantined symptomatic cases \\ \(\beta_{a}\) and \(\beta_{s}\) & rate coefficient for latency of asymptomatic and symptomatic cases, respectively \\ \(\theta\) & rate coefficient for mortality of hospitalized cases \\ \(\gamma_{a}\), \(\gamma_{\text{var}}\) and \(\gamma_{\text{ex}}\) & rate coefficients for recovery \\ \(\delta_{\text{ex}}\) and \(\delta_{\text{ex}}\) & rate coefficients for successively stronger symptoms \\ \(k_{s}\), \(k_{s}\) and \(k_{s}\) & rate coefficients accounting for testing \\ \(\mathcal{R}_{0}\) & basic reproduction number without mitigation \\ \(\mathcal{R}_{\text{eff}}^{a\prime\prime}\) & effective reproduction number with mitigation \\ \(\mathcal{R}_{\text{eff}}^{a\prime\prime}\) & effective reproduction number of symptomatic and asymptomatic cases, respectively \\ \(\mathcal{R}_{\text{eff}}^{a\prime\prime}\), \(\mathcal{R}_{\text{eff}}^{a\prime\prime}\) & \(\mathcal{R}_{\text{eff}}^{a\prime\prime\prime}\) - \(\mathcal{R}_{\text{eff}}^{a\prime\prime}\) - and \(\mathcal{R}_{\text{eff}}^{a\prime\prime}\) - \\ \(\zeta\) & percentage of app users among smart-phone owners \\ \(\zeta^{(\text{anti})}\) and \(\theta^{(\text{th})}\) & rate coefficient for mortality of hospitalized cases without and with intensive care units, respectively \\ \(\gamma_{\text{var}}^{(\text{anti})}\) and \(\gamma_{\text{tri}}^{(\text{th})}\) & rate coefficient for recovery of hospitalized cases without and with intensive care units, respectively \\ \(N\) & testing interval \\ \(N^{-1}\) & testing frequency \\ \(\eta\) & fraction of false negative test results \\ \(C^{(\text{anti})}/2.5\) & fraction of total population for which intensive care units are available \\ \(m\) and \(k_{c}\) & lower and higher cut-off of the connectivity distribution, respectively \\ \(\mathcal{T}\) & difference between the exponent of the power law model and 2 \\ disease transmissibility & disease transmissibility \\ \(\mathcal{E}\), \(\mathcal{E}^{ST-A}\), \(\mathcal{E}^{ST-B}\) and \(\mathcal{E}^{ST-C}\) & efficacy of contact counting, STeCC-A, STeCC B and STeCC C, respectively \\ \hline
## operator \& function
& \\ \hline \(\mathbb{E}(\cdot)\) & expectation \\ \(\mathcal{P}_{\mathcal{R}}\) and Prob(\(\mathcal{A}\)) & probability of the event \(\mathcal{A}\) \\ \(\mathbb{E}_{\text{mel}_{\mu}}(i,s)\) & cyphertext for ID \(i\), random seed \(s\) and public key \(\mathbf{p}_{k}\) \\ \(\hat{n}_{a}\) & bitwise XOR \\ \(\hat{b}\) & NOT operator over \(b\) \\ \(\&\) & AND operator \\ \hline \end{tabular}
\end{table}
Table 1: Terminology and nomenclature of model parameters and variablesby the following ordinary differential equations:
\[\dot{n}_{s} = -\alpha(n_{ia}/2+n_{im}+\epsilon n_{ms})\frac{n_{s}}{n_{s}^{0}}\ -\ Q \frac{n_{s}}{n_{s}^{0}}, \tag{1}\] \[\dot{n}_{e} = \alpha(n_{ia}/2+n_{im}+\epsilon n_{ms})\frac{n_{s}}{n_{s}^{0}}\ -\ (\beta_{a}+\beta_{s})n_{e}\ +\ Q\frac{n_{s}}{n_{s}^{0}}\ -\ k_{e}n_{e},\] \[\dot{n}_{ia} = \beta_{a}n_{e}\ -\ \gamma_{a}n_{ia}\ -\ k_{a}n_{ia},\] \[\dot{n}_{im} = \beta_{s}n_{e}\ -\ \xi_{ms}n_{im}\ -\ k_{s}n_{im},\] \[\dot{n}_{ra} = \gamma_{a}n_{ia},\] \[\dot{n}_{ms} = \xi_{ms}n_{im}\ -\ (\gamma_{ms}+\xi_{ss})n_{ms},\] \[\dot{n}_{ss} = \xi_{ss}n_{ms}\ -\ (\gamma_{ss}+\theta)n_{ss},\] \[\dot{n}_{rs} = \gamma_{ss}n_{ss}\ +\ \gamma_{ms}n_{ms}\ \ \ \mbox{and}\] \[\dot{n}_{d} = \theta n_{ss}. \tag{9}\]
Note that \(\epsilon\in\) is the transmission reduction factor of the self-isolated individuals. It is assumed that those infected persons who were detected by testing or hospitalized infect much less due to strong isolation and other precautions. Therefore, their effect on the infection rate is neglected here. In order to parametrize the model, besides the rates \(\alpha\), \(\beta_{a}\), \(\beta_{s}\), \(\gamma_{a}\), \(\gamma_{ms}\), \(\gamma_{ss}\), \(\xi_{ms}\), \(\xi_{ss}\) and \(\theta\), also the relative rate \(Q\) of infections from outside, i.e., by travel or from the animal world, has to be determined. Further, the initial values of \(n_{s}(t)\), \(n_{e}(t)\), \(n_{ia}(t)\), \(n_{im}(t)\), \(n_{ra}(t)\), \(n_{ms}(t)\), \(n_{ss}(t)\), \(n_{rs}(t)\) and \(n_{d}(t)\) have to be chosen. The variables \(\bar{n}_{e}(t)\), \(\bar{n}_{ia}(t)\), \(\bar{n}_{im}(t)\), \(\bar{n}_{ra}(t)\), \(\bar{n}_{ms}(t)\), \(\bar{n}_{ss}(t)\), \(\bar{n}_{rs}(t)\) and \(\bar{n}_{d}(t)\) denote the respective numbers of persons who were tested positive and thus are removed from transmission. The detection rates of exposed (\(n_{e}\)), asymptomatic (\(n_{ia}\)) and mild symptomatic (\(n_{im}\)) persons due to testing are proportional to \(k_{e}\), \(k_{a}\) and \(k_{s}\), respectively. These individuals are then accounted for by the respective numbers \(\bar{n}_{e}(t)\), \(\bar{n}_{ia}(t)\) and \(\bar{n}_{im}(t)\); see Fig. S1. Note that the graph in Fig. S1 is very similar as the one in Fig. 1, except that there is no node for susceptible persons (since by definition a susceptible person can not be detected infected) and that there exist sources due to testing (dotted arrows) instead of sinks.
\[\dot{\bar{n}}_{e} = -(\beta_{a}+\beta_{s})\bar{n}_{e}\ +\ k_{e}n_{e}, \tag{10}\] \[\dot{\bar{n}}_{ia} = \beta_{a}\bar{n}_{e}\ -\ \gamma_{a}\bar{n}_{ia}\ +\ k_{a}n_{ia},\] \[\dot{\bar{n}}_{im} = \beta_{s}\bar{n}_{e}\ -\ \xi_{ms}\bar{n}_{im}\ +\ k_{s}n_{im},\] \[\dot{\bar{n}}_{ra} = \gamma_{a}\bar{n}_{ia},\] \[\dot{\bar{n}}_{ms} = \xi_{ms}\bar{n}_{im}\ -\ (\gamma_{ms}+\xi_{ss})\bar{n}_{ms},\] \[\dot{\bar{n}}_{ss} = \xi_{ss}\bar{n}_{ms}\ -\ (\gamma_{ss}+\theta)\bar{n}_{ss},\] \[\dot{\bar{n}}_{rs} = \gamma_{ss}\bar{n}_{ss}\ +\ \gamma_{ms}\bar{n}_{ms}\ \ \ \mbox{and}\] \[\dot{\bar{n}}_{d} = \theta\bar{n}_{ss}. \tag{17}\]
The effect of testing is further discussed in Section 3. Next it is described how the parameters can be estimated based on literature data.
## 2 Parameter Estimation
Our devised generalized SEIR model becomes closed once we tune the rate coefficients. These coefficients were computed mainly based on data provided in recently published reports.
## Fig. S 1.
Graph showing the dependencies of the compartments describing the dynamics of the positively tested people.
Note that \(\mathcal{R}_{0}\) represents "the expected number of secondary cases produced, in a completely susceptible population, by a typical infective individual". If \(\mathcal{R}_{0}\) becomes \(<1\), virus spread will decline, and if \(\mathcal{R}_{0}>1\), virus spread will increase. To compute \(\mathcal{R}_{0}\), we split the dynamics of the infected population into the infection driven propagation \(f\) and the remainder \(V\), i.e.,
\[\begin{bmatrix}\dot{n}_{e}\\ \dot{n}_{ia}\\ \dot{n}_{im}\\ \dot{n}_{ms}\\ \dot{n}_{ss}\end{bmatrix}=\overbrace{\begin{bmatrix}0&\alpha/2&\alpha&\epsilon& 0\\ 0&0&0&0&0\\ 0&0&0&0&0\\ 0&0&0&0&0\end{bmatrix}}^{f}\begin{bmatrix}n_{e}\\ n_{ia}\\ n_{im}\\ n_{ms}\end{bmatrix}^{V}=\overbrace{\begin{bmatrix}\beta_{a}+\beta_{s}&0&0&0&0\\ -\beta_{a}&\gamma_{a}&0&0&0\\ -\beta_{s}&0&\xi_{ms}&0&0\\ 0&0&-\xi_{ms}&\xi_{ss}+\gamma_{ms}&0\\ 0&0&0&-\xi_{ss}&\theta+\gamma_{ss}\end{bmatrix}}^{V}\begin{bmatrix}n_{e}\\ n_{ia}\\ n_{im}\\ n_{ms}\end{bmatrix}}^{V}. \tag{18}\]
Note that testing is not considered here, i.e., \(k_{e}\), \(k_{a}\) and \(k_{s}\) are zero.
\[\mathcal{R}_{0} = \rho(fV^{-1})\;=\;\frac{\alpha\beta_{s}}{\beta_{a}+\beta_{s}} \left[\frac{\beta_{a}}{2\gamma_{a}\beta_{s}}+\frac{1}{\xi_{ms}}+\frac{\epsilon }{\gamma_{ms}+\xi_{ss}}\right]. \tag{19}\]
By inspecting Eq., we observe that we can move towards a stable state (corresponding to \(\mathcal{R}_{0}\leq 1\)) by reducing the infection rate \(\alpha\) via mitigation policies such as social distancing. Importantly, as shown later, \(\mathcal{R}_{0}\) can be reduced as well by introducing mass testing, contact tracing, smart testing and subsequent isolation of detected infected individuals.
Next, to clarify our choice of model coefficients, we discuss the rates which appear in transmissive and non-transmissive compartments separately. Finally, the increase of mortality due to lack of intensive care units is modeled.
1. _Transmissive_ : We model the incubation time to be log-normally distributed with mean 5.84 (day) and standard deviation 2.98 (day). In accordance with we take the latency time \(x_{l}\) such that in average it becomes half a day shorter than the incubation time. Similar to the incubation time, we adopt a log-normal distribution for \(x_{l}\) but with mean 5.34 (day) and standard deviation 2.7249 (day). We assume that \(1/3\) of the cases won't have noticeable symptoms and \(2/3\) become symptomatic half a day after latency. This leads to \(\beta_{a}=\frac{1}{3}\mathbb{E}(1/x_{l})=0.078\) (1/day), where \(\mathbb{E}(\cdot)\) denotes the expectation which gives us the average latency rate. Due to the ratio of \(1/3\) to \(2/3\) between asymptomatic and symptomatic cases we get the transfer rate from being exposed to infectious symptomatic as \(\beta_{s}=2\beta_{a}=0.156\) (1/day). We suppose that it takes around 1 day from onset of symptoms to self-isolation. Since it takes half a day time delay from becoming infectious to symptomatic, we get \(\xi_{ms}=1/1.5=0.6667\) (1/day). The average onset to discharge time of clinical cases is around 22 days. We assume that for mild-symptomatic cases the onset to recovery time would be half of this amount, i.e., around 11 days. Therefore the average recovery time from end of the latency period becomes 11.5 days for mild-symptomatic cases. We set the same recovery time for asymptomatic cases which leads to \(\gamma_{a}=1/11.5=0.087\) (1/day). A range of values have been suggested for infectiousness of asymptomatic cases; one finds 0.1 in, 2/3 in and 1 in. We assume that the asymptomatic cases are 50% less infectious. Furthermore we consider the self quarantined patients to be 90% less infectious, i.e., \(\epsilon=0.1\) is adopted. To compute the infection rate \(\alpha\), we assume \(\mathcal{R}_{0}=2.4\). Following Eq., the infection rate becomes \(\alpha=0.6711\) (1/day). Since the basic reproduction number is the most important single parameter of the system, we performed sensitivity studies by changing \(\mathcal{R}_{0}\).
2. _Non-transmissive_: The mean delay time from appearance of symptoms to hospitalization has been reported to be around 11 days. However, 80% of symptomatic cases would not require hospitalization. For those who develop strong symptoms, the delay from self-isolation to hospitalization then becomes \(11-1=10\) days. Hence we get \(\xi_{ss}=0.2\times 1/10=0.02\) (1/day) and \(\gamma_{ms}=0.8\times 1/10=0.08\) (1/day). Note that the latter gives onset to recovery time of 11 days for mild cases consistent with our earlier assumption. The average hospital treatment time is 11 days. In case of availability of intensive care units we assume that 20% of hospitalized cases die. Accordingly, we get \(\gamma_{ss}^{}=0.8\times 1/11=0.0727\) (1/day) and \(\theta^{}=0.2\times 1/11=0.0182\) (1/day).
3. _Fatality increase_: We assume that the case fatality ratio increases by two-fold in saturation of the health system. This is justified by noting that the case fatality ratio has increased from approximately 5% in China to roughly 10% in Wuhan while it was the epicentre of the outbreak. By taking this factor into account, and assuming that the average time of hospital treatment remains 11 days, we can compute the death rate of hospitalized cases once saturation of intensive care units is reached as \(\theta^{(sat)}=0.4\times 1/11=0.0364\) (1/day). Note that consistently one obtains \(\gamma_{ss}^{(sat)}=0.6\times 1/11=0.0546\) (1/day). It is assumed that there exist eight intensive care beds per 100'000 persons and that 40% of the hospitalized cases need such treatment. Accordingly, saturation is reached once the number of hospitalized cases, i.e., \(n_{ss}\), exceeds \(C^{(\text{sat})}=0.02\%\) of the total population. The adjusted rate \[\theta(n_{ss}^{tot}) = \frac{n_{s}^{0}}{n_{ss}^{tot}}\left(\min\left\{C^{(\text{sat})}, \frac{n_{ss}^{tot}}{n_{s}^{0}}\right\}\theta^{}+\max\left\{0,\frac{n_{ss}^ {tot}}{n_{s}^{0}}-C^{(\text{sat})}\right\}\theta^{(\text{sat})}\right)\] then quantifies the death rate of hospitalized cases as the weighted average of \(\theta^{}\) and \(\theta^{(\text{sat})}\); the consistently adjusted recovery rate becomes \[\gamma_{ss}(n_{ss}^{tot}) = \gamma_{ss}^{}+\theta^{}-\theta(n_{ss}^{tot}).\]
All estimates here are summarized in Table S2; note that these values can easily be adapted, if more reliable data becomes available. The resulting parameter values for our base case are provided in Table S3.
Results with \(\mathcal{R}_{0}\in\{1.9,2.9\}\) are shown in Fig. S2A,B. Dashed lines represent the immune plus deceased plus infected (\(n_{s}^{0}-n_{s}\)), dash-dotted lines the infected (\(n_{i}^{under}+n_{i}^{det}\)) and solid lines the deceased (\(n_{d}^{tot}\)) population. For bigger values of \(\mathcal{R}_{0}\), a larger immune population is needed to achieve herd immunity (right half of the graphs), and the peak in the number of infections is higher and sharper.
The plot in Fig. S2C shows the case with \(\mathcal{R}_{0}=2.4\) without intensive care unit limitation; compare with Fig. 2A, which shows the same case with intensive care unit limitation (our base case). In both cases 87% of the population will become immune, which compares well with 81% infected people predicted by for the UK and US populations in the absence of mitigation plans. Without intensive care the chance of dying is roughly twice as high for strong symptomatic people than with proper treatment (4.6% vs. 2.3%). While these numbers are subject to errors (mainly due to uncertainties in the parameter values and efforts to increase intensive care and respirator availability), it can be expected that the relevant dynamics is captured to a high degree. If the results are regarded with respect to the base case, much insight can be gained, e.g. how social distancing, mass testing and smart testing can be combined most effectively.
\begin{table}
\begin{tabular}{|l|l||c|c|} \hline
## probability** & **conditional on** & **expression** & **base case value
\\ \hline \hline \(\rightarrow\) pre- and mild sympt. (no self isol.) & asympt. & \(S^{(m)}\) & \(2/3,[1/2,2/3]\) \\ \hline \(\rightarrow\) strong sympt. (hospital.) & mild sympt. (self isol.) & \(S^{(s)}\) & \(1/5\) \\ \hline \(\rightarrow\) deceased & hospit.; with ieu & \(M^{}\) & \(1/5\) \\ \hline \(\rightarrow\) deceased & hospit.; no ieu & \(M^{(sat)}\) & \(2/5\) \\ \hline \hline
## char. time scale (days)
& & & \\ \hline \hline \(\rightarrow\) pre- and mild sympt. (no self isol.) & exposed & \(\bar{S}^{(m)}\beta_{s}^{-1}\) & \(4.27\) \\ \hline \(\rightarrow\) mild sympt. (self isol.) & pre- and mild sympt. (no self isol.) & \(t_{\text{in}}=\xi_{m}^{-1}\) & \(1.5\) \\ \hline \(\rightarrow\) strong sympt. (hospit.) & mild sympt. (self isol.) & \(t_{\text{in}}=S^{(s)}\xi_{m}^{-1}\) & \(10\) \\ \hline \(\rightarrow\) deceased & str. sympt. & \(M^{(0,sat)}/\theta^{(0,sat)}\) & \(11\) \\ \hline \(\rightarrow\) recovered & asymptomatic & \(t_{\text{in}}=\gamma_{\text{e}}^{-1}\) & \(11.5\) \\ \hline \hline
## further parameters
& & & \\ \hline \hline basic reproduction number & & \(\mathcal{R}_{0}\) & \(2.4\) \\ \hline infection rate reduction factor & mild sympt. (self isol.) & \(\epsilon\) & \(0.1\) \\ \hline rel. intensive care capacity & & \(C^{(sat)}/2.5\) & \(0.00008\) \\ \hline \hline
## social distancing, contact tracing and testing
& & & \\ \hline \hline infection rate reduction factor & social distancing & \(\lambda\) & \(0\) \\ \hline testing frequency (1/days) & testing & \(N^{-1}\) & \(0\) \\ \hline testing process time (days) & testing & \(\tau_{\text{force}}\) & \(1\) \\ \hline fraction of false negative test results & testing & \(\eta\) & \(0.05,\{0.5,0.15,0.25\}\) \\ \hline success rate of contact tracing & contact tracing & \(\zeta\) & \([0.3,1]\) \\ \hline fraction of exposed people who develop no symptoms & contact tracing & \(r_{1}\) & \([1/3,1/2]\) \\ \hline fraction of exposed people who develop no symptoms & contact tracing & \(r_{2}\) & \([0.1,0.5]\) \\ \hline \hline \end{tabular}
\end{table}
Table S 2: Estimations made for the model closure, social distancing, contact tracing and testing.
\begin{table}
\begin{tabular}{|c|l|} \hline
## parameter** & **value
\\ \hline \hline \(\alpha\) & \(0.670\) (\(1/\)day) \\ \(\epsilon\) & \(0.1\) \\ \(\beta_{a}\) & \(0.078\) (\(1/\)day) \\ \(\beta_{s}\) & \(0.156\) (\(1/\)day) \\ \(\gamma_{a}\) & \(0.087\) (\(1/\)day) \\ \(\xi_{ms}\) & \(0.667\) (\(1/\)day) \\ \(\gamma_{ms}\) & \(0.08\) (\(1/\)day) \\ \(\xi_{ss}\) & \(0.02\) (\(1/\)day) \\ \(\gamma_{ss}^{}\) & \(0.072\) (\(1/\)day) \\ \(\theta^{}\) & \(0.0182\) (\(1/\)day) \\ \(\theta^{(sat)}\) & \(0.0364\) (\(1/\)day) \\ \hline \hline
## initial condition** & **value
\\ \hline \hline \(n_{s}^{0}\) & \(6\)’\(384\)’\(631\)’\(490\) (world population outside of China) \\ \(n_{e}\) & \(1\)’\(000\) \\ \hline \end{tabular}
\end{table}
Table S 3: List of estimated parameters and initial values. Note that our model allows to easily replace any of these parameters by more precise estimates, as more data become available. The initial values of all numbers except \(n_{e}\) are set to zero.
## 3 Mass Testing - How the Number of Tests Relates to \(\mathcal{R}_{\text{eff}}\)
Here we analyze how many tests are needed to mitigate the Covid-19 pandemic if no other mitigation strategies were applied. If we can use more tests than that, the effective reproduction number \(\mathcal{R}_{\text{eff}}\) will drop below one, the incidence would decline and the pandemic would eventually end, even if no vaccines or infection therapies become available. Therefore we studied how \(\mathcal{R}_{\text{eff}}\) varies once confirmed cases get isolated (in addition to self-quarantined and hospitalized individuals). Of particular value is the relationship between \(\mathcal{R}_{\text{eff}}\) and the interval of testing the susceptible population (i.e., the frequency of testing needed for reducing \(\mathcal{R}_{\text{eff}}\) below one). Thereby we can determine the key technical parameter of interest, i.e., the number of tests per 100'000 people that must be tested per day in order to achieve the desired \(\mathcal{R}_{\text{eff}}\) value; we chose \(\mathcal{R}_{\text{eff}}=1\) as the target value for our analyses (if not indicated otherwise), which would suffice to keep the number of infected people constant.
To be realistic, we suppose that the processing time \(\tau_{\textit{proc}}\) of mass testing would be somewhere between half a day and two days. Furthermore, a fraction \(\eta=0.05\) of false negative test results is taken into account. It should be noted, however, that this is a rough estimate. The use of standards allows for very high reproducibly of the virus RNA detection results even between different laboratories. The true rate of false negatives and false positives is currently not known. We assume that a false negative rate of 5% is a conservative estimate. The current virus RNA testing capacities in continental Europe reach up to 230 tests per 100'000 people per day (e.g. in Switzerland). If equipment and supplies are not limiting for testing, e.g. by using a quantitative polymerase chain reaction (qPCR) method 1, we estimate that up to around 1'000 samples within a time frame of eight hours can be analyzed per machine. Mass testing (i.e., if \(>500-1\)'000 tests per 100'000 people per day would be required) could be realizable by taking advantage of next-generation RNA extraction, reverse transcription and sequencing (combined with reverse transcription and PCR)
Figure S 2: Alternative model outcomes when changing \(\mathcal{R}_{0}\) of the pandemic, or relaxing the assumption that ICU beds are limiting. Dashed blue lines represent recovered and deceased, dashed-dotted green lines infected, and solid red lines deceased people. Changing \(\mathcal{R}_{0}\) to (A) 1.9 and (B) 2.9 changes the outcomes quantitatively, but does not change the overall picture. (C) Model outcome if the assumption that full ICUs increase the death rate is dropped.
For example, in a massively parallel diagnostic assay is described for testing up to 19'200 patient samples per work flow. In principle, such very high throughput approaches can be parallelized (and potentially optimized) to provide millions of tests per day. In reality, the logistics of collecting these millions of samples would however be a major hurdle. First, we want to assess how many tests were indeed necessary to stop the virus spread (i.e., to reach \(\mathcal{R}_{\text{eff}}\leq 1\) if no other mitigation strategies were applied).
Obviously, the scenario that the whole susceptible population is tested perfectly at once would lead to a trivial disease free state. However, this is an unrealistic scenario, not only because of a lack of test capacity, but also due to logistic and compliance concerns. Therefore, it is only realistic to assume that individuals would be tested at different schedules. Let us consider a situation where each person is tested once every \(N\) days. Note that this is equivalent to testing a random fraction of \(1/N\) of the susceptible population every day. Therefore we focus on the set \(\{1,...,N\}\) of days. An individual is infected at some random time \(x\). To characterize \(x\), we assume that the likelihood of getting infected does not vary much during these days, which is justified if testing is applied at an intensity such that \(\mathcal{R}_{\text{eff}}\approx 1\). Hence \(x\) becomes uniformly distributed in the interval \([1,N]\). The time delay between infection and detection would then be \(\tau_{det}=N-x+\tau_{proc}\). Finally, we sample the latency time \(x_{l}\) from a log-normal distribution with \(5.34\pm 2.7249\) (see Section 2).
Intuitively, by conducting mass testing on individuals who are neither self-quarantined nor hospitalized, positive cases will be detected from exposed, asymptomatic and mild-symptomatic compartments. To quantify each detection rate, it is essential to compare detection time versus the latency period; therefore we consider the effect of testing on these three compartments individually:
1. _Exposed_: Once testing occurs during the latency period of an infected individual, they would be detected from the exposed compartment. This translates into an event set \(\mathcal{A}:\tau_{det}\leq x_{l}\). The rate of detecting individuals by testing from the exposed population then reads \[k_{e} = (1-\eta)\mathcal{P}_{\mathcal{A}}\mathbb{E}_{\mathcal{A}}\left[ \tau_{det}^{-1}\right],\] where \(P_{\mathcal{A}}\) and \(\mathbb{E}_{\mathcal{A}}\) denote frequency of such events and conditional expectation, respectively.
2. _Mild-symptomatic_: Once testing occurs after the latency period, one has to distinguish between two types of infection developments. According to our setting, two thirds of the infected individuals would develop symptoms that will lead them to self-isolate. Please note, that the fraction of infected individuals that remain asymptomatic may range between 33%-50%; see Table S2. Therefore, we have also tested scenarios where 60% or 50% of infected will will progress to develop symptoms; see Fig. S5. These individuals may in fact turn to testing centers in order to detect the virus and incentivize the decision for self-quarantine. They can be detected by testing and therefore sent into quarantine in the span of one and a half days after becoming infectious. The relevant event set is \(\mathcal{B}:(\tau_{det}\geq x_{l})\cap(\tau_{det}\leq(x_{l}+3/2))\), from which one obtains \[k_{s} = \frac{2}{3}(1-\eta)\mathcal{P}_{\mathcal{B}}\mathbb{E}_{\mathcal{ B}}\left[\tau_{det}^{-1}\right]\] for the test detection rate of mild-symptomatic persons.
3. _Asymptomatic_: This is arguably the most important group to consider, because they will not know that they are infected and they can make up as much as 50% of the entire group of the infected people. Importantly, they are very hard to identify using the current mitigation strategies, including app based contact tracing. Wewill discuss this in more detail, below. Testing may catch asymptomatic cases. These individuals won't have symptoms and would then recover after 11.5 days. In their first one and a half days they share same the time-line as mild symptomatic ones. Therefore, in this scenario two event sets \(\mathcal{B}:(\tau_{det}\geq x_{l})\cap(\tau_{det}\leq(x_{l}+3/2))\) and \(\mathcal{C}:((\tau_{det}\geq(x_{l}+3/2))\cap(\tau_{det}\leq(x_{l}+11.5))\) become relevant. We obtain the detection rate from the asymptomatic compartment as \[k_{a} = \frac{1}{3}(1-\eta)\mathcal{P}_{\mathcal{B}}\mathbb{E}_{\mathcal{ B}}\left[\tau_{det}^{-1}\right]+(1-\eta)\mathcal{P}_{\mathcal{C}}\mathbb{E}_{ \mathcal{C}}\left[\tau_{det}^{-1}\right].\]
Before finding the map from testing frequency \(N^{-1}\) to \(\mathcal{R}_{\text{eff}}\), we need to find out how \(\mathcal{R}_{\text{eff}}\) varies with respect to the test detection rates \(k_{e}\), \(k_{a}\) and \(k_{s}\). Hence, let us define \(\mathcal{R}_{\text{eff}}^{wt}\) as the reproduction number subject to testing. To compute \(\mathcal{R}_{\text{eff}}^{wt}\), the main dynamics of the infected population, which can be described by \([n_{e}(t),n_{ia}(t),n_{im}(t),n_{ms}(t),n_{ss}(t),\tilde{n}_{e}(t),\tilde{n}_{ ia}(t),\tilde{n}_{im}(t),\tilde{n}_{ms}(t),\tilde{n}_{ss}(t)]^{T}\), is split into the rate of appearance \(f\) of new infected individuals and transfer \(\tilde{V}\) of infected ones across different compartments, i.e.,
\[f = \begin{bmatrix}0&\alpha/2&\alpha&\epsilon&0&0&0&0&0&0\\ 0&0&0&0&0&0&0&0&0&0\\ 0&0&0&0&0&0&0&0&0&0\\ 0&0&0&0&0&0&0&0&0&0\\ 0&0&0&0&0&0&0&0&0&0\\ 0&0&0&0&0&0&0&0&0&0\\ 0&0&0&0&0&0&0&0&0&0\\ 0&0&0&0&0&0&0&0&0&0\\ 0&0&0&0&0&0&0&0&0&0\\ 0&0&0&0&0&0&0&0&0&0\\ 0&0&0&0&0&0&0&0&0&0\\ 0&0&0&0&0&0&0&0&0&0\end{bmatrix} \tag{25}\]
and
\[\tilde{V}=\begin{bmatrix}\beta_{a}+\beta_{s}+k_{e}&0&0&0&0&0&0&0&0&0&0\\ -\beta_{a}&\gamma_{a}+k_{a}&0&0&0&0&0&0&0&0&0\\ -\beta_{s}&0&\xi_{ms}+k_{s}&0&0&0&0&0&0&0&0\\ 0&0&-\xi_{ms}&\xi_{ss}+\gamma_{ms}&0&0&0&0&0&0\\ 0&0&0&-\xi_{ss}&\theta+\gamma_{ss}&0&0&0&0&0\\ -k_{e}&0&0&0&0&\beta_{a}+\beta_{s}&0&0&0&0\\ 0&-k_{a}&0&0&0&-\beta_{a}&\gamma_{a}&0&0&0\\ 0&0&-k_{s}&0&0&-\beta_{s}&0&\xi_{ms}&0&0\\ 0&0&0&0&0&0&-\xi_{ms}&\xi_{ss}+\gamma_{ss}&0\\ 0&0&0&0&0&0&0&-\xi_{ss}&\theta+\gamma_{ss}\end{bmatrix}, \tag{26}\]
which leads to
\[\mathcal{R}_{\text{eff}}^{wt} = \rho(f\tilde{V}^{-1})\;=\;\frac{\alpha\beta_{s}}{\beta_{a}+\beta_ {s}+k_{e}}\left[\frac{\beta_{a}}{2(\gamma_{a}+k_{a})\beta_{s}}+\frac{1}{\xi_ {ms}+k_{s}}\left(1+\frac{\epsilon\xi_{ms}}{\gamma_{ms}+\xi_{ss}}\right) \right]. \tag{27}\]
It is important to emphasize that in contrast to social distancing the effect of testing on the reproduction number is not through reducing the infection rate (i.e., \(f\) remains the same), but rather through transfer of infected individuals to quarantine, either at home or in hotel rooms, or in care units with strict hygiene barriers, all of which would reduce the likelihood of transmission (i.e., changing \(V\) to \(\tilde{V}\)).
Using Monte-Carlo to estimate the test detection rates given by Eqs. and one can compute the ratio \(\mathcal{R}_{\text{eff}}^{wt}/\mathcal{R}_{0}\) with respect to the testing frequency \(N^{-1}\). The plots in Figs. S3A,B show the number of tests required to reach \(\mathcal{R}_{\text{eff}}=1\). It depends on the time from sampling to result (note: we assume immediate notification and immediate implementation of quarantine measures upon notification) and on the false negative rate (5% in Fig. S3A and 15% in Fig. S3B). The horizontal green dashed lines indicate \(\mathcal{R}_{\text{eff}}^{wt}=1\), if the virus reproduction rate in the case without any mitigation is \(\mathcal{R}_{0}=2.4\).
One can see for example that reducing the initial \(\mathcal{R}_{0}=2.4\) to one would require to test the entire susceptible population roughly once every eight days, if the false negative rate is 5%, if testing results are available after one day and quarantine of the detected individuals commences immediately. Corresponding results are depicted in Fig. S4B, which shows model outcomes if \(\mathcal{R}_{\text{eff}}\) is reduced to one by testing 12'600 per 100'000 people per day. Note that this corresponds to a testing interval of 7.92 days or equivalently to a fraction of 1/7.92 which has to be tested every day. Figure S4A shows the outcome when social distancing is applied to reduce \(\mathcal{R}_{\text{eff}}\) to one, which is equivalent to a 58% reduction of the infection rate. We define this as moderate social distancing; see Table S1. By comparing Figs. S4A and S4B one observes that mass testing and social distancing yield qualitatively equivalent results. For half a day delay time the testing interval can be increased to roughly twelve days and for a delay time of one and a half days it would be five days. This information is important for optimizing technical development decisions. The overall testing capacity needs to be larger, if the testing method requires more time or if delays in case-notification or implementation of quarantine measures occur. This could be justified, if a low-cost technique (such as next generation sequencing) could be devised. Alternatively, one could aim for fewer tests, if they are completed in less than half a day. If combined with social distancing, the effective reproduction number can be reduced by the factor \((1-\lambda)\mathcal{R}_{\text{eff}}^{wt}/\mathcal{R}_{0}\), where \(\lambda\in\) is the intensity of social distancing (\(\lambda=0\) means no social distancing and \(\lambda=1\) means complete isolation of everybody).
Fig. S 3: Mass testing: The number of tests required to reach \(\mathcal{R}_{\text{eff}}=1\) depends on the time from sampling to result. A mitigation strategy relying on mass testing alone is assumed and we computed the number of tests performed per day, which are needed to achieve a particular test-speed dependent \(\mathcal{R}_{\text{eff}}^{wt}/\mathcal{R}_{0}\) ratio; for (A) 5% and (B) 15% false negative test results are assumed. The green lines indicate \(\mathcal{R}_{\text{eff}}^{wt}=1\). Test speeds were: 0.5 days (black line), 1 day (orange line), 1.5 days (blue line) and 2 days (purple line).
Contact Tracing - How Size and Infectiousness of the Asymptomatic Population Relates to \(\mathcal{R}_{\text{eff}}\)
Contact tracing has been proposed to slow down or even stabilize the pandemic. The strategy is that symptomatic individuals who go into self quarantine will use an App to alert all proximity contacts of the past two weeks. Subsequently, these identified individuals self-isolate themselves. For the following analysis we assume that the notice-to-quarantine time delay is negligible.
To analyze the effect of contact tracing on the effective reproduction number, the expected infectiousness \(A(\tau)\) at time \(\tau\) after infection plays a central role.
\[\mathcal{R}_{0} = \int_{0}^{\infty}A(\tau)d\tau. \tag{28}\]
Note that the above equation is consistent with our previous computation of \(\mathcal{R}_{0}\) in the linear regime.
\[A(\tau) = \sum_{i\in\mathcal{S}_{c}}\mathcal{P}_{i}A_{i}(\tau), \tag{29}\]
Correspondingly, we denote the time spent in each compartment as \(t_{i\in\mathcal{S}_{c}}\). From Eqs.
\[\mathcal{R}_{0} = \overbrace{\alpha r_{1}r_{2}t_{ia}}^{R_{0}^{\text{error}}}+ \overbrace{\alpha(1-r_{1})\left(t_{im}+\frac{1}{10}t_{ms}\right)}^{\mathcal{R }_{0}^{\text{error}}}, \tag{30}\]
For both \(r_{1}\) and \(r_{2}\) different values are suggested in the literature. For \(r_{1}\) one finds 1/3 in, 0.4 in and 0.5 in, and for \(r_{2}\) one finds 0.1 in, 2/3 in and 1 in. Based on these published numbers we consider \(r_{1}\in[0.3,0.5]\) and \(r_{2}\in[0.1,0.5]\). From Eq. with our base case values \(r_{1}=1/3\) and \(r_{2}=0.5\) one obtains \(\alpha=0.67\) (1/day), which is consistent with our previous parameter estimation. Based on our previous assumptions and on the values in Table S2 we obtain \(t_{ia}=\gamma_{a}^{-1}=11.5\) days, \(t_{im}=\xi_{ms}^{-1}=1.5\) days and \(t_{ms}=S^{(s)}\xi_{ss}^{-1}=10\).
\[\kappa = \frac{\mathcal{R}_{0}^{\text{sym}}}{\mathcal{R}_{0}}\ =\ \frac{ \left(1-r_{1}\right)\left(t_{im}+t_{ms}/10\right)}{r_{1}r_{2}t_{ia}+\left(1-r _{1}\right)\left(t_{im}+t_{ms}/10\right)} \tag{31}\]
Ignoring secondary infections (their probability becomes around 0.8%) we obtain the approximation
\[\mathcal{R}_{\text{eff}}^{ct} \approx \left[1-\zeta\kappa\right]\mathcal{R}_{0} \tag{32}\]
Figures S5A and S5B show the performance of contact tracing for different \(r_{1}\)-, \(r_{2}\)- and \(\zeta\)-values. The numbers attached to the isolines refer to the ratio \(\mathcal{R}_{\text{eff}}^{wt}/\mathcal{R}_{0}\)and the bold contours depict combinations of \(r_{2}\) and \(\zeta\) for which \(\mathcal{R}_{\text{eff}}\) is reduced from 2.4 to \(\mathcal{R}_{\text{eff}}^{\text{cr}}=1\). One can conclude that the effect of contact tracing, if only applied to identify contacts with symptomatic persons, is limited to optimistic assumptions concerning the parameters dictating the Covid-19 pandemic and strongly depends on size and infectiousness of the asymptomatic population relative to size and infectiousness of the symptomatic one. Even if the most optimistic assumptions would hold, more substantial reductions of \(\mathcal{R}_{\text{eff}}\) would be desirable in order to accelerate the end of the pandemic (e.g. even in the absence of effective therapies or vaccines). For our base parameters of \(r_{1}=1/3\) and \(r_{2}=1/2\), contact tracing alone would not lead to an effective reproduction number of one (see Fig. S 5A at 50% infectiousness).
## 5 Smart Testing - How Selectivity Relates to \(\mathcal{R}_{\text{eff}}\)
Here it is studied how the number of required tests can be reduced, if one is able to identify (and propose testing to) a subpopulation with a prevalence higher than the overall population.
Without any additional knowledge, to achieve the discussed detection rates \(k_{e}\), \(k_{a}\) and \(k_{s}\) and corresponding reductions in \(\mathcal{R}_{\text{eff}}\), one has to test the entire undetected population once every \(N\) days (or equivalently every day a random fraction of \(1/N\)). To improve the efficiency of testing, i.e., the probability per test of getting a positive result by avoiding unnecessary testing of people who have a low likelihood of being infected, one can reduce the sample population by the following approaches:
1. _Serological testing_: With serological testing one can remove the recovered population from the pool of undetected individuals, and thus the same number of positive test results can be achieved with fewer tests. However, during an early stage of the pandemic the relative size of the undetected recovered compared to the whole undetected population is very small, and therefore the gain would be negligible. Nevertheless, this approach can easily be integrated into any mass testing strategy once reliable serological tests become available. Here, we can assume that immune individuals will remain immune for an extended period of time (e.g. up to 1-2 years; however, this is still subject to verification). If immune people cannot be infected for a second time (or are infected at a much lower rate than susceptible individuals), one can collect the information on positive test results to exclude the immune individuals from the Covid-19 RNA testing.
2. _Inference from contact tracing_: A more effective approach would be based on an inference model (e.g. by using contact tracing of infected individuals), which allows to divide the sample population \(\mathcal{D}\) into one subpopulation \(\tilde{\mathcal{D}}\) with a higher and the remainder with a lower percentage of infected individuals. For the following analysis we denote the size of \(\mathcal{D}\) with \(n\) and that of \(\tilde{\mathcal{D}}\) with \(\tilde{n}\). Further, \(\tilde{p}\) is the fraction of infected persons in \(\tilde{\mathcal{D}}\) and \(p\) that in \(\mathcal{D}\). Testing every person in \(\tilde{\mathcal{D}}\) at a frequency of \(1/N\) would require \(\tilde{n}/N\) tests per day; opposed to \(n/N\) tests, if the whole sample population was tested. The respective numbers of positive test results per day, on the other hand, would be \(\tilde{P}(N)=\tilde{p}\tilde{n}/N\) opposed to \(P(N)=pn/N\). In order to obtain the same number of positive results from the subpopulation \(\tilde{\mathcal{D}}\) as one would get from \(\mathcal{D}\), one has to reduce the test interval \(N\) to \(\tilde{N}\), such that \(\tilde{P}(\tilde{N})=P(N)\). From this one obtains \(\tilde{N}=N(\tilde{p}\tilde{n})/(pn)\) and one can conclude that the number of tests required to achieve the same overall quota reduces by the factor \[r = \frac{\tilde{n}/\tilde{N}}{n/N}\ =\ \frac{N\tilde{n}}{\tilde{N}n}\ =\ \frac{p}{\tilde{p}}.\] In order for this result to be practically meaningful, \(\tilde{N}\) has to be at least one, which translates into the requirement that \[\frac{\tilde{n}}{n}\geq\frac{r}{N}.\] In short, if one can identify a subpopulation \(\tilde{\mathcal{D}}\subset\mathcal{D}\) for which the percentage of infections is higher by a factor of \(r^{-1}\) than in \(\mathcal{D}\), and which is larger than \(nr/N\), then the number of tests needed to obtain the same reproduction number reduces by the factor \(r\). The curves in show the relationship between number of tests per 100'000 people per day needed to achieve \(\mathcal{R}_{\text{eff}}=1\) and the prevalence ratio between sub- and overall population; in combination with mild social distancing (solid line) and without social distancing (dashed line).
## 6 Contact Counting - How to Screen Large Enough Subpopulations with High Prevalence
Here we devise a way to screen large enough subpopulations with a much higher prevalence and infectiousness than the overall population, which is a prerequisite for smart testing.
We study three subpopulations as potential candidates for our smart testing mitigation approach; of interest are their prevalence, their infectiousness and their size. Next we describe them and provide quantitative estimates for the most relevant subpopulation.
1. _Contacts of symptomatic cases:_ A straight-forward approach would be to choose the contacts of symptomatic cases as our subpopulation. While this group is highly likely to be infected, this approach has one major drawback. In fact, the outcome of testing contacts of symptomatic cases would not be much different than that of contact tracing mentioned before (and discussed in detail by Ferretti et al.). Therefore, it suffers from the same limitation of not catching sufficient numbers of asymptomatic infections. Besides tracing contacts which potentially got infected by a symptomatic individual, one may also find the contact by whom it got infected. That person has most likely recovered, since he/she got infected roughly 10-14 days ago. Therefore this contact would not be tested positive (as virus titers may already be low and as we still lack reliable serological tests) and hence testing contacts of symptomatic ones would not lead us to a larger group with a sufficient number of asymptomatic cases.
2. _Direct and indirect contacts of symptomatic cases:_ One way to cope with the issue arising from lack of enough asymptomatic cases in the contacts of symptomatic ones is to enlarge our sample population and include also indirect contacts of symptomatic individuals in the past two weeks. This strategy, while most probably catching enough asymptomatic cases, may not reduce the burden of mass testing, since now the size of the subpopulation becomes simply too large. This problem has also been noted by others. For example at a prevalence of 1% in the total population, and assuming 10 contacts per person, the size of this subpopulation becomes almost as large as the whole population.
3. _High-contact individuals_: In this scenario we only test those with significantly more contacts than the average. In the following we show that indeed this strategy allows to screen a high prevalence subpopulation which is also large enough to stop the pandemic. It is also important to emphasize that the prerequisite of this strategy is to utilize a contact counter, which may be integrated into an existing contact tracing app that uses bluetooth technology.
While the improvements resulting from contact counting can be estimated based on the prevalence ratio, the contact counting scheme has a more fundamental feature that exhibits itself directly in the effective reproduction number. In fact by cutting out the highly transmissive parts of the population network, we reduce the effective reproduction number significantly. This reduction in \(\mathcal{R}_{\text{eff}}\) can be evaluated by considering the transmissibility of the disease \(T\). In short, considering a normalized recovery rate, \(T\) is the probability that an infected person infects one of their contacts per unit of time.
\[T = \mathcal{R}_{0}\frac{\mathbb{E}[\mathcal{K}]}{\mathbb{E}[\mathcal{ K}^{2}-\mathcal{K}]}. \tag{35}\]
Now imagine a scenario where we halt the virus-spread among all individuals with a degree of connectivity above \(\mathcal{K}_{0}\); for example via vaccinating every person who has contact numbers above \(\mathcal{K}_{0}\).
\[\mathcal{R}_{\text{eff}}^{m} = \frac{\mathbb{E}[\mathcal{K}^{2}-\mathcal{K}]\mathcal{K}\leq \mathcal{K}_{0}]}{\mathbb{E}[\mathcal{K}^{2}-\mathcal{K}]}\frac{\mathbb{E}[ \mathcal{K}]}{\mathbb{E}[\mathcal{K}[\mathcal{K}\leq\mathcal{K}_{0}]}\mathcal{ R}_{0}, \tag{36}\]
For a specified size of the new network, this results in a significant reduction of the reproduction number as the tail of the contact distribution is removed. However, in practice there are failures in containing the virus-spread through highly connected people. The efficacy \(\mathcal{E}\) of a smart testing based on contact counting thus depends on the number of highly connected people who would employ the contact counting app, as well as the accuracy of the tests. In the following we compute how these boundary conditions affect STeCC. However, before proceeding, notice that we suppose that the isolated individuals have negligible contributions to the virus-spread. Furthermore, we assume that elderly people (above 70 years of age) are shielded by isolation and that children below 10 years would not contribute to the infection dynamics. Therefore our target subpopulation is considered to be in possession of smart-phones.
Let us define a testing regime, where we screen through app users with number of connections \(\mathcal{K}\geq\mathcal{K}_{0}^{}\) at day 1, \(\mathcal{K}_{0}^{}\leq\mathcal{K}_{0}\leq\mathcal{K}_{0}^{}\) at day 2 and so-forth until testing \(\mathcal{K}_{0}^{(T_{t})}\leq\mathcal{K}_{0}\leq\mathcal{K}_{0}^{(T_{t}-1)}\) at day \(T_{t}\). Consequently, based on the test results, we ask the positively tested individuals to quarantine themselves. We fix the testing cycle to \(T_{t}=7\) days (see Fig. 4). Consider \(\zeta\) to be the fraction of smart-phone owners who utilize the app. The portion of the network besides the fraction \(\zeta\) that we can disconnect from the population depends on the probability of the event that a positively tested highly connected individual could pass on the virus to at least one person in the past \(T_{t}+\tau_{proc}\) days.
Let us denote such an event by \(\mathcal{A}_{out}\) and consider the test processing time \(\tau_{proc}\).
\[\mathcal{R}_{\text{eff}}^{an} = \frac{\mathcal{P}_{\mathcal{K}\leq\mathcal{K}_{0}^{(T_{s})}}\ \mathbb{E}[\mathcal{K}^{2}-\mathcal{K}|\mathcal{K}\leq\mathcal{K}_{0}^{(T_{s})}]+(1-\mathcal{E})\mathcal{P}_{\mathcal{K}\geq\mathcal{K}_{0}^{(T_{s})}}\ \mathbb{E}[\mathcal{K}^{2}-\mathcal{K}|\mathcal{K}\geq\mathcal{K}_{0}^{(T_{s})}]}{ \mathcal{P}_{\mathcal{K}\leq\mathcal{K}_{0}^{(T_{s})}}\ \mathbb{E}[\mathcal{K}|\mathcal{K}\leq\mathcal{K}_{0}^{(T_{s})}]+(1-\mathcal{E}) \mathcal{P}_{\mathcal{K}\geq\mathcal{K}_{0}^{(T_{s})}}\ \mathbb{E}[\mathcal{K}|\mathcal{K}\geq\mathcal{K}_{0}^{(T_{s})}]}{\mathbb{E}[ \mathcal{K}^{2}-\mathcal{K}]}\mathcal{R}_{0}, \tag{37}\]
where \(\mathcal{E}\) is the efficacy of STeCC and can be computed via
\[\mathcal{E} = 1-\left((\mathcal{P}_{\mathcal{A}_{out}}(1-\eta)+\eta)\zeta+(1- \zeta)\right). \tag{38}\]
Note that \(\eta\) is the fraction of false negative test results, \(\mathcal{P}_{\mathcal{A}_{out}}\) is the probability of the event \(\mathcal{A}_{out}\), \(\mathcal{P}_{\mathcal{K}\leq\mathcal{K}_{0}^{(T_{s})}}\) is the probability that an individual has contacts below \(\mathcal{K}_{0}^{(T_{s})}\) and \(\mathcal{P}_{\mathcal{K}\geq\mathcal{K}_{0}^{(T_{s})}}=1-\mathcal{P}_{ \mathcal{K}\leq\mathcal{K}_{0}^{(T_{s})}}\). It is evident that \(\mathcal{R}_{\text{eff}}^{an}\) and \(\mathcal{E}\) would now depend on the network topology and latency time, respectively.
### Network Topology
In order to model the heterogeneity of a population relevant for disease modeling, scale-free networks offer appropriate features. Scale-free networks are characterized by a power-law distribution which determines the probability density function \(P_{k}\) of the degree of connectivity \(k\) per node.
\[P_{k}=\alpha_{p}k^{-(2+\gamma)}\quad(m\leq k\leq k_{c})\ \ \&\ \ \ (0\leq\gamma\leq 1), \tag{39}\]
where
\[\alpha_{p} = \frac{(1+\gamma)m^{1+\gamma}}{1-(k_{c}/m)^{-(1+\gamma)}}. \tag{40}\]
Notice that by contacts we mean disease relevant contacts. We adopt \(\gamma=0.3\) and fix the upper and lower cut-offs by \(k_{c}=552\) and \(m=4\), respectively. These choices were made in order to have a realistic range for number of contacts and obtain an average number of contacts of \(\mu=13.4\), which is consistent with the data provided in. Two extreme choices of \(\gamma\) include \(\gamma=1\) and \(\gamma=0\). While the former leads to the celebrated Barabasi and Albert (BA) model; the latter has been used in disease spread models, e.g. see. Note that we conducted a sensitivity analysis of our results with respect to \(\gamma\), see Figs. S7 and S8.
With the choice of the degree of connectivity distribution we can compute the relative size of the population with a degree of connectivity above a certain \(\mathcal{K}_{0}^{(T_{s})}\):
\[\mathcal{P}_{\mathcal{K}\geq\mathcal{K}_{0}^{(T_{s})}} = \frac{\alpha_{p}}{1+\gamma}\left(\mathcal{K}_{0}^{(T_{s})-(1+ \gamma)}-k_{c}^{-(1+\gamma)}\right). \tag{41}\]
Before proceeding further, let us mention that for the perfect efficacy \(\mathcal{E}=1\), we can reach \(\mathcal{R}_{\text{eff}}^{an}=1\) with \(\mathcal{K}_{0}^{(T_{s})}=138.8\). This accounts for \(0.83\%\) of the population with highest degree of connectivity. Now, to translate \(\mathcal{P}_{\mathcal{K}\geq\mathcal{K}_{0}^{(T_{s})}}\) of the population into the equivalent number of tests, suppose we conduct \(N_{test}\) per day per \(100\,000\) people.
\[\mathcal{K}_{0}^{(T_{s})} = \left(\frac{(1+\gamma)N_{test}T_{t}}{10^{5}\alpha_{p}\zeta}+k_{c} ^{-(1+\gamma)}\right)^{-1/(\gamma+1)}. \tag{42}\]
### Uncontained Virus Spread
Since we test these high-contact individuals once every \(T_{t}=7\) days (test cycle depicted in Fig. 4B), there is a chance that a virus-positive person has already transmitted the virus between two successive tests. The probability of such events depends on the latency time \(\tau_{l}\) and average number of contacts of the individual. The infection time \(\tau_{0}\) is uniformly distributed between 0 and \(T_{t}\).
\[\mathcal{P}_{\mathcal{A}_{\text{test}}} = \text{Prob}\Bigg{\{}(\tau_{0}+\tau_{1})\leq(T_{t}+\tau_{proc}) \Bigg{\}}, \tag{43}\]
### Scenario Analysis
Now we are ready to consider the following scenarios and compute the reduction of the effective reproduction number as a function of number of app users.
1. _Scenario A:_ In this STeCC alone scenario we identify high-contact individuals in cycles of 7 days, ask them to be tested and ask the positively tested individuals to go into self-quarantine. We compute the reduced effective reproduction number \(\mathcal{R}_{\text{eff}}^{ST-A}\) using Eq. with the efficacy equation. For our base parameters together with the network topology with \(\gamma=0.3\), \(m=4\) and \(k_{c}=552\), Fig. S 6 shows the performance of STeCC-A. While up to 30% reduction of \(\mathcal{R}_{\text{eff}}\) can be achieved with a combination of 90% app users among smart phone users (which would only be achieved in very optimistic scenarios) and 200 tests per 100'000 per day, it is clearly insufficient to halt the pandemic. The reason lies in the fact that we would not be able to contain the virus spread from almost 40% of highly connected people resulting from the transmission events that occur between their infection and the date of the virus test. Next, we introduce a combination that can significantly reduce this virus spread.
2. _Scenario B:_ Here we consider a variant of STeCC in which besides the positively tested ones also their contacts are asked to quarantine. This results in a much lower effective reproduction number of \(\mathcal{R}_{\text{eff}}^{ST-B}\), which is obtained from Eq. with the improved efficacy \[\mathcal{E}\;=\;\mathcal{E}^{ST-B} = 1-\left(\left(\mathcal{P}_{\mathcal{A}_{\text{test}}}(1-\eta) \overbrace{(1-\zeta)}^{\text{due to quarantine}}+\eta\right)\zeta+(1-\zeta)\right).\] The results shown in predict a much stronger effect than STeCC alone (Fig. S 6). The combination of 90% user percentage and almost 400 tests per 100'000 per day now lead to \(\mathcal{R}_{\text{eff}}^{ST-B}=1\). Again, this approach alone will likely not suffice to halt the pandemic under realistic conditions.
3. _Scenario C:_ Since the app already provides the contacts, we can further improve the STeCC based mitigation by combining it with conventional contact tracing (see SS4). This is especially interesting since neither contact tracing nor STeCC alone are effective enough to halt the pandemic under realistic conditions. Therefore, on top of scenario B, we also ask the contacts of symptomatic cases to quarantine, which leads to an effective reproduction number of \[\mathcal{R}_{\text{eff}}^{ST-C} = \frac{\mathcal{P}_{\mathcal{K}\leq\mathcal{K}_{0}^{(T_{c})}}\; \mathbb{E}[\mathcal{K}^{2}-\mathcal{K}|\mathcal{K}\leq\mathcal{K}_{0}^{(T_{c} )}]+(1-\mathcal{E}^{ST-B})\mathcal{P}_{\mathcal{K}\geq\mathcal{K}_{0}^{(T_{c} )}}\;\mathbb{E}[\mathcal{K}^{2}-\mathcal{K}|\mathcal{K}\geq\mathcal{K}_{0}^{(T _{c})}]}{\mathcal{P}_{\mathcal{K}\leq\mathcal{K}_{0}^{(T_{c})}}\;\mathbb{E}[ \mathcal{K}|\mathcal{K}\leq\mathcal{K}_{0}^{(T_{c})}]+(1-\mathcal{E}^{ST-B}) \mathcal{P}_{\mathcal{K}\geq\mathcal{K}_{0}^{(T_{c})}}\;\mathbb{E}[\mathcal{K} |\mathcal{K}\geq\mathcal{K}_{0}^{(T_{c})}]}\frac{\mathbb{E}[\mathcal{K}]}{ \mathbb{E}[\mathcal{K}^{2}-\mathcal{K}]}\mathcal{R}_{\text{eff}}^{ct},\] where \(\mathcal{R}_{\text{eff}}^{ct}=(1-\zeta\kappa)\,\mathcal{R}_{0}\) and \(\kappa=\mathcal{R}_{0}^{\text{sym}}/\mathcal{R}_{0}\) (see SS4). The result corresponding to this scenario is shown in Accordingly, we predict that \(\mathcal{R}_{\text{eff}}^{ST-C}=1\) can be achieved with 72% app users among smart phone users and 166 tests per 100'000 per day. This is very encouraging, since 72% app users among smart phone users corresponds to only about 50% app users of the whole population. Furthermore, a testing capacity of 166 per 100'000 per day already is available in several developed countries, including Switzerland.
### Sensitivity Study
In order to gain further confidence in our STeCC related mitigation scenarios, we conducted studies to investigate the sensitivity of the effective reproduction number for \(\mathcal{R}_{0}\in\{1.9,2.9,3.4\}\). The parameters which we varied are \(\gamma\in\{2,2.5,3.5\}\) in the exponent of the power-law distribution of the degree of connectivity, the ratio \(\eta\in\{0.1,0.15\}\) of false negatives and the test processing time \(\tau_{proc}\in\{0.5,1.5\}\) (day). Note that our base setting is the combination of \(\mathcal{R}_{0}=2.4\), \(\gamma=0.3\), \(\eta=0.05\) and \(\tau_{proc}=1\) (day). Figures S 7 and 8 show the sensitivity of STeCC-B and-C scenarios, respectively, for varying \(\mathcal{R}_{0}\) and \(\gamma\) values. Figure S9 depicts the sensitivity of STeCC-C with respect to the fraction of false negatives and test processing time. We observe that for a large range of parameters considered the combination of STeCC and conventional contact tracing leads to stopping the pandemic with realistic app user percentage (i.e., 60% to 85%) and number of tests per day (i.e., 50 to 350 tests per 100'000).
Figure S7: STeCC plus isolation of contacts with positively tested individuals (STeCC-B): \(\mathcal{R}_{\text{eff}}^{ST-B}/\mathcal{R}_{0}\) as function of number of smart tests per \(100^{\prime}000\) per day and the percentage of smart-phone owners who participate in STeCC (scenario B). For (\(\gamma=0.3,k_{c}=552\)) and (A) \(\mathcal{R}_{0}=1.9\), (C) \(\mathcal{R}_{0}=2.9\) and (E) \(\mathcal{R}_{0}=3.4\); for \(\mathcal{R}_{0}=2.4\) and (B) (\(\gamma=0.2,k_{c}=227\)), (D) (\(\gamma=0.25,k_{c}=327\)) and (F) (\(\gamma=0.35,k_{c}=1325\)). A corresponding map with \(\mathcal{R}_{0}=2.4\) and \(\gamma=0.3\) is shown in The bold lines indicates the combinations for which \(\mathcal{R}_{\text{eff}}^{ST-B}=1\).
STeCC plus isolation of contacts with positively tested individuals plus classical contact tracing (STeCC-C): \(\mathcal{R}_{\text{eff}}^{ST-C}/\mathcal{R}_{0}\) as function of number of smart tests per \(100^{\prime}000\) per day and the percentage of smart-phone owners who participate in STeCC (scenario C). For (\(\gamma=0.3,k_{c}=552\)) and (A) \(\mathcal{R}_{0}=1.9\), (C) \(\mathcal{R}_{0}=2.9\) and (E) \(\mathcal{R}_{0}=3.4\); for \(\mathcal{R}_{0}=2.4\) and (B) (\(\gamma=0.2,k_{c}=227\)), (D) (\(\gamma=0.25,k_{c}=327\)) and (F) (\(\gamma=0.35,k_{c}=1325\)). A corresponding map with \(\mathcal{R}_{0}=2.4\) and \(\gamma=0.3\) is shown in The bold lines indicates the combinations for which \(\mathcal{R}_{\text{eff}}^{ST-C}=1\).
## 7 Contact Counting App - One Approach to Ensure Data Privacy
Here we outline one option how an efficient centralized contact counting scheme could be implemented using Fully Homomorphic Encryption (FHE). By centralized we mean that the number of contacts of each user is gathered on a central server every day, which allows to compute the distribution of contacts among the population. Given this distribution allows to determine and broadcast a threshold, beyond which testing is recommended. Subsection 7.1 provides an introduction to FHE, in subsection 7.2 a solution is presented and privacy concerns are discussed in subsection 7.3.
### Fully Homomorphic Encryption
Fully Homomorphic Encryption (FHE) has been the holy grail of cryptographers for a very long time. It is only since 2009, with the seminal work of Gentry, that the first concrete and secure construction appeared. However, these initial constructions were far from being practical, and even their mere implementation took few years; see e.g.. Whereas in the beginning performances were catastrophic (keys of few gigabytes and hours to perform operations), recent constructions have proven rather efficient and are now usable in industry. Most notably, the implementation of HElib2, Seal3, and TFHE4 have shown to be of practical value.
Footnote 2: [https://github.com/shaih/HElib](https://github.com/shaih/HElib)
Footnote 3: [https://www.microsoft.com/en-us/research/project/microsoft-seal/](https://www.microsoft.com/en-us/research/project/microsoft-seal/)
Footnote 4: [https://tfhe.github.io/tfhe/](https://tfhe.github.io/tfhe/)
A FHE scheme allows to compute on encrypted data. More precisely, let Enc (respectively Dec) be an (asymmetric) encryption algorithm (respectively its corresponding decryption algorithm). These algorithms are non-deterministic, however for the following explanations we will explicitly write the random seed parameter to make the function deterministic (for the same seed value). Let \(m_{1},\ldots m_{n}\in\mathcal{M}\) be plaintexts (here IDs), and let \(f:\mathcal{M}^{n}\rightarrow\mathcal{M}\) be any computational circuit. Let also \(c_{1},\ldots c_{n}\in\mathcal{C}\) be the corresponding ciphertexts, i.e., \(c_{i}=\text{Enc}(m_{i})\). Then there exists a circuit \(\tilde{f}\) which is efficiently computable such that \(\text{Dec}(\tilde{f}(c_{1},\ldots,c_{n}))=f(m_{1},\ldots,m_{n})\), i.e., there is the possibility to apply a function on the plain-texts without decrypting the ciphertexts without knowing their content. It is important to note that most of the practical constructions work at the bit level, which means that only bit operations can be performed on the plaintexts.
### Our Construction
The goal of our construction is that at the end of each day the central server is aware of the distribution of number of contacts per user, without knowing which user has how many contacts. However, we want to minimize the size of the exchanged messages, i.e., of all the beacons seen that day.
Our idea is to homomorphically update an encrypted counter on each device. This counter will be encrypted with the public key of the server and, thus, only this server will be able to know its value. In more detail:
1. Initially, the central server generates a pair of public/private keys \((\mathbf{pk}_{c},\mathbf{sk}_{c})\) for an asymmetric fully homomorphic encryption scheme.
2. Every device will select each day \(t\) a new ID that we denote \(\text{ID}_{t}\). This ID is going to be used for contact counting.
3. During each epoch, each device broadcasts a ciphertext of \(\text{ID}_{t}\) with fixed randomness. This means that during one epoch, the same ciphertext is broadcast. More precisely, at epoch \(i\) we broadcast the ciphertext \(c_{i}=\text{Enc}_{\mathbf{pk}}(\text{ID}_{t},r_{i})\) for some random coins \(r_{i}\). Therefore, between different epochs the ciphertexts will not be linkable, unless one possesses the private key \(\mathbf{sk}_{c}\).
4. Now we deal with the contact counter ctr. Every day this counter is set to zero; its encryption thus is \(ctr=\)Enc\({}_{pk_{c}}\)5. Footnote 5: Note that since our scheme operates at bit level, one needs to encode this for many bits.
5. Every device will also keep a database of all the beacons seen that day.
6. Upon reception of a beacon \(c^{*}\), which is a ciphertext of an ID, we need to update the counter only if the ID is a new one. We do this by computing the following circuit homomorphically. Let \(c_{1},\ldots,c_{n}\) be the beacons that are already stored in the database. We homomorphically compute \(d_{i}=(c^{*}\oplus c_{i})\) for \(i\in[1,\ldots n]\), where \(\oplus\) is the bitwise XOR. Hence, the plaintext corresponding to \(d_{i}\) is zero, if and only if \(c^{*}\) and \(c_{i}\) come from the same ID.
7. The counter then has to be updated by one only if all the \(d_{i}\) have a corresponding plaintext different from zero. Let \(d_{i,1},\ldots,d_{i,m}\) denote the bits of \(d_{i}\). We will apply the following function \(g\) on each \(d_{i}\): \[g(d_{i})=\overline{\overline{d_{i,1}}\&\ldots\&\overline{d_{i,m}}}\,\] where \(\overline{b}\) denotes the NOT operator over the bit \(b\). Note that the output of \(g\) is the ciphertext of 0, if \(d_{i}\) is the ciphertext of zero, and Dec(\(g\))=1 otherwise. Hence, we then homomorphically compute ctr=ctr+\(g(d_{1})\&g(d_{2})\&\ldots\&g(d_{n})\), where, & denotes the AND operator.
8. At the end of the day this encrypted counter is sent to the central server.
Note that the homomorphic computations can be computationally expensive, which might be problematic on devices that run on a battery (e.g. a mobile phone). A solution to this problem is to delay these homomorphic computations as much as possible (e.g. waiting for the phone to get plugged in). Further, one may reduce the frequency at which beacons are broadcast, thus reducing the number of beacons on which homomorphic computations have to be performed.
Note that minimal communication with the server is required, i.e., only one message has to be sent each day (the encrypted counter).
### Privacy Discussion
Our scheme has the important advantage of not letting users know whether different beacons at different epochs belong to the same person. Indeed, the properties of the non-deterministic FHE scheme ensures that two ciphertexts of the same plaintext, but with different random coins, are not relatable (IND-CPA security). However, since the central authority knows the associated private key, it could decrypt beacons on the fly and therefore could use this information to track/follow users, i.e. the central authority must be trusted. Attacks that are possible in the DP-3T setting also exist here, e.g. replay and Sybil attacks.
Since some users may have concerns with a centralized scheme, we also study how different mixes of contact counting and contact tracing users would affect the performance of SteCC-C, as shown in
## 8 Model Implementation
The dynamic model was implemented with Maple 2018. The calculations for mass testing, contact tracing and smart testing were implemented with MATLAB and the Statistics Toolbox Release 2018b. The corresponding codes are available on GitHub server via [https://github.com/gorjih2/STeCC_preliminary](https://github.com/gorjih2/STeCC_preliminary).
|
053355_file02 | ## Detailed methods and R summary model output
### GAMM models
#### Summary model output
This is a representation of the fitted values in the final model for test sensitivity as returned by mgcv::summary in R:
\begin{tabular}{l c c c c} _Predictors_ & _Estimate_ & _SE_ & \(p\) & _df (edf for smooth)_ \\ \hline Intercept (inc. Nasal swab) & 0.87 & 0.19 & **<0.001** & - \\ Swab type (Throat) & -1.00 & 0.28 & **0.0002** & 1 \\ Smooth term (Days since symptom onset) & - & & **<0.001** & 1.06 \\ RE Smooth term (Patient) & - & & **<0.001** & 63.13 \\ \hline R\({}^{2}\) adj & 36.20 \% & & & \\ AIC & 805.31 & & & \\ \end{tabular}
### Sensitivity of Zou et al estimates
We utilise data from Zou et al. who use a combination of mid-turbinate and nasopharyngeal swabs to constitute nasal samples. To determine if there is an effect of using this combination of different swab types on results, we coded the "swab type" variable to have a separate level corresponding to the nasal samples for Zou et al, then compared it to the best fitting model with only two levels in the swab type variable (AIC = 805.31). The inclusion of a Zou-specific correction was not supported (AIC = 805.81, \(\Delta\)AIC = 0.50).
#### Estimating the false-negative error rate in cohorts of tested individuals
Using the GAMM model, we estimated the aggregate false negative rate for hypothetical cohorts of tested patients. To do this, we considered a range of Gamma distributions as parameterised by the mode and standard deviation. These distributions were used to describe the time between the onset of symptomsand patients being tested. The shape (S) and rate (R) parameters were written as functions of the mode (M) and standard deviation (s):
\[R = \frac{M+\sqrt{(M^{2}+4\sigma^{2})}}{2\sigma^{2}}\] \[S = 1+MR\]
We explored arrival time distributions with modes ranging from 0.1 to 5 days and standard deviations ranging from 0.5 to 5. We discretised the arrival time distribution (\(\Gamma(x)\)) to give the proportion of patients in a cohort being tested on a given day. These fractions were then multiplied by the estimated probability of a false negative predicted by the GAMM function (f(x)) for a single nasal swab on that day; summing these together gave the aggregate false negative rate (_P(Neg|Inf)_) for cohorts tested according to this particular arrival time distribution. To get the probability of 2 false-negatives 1 day apart, we simply took the product f(x).f(x+1) and used this in place of f(x).
### Estimating the time to test
Let
* \(\tau_{i}\) correspond to being tested on day i
* \(\psi\) correspond to having a positive test result
* \(\eta\) correspond to being infected
Then
\[P(\tau_{i}\cap\eta) = \frac{P(\tau_{i}\cap\eta\mid\psi)\times P(\psi)}{P(\psi\mid\tau_{i }\cap\eta)}\]
We assumed the test has perfect sensitivity, such that \(P(\tau_{i}\cap\eta\mid\psi)\equiv P(\tau_{i}\mid\psi)\) since all individuals with positive tests must be infected, and so we estimated this for each day using the distribution of time to positive test results for symptomatic individuals from Bi et al. (a gamma distribution with shape 2.12 and rate 0.39). We discretised this distribution (such that [0, 0.5) corresponds to 0 days from symptom onset, [0.5, 1.5) corresponds to 1 day after symptom onset etc) and truncated it to 31 days, which is the maximum number of days from symptom onset present in the data we analysed. This truncation has no practical impact because > 99.99% of the density of this particular gamma distribution is accounted for at this point.
Meanwhile \(P(\psi\mid\tau_{i}\cap\eta)\) is the probability of a positive test result for infected individuals given the day of the test, which is exactly what we estimated in this study. Of course, \(P(\psi)\) is unknown.
Supposing that all tests were performed the same number of days after symptom onset; we defined:
* \(a\) as the (unknown) true prevalence among those tested
* \(\beta\) as the false-positive rate i.e. P(positive test | uninfected)
* \(\gamma\) as the false-negative rate for tests done on that day i.e.
Then the true prevalence among those tested for infection is equal to the sum of (a) P(infected|positive test) multiplied by the number of positive tests and (b) P(infected|negative test) multiplied by the number of negative tests (i.e sum of the true positives and false negatives). These conditional probabilities can be separately rearranged via Bayes' Theorem and then added together to give:
\(\alpha T=qT\)\(\frac{a(1\neg\gamma)}{a(1\neg\gamma)+(1\neg\alpha)\beta}+(1-q)T\)\(\frac{\alpha\gamma}{a+(1\neg\alpha)(1\neg\beta)}\)
When rearranging, this as a quadratic in \(a\) then we discover it has 2 roots:
\(\alpha=\frac{q-\beta}{1-\gamma-\beta}\)
\(\alpha=1\)
And so the first root allows us to estimate the true prevalence among the test cohort, while accounting for the false-negative test probability for those tested on that day.
In reality, however, individuals are tested on different days on which the false negative test probability depends, which makes it much harder to estimate \(a\) in this way. One way it can be done is to use the distribution for time to test to calculate the average false-negative test probability across all tests conducted, again assuming that all tests are done by nasal swab - here this gives a false-negative test probability of 16.71%. If we do this, then we can still apply the same equations as above and explore how accounting for the false-negative and false-positive test probabilities affects the consequent estimates of the true prevalence among those tested, which we illustrate for some different scenarios in the main text.
Importantly, this only tells us about prevalence in the test cohort and not in the wider population i.e. this does nothing to correct for not finding and not testing mild/asymptomatic cases (as discussed in the main text). |
054338_file03 | ## Chicago, IL
\begin{tabular}{|l|l|} \hline _County_ & _FIPS_ \\ \hline Cook County & 17031 \\ \hline DuPage County & 17043 \\ \hline Grundy County & 17063 \\ \hline Kendall County & 17093 \\ \hline McHenry County & 17111 \\ \hline Will County & 17197 \\ \hline \end{tabular}
#### New York City, NY
\begin{tabular}{|l|l|} \hline _County_ & _FIPS_ \\ \hline Bergen County & 34003 \\ \hline Hudson County & 34017 \\ \hline Middlesex County & 34023 \\ \hline Monmouth County & 34025 \\ \hline Ocean County & 34029 \\ \hline Passaic County & 34031 \\ \hline Orange County & 36071 \\ \hline Rockland County & 36087 \\ \hline Westchester County & 36119 \\ \hline New York City & 36061 \\ \hline \end{tabular}
## Figure S1.
The autocorrelation of accepted parameters using the Metropolis-Hasting algorithm after thinning and burn-in are shown for Italy with unconstrained priors of \(\theta\).
## Figure S2.
The autocorrelation of accepted parameters using the Metropolis-Hasting algorithm after thinning and burn-in are shown for Spain with unconstrained priors of \(\theta\).
## Figure S3.
The autocorrelation of accepted parameters using the Metropolis-Hasting algorithm after thinning and burn-in are shown for South Korea with unconstrained priors of \(\theta\).
## Figure S4.
The autocorrelation of accepted parameters using the Metropolis-Hasting algorithm after thinning and burn-in are shown for New York City with unconstrained priors of \(\theta\).
## Figure S5.
The autocorrelation of accepted parameters using the Metropolis-Hasting algorithm after thinning and burn-in are shown for Chicago with unconstrained priors of \(\theta\).
## Figure S6.
The autocorrelation of accepted parameters using the Metropolis-Hasting algorithm after thinning and burn-in are shown for Italy with priors of \(\theta<50\%\).
## Figure S7.
The autocorrelation of accepted parameters using the Metropolis-Hasting algorithm after thinning and burn-in are shown for Spain with priors of \(\theta<50\%\).
## Figure S8.
The autocorrelation of accepted parameters using the Metropolis-Hasting algorithm after thinning and burn-in are shown for South Korea with priors of \(0<50\%\).
## Figure S9.
The autocorrelation of accepted parameters using the Metropolis-Hasting algorithm after thinning and burn-in are shown for New York City with priors of \(\theta<50\%\).
## Figure S10.
The autocorrelation of accepted parameters using the Metropolis-Hasting algorithm after thinning and burn-in are shown for Chicago with priors of \(\theta<50\%\).
## Figure S11.
The autocorrelation of accepted parameters using the Metropolis-Hasting algorithm after thinning and burn-in are shown for Italy with priors of \(\theta<10\%\).
## Figure S12.
The autocorrelation of accepted parameters using the Metropolis-Hasting algorithm after thinning and burn-in are shown for Spain with priors of \(\theta<10\%\).
## Figure S13.
The autocorrelation of accepted parameters using the Metropolis-Hasting algorithm after thinning and burn-in are shown for South Korea with priors of \(0<10\%\).
## Figure S14.
The autocorrelation of accepted parameters using the Metropolis-Hasting algorithm after thinning and burn-in are shown for New York City with priors of \(\theta<10\%\).
## Figure S15.
The autocorrelation of accepted parameters using the Metropolis-Hasting algorithm after thinning and burn-in are shown for Chicago with priors of \(\theta<10\%\).
## Figure S16.
The trace plot of accepted parameters using the Metropolis-Hasting algorithm after thinning and burn-in are shown for Italy with unconstrained priors of \(\theta\).
## Figure S17.
The trace plot of accepted parameters using the Metropolis-Hasting algorithm after thinning and burn-in are shown for Spain with unconstrained priors of \(\theta\).
## Figure S18.
The trace plot of accepted parameters using the Metropolis-Hasting algorithm after thinning and burn-in are shown for South Korea with unconstrained priors of \(\theta\).
## Figure S19.
The trace plot of accepted parameters using the Metropolis-Hasting algorithm after thinning and burn-in are shown for New York City with unconstrained priors of \(\theta\).
## Figure S20.
The trace plot of accepted parameters using the Metropolis-Hasting algorithm after thinning and burn-in are shown for Chicago with unconstrained priors of \(\theta\).
## Figure S21.
The trace plot of accepted parameters using the Metropolis-Hasting algorithm after thinning and burn-in are shown for Italy with priors of \(\theta<50\%\).
## Figure S22.
The trace plot of accepted parameters using the Metropolis-Hasting algorithm after thinning and burn-in are shown for Spain with priors of \(0<50\%\).
## Figure S23.
The trace plot of accepted parameters using the Metropolis-Hasting algorithm after thinning and burn-in are shown for South Korea with priors of \(\theta<50\%\).
## Figure S24.
The trace plot of accepted parameters using the Metropolis-Hasting algorithm after thinning and burn-in are shown for New York City with priors of \(0<50\%\).
## Figure S25.
The trace plot of accepted parameters using the Metropolis-Hasting algorithm after thinning and burn-in are shown for Chicago with priors of \(\theta<50\%\).
## Figure S26.
The trace plot of accepted parameters using the Metropolis-Hasting algorithm after thinning and burn-in are shown for Italy with priors of \(\theta<10\%\).
## Figure S27.
The trace plot of accepted parameters using the Metropolis-Hasting algorithm after thinning and burn-in are shown for Spain with priors of \(\theta<10\%\).
## Figure S28.
The trace plot of accepted parameters using the Metropolis-Hasting algorithm after thinning and burn-in are shown for South Korea with priors of \(\theta<10\%\).
## Figure S29.
The trace plot of accepted parameters using the Metropolis-Hasting algorithm after thinning and burn-in are shown for New York City with priors of \(0<10\%\).
## Figure S30.
The trace plot of accepted parameters using the Metropolis-Hasting algorithm after thinning and burn-in are shown for Chicago with priors of \(\theta<10\%\).
## Figure S31.
Using Markov Chain Monte Carlo (MCMC) methods, we sampled from the posterior distribution of the model parameters for three Bayesian priors which assumes \(\theta\) is less than 10%, 50% and 99%. The posterior distribution of \(\theta\) and the inverse of sum of squared residuals (SSR\({}^{-1}\)) for Chicago and New York City are shown in A, B, and C, and the same set of priors for Italy, Spain, and South Korea are shown in D, E, and F. The marginal posterior density of \(\theta\) and SSR\({}^{-1}\) are displayed on the right and top of the scatter plot, respectively. The ellipses encircle 95% of simulation runs for each location.
Page **33** of **44**
## Figure S32.
Using Markov Chain Monte Carlo (MCMC) methods, we sampled from the posterior distribution of the model parameters for three Bayesian priors which assumes \(\theta\) is less than 10%, 50% and 99%. The posterior distribution of \(\theta\) and \(R_{0}\) for the three priors of Chicago and New York City are shown in A, B, and C, and the same set of priors for Italy, Spain, and South Korea are shown in D, E, and F. The marginal posterior density of \(R_{0}\) and \(\theta\) are displayed on the right and top of the scatter plot, respectively. The ellipses encircle 95% of simulation runs for each location.
## Figure S33.
The posterior distribution of R\({}_{0}\) is generated from the MCMC sampling for each location are shown for the symptomatic rate \(\theta\). The three groupings represent the Bayesian priors for \(\theta\), where 0<10%, 0 <50%, and \(\theta\) is unconstrained.
## Figure S34.
The simulated and actual cumulative infections for each location (Spain, Italy, South Korea, Chicago, IL, and New York City, NY are shown) for three different prior distributions of the symptomatic rate (\(\theta\)). The turquoise line (simulated) corresponds with the simulated outputs for cumulative confirmed cases, which were fitted to the yellow line (trained) representing the actual data. The red dashed line represents the actual data after the explosion date, which is demarcated by the vertical black dotted line. The grey ribbon represents the upper and lower bounds of the MCMC sampling for all cases for each day.
## Figure S35.
Simulated and actual cumulative hospitalizations and cumulative infections for New York City for three different prior distributions of the symptomatic rate (\(\theta\)). The turquoise line (simulated) corresponds with the simulated outputs for cumulative confirmed cases, which were fitted to the yellow line (trained) representing the actual data. The red dashed line represents the actual data after the explosion date which is demarcated by the vertical black dotted line. The grey ribbon represents the upper and lower bounds of the MCMC sampling for all cases for each day.
|
055574_file02 | ## Supplementary Table S2.
The spearman correlations between the vectors of 23 statistics, one value for each disease. Imp. refers to the improvement, or difference in models that include or do not include the polygenic risk score.
## Supplementary Table S3.
Count of individuals moving into and out of the top 5% risk group with the incusion of the polygenic risk score in the underlying risk model.
## Supplementary Table S4.
The Net Reclassification Improvement (NRI) values for each disease using the 95th percentile risk as the cutoff within the categorical computation.
## Supplementary Table S5.
The integrated discrimination index (IDI) values computed for each disease. The definition of IDI is provided within _Evaluating the added predictive ability of a new marker: From area under the ROC curve to reclassification and beyond_ by Pescina et al.
## Supplementary Table S6.
Brier values computed from models that either contain the base covariates, or a model that also includes the best respective polygenic risk score.
## Supplementary Table S7.
The true positive rates determined for the top 5% risk group.
## Supplementary Table S8.
The hazards at the final time-point in the study generated from models that include age, sex, top, ten genetic principal components and the respective polygenic risk score
## Supplementary Table S9.
The hazards at the final time-point in the study generated from models that included the polygenic risk score minus the hazards at the same time point but for models without the polygenic risk score.
## Supplementary Table S10.
The AUCs generated from models that include age, sex, top ten genetic principal components and either a polygenic risk score or extra covariates as specified.
## Supplementary Table S11.
The AUCs generated from models that contain age, sex, top ten genetic principal components and the polygenic risk score specified.
## Supplementary Table S12.
The maximum standardized net benefits corresponding to both base models that include the covariates of age, sex, and the top ten genetic principal components, and the score included models also includes the polygenic risk score to the base covariates.
## Supplementary Table S13.
Standardized net benefits corresponding to both base models that include the covariates of age, sex, and the top ten genetic principal components, and the score included models also includes the polygenic risk score to the base covariates, computed at the thresholds described in the column headers.
## Supplementary Table S14.
The range of thresholds for each disease in which the score included model generated standardized net benefits that exceeded those of the base model. Base models include the covariates of age, sex, and the top ten genetic principal components, and the score included models also include the polygenic risk score to the base covariatesSupplementary Table S15. The absolute risks calculated for each lifestyle and PRS grouping, listed for all significant disease and lifestyle factor combinations.
\begin{tabular}{l l l l l l l l} \hline \hline
## Disease** & **Lifestyle Factor** & **P - Low** & **P - Inter.** & **P - High** & **OR - Low** & **OR - Inter.** & **OR - High
\\ \hline A. Fib. & Alcohol & 0.726 & 0.000163 & 0.000197 & 0.968 & 1.16 & 1.22 \\ A. Fib. & Smoking Status & 0.000538 & 9.91e-07 & 3.01e-05 & 0.677 & 0.77 & 0.748 \\ A. Fib. & BMI & 1.6e-24 & 1.1e-85 & 3.58e-45 & 0.374 & 0.398 & 0.408 \\ A. Fib. & Walking Pace & 1.59e-51 & 1.25e-150 & 1.63e-69 & 4.7 & 3.64 & 3.3 \\ A. Fib. & TV & 2.75e-19 & 3.99e-66 & 1.21e-28 & 0.523 & 0.56 & 0.602 \\ A. Fib. & Meat & 3.92e-05 & 1.45e-15 & 4.8e-10 & 0.733 & 0.755 & 0.744 \\ A. Fib. & Water Intake & 0.178 & 0.0532 & 6.96e-06 & 1.12 & 1.08 & 1.26 \\ Asthma & Smoking Status & 5.64e-05 & 1.54e-10 & 2.36e-05 & 0.608 & 0.66 & 0.655 \\ Asthma & BMI & 3.62e-15 & 2.46e-48 & 3.46e-14 & 0.412 & 0.413 & 0.501 \\ Asthma & Walking Pace & 2.01e-29 & 7.4e-109 & 2.4e-60 & 3.81 & 4.16 & 4.71 \\ Asthma & TV & 5.06e-09 & 3.44e-38 & 9.74e-17 & 0.606 & 0.559 & 0.57 \\ Migraine & Alcohol & 0.0028 & 3.22e-13 & 5.02e-08 & 0.572 & 0.515 & 0.49 \\ Migraine & Hours Sleep & 0.00956 & 0.0396 & 0.00514 & 1.53 & 1.18 & 1.38 \\ MS & Walking Pace & 0.0107 & 5.21e-11 & 1.01e-08 & 5.55 & 7.27 & 5.26 \\ Gout & Alcohol & 0.00063 & 6.63e-13 & 6.29e-07 & 1.86 & 1.85 & 1.75 \\ Gout & Smoking Status & 0.162 & 0.000177 & 9.76e-05 & 0.707 & 0.652 & 0.574 \\ Gout & BMI & 1.05e-18 & 2.19e-86 & 2.1e-47 & 0.106 & 0.105 & 0.127 \\ Gout & Walking Pace & 6.2e-20 & 3.22e-68 & 3.58e-27 & 6.87 & 5.41 & 4.27 \\ Gout & TV & 0.000197 & 1.05e-22 & 5.55e-18 & 0.559 & 0.497 & 0.443 \\ Gout & Driving & 0.000781 & 5.05e-10 & 0.00045 & 0.577 & 0.607 & 0.686 \\ Gout & Fruit & 0.00112 & 4.58e-06 & 0.0204 & 1.68 & 1.4 & 1.25 \\ Gout & Meat & 1.64e-07 & 1.32e-25 & 5.67e-17 & 0.42 & 0.46 & 0.432 \\ Crohns Disease & Walking Pace & 0.0062 & 6.76e-09 & 0.0405 & 2.69 & 2.4 & 1.64 \\ Ulcerative Colitis & Walking Pace & 0.00795 & 9.29e-06 & 0.000519 & 3.23 & 2.73 & 2.64 \\ Ulcerative Colitis & TV & 0.239 & 0.00123 & 2.73e-05 & 0.668 & 0.586 & 0.451 \\ Type 2 Diabetes & Alcohol & 1.7e-17 & 1.74e-68 & 9.8e-36 & 0.502 & 0.503 & 0.486 \\ Type 2 Diabetes & Smoking Status & 2.95e-12 & 4.69e-40 & 1.81e-12 & 0.501 & 0.533 & 0.614 \\ Type 2 Diabetes & BMI & 5.04e-156 & 0 & 2.15e-247 & 0.0794 & 0.0727 & 0.0847 \\ Type 2 Diabetes & Min. Walked & 0.00664 & 0.000572 & 0.0441 & 1.29 & 1.17 & 1.14 \\ Type 2 Diabetes & Mod. Activity & 2.51e-05 & 1.91e-24 & 6.87e-10 & 1.44 & 1.53 & 1.46 \\ Type 2 Diabetes & Walking Pace & 2.73e-110 & 0 & 3.61e-216 & 8.6 & 8.32 & 8.22 \\ Type 2 Diabetes & TV & 2.07e-50 & 4.94e-208 & 4.98e-85 & 0.36 & 0.367 & 0.398 \\ Type 2 Diabetes & Hours Sleep & 0.00328 & 0.00484 & 0.0013 & 1.24 & 1.1 & 1.18 \\ Type 2 Diabetes & Vegetable & 0.103 & 1.04e-07 & 0.000276 & 1.12 & 1.19 & 1.19 \\ Type 2 Diabetes & Meat & 6.76e-17 & 5.44e-71 & 1.34e-27 & 0.555 & 0.549 & 0.588 \\ Type 2 Diabetes & Cheese Intake & 6.21e-05 & 2.53e-21 & 8.67e-10 & 1.36 & 1.41 & 1.38 \\ Type 2 Diabetes & Water Intake & 0.0191 & 0.0132 & 0.0134 & 0.838 & 0.914 & 0.879 \\ Stroke & Smoking Status & 1.82e-10 & 1.53e-29 & 1.13e-17 & 0.433 & 0.465 & 0.421 \\ Stroke & BMI & 0.00161 & 2.96e-17 & 3.97e-05 & 0.663 & 0.564 & 0.645 \\ Stroke & Walking Pace & 7.69e-28 & 5.27e-113 & 6.54e-46 & 4.45 & 4.62 & 4.41 \\ Stroke & TV & 2.09e-13 & 5.57e-58 & 3.01e-15 & 0.511 & 0.455 & 0.553 \\ Stroke & Meat & 0.131 & 2.06e-09 & 0.000569 & 0.863 & 0.738 & 0.759 \\ Stroke & Water Intake & 0.042 & 0.00223 & 0.0327 & 1.24 & 1.18 & 1.21 \\ Breast Cancer & Walking Pace & 0.00217 & 1.72e-10 & 0.011 & 1.92 & 1.76 & 1.33 \\ Breast Cancer & TV & 0.000554 & 0.14 & 0.00205 & 0.544 & 0.902 & 0.767 \\ NAFLD & Alcohol & 2.34e-05 & 2.01e-06 & 2.81e-05 & 0.428 & 0.638 & 0.539 \\ NAFLD & Smoking Status & 0.0128 & 3.94e-13 & 0.000194 & 0.58 & 0.453 & 0.532 \\ NAFLD & BMI & 2.43e-21 & 1.04e-75 & 1.04e-28 & 0.0951 & 0.112 & 0.137 \\ NAFLD & Mod. Activity & 0.0263 & 4.56e-05 & 0.012 & 1.65 & 1.54 & 1.49 \\ NAFLD & Walking Pace & 2.04e-17 & 1.95e-55 & 1.76e-24 & 6.37 & 5.75 & 5.85 \\ NAFLD & TV & 5.47e-11 & 6.77e-21 & 4.32e-11 & 0.334 & 0.466 & 0.454 \\ NAFLD & Cheese Intake & 0.00339 & 9.91e-06 & 0.00609 & 1.68 & 1.49 & 1.45 \\ NAFLD & Water Intake & 0.136 & 0.0719 & 0.000349 & 0.761 & 0.849 & 0.63 \\ \hline \end{tabular} Table 1: The effect of the effectSupplementary Table S16. The P-values and odds ratios computed from Fisher Exact tests that considered lifestyle factors within low, intermediate and high polygenic risk score groups. Listed are the disease and lifestyle factor combinations that were determined to be significant.
## Supplementary Table S17.
The absolute risks calculated for each medication/supplement and PRS grouping, listed for all significant disease and lifestyle factor combinations. On means the group of people on or taking the medication/supplement.
## Supplementary Table S18.
The P-values and odds ratios computed from Fisher Exact tests that considered medication/supplements within low, intermediate and high polygenic risk score groups. Listed are the disease and medication/supplement combinations that were determined to be significant.
## Supplementary Table S19.
The AUC and their 95% CI generated from models that utilized either only male or female individuals.
## Supplementary Table S20.
The AUC and their 95% CI generated from models that utilized either only young or old individuals as determined by the median age of cases for each respective disease.
## Supplementary Table S21.
Validity check by splitting the total population according to time at Current Address. The low group is less than or equal to 20 years and the higher group is greater than 20 years.
## Supplementary Table S22.
Validity check by splitting the total population according to income. The low group is less than PS40,000 and the higher group is greater than PS40,000.
## Supplementary Table S23.
Validity check by splitting the total population according to number of individuals in the household. The low group is 1-2 persons and the higher group is 3 or more persons.
## Supplementary Table S24.
Validity check by splitting the total population according to the age education was completed. The low group is 1-19 years and the higher group is 20 or more years.
## Supplementary Table S25.
Validity check by splitting the total population according to the census measurement of median age. The lower group is less than 42 years and the higher group is greater than 42 years.
## Supplementary Table S26.
Validity check by splitting the total population according to the census measurement of unemployment. The lower group is less than 38 persons and the higher group is greater than 38 persons.
## Supplementary Table S27.
Validity check by splitting the total population according to census measurement of very good health. The lower group is less than 719 persons and the higher group is greater than 719 persons.
## Supplementary Table S28.
Validity check by splitting the total population according to the census measurement of population density. The lower group is less than 32 persons per hectare and the higher group is great than 32 persons per heactare.
## Supplementary Table S29.
The mean of each population group's polygenic risk score (that was utilized in the testing) phase minus the mean of the British population group's polygenic risk score. Before the mean was taken each polygenic risk score was standardized to have a minimum of zero and maximum of 100. No additional standardization/scaling was done.
## Supplementary Table S30.
The P-values generated when comparing polygenic risk score distributions of one population group to another, as indicated in the column header, with a Student's T-Test. The polygenic risk score distributions used in the test are the same as the distributions described in the previous table. P-values less than 1e-300 are reported at 1e-300.
## Supplementary Table S31.
The AUC values generated from models assessed on the testing set, with phenotype defintions as described in the column headers, minus the AUC values generated from models assessed on the testing set and the phenotype definition of either ICD or Self-Reported. The ICD or self-reported method is the same method used throughout the majority of analyses. Please note that values of 0 are in fact greater than 0 but round to 0 when only keeping values greater than \(1\times 10^{-4}\)
## Supplementary Table S32.
The mean AUC and rank as determined by the AUC across all diseases for each polygenic risk score generative method
## Supplementary Table S33.
The mean concordance and rank as determined by the concordance across all diseases for each polygenic risk score generative method
## Supplementary Table S34.
The mean odds ratio and rank as determined by the odds ratio across all diseases for each polygenic risk score generative method
## Supplementary Table S35.
The mean cumulative hazard and rank as determined by the cumulative across all diseases for each polygenic risk score generative method
## Supplementary Table S36.
The count of methods amongst the top ten AUCs weighted by the attribute listed. The best AUC for each disease and method combination was utilized for weighting and ranking.
## Supplementary Table S37.
Continued from above. The count of methods amongst the top ten AUCs weighted by the attribute listed. The best AUC for each disease and method combination was utilized for weighting and ranking.
## Supplementary Table S38.
The number of variants in each polygenic risk score used in the testing phase.
## Supplementary Table S39.
For each disease the variants of the polygenic risk score used in the testing phase were ordered by absolute effect, and split into four groups such that the sum of effects in each group were equal. The size of each group, standardized such that the minimum was zero and maximum was one, were calculated.
## Supplementary Table S40.
The functional annotation scores. Computed for each disease, with the variants of the polygenic risk score used in the testing phase identified as belonging to any of 44 functional annotation groups. The mean of the absolute effects of the variants in each group were calculated, and normalized such that the sum of resulting functional annotation weights for each disease summed to one.
## Supplementary Table S41.
Functional annotation weights, continued
## Supplementary Table S42.
Functional annotation weights, continued
## Supplementary Table S43.
Functional annotation weights, continued
## Supplementary Table S44.
Functional annotation weights, continued
\begin{tabular}{l c c c c c c c} \hline \hline
## Disease** & **Promoter** & **Liver** & **Conserved** & **Conserved** & **H3K9ac** & **TSS** & **Kidney** \\ & **Cell Type** & **Primate** & **Peak** & **Peak**s & **TSS** & **Cell Type
\\ \hline Lupus & 0.0346 & 0.0131 & 0.0274 & 0.0371 & 0.0173 & 0.0583 & 0.012 \\ A. Fib. & 0.0194 & 0.0209 & 0.0469 & 0.0426 & 0.0226 & 0.019 & 0.0167 \\ Asthma & 0.0275 & 0.0236 & 0.0151 & 0.0141 & 0.0267 & 0.0429 & 0.0238 \\ Celiac Disease & 0.0191 & 0.0221 & 0.0107 & 0.00537 & 0.0219 & 0.0739 & 0.0324 \\ Migraine & 0.0183 & 0.0185 & 0.0327 & 0.0284 & 0.0206 & 0.0358 & 0.0237 \\ MS & 0.0368 & 0.0229 & 0.014 & 0.0123 & 0.0397 & 0.0631 & 0.0307 \\ Vitiligo & 0.0241 & 0.0105 & 0.0359 & 0.0294 & 0.0245 & 0.0245 & 0.018 \\ Gout & 0.115 & 0.00389 & 0.0742 & 0.0576 & 0.0119 & 0 & 0.0471 \\ Crohn's Disease & 0.0174 & 0.0197 & 0.0333 & 0.0383 & 0.0197 & 0.0243 & 0.021 \\ Ulcerative Colitis & 0.0209 & 0.0215 & 0.0261 & 0.0258 & 0.0228 & 0.0299 & 0.0226 \\ Type 2 Diabetes & 0.0115 & 0.0296 & 0.0209 & 0.0191 & 0.0272 & 0.03 & 0.0259 \\ Stroke & 0.0182 & 0.0231 & 0.0241 & 0.0233 & 0.0259 & 0.0259 & 0.031 \\ Breast Cancer & 0.0179 & 0.0234 & 0.0247 & 0.0187 & 0.0269 & 0.0319 & 0.0313 \\ NAFLD & 0.00164 & 0.0677 & 0.00305 & 0.1 & 0.00414 & 0.00258 & 0.11 \\ CAD & 0.0177 & 0.0274 & 0.0252 & 0.0237 & 0.0242 & 0.0308 & 0.0255 \\ Rheumatoid Arthritis & 0.0463 & 0.0155 & 0.0103 & 0.00662 & 0.0201 & 0.0709 & 0.0262 \\ Type 1 Diabetes & 0.0614 & 0.0291 & 0.038 & 0.0296 & 0.016 & 0.0288 & 0.0151 \\ Ovarian Cancer & 0.0432 & 0.0231 & 0.0277 & 0.0236 & 0.0196 & 0.0684 & 0.0282 \\ ALS & 0.0253 & 0.0191 & 0.0362 & 0.032 & 0.0284 & 0.022 & 0.0273 \\ Prostate Cancer & 0.0198 & 0.0232 & 0.0258 & 0.0212 & 0.0201 & 0.0344 & 0.0285 \\ Heart Failure & 0.024 & 0.0183 & 0.0327 & 0.0256 & 0.0263 & 0.0344 & 0.0251 \\ Psoriasis & 0.036 & 0.0219 & 0.0208 & 0.0186 & 0.0252 & 0.0371 & 0.0295 \\ Depression & 0.00506 & 0.0102 & 0.0392 & 0.0392 & 0.0286 & 0.0226 & 0.0161 \\ \hline \hline \end{tabular}
## Supplementary Table S45.
Functional annotation weights, continued
\begin{tabular}{l c c c c c c} \hline \hline
## Disease** & **Hematopoetic** & **TFBS** & **Enhancer-2** & **Dispersed** & **GI** & **Conserved** \\ & **Cell Type** & **Primate** & **Peak** & **Peak** & **Peak** & **Peak
\\ \hline Lupus & 0.0245 & 0.0252 & 0.0162 & 0.0207 & 0.0167 & 0.0364 \\ A. Fib. & 0.017 & 0.0196 & 0.0206 & 0.0138 & 0.0219 & 0.0402 \\ Asthma & 0.0227 & 0.0197 & 0.0313 & 0.0178 & 0.021 & 0.0139 \\ Celiac Disease & 0.0225 & 0.0222 & 0.0269 & 0.0205 & 0.0181 & 0.00534 \\ Migraine & 0.0126 & 0.016 & 0.019 & 0.0148 & 0.0162 & 0.0274 \\ MS & 0.0295 & 0.0251 & 0.0201 & 0.0161 & 0.0217 & 0.0177 \\ Vitiligo & 0.0237 & 0.0233 & 0.0156 & 0.025 & 0.0156 & 0.0258 \\ Gout & 0.0193 & 0.0128 & 0 & 0.0276 & 0.00981 & 0.0657 \\ Crohn's Disease & 0.0122 & 0.0203 & 0.0257 & 0.0177 & 0.0187 & 0.0374 \\ Ulcerative Colitis & 0.0196 & 0.0232 & 0.0311 & 0.0183 & 0.0238 & 0.0277 \\ Type 2 Diabetes & 0.0224 & 0.026 & 0.033 & 0.0201 & 0.0265 & 0.0213 \\ Stroke & 0.0161 & 0.0176 & 0.0254 & 0.0164 & 0.0229 & 0.0224 \\ Breast Cancer & 0.0164 & 0.0203 & 0.0244 & 0.0166 & 0.0221 & 0.0211 \\ NAFLD & 0.0254 & 0.00341 & 0.00471 & 0.00367 & 0.00563 & 0.00101 \\ CAD & 0.0181 & 0.0153 & 0.0197 & 0.0156 & 0.0214 & 0.0266 \\ Rheumatoid Arthritis & 0.0199 & 0.0212 & 0.0226 & 0.0138 & 0.0144 & 0.0121 \\ Type 1 Diabetes & 0.0319 & 0.0209 & 0.0311 & 0.0269 & 0.0185 & 0.0341 \\ Ovarian Cancer & 0.0103 & 0.0223 & 0.0206 & 0.034 & 0.0176 & 0.0249 \\ ALS & 0.0149 & 0.0145 & 0.0155 & 0.0149 & 0.018 & 0.034 \\ Prostate Cancer & 0.0146 & 0.0152 & 0.0247 & 0.0123 & 0.017 & 0.02 \\ Heart Failure & 0.0172 & 0.0165 & 0.0257 & 0.0152 & 0.0209 & 0.0261 \\ Psoriasis & 0.0172 & 0.0212 & 0.0188 & 0.0212 & 0.0213 & 0.0206 \\ Depression & 0.0161 & 0.0204 & 0.0245 & 0.0152 & 0.0207 & 0.0399 \\ \hline \hline \end{tabular}
## Supplementary Table S46.
Functional annotation weights, continued
## Supplementary Table S46.
Functional annotation weights, continued
## Supplementary Table S47.
The deleterious weights. Computed for each disease, with the variants of the polygenic risk score used in the testing phase identified aligned to deleterious scores computed for 9 different methods. The sum of the product between each variant's absolute effect and the deleterious score of were calculated, divided by the total variants aligned to each deleterious score, and then normalized such that the sum of resulting deleterious weights for each disease summed to one.
## Supplementary Table S48.
Deleterious weights continued |
057869_file03 | ### Competing risks analysis
In the Main Text, we note that the analyses performed using univariate and multivariate Cox proportional hazards (PH) models pertained to the cause-specific hazard (CSH) of progression to advanced neoplasia (AN) as an event separate to the event of colectomy, the latter of which served as a condition for censoring. In each of the patient datasets analysed, censoring due to colectomy occurred to 11% of patients during the study period (27/249 in discovery set and 24/211 in validation set). In practice, colectomy surgeries may be performed due to medically refractory symptomatic colitis, a cancer diagnosis or if there is a high risk of cancer in the future. The aim of our study is to determine which patients diagnosed with low-grade dysplasia (LGD) are considered to be at a considerable risk of progression to advanced neoplasia (AN) and thus a recommendation for colectomy in their case is justified. We acknowledge that censoring patients at colectomy before they have had time to progress to AN may affect estimates of overall absolute risk. Therefore, we performed additional analyses including competing risk of colectomy on study and summarize the results below.
First, we considered event-free survival method for Kaplan-Meier (KM) estimation, which focuses on the non-occurrence of events (event-free status, Figure S8A). In the KM plot produced using R package _cmprsk_ for competing risks, the curve estimates the proportion of patients within each risk factor set (see Main Text) who have not experienced either of the endpoints since baseline LGD diagnosis (colectomy nor AN progression) in the discovery set. We noted that the curves are qualitatively similar to those using the same stratification for cause-specific hazard estimation, implying that the more high-risk patients designated by our risk factor criteria were also those more likely referred to colectomy. Furthermore, the cumulative incidence functions (CIFs) for both events of AN progression (event = 1) and colectomy (event = 2) are estimated to be very similar in the first years of follow-up in the presence of the competing risk event (Figure S8B created with function 'ggcompetingrisks' in R package _survminer_). This suggests patients received colectomy at a similar rate to advancing to neoplasia in our discovery set; patients who were at such high-risk for AN progression likely should have all been assigned the group who received colectomy during the study period if they were able.
Lastly, we graphically compared the CIFs and 1 - CSH KM curves in Figure S8C. The 1 - CSH KM (dotted lines) are nearly identical for the bottom 2 risk groups but overestimate the progression to AN in the top 2 risk groups in later follow-up years. Again, CIF curves (solid and dashed lines by event type AN progression and colectomy, respectively) describe the occurrence of each event type in the presence of the other, i.e., it describes the outcomes for each risk group in the data, and Gray tests were performed that found significant differences in risk of either event by risk score group (p < 10-6 for both events)3. The 1 - CSH KM curves describe the progression risk for one type of event in the absence of the other, which is relevant for inference of the biological relationship between a certain event and given covariates. It overestimates the incidence because in the absence of the competing risk of a colectomy event, the event has more chance to occur. Overall, we found using competing risk formulation that the risks were similar for colectomy and AN progression in our discovery set, validating the hazard ratios used in our prognostic risk function in _UC-CaRE_.
\begin{table}
\begin{tabular}{l c c} \hline Risk factor in final model & Internal rate & \(\frac{\text{Cov}}{\text{Cov}}\) \\ (ES24) & & \\ \hline
## Visible index LGD size 10mm or more
& 4.1 (1.8 - 9.2) & 0.0008 \\ \hline
## Index LGD not endoscopically resected or incomplete resection
& 5.8 (2.6 - 12.6) & 1.14e-05 \\ \hline
## Multifocal LGD at time of index LGD diagnosis
& 1.1 (0.5 - 2.5) & 0.8726 \\ \hline
## Moderate or severe active histological inflammation
& 1.7 (0.8 - 3.8) & 0.1738 \\ \hline \end{tabular}
\end{table}
Table S6: Multivariate model for cause-specific progression to colectomy outcome within the discovery set. Risk factors for occurrence of colectomy (MULTIVARIATE Cox regression analysis). N=246, including 27 who received colectomy as outcome for censoring.
Figure S8. Competing risk analysis of advanced neoplasia (AN) and colectomy within the discovery set. (A) Event-free survival (combined colectomy and AN progression) derived from Kaplan-Meier estimation in discovery set (n=246) using same risk score groups from Main Text. (B) Cumulative incidence functions in the face of competing risks for event 1 (AN progression) and event 2 (colectomy) were found to be similar in this cohort. (C) Event outcomes in the data (CIFs) and model estimated survival (1 - CSH) by risk factor groups.
Figure S7. Variance-covariance matrix for final multivariate model for cause-specific progression to advanced neoplasia (AN) outcome derived from the Discovery Set.
Patients were not directly involved in the retrospective design and conduct of this study but previous qualitative work involving patient questionnaires and interviews revealed aspects that we aimed to include in the construction of our visual web-tool _UC-CoRE_. To summarize, patients described both a lack of quantitative risk communication and a lack of personalised discussion of treatment options as barriers to patient decision-making.4 Thus we included calculations of such personalised, quantitative risks (percentages by follow-up year) in easy to interpret visual diagrams (Paling charts) as part of this study. We plan to disseminate our conclusions to patients by implementing UC-CoRE for use in shared treatment decision-making and obtaining feedback/critique on their experiences for future improvements.
|
071357_file03 | ## continued on next page_Table S4 _- continued from previous page
\begin{tabular}{c c c c c c c c c c} \hline logFC & CLL & CLR & AveExpr & t & P.Value & adj.P.Val & B & SE & Chromosome & Symbol \\ \hline
3 & 2.1 & 3.8 & -0.32 & 7.1 & \(4.6\times 10^{-9}\) & 0.00022 & 5.3 & 0.23 & 12 & VWF \\ -2.5 & -3.3 & -1.7 & -0.24 & -6.4 & \(5.7\times 10^{-8}\) & 0.0014 & 4 & 0.15 & Y & CSF2RA \\
2.3 & 1.5 & 3.1 & 0.25 & 5.5 & \(1.3\times 10^{-6}\) & 0.021 & 2.3 & 0.26 & 20 & MYL9 \\ -2.2 & -3 & -1.3 & -0.22 & -5.4 & \(2.3\times 10^{-6}\) & 0.028 & 2 & 0.21 & Y & CSF2RA \\
0.71 & 0.43 & 0.98 & -0.017 & 5.2 & \(3.9\times 10^{-6}\) & 0.038 & 1.7 & 0.17 & 2 & SPC25 \\
1.3 & 0.74 & 1.8 & 0.17 & 4.9 & \(1.2\times 10^{-5}\) & 0.099 & 1 & 0.18 & X & BEND2 \\
2.5 & 1.4 & 3.5 & 0.089 & 4.7 & \(2.1\times 10^{-5}\) & 0.14 & 0.72 & 0.18 & 17 & ITGA2B \\
3.3 & 1.9 & 4.8 & 0.11 & 4.7 & \(2.4\times 10^{-5}\) & 0.14 & 0.64 & 0.29 & 4 & PPBP \\
1.1 & 0.6 & 1.5 & -0.18 & 4.6 & \(2.6\times 10^{-5}\) & 0.14 & 0.6 & 0.19 & 14 & SYNES3 \\
0.71 & 0.39 & 1 & -0.062 & 4.5 & \(4.4\times 10^{-5}\) & 0.18 & 0.29 & 0.19 & 12 & ANKS1B \\ -1 & -1.5 & -0.55 & 0.02 & -4.5 & \(4.5\times 10^{-5}\) & 0.18 & 0.28 & 0.23 & 11 & POU2AF1 \\
0.69 & 0.37 & 1 & -0.11 & 4.4 & \(6.8\times 10^{-5}\) & 0.26 & 0.041 & 0.28 & X & GAGE4 \\ -1.6 & -2.4 & -0.87 & -0.034 & -4.3 & \(8.2\times 10^{-5}\) & 0.26 & -0.07 & 0.2 & 17 & KRT23 \\ -0.8 & -1.2 & -0.43 & 0.032 & -4.3 & \(8.3\times 10^{-5}\) & 0.26 & -0.073 & 0.2 & 8 & ENPP2 \\
0.75 & 0.4 & 1.1 & -0.14 & 4.3 & \(8.9\times 10^{-5}\) & 0.26 & -0.11 & 0.22 & 16 & CDH8 \\
0.79 & 0.42 & 1.2 & -0.056 & 4.3 & \(9.2\times 10^{-5}\) & 0.26 & -0.14 & 0.18 & 15 & TMOD3 \\
2.3 & 1.2 & 3.4 & 0.04 & 4.2 & 0.0001 & 0.27 & -0.21 & 0.37 & 11 & JAM3 \\ -0.92 & -1.4 & -0.47 & -0.12 & -4.1 & 0.00017 & 0.41 & -0.49 & 0.19 & Y & SFRS17A \\ -1 & -1.5 & -0.52 & -0.1 & -4 & 0.00019 & 0.44 & -0.56 & 0.17 & 2 & WIPF1 \\
1.7 & 0.83 & 2.5 & 0.34 & 4 & 0.00023 & 0.48 & -0.68 & 0.3 & 18 & GTSCR1 \\
1.1 & 0.55 & 1.7 & -0.14 & 4 & 0.00024 & 0.48 & -0.71 & 0.22 & 1 & ADAM15 \\ -1.4 & -2.1 & -0.7 & 0.25 & -4 & 0.00024 & 0.48 & -0.71 & 0.24 & Y & TMSB4Y \\
1.5 & 0.75 & 2.3 & 0.054 & 4 & 0.00025 & 0.48 & -0.71 & 0.2 & 4 & GUCY1A3 \\
0.78 & 0.38 & 1.2 & -0.033 & 3.9 & 0.00026 & 0.5 & -0.76 & 0.22 & 5 & PIK3R1 \\
0.87 & 0.42 & 1.3 & 0.035 & 3.9 & 0.00029 & 0.5 & -0.81 & 0.22 & 17 & MEOX1 \\
1 & 0.5 & 1.6 & 0.012 & 3.9 & 0.00031 & 0.5 & -0.85 & 0.19 & 15 & ACSBG1 \\
0.92 & 0.44 & 1.4 & -0.04 & 3.8 & 0.00035 & 0.5 & -0.92 & 0.28 & 19 & ZNF266 \\
2.6 & 1.3 & 4 & -0.73 & 3.8 & 0.00036 & 0.5 & -0.94 & 0.17 & 8 & DEFCR24 \\
0.55 & 0.26 & 0.84 & 0.038 & 3.8 & 0.00037 & 0.5 & -0.96 & 0.17 & 10 & CYP26A1 \\ -0.73 & -1.1 & -0.34 & 0.13 & -3.8 & 0.00041 & 0.5 & -1 & 0.2 & 16 & TAOK2 \\ \hline \end{tabular} Table S5: Top-30 DE genes in LOY individuals
\begin{table}
\begin{tabular}{r r r r r r r r r r r} \hline logFC & CIL & CLR & AveExpr & t & P.Value & adj.P.Val & B & SE & Chromosome & Symbol \\ \hline -2.5 & -3.3 & -1.7 & -0.24 & -6.4 & \(5.7\times 10^{-8}\) & 0.0014 & 4 & 0.15 & Y & CSF2RA \\ -2.2 & -3 & -1.3 & -0.22 & -5.4 & \(2.3\times 10^{-6}\) & 0.028 & 2 & 0.21 & Y & CSF2RA \\ -0.92 & -1.4 & -0.47 & -0.12 & -4.1 & 0.00017 & 0.41 & -0.49 & 0.19 & Y & SFRS17A \\ -1.4 & -2.1 & -0.7 & 0.25 & -4 & 0.00024 & 0.48 & -0.71 & 0.24 & Y & TMSB4Y \\ -2.3 & -3.5 & -1.1 & 0.11 & -3.7 & 0.00049 & 0.5 & -1.1 & 0.2 & Y & EIF1AY \\ -5.2 & -8 & -2.3 & 1.1 & -3.6 & 0.00074 & 0.53 & -1.4 & 0.18 & Y & EIF1AY \\ -0.8 & -1.3 & -0.31 & 0.036 & -3.3 & 0.0018 & 0.69 & -1.9 & 0.21 & XY & ASMTL \\ -0.89 & -1.5 & -0.33 & 0.079 & -3.2 & 0.0024 & 0.77 & -2.1 & 0.2 & Y & TLNGY \\ -0.66 & -1.1 & -0.22 & -0.044 & -3 & 0.0041 & 0.89 & -2.4 & 0.25 & Y & BCORL2 \\ -1.9 & -3.3 & -0.53 & 0.43 & -2.8 & 0.0074 & 0.99 & -2.7 & 0.17 & Y & KDM5D \\ -0.88 & -1.5 & -0.24 & -0.15 & -2.8 & 0.0076 & 0.99 & -2.7 & 0.24 & Y & SFRS17A \\ -1.7 & -3 & -0.46 & 0.48 & -2.7 & 0.0087 & 1 & -2.8 & 0.19 & Y & TXLNGY \\ -5.5 & -9.7 & -1.3 & 2 & -2.6 & 0.011 & 1 & -3 & 0.21 & Y & RPS4Y1 \\ -1.7 & -3.1 & -0.38 & 0.2 & -2.6 & 0.013 & 1 & -3 & 0.36 & Y & RPS4Y2 \\ -0.75 & -1.3 & -0.17 & -0.086 & -2.6 & 0.013 & 1 & -3 & 0.15 & Y & ZBED1 \\ -0.77 & -1.4 & -0.17 & 0.01 & -2.6 & 0.013 & 1 & -3.1 & 0.21 & Y & ZFY \\
0.49 & 0.1 & 0.87 & -0.0077 & 2.5 & 0.014 & 1 & -3.1 & 0.23 & Y & SHOX \\ -0.38 & -0.68 & -0.073 & 0.058 & -2.5 & 0.016 & 1 & -3.2 & 0.18 & Y & TTTY14 \\
0.39 & 0.054 & 0.73 & -0.018 & 2.3 & 0.024 & 1 & -3.4 & 0.33 & Y & TTTY8 \\ -1 & -2 & -0.11 & 0.29 & -2.2 & 0.029 & 1 & -3.5 & 0.27 & Y & PRKY \\ -0.48 & -0.91 & -0.04 & 0.038 & -2.2 & 0.033 & 1 & -3.6 & 0.21 & Y & UTY \\
0.41 & 0.022 & 0.81 & -0.095 & 2.1 & 0.039 & 1 & -3.7 & 0.18 & Y & PCDH11Y \\ -0.41 & -0.79 & -0.019 & 0.011 & -2.1 & 0.04 & 1 & -3.7 & 0.2 & Y & RBMY1A1 \\
0.45 & 0.0065 & 0.9 & -0.068 & 2 & 0.047 & 1 & -3.8 & 0.25 & XY & SHOX \\ -0.4 & -0.82 & 0.028 & 0.16 & -1.9 & 0.066 & 1 & -4 & 0.21 & Y & PPP2R3B \\ -0.65 & -1.4 & 0.083 & 0.2 & -1.8 & 0.081 & 1 & -4.1 & 0.29 & Y & UTY \\
0.32 & -0.042 & 0.68 & -0.034 & 1.8 & 0.082 & 1 & -4.1 & 0.32 & Y & BPY2B \\ -0.48 & -1 & 0.079 & -0.066 & -1.7 & 0.09 & 1 & -4.2 & 0.15 & Y & ASMTL \\ -0.28 & -0.61 & 0.05 & -0.085 & -1.7 & 0.094 & 1 & -4.2 & 0.21 & Y & TTTY2 \\ -0.52 & -1.2 & 0.12 & -0.19 & -1.6 & 0.11 & 1 & -4.3 & 0.19 & Y & GTPBP6 \\ \hline \end{tabular}
\end{table}
Table S6: Top-30 DE genes in LOY individuals located in gonosomes.
Table S7: Genes located on the human Y chromosome with homolog on X and a possible role in immunity. [See supplementary Excel File]
\begin{table}
\begin{tabular}{r r r r r} \hline & effect & inf & sup & pvalue \\ \hline B cell naive & -1.57 & -2.97 & -0.16 & 0.03454 \\ Neutrophil & -1.15 & -2.23 & -0.06 & 0.04477 \\ NK cell & 0.05 & -0.01 & 0.10 & 0.08817 \\ T cell NK & -0.85 & -1.86 & 0.16 & 0.1077 \\ Monocyte & 0.97 & -0.20 & 2.15 & 0.1115 \\ Macrophage & 1.05 & -0.27 & 2.37 & 0.1258 \\ T cell CD8+ naive & 1.00 & -0.39 & 2.38 & 0.1653 \\ T cell regulatory (Tregs) & 1.12 & -0.49 & 2.74 & 0.1809 \\ Eosinophil & -0.75 & -1.89 & 0.40 & 0.207 \\ B cell memory & -0.85 & -2.25 & 0.55 & 0.2414 \\ B cell plasma & -0.53 & -1.43 & 0.37 & 0.258 \\ T cell CD4+ (non-regulatory) & 0.53 & -0.38 & 1.45 & 0.2599 \\ Macrophage M2 & 0.35 & -0.27 & 0.98 & 0.2738 \\ T cell CD4+ central memory & 0.45 & -0.39 & 1.30 & 0.3009 \\ T cell CD4+ Th2 & -0.26 & -0.77 & 0.24 & 0.3128 \\ Plasmacytoid dendritic cell & -0.73 & -2.18 & 0.72 & 0.3304 \\ T cell CD4+ effector memory & 0.83 & -0.85 & 2.51 & 0.3401 \\ Myeloid dendritic cell & 0.53 & -0.60 & 1.66 & 0.365 \\ T cell CD8+ & -0.51 & -1.79 & 0.76 & 0.4345 \\ Mast cell & 0.27 & -0.41 & 0.95 & 0.4372 \\ Common lymphoid progenitor & 0.18 & -0.31 & 0.67 & 0.4699 \\ Macrophage M1 & 0.33 & -0.72 & 1.38 & 0.5399 \\ Cancer associated fibroblast & -0.43 & -1.83 & 0.98 & 0.5559 \\ T cell CD8+ central memory & 0.35 & -0.89 & 1.59 & 0.5845 \\ T cell gamma delta & 0.00 & -0.00 & 0.00 & 0.6374 \\ Class-switched memory B cell & -0.27 & -1.74 & 1.20 & 0.7227 \\ T cell CD4+ naive & 0.15 & -1.35 & 1.65 & 0.8456 \\ Common myeloid progenitor & 0.11 & -1.18 & 1.39 & 0.8695 \\ Hematopoietic stem cell & -0.04 & -0.52 & 0.45 & 0.884 \\ T cell CD4+ Th1 & 0.11 & -1.59 & 1.81 & 0.9036 \\ T cell CD8+ effector memory & -0.00 & -0.00 & 0.00 & 0.9219 \\ Granulocyte-monocyte progenitor & -2.22 & -3.09 & -1.35 & 1.085e-05 \\ Endothelial cell & 1.40 & 0.77 & 2.02 & 7.856e-05 \\ \hline \end{tabular}
\end{table}
Table S8: Association between cell type composition estimated using bulk transcriptomic data (immunedecov R package) and LOY estatus
\begin{table}
\begin{tabular}{l r r} \hline Description & pvalue & p.adjust \\ \hline blood coagulation & \(6.3\times 10^{-9}\) & \(2.6\times 10^{-6}\) \\ hemostasis & \(7.3\times 10^{-9}\) & \(2.6\times 10^{-6}\) \\ coagulation & \(7.6\times 10^{-9}\) & \(2.6\times 10^{-6}\) \\ platelet degranulation & \(1.6\times 10^{-7}\) & \(4.1\times 10^{-5}\) \\ regulation of body fluid levels & \(4.1\times 10^{-7}\) & \(8.3\times 10^{-5}\) \\ leukocyte migration & \(1.9\times 10^{-6}\) & \(0.00032\) \\ platelet activation & \(8.6\times 10^{-6}\) & \(0.0013\) \\ oxygen transport & \(1.4\times 10^{-5}\) & \(0.0017\) \\ gas transport & \(2.9\times 10^{-5}\) & \(0.0033\) \\ platelet aggregation & \(3.4\times 10^{-5}\) & \(0.0035\) \\ blood coagulation, fibrin clot formation & \(8.5\times 10^{-5}\) & \(0.0079\) \\ homotypic cell-cell adhesion & \(0.0001\) & \(0.009\) \\ cellular oxidant detoxification & \(0.00028\) & \(0.022\) \\ cellular detoxification & \(0.00037\) & \(0.027\) \\ detoxification & \(0.00046\) & \(0.031\) \\ cell-substrate adhesion & \(0.00054\) & \(0.035\) \\ cell-matrix adhesion & \(0.00059\) & \(0.035\) \\ \hline \end{tabular}
\end{table}
Table S9: GO enrichment analysis of DE genes in individuals with LOY. GO terms significant at 5% FDR.
\begin{table}
\begin{tabular}{l r r} \hline Description & pvalue & p.adjust \\ \hline response to virus & \(1.7\times 10^{-21}\) & \(5.9\times 10^{-18}\) \\ defense response to other organism & \(1.5\times 10^{-19}\) & \(2.6\times 10^{-16}\) \\ type I interferon signaling pathway & \(8.8\times 10^{-17}\) & \(7.5\times 10^{-14}\) \\ cellular response to type I interferon & \(8.8\times 10^{-17}\) & \(7.5\times 10^{-14}\) \\ response to type I interferon & \(2\times 10^{-16}\) & \(1.4\times 10^{-13}\) \\ defense response to virus & \(2.6\times 10^{-16}\) & \(1.5\times 10^{-13}\) \\ response to molecule of bacterial origin & \(3.9\times 10^{-16}\) & \(1.9\times 10^{-13}\) \\ response to lipopolysaccharide & \(1.1\times 10^{-15}\) & \(4.6\times 10^{-13}\) \\ response to interferon-gamma & \(8\times 10^{-14}\) & \(3\times 10^{-11}\) \\ regulation of inflammatory response & \(6.3\times 10^{-13}\) & \(2.2\times 10^{-10}\) \\ positive regulation of response to external stimulus & \(2.5\times 10^{-12}\) & \(7.8\times 10^{-10}\) \\ negative regulation of viral genome replication & \(9.4\times 10^{-12}\) & \(2.7\times 10^{-9}\) \\ acute-phase response & \(1.4\times 10^{-11}\) & \(3.6\times 10^{-9}\) \\ acute inflammatory response & \(6.2\times 10^{-11}\) & \(1.5\times 10^{-8}\) \\ regulation of innate immune response & \(8.8\times 10^{-11}\) & \(2\times 10^{-8}\) \\ cellular response to lipopolysaccharide & \(1.1\times 10^{-10}\) & \(2.4\times 10^{-8}\) \\ positive regulation of inflammatory response & \(1.2\times 10^{-10}\) & \(2.5\times 10^{-8}\) \\ cellular response to molecule of bacterial origin & \(2.1\times 10^{-10}\) & \(4\times 10^{-8}\) \\ regulation of viral genome replication & \(2.4\times 10^{-10}\) & \(4.3\times 10^{-8}\) \\ neutrophil mediated immunity & \(2.7\times 10^{-10}\) & \(4.6\times 10^{-8}\) \\ negative regulation of viral process & \(4.1\times 10^{-10}\) & \(6.6\times 10^{-8}\) \\ negative regulation of viral life cycle & \(8.3\times 10^{-10}\) & \(1.3\times 10^{-7}\) \\ cellular response to biotic stimulus & \(1.3\times 10^{-9}\) & \(1.8\times 10^{-7}\) \\ neutrophil activation & \(1.3\times 10^{-9}\) & \(1.8\times 10^{-7}\) \\ positive regulation of MAPK cascade & \(1.3\times 10^{-9}\) & \(1.8\times 10^{-7}\) \\ regulation of response to cytokine stimulus & \(1.8\times 10^{-9}\) & \(2.3\times 10^{-7}\) \\ positive regulation of peptidyl-tyrosine phosphorylation & \(1.9\times 10^{-9}\) & \(2.4\times 10^{-7}\) \\ cornification & \(1.9\times 10^{-9}\) & \(2.4\times 10^{-7}\) \\ positive regulation of innate immune response & \(2.8\times 10^{-9}\) & \(3.2\times 10^{-7}\) \\ regulation of multi-organism process & \(2.8\times 10^{-9}\) & \(3.2\times 10^{-7}\) \\ humoral immune response & \(2.9\times 10^{-9}\) & \(3.2\times 10^{-7}\) \\ regulation of lipid storage & \(3\times 10^{-9}\) & \(3.2\times 10^{-7}\) \\ positive regulation of cytokine production & \(3.2\times 10^{-9}\) & \(3.3\times 10^{-7}\) \\ neutrophil degranulation & \(3.5\times 10^{-9}\) & \(3.5\times 10^{-7}\) \\ neutrophil activation involved in immune response & \(4\times 10^{-9}\) & \(3.9\times 10^{-7}\) \\ viral genome replication & \(4.5\times 10^{-9}\) & \(4.2\times 10^{-7}\) \\ cell chemotaxis & \(4.5\times 10^{-9}\) & \(4.2\times 10^{-7}\) \\ positive regulation of DNA-binding transcription factor activity & \(5.8\times 10^{-9}\) & \(5.3\times 10^{-7}\) \\ positive regulation of smooth muscle cell proliferation & \(6.3\times 10^{-9}\) & \(5.5\times 10^{-7}\) \\ leukocyte migration & \(7.8\times 10^{-9}\) & \(6.7\times 10^{-7}\) \\ \hline \end{tabular}
\end{table}
Table S11: Top GO enrichment of DE genes in the two cell lines infected with SARS-CoV-2.
\begin{table}
\begin{tabular}{l c r r r r r r} Gene & Chr & logFC (LOY) & P.value & logFC (NHBE) & P.value & logFC (A549) & P.value \\ \hline CXCL5 & 4 & 1.7 & 0.014 & 3.5 & \(7.1\times 10^{-31}\) & 0.77 & \(1.7\times 10^{-17}\) \\ IFI44L & 1 & -1.6 & 0.021 & 2.3 & \(0.00028\) & 5.7 & \(2.5\times 10^{-5}\) \\ IFI6 & 1 & -1 & 0.049 & 2.3 & \(3.3\times 10^{-5}\) & 4.3 & \(2.3\times 10^{-261}\) \\ IFIT1 & 10 & -1.2 & 0.032 & 0.82 & \(0.00025\) & 4.3 & \(3\times 10^{-141}\) \\ IFIT3 & 10 & -1.4 & 0.017 & 0.73 & \(5.1\times 10^{-5}\) & 2 & \(1\times 10^{-32}\) \\ ITGB3 & 17 & 1.7 & 0.013 & 1.2 & \(9.1\times 10^{-7}\) & -0.24 & 0.42 \\ KRT23 & 17 & -1.6 & \(8.2\times 10^{-5}\) & 0.59 & \(4.5\times 10^{-7}\) & 1.6 & 0.37 \\ KYNU & 2 & 1.2 & 0.0058 & 0.84 & \(7.8\times 10^{-10}\) & 0.48 & \(1.2\times 10^{-5}\) \\ PROS1 & 3 & 1.5 & 0.0022 & -0.66 & \(4.2\times 10^{-6}\) & 0.3 & 0.027 \\ S100P & 4 & 2.4 & 0.033 & 0.69 & \(3.2\times 10^{-10}\) & -0.11 & 0.51 \\ SLPI & 20 & -1.2 & 0.037 & 0.58 & \(7.3\times 10^{-9}\) & 0.42 & 0.018 \\ TSC22D3 & X & 1 & 0.024 & -0.72 & \(6.9\times 10^{-10}\) & -0.17 & 0.2 \\ VNN1 & 6 & 1.6 & 0.00099 & 1.9 & \(3.4\times 10^{-8}\) & 0.46 & 0.41 \\ \hline \end{tabular}
\end{table}
Table S12: Intersection between significant genes in the analysis of normal vs LOY individuals and in the two cell lines infected with SARS-CoV-2 (NHBE and A549).
**Supplementary figures**Figure S1: Plots of the whole-genome molecular karyotype obtained by SNParray of blood DNA from all 133 individuals of SCOURGE with detectable CMEs.
[See supplementary file FigureS1.pdf]Figure S2: Top differentially expressed genes at genome level. The plots show the gene expression for individuals with (Y) and without (N) LOY. The p-values correspond to a linear model adjusted for age and surrogate variables using limma.
Figure S3: Top differentially expressed genes in chromosome Y. The plots show the gene expression for individuals with (Y) and without (N) LOY. The p-values correspond to a linear model adjusted for age and surrogate variables using limma. |
074351_file02 | ### Charite/World Health Organization (WHO)/Public Health England (PHE) probes and primers:
RdRP_SARS-P2 (6FAM -CAggTggAAACCTCATCAGgAgAgTgC- BBQ) were ordered from TIB MOLBIOL (Germany). RdRP_SARS-F2 (GTGARATGGTCATGTGGCG) and RdRP_SARS-R1 (CARATGTTAAASACATATTGACATA) were ordered from Eurofins. We did not employ RdRP_SARS-P1 (6FAM-CCAggTggWACRTCATCMggTgC- BBQ) except for Supplementary - as this probe is not specific for SARS-CoV-2 but generic for coronaviruses. Probes were HPLC-purified by the manufacturer. W is A/T; R is G/A; M is A/C.
### MagMAX RNA isolation using MagMAX(tm)-96 Total RNA Isolation Kit (AM1830)
After heat treatment/no heat treatment of nasopharyngeal swab within Class I MSC of CL-3 lab, 100 ml of sample was transferred to 1.5mL tubes and 300 ml TRIzol(tm) Reagent (Thermofisher 15596018) added. Samples were vortexed and incubated at room temperature for 5 mins. 40 ml chloroform was added, samples vortexed and incubated for a further 5 mins. Samples were transferred to a CL-2 lab for further processing and spun at 12000g at 4degC for 10 mins. 100ul of the upper aqueous phase was then transferred to a 96-well plate, 50 ml 100% isopropanol added, and samples vortexed/shaken for 1 min. RNA binding beads (Thermofisher Scientific) were first vortexed to resuspend, then 10ul was added to each sample, and the plate vortexed/shaken for a further 3 mins. The plate was placed onto a 96-well magnetic stand (Thermofisher Scientific) for approximately 2 mins, until the supernatant was completely clear. All of the supernatant was removed carefully, without disturbing the beads. 150 ml Wash 2 (Thermofisher Scientific) was added and the plate vortexed/shaken for 1 min. The plate was placed on the magnet until supernatant clear, and the supernatant removed. This step was repeated, using another 150 ml Wash 2. Once the last supernatant was removed the plate was vortexed/shaken for 2 minutes to dry the beads. 50 ml Elution Buffer (Thermofisher Scientific) was added to each sample and the plate vortexed/shaken vigorously for 3 mins. The plate was placed on the magnet, and once clear the supernatant containing total RNA was removed and transferred to a clean 96-well plate.
## Supplemental Figures and Tables
## Supplemental Comparison between three RT-qPCR Master Mix kits with N1 primer-probes.** RNA extraction with the QIAamp kit was done for a set of ten swab samples, previously classified as positive (CPS) by the diagnostics lab. RT-qPCR mixes were done according to each kit manufacturer's indications, maintaining the concentrations of primer-probes between the different mixes. For all panels, dots represent each individual technical duplicate, line connects the average of replicates. Appearance of one dot in samples is due to very tight qPCR replicates. Normality was assessed using D'Agostino & Pearson test prior to analysing the datasets employing ANOVA. *
p<0.001
## Supplemental Plaque assays showing heat inactivation of the B 1.1.7 and original SARS-CoV-2 strains.** Viral stocks for B 1.1.7. **(A)** or original **(B)
Note: plaques in B 1.1.7 infected cells are smaller as compared to the original strain.
## Supplemental Figure 3.****Plaque assays showing partial heat inactivation of the original SARS-CoV-2 strain.
Viral of the original SARS-CoV-2 strains were heat inactivated at 70\({}^{\circ}\)C or 90\({}^{\circ}\)C for 10 or 30 min; however, instead of using a digital thermometer we relied on the water bath temperature and later evaluated that it was set at lower than 70\({}^{\circ}\)C and at around 62-63\({}^{\circ}\)C. Plaques can be observed at the highest concentration of virus (3 × 10\({}^{5}\) pfu/mL). These data show that employing less than 70\({}^{\circ}\)C is not safe for heat inactivation of samples, particularly of those with high viral titres..
## Supplemental Figure 4.****Heat inactivation of nasopharyngeal swab samples and RNA extraction using MagMax (ThermoFisher Scientific) extraction kit (A)
Six positive samples were subjected to different temperatures and incubation times as indicated. RNA was extracted using MagMax (ThermoFisher Scientific). RT-qPCR run with the three different primer-probe sets (N1, N2 and RdRP) with FastVirus Master Mix. Dots represent each individual technical duplicate.
## Supplemental Comparison of RdRP primer-probe sets (A)** Four positive samples assessed employing the combinations of RdRP primer-probe sets (same forward and reverse, different probe combinations). RNA was extracted using QiAmp and RT-qPCR employing FastVirus Master Mix. **(B)
Confirmation of the positivity of these samples (as per previous clinical diagnostics) employing the N1 and N2 primer-probe sets on the same samples, using Luna Master Mix. Dots represent each individual technical duplicates. For CPS_68 and N1 and N2 primer-probes we only obtained one well of amplification.
## Supplemental RNAseP in samples tested in
Samples were tested for RNAse P for each donor except for CNS_55 where there was no RNA left to assess. All samples had detectable RNAse P. We have observed very high Ct values for RNAse P in some water controls related to bad amplification curves which were considered no amplification.
## Supplemental Outliers from Samples heat inactivated vs non inactivated that were detected in one or other treatment were plotted to establish if a Ct cut-off establishes detection. We were not able to determine a Ct cut-off above which samples became undetectable upon heat or vice versa, with certain samples being better detected upon heat and others (more) undetected upon heat.
\begin{tabular}{|l|l|l|l|l|} \hline & \multicolumn{2}{c|}{**N1**} & \multicolumn{2}{c|}{**N2**} \\ \cline{2-5} & **Non-inactivated** & **Heat Inactivated** & **Non-inactivated** & **Heat Inactivated** \\ \hline
## Minimum
& 14.41 & 14.80 & 14.17 & 15.13 \\
## 25\%
& & & & \\
## Percentile
& 19.82 & 20.41 & 19.82 & 20.94 \\ \hline
## Median
& 23.88 & 23.93 & 23.74 & 24.95 \\ \hline
## 75\%
& & & & \\
## Percentile
& 30.76 & 32.89 & 30.95 & 33.23 \\ \hline
## Maximum
& 50.00 & 50.00 & 50.00 & 50.00 \\ \hline
## Range
& 35.60 & 35.21 & 35.83 & 34.88 \\ \hline
## Mean
& 26.46 & 27.76 & 26.13 & 28.06 \\ \hline
## Std.
& & & & \\
## Deviation
& 9.141 & 9.998 & 8.608 & 9.577 \\ \hline
## Std.
& & & & \\
## of Mean
& 0.9744 & 1.066 & 0.9124 & 1.015 \\ \hline
## Number of
& & & & \\
## samples
& 88 & 88 & 89 & 89 \\ \hline \end{tabular}
## Supplemental Table 1
Statistics of samples in Undetermined samples were randomly assigned a value of 50. Non amplified samples in both treatments are not included.
\begin{tabular}{|l|l|l|l|l|} \hline & **qPCRBIO Probe 1-** & **TaqMan Fast Virus** & **TaqMan Fast Virus** & **Luna Universal** \\ & **Step Go Lo-ROX** & **1-Step** & **1-Step** & **Probe** \\ & _CDC Primers_ & _RdRp Primers_ & _CDC Primers_ & _CDC Primers_ \\ \hline
## Reaction
& 5 \(\mu\)L & 5 \(\mu\)L & 5 \(\mu\)L & 10 \(\mu\)L \\
## mix buffer
& & & & \\ \hline
## RT enzyme
& 2 \(\mu\)L RTase Go & (included in buffer) & (included in buffer) & 1 \(\mu\)L Luna \\ & & & & WarmStart \\ \hline
## Primer
& 1.5 \(\mu\)L & 1.2 \(\mu\)L (10 \(\mu\)M) & 1.5 \(\mu\)L & 1.5 \(\mu\)L \\
## Forward
& (All premixed by & RdRP SARSr-F2 & (All premixed by & (All premixed by \\ \hline Primer & IDT) & 1.6 \(\mu\)L (10 \(\mu\)M) & IDT) & IDT) \\
## Reverse
& & RdRP SARSr-R1 & & \\ \hline
## Probe
& & 0.2 \(\mu\)L (10 \(\mu\)M) & & \\ & & RdRP SARSr-P2 & & \\ \hline
## Water
& 5 \(\mu\)L & 7 \(\mu\)L & 8.5 \(\mu\)L & 2.5 \(\mu\)L \\ \hline
## RNA
& & & 5 \(\mu\)L & \\
## template
& & & & \\ \hline \end{tabular}
## Supplemental Table 2
List of components for the different one-step RT-qPCR reagents used.
## Supplemental Table 3
Cycling modes for the different one-step RT-qPCR reagents used (reaction volume is always 20 \(\mu\)L) |
075531_file02 | ### Animal Housing
Animal use was approved by the CCHMC Institutional Animal Use and Care Committee. Mice were housed in a pathogen-free facility with 12-hour light/dark cycles and provided chow and water _ad lib_. Previously generated _Cela1\({}^{\sim}\)_ and wild type mice were all on the C57BL/6 background and derived from our existing colony.
### Porcine Pancreatic Elastase Model of Emphysema
A single dose of 2 units porcine pancreatic elastase (PPE, Sigma, St. Louis, MO) at a concentration of 10 units/mL diluted in PBS was administered by tracheal instillation as previously described to 8-12 week old C57BL/6 mice anesthetized with isoflurane and tracheally cannulated using an 18 gauge angiocatheter.
### Aged Mouse Model of Emphysema
WT and _Cela1\({}^{\sim}\)_ mice were collected at age 70-75 weeks for evaluation of age-dependent alveolar simplification.
### Mouse Lung Tissue Collection and Processing
At predetermined time points, mice were anesthetized with 0.2 mL of ketamine/xylazine/acepromazine and sacrificed by exsanguination. The left lung was ligated before inflation and used for protein and RNA analysis, and the right lung inflated at 25 cm H\(\mathrm{\SIUnitSymbolOhm}\) water pressure with 4% PFA in PBS, fixed,paraffinized, lobes as previously described [], and 5 \(\mu\)m sections created.
### Mouse Lung Morphometry
Using the methods of Dunnill [] on five images from each right lung lobe, mean linear intercepts were determined and used for comparisons.
### CELA1 anti-Sera Generation
100 micrograms of GEHNLSQNDGTEQYVNVQKIVSHPY (U-7318 in this manuscript, Genscript, Piscataway, NJ) peptide in 1 mL of PBS and 1 mL of Freuds complete adjuvant was administered subcutaneously at multiple sites to a New Zealand female rabbit with a subsequent administration of 100 and then 50 micrograms in incomplete Freunds adjuvant on days 21 and 42. Titers were determined by direct ELISA using CELA1-coated plates and titers of <1:5000 considered positive. 7 mL/kg of blood was collected every 2 weeks by marginal vein catheterization using isoflurane anesthesia.
### anti-CELA1 Monoclonal Antibody Generation
CD-1 female mice were immunized with CELA1 peptides (see below) conjugated to CRM197. Each mouse received a primary, subcutaneous immunization of 20 ug of the conjugate with 50% Titermax Gold adjuvant. The mice received subsequent immunizations of 20 ug (day 21) and 10 ug (day 35). Following the day 35 immunization serum samples were obtained and tested for reactivity with CELA1. Based on the results of the serum titration, one mouse was selected for hybridoma production. The mouse received an intravenous immunization of 2 ug of conjugate and three days later the mouse was euthanized and the spleen excised for hybridoma formation with SP2/0.
Supernatants from the resulting hybridomas were tested for reactivity with CELA1 and were subsequently expanded and cloned. Antibodies from the cloned culture, derived from serum-free medium, was used in the studies reported here.
\[\text{Peptides used for mouse immunization}\] \[\text{hHCELA1}\] \[\text{CGFEAGRNSWPSQISLQYRSGSFYH}\] \[\text{hHCELA1}\] \[\text{CRQNWVMTAAHCVDYQKIFRVVAGDH}\] \[\text{hHCELA1}\] \[\text{CVVHPYWNSDNVAAAGYDIALLRLAQSVTLNSY}\] \[\text{hHCELA1}\] \[\text{CGFKTKINGQLAQTLQQAYLPSVDYAI}\] \[\text{hHCELA1}\] \[\text{CLVNGKYSVHGVTSFVSSRGCNVSR}\]
Isotyping was performed using the Iso-Gold Rapid Mouse-Monoclonal Isotyping Kit (BioAssay Works Cat# KSOT03-010)
### Human Lung Tissue Use
Human tissue utilized under a waiver from the CCHMC IRB. Emphysematous lung explants from individuals with COPD and _postmortem_ specimens from aged individuals with no documented lung disease were obtained from the NHLBI lung tissue research consortium (LTRC). "Healthy" lung specimens from non-lung organ donors were obtained from National Jewish Health Human Lung Tissue Consortium in Denver, Colorado. Flash frozen lung specimens of COPD, non-lung organ donors, and aged lung without known lung disease were obtained from the NIH lung tissue consortium and the National Jewish Health Human Lung Tissue Consortium. Portions of specimens were fixed and sectioned and other portions used for biochemical assays.
Left mouse lungs were ligated and collected prior to inflation and fixation of the right lungs. Protein and RNA was extracted from these specimens and used for Western Blot and PCR. Protein and RNA was similarly extracted from human lung specimens but additionally homogenized lung specimens were analyzed using Enzchek elastase, gelatinase, and proteinase assays (Thermo Fisher E12056, E12055, E6639).
### Enzyme-linked Immunoassay (ELISA)
96 well clear bottom plates (Corning) were coated with 20 ug/mL recombinant mCela1, hCELA1, or peptide and incubated at 4degC overnight. After washing, hybridoma supernatants or antibody preparations were incubated for 1 hour at room temperature, washed, and a donkey anti mouse peroxidase conjugated secondary antibody used for detection using TMB. Absorbance at 450 nm was determined using a Spectramax photometer.
### Enzymatic Assays
Frozen human lung specimens were homogenized in RIPA buffer and protein content quantified. Ten \(\mu\)g of protein was used for Enzcheck elastase, gelatinase, and proteinase assays per manufacturer instructions using a Molecular Devices Spectramax M2 plate reader using 4-hour readings for comparisons.
### Proximity Ligation _in situ_ Hybridization (PLISH)
Using oligos in Supplementary Table 1 and previously published methods, PLISH for mouse and human _CELA1_ and mouse _Surfactant protein B_ mRNA was performed. Briefly, sections were incubated with right and left sided oligonucleotides, then linking oligonucleotides, ligation performed with T4 DNAligase (New England Biolabs, M0202L). The sequences amplified by rolling circle amplification using Phi29 polymerase (New England Biolabs M0269L), and these oligos detected using a detection oligonucleotide. DAPI counterstaining was performed and sections imaged on a Nikon NiE microscope.
## Supplemental Table 1: PLISH Primers, Bridges, and Probes
\begin{tabular}{|l|l|} \hline Name & Sequence \\ \hline MsCelal\_705\_L243 & TAGCGCTAACAACTTACGTTGTTATGAAGTCATGGGCCTGTCACA \\ \hline MsCelal\_705\_L742 & TAGCGCTAACAACTTACGTTGTTATGTTCCTGGCACATTACAGCC \\ \hline MsCelal\_705\_L130 & TAGCGCTAACAACTTACGTTGTTATGTGAAGGCCAAAGATTTCCT \\ \hline MsCelal\_705\_L552 & TAGCGCTAACAACTTACGTTGTTATAGGCACGCTGGCAGG \\ \hline MsCelal\_705\_L100 & TAGCGCTAACAACTTACGTTGTTATGTATCCCCGAGTACCAAAGAC \\ \hline MsCelal\_705\_R243 & CTCTCCGACAACCACTCGATTATACGTCGAGTGAACGTCGTAACA \\ \hline MsCelal\_705\_R742 & CTCTGGTGAGAACGGTGGGCTTATACGTTGAGTTGAACGTCGAACA \\ \hline MsCelal\_705\_R130 & ACTGGTACTGGAGGGAAAATCTTATACGTCGAGTGAACGTCGTAACA \\ \hline MsCelal\_705\_R552 & AAGAGGAGCTGGGAGCCAGATGCTTATACGTCGAGTGAACGTCGTAACA \\ \hline MsCelal\_705\_R100 & CTTTTCATTAACCCCCCACCTTATACGTCGAGTGAACGTCGTAACA \\ \hline MsSftpb\_594\_L211 & TTAGTAGGCGAACTTACGTTGTTATGATCATGCCCTTCCCTGGC \\ \hline MsSftpb\_594\_L1129 & TTAGTAGGCGAACTTACGTTGTTATGTCTCTGAGCCATCTTCATG \\ \hline MsSftpb\_594\_L808 & TTAGTAGGCGAACTTACGTTGTTATAGTTTTACAGACTTCCACCGGTT \\ \hline MsSftpb\_594\_L1398 & TTAGTAGGCGAACTTACGTTGTTATGTGTCTCGCTCACTCGGGGCCTA \\ \hline MsSftpb\_594\_L362 & TTAGTAGGCGAACTTACGTTGTTGTTATGTCTACTCATGTCCATTT \\ \hline MsSftpb\_594\_R211 & GAATCGGACTCGGAAACCAGTTTTATACGTCGAGTGAACATAAGTGCG \\ \hline MsSftpb\_594\_R1129 & AGCCTCAAAGACTAGGGATGCTTATACGTTGAGATCAAAGTGCG \\ \hline MsSftpb\_594\_R808 & CGTAGGAGAGACACCTTCCTTATACGTTGAGATCAAAGTGCG \\ \hline MsSftpb\_594\_R1398 & GAAAAGGTAGGCATGGTGCTTATACGTCGAGTTGAACATAAGTGCG \\ \hline MsSftpb\_594\_R362 & GGACTCTCCATCAGGACCTCTTATACGTCGAGTTGAACATAAGTGCG \\ \hline HuCELA1\_705\_L707 & TAGCGCTAACAACTTACGTTGTTATGTGGACACAAGCTGGTCACT \\ \hline \end{tabular}
## Immunofluorescence
Human lung sections were incubated overnight with 1:500 dilution rabbit anti-CELA1 and 1:500 guinea pig anti-SCGB1A1 antibodies (gift of Jeffrey Whitsett) in 5% donkey serum with subsequent incubation with 1:5000 fluorophore-conjugated secondary antibodies, counterstained with DAPI, and mounted in prolong gold. Images were obtained using a Nikon NiE microscope.
### Immunohistochemistry
Human lung sections were immunostained for CELA1 using anti-CELA1 guinea pig antibody (?) with secondary alone control using the ABC Vectastain kit (Vector Labs, Burlingame, CA). 4X tile scanned and 20X images were obtained using a Nikon 90i inverted microscope. Using Nikon elements software, the number of Cela1-positive cells per lung section were morphometrically determined in 4x tile scanned sections.
### Western Blot
Mouse lung homogenates were electrophoretically separated, transferred to PVDF membranes, and total protein quantified using a total protein stain (LICOR, 926-11011). Blots were immunostained with anti-CELA1 guinea pig antibody (1:5,000 dilution) and anti-tropoelastin antibody (ab21600, Abcam, 1:5,000 dilution), anti-p16INK (Sigma SAB45000-72, 1:500), p19ARF antibody (Novus Biologics, NB200-169, 1:500), anti-p21 antibody (Novus Biologics, NBP2-29463, 1:500), anti-p53 antibody (Abcam, ab131442, 1:500) and evaluated by densitometry using an Odyssey system (LI-COR Biotechnology, Lincoln, NE). Fold-change values from total protein (ReVERT 700 Total Protein Stain, LI-COR Biotechnology) normalized values were used for calculations.
### Pcr
RNA was extracted from lung homogenates using RNEasy Mini columns (Qiagen, Valencia, CA) and cDNA library synthesized using a High Capacity cDNA Reverse Transcriptase Kit (Applied Biosystems, Foster City, CA). For human specimens, Taqman PCR was performed using the primers listed inSupplemental Table 2 and a QuantStudio6 device (all Applied Biosystems). For mouse specimens Sybr Green PCR was performed using the primers in (Supplemental Table 3) and PowerUp SYBR Green (Applied Biosystems, AB25780).
## Supplemental Table 2: Taqman Primers
## Human _Ex vivo_ Lung Stretch
Ten mm cores of frozen human lung tissue were created using a coring device and hand-cut 100-200 \(\mu\)m sections were cut using a scalpel on dry ice. These sections were mounted onto a silicone mold and then subjected to biaxial stretch or imaged sequentially over time using a previously published 3D-printed confocal microscope-compatible stretching device with Enzcheck elastin zymography substrate (10 \(\mu\)g/mL), Texas-Red conjugated albumin (Thermo Fisher A23017, 1 \(\mu\)g/mL) and AF647-conjugated CELA1 (1 \(\mu\)g/mL). A 100 \(\mu\)m Z-stack at 10x magnification was obtained using a Nikon A1 confocal microscope and the signal for each analyte at sequential levels of biaxial stretch were quantified and normalized to tissue autofluorescence. The rate of elastase activity, albumin binding, and CELA1 binding per fold change in area or time equivalent was measured per section and sections assayed in triplicate. The average rate of change per specimen was used for comparisons.
### Human Genomic Studies
CELA1 gene variants were downloaded from the Broad Institute, dbGAP and Ensembl. Functional significance of variants was predicted using SIFT and PolyPhen-2.
### Statistical Methods
Using R version 4.0.2, the following packages were used for statistical comparisons and graphics generation: ggpubr, gridExtra, cowplot, ggpltoify, corplot, and rstatix. For parametric data, Welch's t-test and ANOVA with Holm-Sidac _post hoc_ test were used, and for non-parametric data, Wilcoxon rank-sum and Kruskal-Wallis with Dunn's _post hoc_ test were used. Forcorrelative analyses, Pearson's correlation with Bonferroni correction for multiple comparisons was used. Parametric data is displayed as line and whisker plots with center line representing mean and whiskers standard deviation. Non-parametric data is displayed as box plots with center line representing median value, boxes representing 25th to 75th percentile range, and lines representing 5th to 95th percentile range. For both plot types dots represent individual data points. For all analyses p-values of less than 0.05 were considered significant.
### Analysis of Bulk Human Lung Organoid Data
Datasets from native __ and induced pluripotent stem cell __ alveolar type 2 cell organoids infected with SARS-CoV-2 virus and CELA1 expression was expressed using a publicly available webtool __.
### Re-analysis of Single Cell Data
For Human Lung Cell Atlas __ data, annotated patient data and analysis code was downloaded and modified to remove the 80% cell filtering step and then clustered and analyzed using Seurat __. Human fetal lung datasets __ and AT2 cell organoid __ matrix files were downloaded from Array Express and GEODatasets respectively and analyzed in Seurat. Human control, COPD, and IPF single cell data __, mouse lipopolysaccharide lung injury __, and mouse lung bleomycin single cell data __ were analyzed using publicly available web tools described in each manuscript __.
## Aged Mouse Lung Supplemental Data
There was no difference in Cela1 protein levels in aged vs. young WT mice (Supplemental Figure 2A). Quantitative morphometry of Hart stained WT and _Cela1\({}^{\times}\)_ lung specimens showed a trend towards more insoluble elastin in _Cela1\({}^{\times}\)_ lungs (Supplemental Figure 2B). There was no difference in the amount of senescence-related proteins in aged WT and _Cela1\({}^{\times}\)_ lung (Supplemental Figure 2C).
Supplemental Additional Aged Mouse Lung Data. (A) Western blot of young (8-12 week-old) and aged (70-75 week-old) wild type mouse lung revealed no differences in Cela1 protein levels. (B) Quantitative image analysis of elastin-stained mouse lung issues identified a trend towards increased total lung elastin in aged _Cela1\({}^{\times}\)_ mouse lungs. (C) Quantification of lung senescence proteins showed no differences except for a trend towards reduced p53 in aged _Cela1\({}^{\times}\)_ lung.
## Mouse Cela1-expressing Cells During Lung Development
Time course single cell mRNA-Seq data from C57BL/6 mouse lung shows low level expression in distal lung epithelial and immune cells at all time points except E18.5 when an increase in distal lung epithelial expression is notable (Supplemental Figure 3).
Supplemental _Cela1_-expressing Cells Over the Course of Mouse Lung Development. A-H, U-maps and feature plots for Cela1 of single cell mouse lung data from LungGENS database.
## CELA1 in Human Fetal Lung
In a dataset of tissues from four different human fetal lung specimens, _CELA1_ mRNA was detected in none of the lung epithelial cells. Only rare lymphocytes had _CELA1_ mRNA. Notably, the oldest age specimen with distal lung sampling was 18 weeks of age (Supplemental Figure 4)
Supplemental Identification of _CELA1_-expressing Cells in Human Fetal Lung. (A) U-map of cells from four different specimens with segregation into tracheal, small conducting airway, and distal lung as the specimen allowed. (B) Feature plot with virtually no _CELA1_-expressing cells. (C) Violin pot showing T-cell and lymphocyte CELA1-expressing cells in large airways. (D) Violin plot by specimen showing that the cells were only found in the trachea.
### _Cela1_ in Adult Human Lung
Query of the Human Lung Cell Atlas identified CELA1 as being only very rarely expressed in adult immune and AT2 cells (Supplemental Figure 5A-C). Query of sorted human lung cells in LungGENS identified CELA1 transcripts as being elevated in epithelial and immune cells in infant and child lung specimens (Supplemental Figure 5D). Native and induced alveolar type 2 cell organoids showed increased CELA1 expression after infection with SARS-CoV-2 virus (Supplemental Figure 5E).
Lung Cell Atlas U-map of datasets without the 80% cell number reduction reported in the original paper. (B) Feature plot for _CELA1_ showing very few positive cells. (C) Violin plot showing that the few positive cells are mostly immune cells with a few AT2 cells. (D) mRNA-seq of sorted human lung cells at different ages with each point representing a subject. _CELA1_ mRNA levels were higher in immune and AT2 cells during lung development. (E) Human lung organoids created from native AT2 cells or induced pluripotent stem cells express _CELA1_ mRNA after infection.
Identification of CELA1-expressing Cells in Postnatal Human Lung. (A) Human Lung Cell Atlas U-map of datasets without the 80% cell number reduction reported in the original paper. (B) Feature plot for _CELA1_ showing very few positive cells. (C) Violin plot showing that the few positive cells are mostly immune cells with a few AT2 cells. (D) mRNA-seq of sorted human lung cells at different ages with each point representing a subject. _CELA1_ mRNA levels were higher in immune and AT2 cells during lung development. (E) Human lung organoids created from native AT2 cells or induced pluripotent stem cells express _CELA1_ mRNA after infection.
## COPD-Associated Proteases in Human Lung
Among the proteases reportedly important in emphysema pathogenesis, the majority were elevated in COPD specimens compared to non-smoker and smoker controls (Supplemental Figure 6).
MMP=matrix metalloproteinase. Indicated p-values are by Kruskal-Wallis test.
## Aged Human Lung Supplemental Data
Western blot for CELA1 in aged smoker and non-smoker lung homogenates (Supplemental Figure 7).
Supplemental Aged Human Lung Western Blot. (A) CELA1 and (B) total protein stain of smoker and non-smoker aged human lung.
## Lung Stretching Supplemental Data
Image of 3D-printed confocal microscope stretching device (Supplemental Figure 8A&B). Quantification of biaxial strain applied by device (Supplemental Figure 8C).
3D-printed Confocal Microscope Lung Stretching Device. (A) Four motors are housed within a plastic case that fits within the microscope mounting plate. A silicone mold (circle) is secured by four clips attached to the motors by Tyvek strips. (B) Image of lung before stretching and after stretching (inset). (C) Quantification of the increase in mold aperture area with number of stretch (steps). The steps used for imaging are shown. |
076075_file02 | ### Proof of convergence
We start by introducing the relevant terminology. Let \(\Pi\subset\mathbb{R}^{L+1}\) be a closed set of parameters, and let \(f\) be a continuous functional on \(\Pi\). Assume that \(B\subset\mathbb{R}\) is compact and that \(g:\,\Pi\mapsto\mathcal{C}(B)\) is a continuous mapping from \(\Pi\) into \(\mathcal{C}(B),\) where \(\mathcal{C}(B)\) is the space of continuous functions over \(B\) equipped with the supremum norm \(||\cdot||_{\infty}.\) For each \(D\subset B\) let
\[M(D)=\{\mathbf{c}\in\Pi|\,g(\mathbf{c},x)\leq 0,x\in D\}\]
denote the set of feasible points of the optimization problem
\[\text{min }f(\mathbf{c})\text{ over }\mathbf{c}\in M(D).\]
Assuming that \(M(D)\neq\emptyset\), let
\[\mu(D)=\inf\{f(\mathbf{c})|\mathbf{c}\in M(D)\},\]
and define the level set
\[\text{Level}(\mathbf{c}_{0},D)=\{\mathbf{c}\in\Pi|\,f(\mathbf{c}) \leq f(\mathbf{c}_{0})\}\cap M(D).\]
We also make the following two assumptions:
* Assumption 1: Fine grid Let \(\mathbb{N}_{0}=\mathbb{N}\cup\{0\}\). There exists a sequence \(\{B_{i}\}\) of compact subsets of \(B\) with \(B_{i}\subset B_{i+1},\,i\in\mathbb{N}_{0},\) for which \(\lim_{i\to\infty}h(B_{i},B)=0,\) such that \[h(B_{i},B)=\sup_{x\in B}\inf_{y\in B_{i}}||x-y||.\]
* Assumption 2: Bounded level set \(M(B)\) is nonempty, and there exists a \(\mathbf{c}_{0}\in M(B)\) such that the level set \(\text{Level}(\mathbf{c}_{0},B_{0})\) is bounded and hence compact in \(\mathbb{R}^{L+1}\).
Convergence of the discretized method, Theorem 2.1 from:
Under assumptions 1.3 and 1.3, the solution of the discretized problem converges to the optimal solution.
\[\mu(B_{i})\leq\mu(B_{i+1})\leq\mu(B),\forall t\in\mathbb{N}_{0}\] \[\lim_{i\to\infty}\mu(B_{i})=\mu(B).\]
If \(\mathbf{c}^{*}\) is the unique optimal solution of the original problem, and \(\mathbf{c}_{i}^{*}\) is the optimal solution of the discretized relaxation with grid \(B_{i}\), then
\[\lim_{i\to\infty}||\mathbf{c}^{*}-\mathbf{c}_{i}^{*}||_{2}=0.\]
It is straightforward to see that our chosen grid is arbitrary fine. Hence, we only need to prove that there exists a \(\mathbf{c}_{0}\) such that the level set \(\text{Level}(\mathbf{c}_{0},D)\) is bounded.
Let \(\mathbf{c}=(\mathbf{a};t)\) and note that in our setting, \(f(\mathbf{c})=t\).
\[g(\mathbf{c},\lambda)=\mathbf{a}^{T}\mathbf{M}(\lambda)\mathbf{a} +\mathbf{a}^{T}\mathbf{\Lambda}\mathbf{\Lambda}^{T}\mathbf{a}-t,\]
where
\[\mathbf{\Lambda}\triangleq e^{-\lambda}(\lambda^{0},\lambda^{1},...,\lambda^{L})^{T}.\]
Note that only \(a_{1},...a_{L}\) are allowed to vary since we fixed \(a_{0}=-1\). Obviously, \(\mathbf{\Lambda}\mathbf{\Lambda}^{T}\) is positive semi-definite and the previously introduced \(\mathbf{M}(\lambda)\) is positive definite for all \(\lambda>0\). Since the constraints on \(g\) are positive definite with respect to \(a_{1},...a_{L},\,g\) is coercive in \(a_{1},...a_{L}\). Furthermore, for any given \(t\), the set of feasible coefficients \(a_{1},...a_{L}\) is bounded. Therefore, given a \(t_{0}\), the level set \(\text{Level}(\mathbf{c}_{0},B_{0})\) is bounded. This ensures that Assumption 1.3 holds for our optimization problem.
Next, we prove the uniqueness of the optimal solution \(\mathbf{c}^{\star}\). Note that proving this result is equivalent to proving the uniqueness of \(\mathbf{a}^{\star}\).
\[\inf_{\mathbf{a}:a_{0}=-1}\sup_{\lambda\in[\frac{\pi}{6},6.5L]} \mathbf{a}^{T}(\mathbf{M}(\lambda)+\mathbf{\Lambda}\mathbf{\Lambda}^{T}) \mathbf{a}\triangleq\inf_{\mathbf{a}:a_{0}=-1}\sup_{\lambda\in[\frac{\pi}{6},6.5L]}h_{\lambda}(\mathbf{a}) \tag{2}\]Clearly, \(\forall\lambda\in[\frac{n}{k},6.5L]\), the function \(h_{\lambda}(\mathbf{a})\) is strictly convex since \((\mathbf{M}(\lambda)+\mathbf{\Lambda}\mathbf{\Lambda}^{T})\succ 0,\ \forall\lambda\in[ \frac{n}{k},6.5L]\).
\[\sup_{\lambda\in[\frac{n}{k},6.5L]}h_{\lambda}(\mathbf{\theta} \mathbf{x}+(1-\theta)\mathbf{y})\] \[<\sup_{\lambda\in[\frac{n}{k},6.5L]}\theta h_{\lambda}(\mathbf{x })+(1-\theta)h_{\lambda}(\mathbf{y})\] \[\leq\sup_{\lambda\in[\frac{n}{k},6.5L]}\theta h_{\lambda}( \mathbf{x})+\sup_{\lambda^{\prime}\in[\frac{n}{k},6.5L]}(1-\theta)h_{\lambda^ {\prime}}(\mathbf{y}).\]
Hence \(\sup_{\lambda\in[\frac{n}{k},6.5L]}h_{\lambda}(\mathbf{a})\) is strictly convex, which consequently implies the uniqueness of \(\mathbf{a}^{*}\) and hence \(\mathbf{c}^{*}\).
For the case of samples passed through a Poisson channel, it is not hard to see that the constraints are again strictly convex in \(\mathbf{a}\), where one only need to replace \(\mathbf{M}(\lambda),\mathbf{\Lambda}\) by
\[\frac{1}{k}e^{-\lambda(1-e^{-\eta})}\ Diag(0!\eta^{0}M_{N^{*}}^{( 0)},1!\eta^{1}M_{N^{*}}^{},...,L!\eta^{L}M_{N^{*}}^{(L)})\] \[e^{-\lambda(1-e^{-\eta})}(\eta^{0}M_{N^{*}}^{},\eta^{1}M_{ N^{*}}^{},...,\eta^{L}M_{N^{*}}^{(L)})^{T}\]
Thus, a similar analysis is possible and the details are omitted. The proof above along with the previous observation proves the convergence result.
### Proof for the convergence rate
In what follows, and for reasons of simplicity, we omit the constraint \(a_{0}=-1\) in the SIP formulation. The described proof only requires small modifications to accommodate \(a_{0}=-1\).
Recall that we used \(B_{d}\) to denote the grid with grid spacing \(d\). In order to use the results in, we require the convergence assumption below.
* Assumption Let \(\bar{\mathbf{c}}\) be a local minimizer of an SIP. There exists a local solution \(\mathbf{c}_{d}\) of the discretized SIP with grid \(B_{d}\) such that \[||\mathbf{c}_{d}-\bar{\mathbf{c}}||\to 0.\] This assumption is satisfied for the SIP of interest as shown in the first part of the proof.
* Assumption The following hold true:
* There is a neighborhood \(\bar{U}\) of \(\bar{\mathbf{c}}\) such that the function \(\frac{\partial^{2}}{\partial\lambda^{2}}g(\mathbf{c},\lambda)\) is continuous on \(\bar{U}\times B\).
* The set \(B\) is compact, nonempty and explicitly given as the solution set of a set of inequalities, \(B=\{\lambda\in\mathbb{R}|v_{i}(\lambda)\leq 0,i\in I\}\), where \(I\) is a finite index set and \(v_{i}\in C^{2}(B)\).
* For any \(\bar{\lambda}\in B\), the vectors \(\frac{\partial}{\partial\lambda}v_{i}(\bar{\lambda}),i\in\{i\in I|v_{i}(\bar{ \lambda})=0\}\) are linearly independent. Recall that our objective is of the form \[g(\mathbf{c},\lambda)=\mathbf{a}^{T}\mathbf{M}(\lambda)\mathbf{a}+\mathbf{a}^ {T}\mathbf{\Lambda}\mathbf{\Lambda}^{T}\mathbf{a}-t,\] where \[\mathbf{\Lambda}\triangleq e^{-\lambda}(\lambda^{0},\lambda^{1},...,\lambda^{L})^{T},\ \mathbf{c}=(\mathbf{a};t),\] \[\mathbf{M}(\lambda)\triangleq\frac{e^{-\lambda}}{k}\ Diag( \lambda^{0}0!,\lambda^{1}!,...,\lambda^{L}L!).\] It is straightforward to see that the first condition in Assumption 1.4 holds. For the second condition, recall that \(B=[\frac{n}{k},6.5L]\). Hence, the second condition can be satisfied by choosing \(I=\{1\}\), \(v_{1}(\lambda)=(\lambda-\frac{n}{k})(\lambda-6.5L)\). Since we only have one variable \(v_{1}\), it is also easy to see that the third condition is met.
* Assumption The set \(B\) satisfies Assumption 1.4 and all the sets \(B_{d}\) contain the boundary points \(\frac{n}{k},6.5L\). This assumption also clearly holds for the grid of choice. Note that it is crucial to include the boundary points for the proof in to be applicable.
* Assumption \(\nabla_{\mathbf{c}}g(\mathbf{c},\lambda)\) is continuous on \(\bar{U}\times B\), where \(\bar{U}\) is a neighborhood of \(\bar{\mathbf{c}}\). Moreover, there exists a vector \(\xi\) such that \[\nabla_{\mathbf{c}}g(\bar{\mathbf{c}},\lambda)^{T}\xi\leq-1,\ \forall\lambda\in B.\] Note that \(\nabla_{\mathbf{c}}g(\mathbf{c},\lambda)=[\nabla_{\mathbf{a}}g(\mathbf{c}, \lambda);\nabla_{t}g(\mathbf{c},\lambda)]\) and \[\nabla_{\mathbf{a}}g(\mathbf{c},\lambda)=2(\mathbf{M}(\lambda)+\mathbf{\Lambda }\mathbf{\Lambda}^{T})\mathbf{a}.\] Also note that \(\forall\lambda\in B\), \(\mathbf{M}(\lambda)+\mathbf{\Lambda}\mathbf{\Lambda}^{T}\) is positive definite. Hence choosing \(\xi\) to be colinear with and of the same direction as \([-\mathbf{a}^{T}\ 1]^{T}\), as well as of sufficiently large norm will allow us to satisfy the inequality \[\nabla_{\mathbf{c}}g(\bar{\mathbf{c}},\lambda)^{T}\xi\leq-1,\ \forall\lambda\in B.\] Hence, Assumption 1.4 holds as well. The next results follow from the above assumptions and observations, and the results in.
Corollary 1 in
Let \(t_{d}\) be the optimal objective value of the discretized SIP used for support estimation with the grid \(B_{d}\), and let \(t^{\star}\) be the optimal objective value for the original SIP. Since Assumptions 1.4,1.4,1.4,1.4 hold, then for some \(c_{3}>0\) and \(d\) sufficiently small, we have
\[0\leq t^{\star}-t_{d}\leq c_{3}d^{2}.\]
Consequently, \(t_{d}\to t^{\star}\) with a convergence rate of \(O(d^{2})\).
Theorem 2 in
Assume that all assumptions in Lemma 1.4 hold.
\[t-\bar{t}\geq c_{4}||\mathbf{c}-\bar{\mathbf{c}}||,\ \forall\mathbf{c}\in M(B) \cap\bar{U},\]
then for sufficiently small \(d\) and \(\sigma>0\) we have
\[||\mathbf{c}_{d}-\bar{\mathbf{c}}||\leq\sigma d^{2}.\]
This result implies that if \(\bar{\mathbf{c}}\) is also a strict minimum of order one, then the solution of the discretized SIP converges to that of the the original SIP with rate \(O(d^{2})\). For the Poisson repeat channel, the constraints are also strictly convex in \(\mathbf{a}\). Therefore, a similar analysis is possible and the details are omitted once again. Combining these results completes the proof.
### Additional theoretical results
The result described in the main text follows from Theorem 6.2 in.
Theorem 6.2 from Let \(W(x)=\exp(-Q(x))\) be a weight function, where \(Q:\mathbb{R}\mapsto[0,\infty)\) is even, convex, diverging for \(x\to\infty\), and such that
\[0=Q<Q(x),\forall x\neq 0.\]
Then, for any polynomial \(P(x)\) of degree \(\leq L\), not identical to zero, one has
\[\sup_{x\in\mathbb{R}}|P(x)W(x)|=\sup_{x\in[-M_{L},M_{L}]}|P(x)W(x )|,\] \[\sup_{x\in\mathbb{R}\setminus[-M_{L},M_{L}]}|P(x)W(x)|<\sup_{x\in[ -M_{L},M_{L}]}|P(x)W(x)|.\]
Here, \(M_{L}\) stands for the _Mhaskar-Rakhmanov-Saff_ (MSF) number, which is the smallest positive root of the integral equation
\[L=\frac{2}{\pi}\int_{0}^{1}\frac{M_{L}tQ^{\prime}(M_{L}t)}{\sqrt{1-t^{2}}}dt. \tag{3}\]
In our setting, the weight equals \(\exp(-x)\). Solving gives us an MSF number equal to \(M_{L}=\frac{\pi}{2}L\). Thus, we can restrict our optimization interval to \([\frac{n}{k},\frac{\pi}{2}L+\frac{n}{k}]\). If there is no regularization term, the optimal interval reduces to \([\frac{n}{k},\frac{\pi}{2}L+\frac{n}{k}]\).
### Construction of the RWC-S estimator
We introduce the optimization problem needed for minimizing the risk \(E\left(\frac{S-\hat{S}}{S}\right)^{2}\).
\[\mathbb{E}\left(\frac{S-\hat{S}}{S}\right)^{2}=\frac{1}{S^{2}}\bigg{\{}\sum_{i \in\mathcal{L}}\bigg{(}\sum_{l=0}^{L}e^{-\lambda_{i}}a_{l}^{2}\lambda_{i}^{l}l! \bigg{)}+\sum_{i\neq j\in\mathcal{L}}\bigg{(}e^{-\lambda_{i}}\sum_{l=0}^{L}a_{l }\lambda_{i}^{l}\bigg{)}\bigg{(}e^{-\lambda_{j}}\sum_{l=0}^{L}a_{l}\lambda_{j}^ {l}\bigg{)}\bigg{\}}.\]
Taking the supremum over \(D_{k}\), one can further upper bound the risk as
\[\leq\sup_{\lambda\in[\frac{n}{k},n],\ \ell\in\mathcal{L}}\frac{1}{S^{2 }}\bigg{\{}\sum_{i\in\mathcal{L}}\bigg{(}\sum_{l=0}^{L}e^{-\lambda_{i}}a_{l}^ {2}\lambda_{i}^{l}l!\bigg{)}+\sum_{i\neq j\in\mathcal{L}}\bigg{(}e^{-\lambda_{ i}}\sum_{l=0}^{L}a_{l}\lambda_{i}^{l}\bigg{)}\bigg{(}e^{-\lambda_{j}}\sum_{l=0}^{L}a_ {l}\lambda_{j}^{l}\bigg{)}\bigg{\}}\] \[\leq\sup_{\lambda\in[\frac{n}{k},n]}\bigg{\{}\frac{1}{S}\bigg{(} \sum_{l=0}^{L}e^{-\lambda}a_{l}^{2}\lambda^{l}l!\bigg{)}+\bigg{(}e^{-\lambda} \sum_{l=0}^{L}a_{l}\lambda^{l}\bigg{)}^{2}\bigg{\}}\] \[\leq\sup_{\lambda\in[\frac{n}{k},n]}\bigg{\{}\frac{1}{S_{c}} \bigg{(}\sum_{l=0}^{L}e^{-\lambda}a_{l}^{2}\lambda^{l}l!\bigg{)}+\bigg{(}e^{- \lambda}\sum_{l=0}^{L}a_{l}\lambda^{l}\bigg{)}^{2}\bigg{\}}, \tag{4}\]
Note that the only difference between and the corresponding optimization problem described in the main text is in terms of changing the normalization from \(1/k\) to \(1/\hat{S}_{c}\) in the first term. The expression is optimized by the solution of the following problem:
\[\min_{t,\mathbf{a}\in Poly(L)}t\quad\text{s.t.} \tag{5}\] \[\bigg{\{}\frac{1}{\hat{S}_{c}}\bigg{(}\sum_{l=0}^{L}e^{-\lambda} a_{l}^{2}\lambda^{l}l!\bigg{)}+\bigg{(}e^{-\lambda}\sum_{l=0}^{L}a_{l} \lambda^{l}\bigg{)}^{2}\bigg{\}}\leq t,\ \forall\lambda\in\text{Grid}([\frac{n}{k},6.5L],s).\]
Figure S1: The results are obtained over \(100\) independent trials. The first two figures shows the mean and standard deviation of the estimators, while the latter two figures shows the MSE normalized by \(S^{2}\).
|
076612_file03 | ## Supplementary
- All agents. Generalised odds ratios (OR) for ordinal outcome forest plot. Generalised OR shown for each study with 95% confidence interval and day at which ordinal outcome recorded. Sample sizes given for patients receiving intervention (n) alongside total included (N) in study. Summary estimates presented separately for prospective and retrospective studies.
* non peer-reviewed preprint studies
## Supplementary - All studies mean duration of hospitalisation (days) forest plot. A: Mean duration of hospital stay. B: Mean difference compared with controls in duration of hospital stay. Effect sizes and associated 95% confidence intervals presented for each study. Sample sizes given for patients receiving intervention (n) and total included in study (N). Summary estimates presented separately for prospective and retrospective studies. Drugs labelled where T = toclimumab, S = sarilumab, Si = slituzumab. * non peer-reviewed preprint studies # randomised controlled trials
## Supplementary - All studies, adjusted hazard ratios (HR) for overall mortality forest plot. Adjusted HRs with associated 95% confidence interval and day of censorship presented for each study. Sample sizes given for patients receiving intervention (n) and total included (N) in study. Summary estimates presented separately for prospective and retrospective studies. Drugs labelled where T = toclilizumab, A = anakina, S = sarilumab, Si = siltuximab. * non peer-reviewed preprint studies # randomised controlled trials NR, not reported
## Supplementary -
All agents, mortality risk ratios (RR) forest plot. Risk ratios with associated 95% confidence interval and day of censorship presented for each study. Sample sizes given for patients receiving intervention (n) and total included in study (N). Summary estimates presented separately for prospective and retrospective studies. Drugs labelled where T = toclilizumab, A = anakina, Si = siltuximab.
* non peer-reviewed preprint studies
# randomised controlled trials
NR, not reported
*
\begin{tabular}{|c|c|c|c|c|c|c|c|c|} \hline \multicolumn{1}{|c|}{\multirow{2}{*}{Variables}} & \multicolumn{5}{c|}{Retrospective studies} \\ \cline{2-9} & \multicolumn{2}{c|}{Generalised odds ratios for} & \multicolumn{2}{c|}{Difference in duration of} & \multicolumn{2}{c|}{Adjusted hazard ratios for} & \multicolumn{2}{c|}{Risk ratios for mortality (N=26)} \\ & \multicolumn{2}{c|}{ordinal outcomes (N=8)} & \multicolumn{2}{c|}{hospitalisation (N=6)} & \multicolumn{2}{c|}{mortality (N=14)} & \multicolumn{2}{c|}{} \\ \hline \(\text{R}^{2}\) & \(\text{P}\) value & \(\text{R}^{2}\) & \(\text{P}\) value & \(\text{R}^{2}\) & \(\text{P}\) value \\ \hline Steroid use & 0.00 & 0.7921 & 0.00 & 0.3882 & 0.00 & 0.3097 & 0.00 & 0.9813 \\ Peer review & 0.00 & 0.5067 & N/A & N/A & 86.89 & 0.7388 & 0.35 & 0.3137 \\ \hline Drug delivery & 4.75 & 0.3526 & 94.37 & p\textless{}0.001 & 0.00 & 0.3062 & 8.33 & 0.1146 \\ \hline Single centre & 0.00 & 0.6028 & N/A & N/A & 0.00 & 0.4138 & 0.00 & 0.6616 \\ Outcome day & 0.00 & 0.7921 & N/A & N/A & 30.84 & 0.7910 & 30.37 & 0.013 \\ \hline \hline \multicolumn{1}{|c|}{\multirow{2}{*}{Variables}} & \multicolumn{5}{c|}{Prospective studies} \\ \cline{2-9} & \multicolumn{2}{c|}{Generalised odds ratios for} & \multicolumn{2}{c|}{Difference in duration of} & \multicolumn{2}{c|}{Adjusted hazard ratios for} & \multicolumn{2}{c|}{Risk ratios for mortality (N=5)} \\ & \multicolumn{2}{c|}{ordinal outcomes (N=5)} & \multicolumn{2}{c|}{hospitalisation (N=0)} & \multicolumn{2}{c|}{mortality (N=3)} & \multicolumn{2}{c|}{} \\ \hline \(\text{R}^{2}\) & \(\text{P}\) value & \(\text{R}^{2}\) & \(\text{P}\) value & \(\text{R}^{2}\) & \(\text{P}\) value & \(\text{R}^{2}\) & \(\text{P}\) value \\ \hline Steroid use & 99.99 & \textless{}0.0001 & N/A & N/A & 93.3 & 0.7960 & 81.92 & 0.1819 \\ Peer review & 0.00 & 0.4165 & N/A & N/A & N/A & N/A & N/A & N/A \\ Drug delivery & N/A & N/A & N/A & N/A & 93.3 & 0.7960 & 99.62 & 0.3689 \\ Single centre & 0.00 & 0.5332 & N/A & N/A & 93.3 & 0.7960 & 7.17 & 0.1677 \\ Outcome day & 0.00 & 0.5351 & N/A & N/A & 11.3 & 0.9103 & 19.21 & 0.8795 \\ \hline \end{tabular}
## Supplementary Table 4
- Results of meta-regression for variables assessed separated by study design (retrospective and prospective) and study outcomes. Sample sizes for each outcome shown (N). \(\text{R}^{2}\) and \(\text{P}\) values from meta-regression shown were applicable.
N/A, not applicable.
## Supplementary Table S(a)
- Risk of bias assessment for randomised clinical trials using Cochrane risk of bias 2 tool. Risk of bias was assessed in six categories and scored as either low risk of bias, some concern, or high risk of bias, before an overall risk of bias was given to each study.
* non peer-reviewed preprint study
## Supplementary Table 5(b).
Risk of bias assessment for prospective studies. Questions numbered in the first column. 1. Was the research question or objective in this paper clearly stated? 2. Was the study population clearly specified and defined? 3. Was the participation rate of eligible persons at least 50%? 4. Were all the subjects selected or recruited from the same or similar populations (including the same time period)? Were inclusion and exclusion criteria for being in the study prespecified and applied uniformity to all participants? 5. Was a sample size justification, power description, or variance and effect estimates provided 6. For the analyses in this paper, were the exposure(s) of interest measured prior to the outcome(s) being measured? 7. Was the timeframe sufficient so that one could reasonably expect to see an association between exposure and outcome if it existed? 8. For exposures that can vary in amount or level, did the study examine different levels of the exposure as related to the outcome (e.g., categories of exposure, or exposure measured as continuous variable?) 9. Were the exposure measures (independent variables) clearly defined, valid, reliable, and implemented consistently across all study participants? 10. Was the exposure(s) assessed more than once over time? 11. Were the outcome measures (dependent variables) clearly defined, valid, reliable, and implemented consistently across all study participants? 12. Were the outcome assessors blinded to the exposure status of participants? 13. Was loss to follow-up after baseline 20% or less? 14.
|
084319_file02 | ## Supplementary Text 2.
Direction of causation for non-genetic, intergenerational effects
As a follow-up analysis to the presented Children-of-Twins model, we ran a direction of causation model that included causal paths running from offspring-to-parent and parent-to-offspring (Figure S3). The logic underlying direction of causation models has been discussed elsewhere, as has the application of these models to combined Children-of-Twins and child twin data.
In short, direction of causation can be tested using cross-sectional family data for variables that differ in their aetiology (i.e., relative magnitudes of direct genetic and shared environmental influences). When there is a causal relationship between two traits, and these traits differ in their aetiology, the covariance between the traits can be used to determine the direction of causation. For example, if X causes Y, and X is more heritable than Y, then the covariance between X and Y will be driven by genetic factors. As such, the covariance decomposition between X and Y can be used to trace the origins of their association. Put another way, the variance components of X can be thought of as instrumental variables in their prediction of Y, as they only become associated with Y via causal influence of X on Y.
We adapted the model specification introduced by Narusyte et al., where causal intergenerational paths run from parent-to-offspring (m) _and_ offspring-to-parent (n) traits, alongside the A1' path for genetic transmission (Figure S3). We made the same amendments to the model specification as discussed in Supplementary Text 1 for the standard model (i.e., we include rEmz and rEdz parameters; and specify the model to ensure that MZ twin children share an identical A1' factor). Further, we ran several iterations of the model to account for possible bias introduced by measurement error.
Measurement error is an important consideration in all tests of causality between variables. If significant measurement error is present (as is the norm in behavioural science, where variables are rarely measured without considerable error), then this must be modelled to avoid biasing other parameter estimates. In direction of causation twin models, measurement error (\(\varepsilon\)) is not subsumable as unshared environmental variation (E), as is the case in the standard factor models. When researchers lack the data required to specify a value for \(\varepsilon\) a priori (i.e., when measurement error is unknown, as was the case in our analyses), then \(\varepsilon\) should be freely estimated within the model. In direction of causation Children-of-Twins models, it is not possible to estimate \(\varepsilon\) separately for two variables alongside the causal paths m and n - this model (as shown in Figure S3) is not identified.
Narusyte et al. incorporate a freely estimated \(\varepsilon\) parameter in their reciprocal direction of causation Children-of-Twins model, with \(\varepsilon\) contributing directly to variance in both generations. Their model is identified because \(\varepsilon\) is fixed to be equal across both variables (i.e., fixing \(\varepsilon\)1 and \(\varepsilon\)2 to equality in Figure S3). However, the validity of this method is undermined if true measurement error differs between variables. To avoid this pitfall, we followed a protocol suggested by Heath et al., who showed that measurement error need only be estimated for the _predictor_ variable in unidirectional causal models (i.e., estimating only \(\varepsilon\)1 if modelling only a parent-to-offspring causal path; and estimating only \(\varepsilon\)2 if modelling only an offspring-to-parent path), and doing so gives an unbiased estimate of the causal influence of predictor on outcome. We ran sequential univariate causal models to derive parameter estimates that were not biased. Results are presented in Table S5, panel A, and show that our data were explained equally well by causal paths in either direction. Model fit statistics provided no clear reason to choose one model over the other. Because these models showed overlapping confidence intervals for \(\varepsilon\) estimates in both generations, we next followed the Narusyte et al. method of fixing \(\varepsilon\) estimates in both generations to equality, to simultaneously estimate parentto-child and child-to-parent effects. Results are provided in Table S5, panel B, and show that neither causal path was estimated as significantly different from zero. Further, it was possible to drop either the parent-to-offspring (m) _or_ the offspring-to-parent (n) paths from this model without compromising model fit.
By applying these tests regarding the direction of causality, we hoped to identify whether the non-genetic association between parental criticism and offspring internalising symptoms could best be conceptualised as a unidirectional parent-to-offspring or offspring-to-parent effect, or by bidirectional effects in both directions. We found no clear evidence to help in differentiating between these possibilities (Table S5).
There are a number of interrelated possibilities that may explain our inability to distinguish direction of causation. Primarily, the aetiological structures of our phenotypes were likely too similar to distinguish reciprocal causation. Although adolescent internalising symptoms were more heritable than parental criticism, their overall aetiologies were perhaps not different enough to be distinguishable in our sample. This is shown by the overlapping confidence intervals for parent and offspring trait heritability (A1 and A2) in the bidirectional model (Table S5, panel B). It may have been easier to distinguish the'm' and 'n' paths if C2 were significant, because C2 would impact upon the parent-offspring covariance structure via the offspring-to-parent 'n' path. Further, variance explained by measurement error (\(\varepsilon\)) did not differ significantly between variables, again adding to their homogenous composition. As demonstrated via previously published power calculations, statistical power to establish causality depends on the relative degrees of measurement error in both variables, as well as the underlying aetiological structure of the phenotype. Finally, causality between variables, in either direction, is a major assumption in direction of causation analyses. Although we show that the association between parental criticism and adolescent internalising symptoms was not attributable to genetic factors in our sample, influence by common causes in the nuclear family environment (e.g., neighbourhood stressors, socio-economic factors, or other family members) remained possible. Influence by non-genetic confounders may have contributed to our inability to distinguish intergenerational causal paths.
1. Heath AC, Kessler RC, Neale MC, Hewitt JK, Eaves LJ, Kendler KS. Testing hypotheses about direction of causation using cross-sectional family data. _Behav Genet._ 1993;23:29-50.
2. Narusyte J, Neiderhiser JM, D'Onofrio BM, et al. Testing different types of genotype-environment correlation: an extended children-of-twins model. _Dev Psychol._ 2008;44:1591-1603.
3. Duffy DL, Martin NG. Inferring the direction of causation in cross-sectional twin data: theoretical and empirical considerations. _Genet Epidemiol._ 1994;11:483-502.
4. McAdams TA, Rijsdijk FV, Zavos HM, Pingault J-B. Twins and causal inference: Leveraging nature's experiment. _Cold Spring Harbor Perspectives in Medicine._ 2020.
## Figure S3.
Model specification for a two-sample direction of causation Children-of-Twins model, used to decompose the association between parental criticism and adolescent internalising symptoms a. Sample of M2G2 wine with one adolescent latins with one percent per twin pair.
**A. Testing unidirectional causation: measurement error estimated for the predictor variable** |
092965_file03 | ## S2 Burst model
The continuous-production model is more likely to be relevant for SARS-CoV-2 (Park et al., 2020), and was therefore chosen in the main text. Here we examine how a burst model would affect our findings. In a burst model, we assume that virus is produced in an infected cell but is only released to the environment upon cell death. The number of virus particles released is therefore a random number which we again denote by \(N\).
In the corresponding reactions in Eq. (S1), we need to replace the virus production and cell death lines by
\[I_{2}\overset{\delta}{\longrightarrow}\eta NV_{I}+(1-\eta)NV_{N1}.\] (S4)
In order to be consistent with the continuous-production model, we set the mean of the burst size to \(p/\delta\).
In the following we assume that the overall burst size \(N\) is Poisson-distributed. There are two reasons for this choice: (i) it is analytically relatively easy to handle, and (ii) it represents the other end of the spectrum of negative-binomially distributed burst sizes when compared to the continuous-production model which is equivalent to a geometrically-distributed burst size and thus providing an upper bound for the establishment probability of a viral infection under different forms of virus release from infected cells. A negative binomial distribution is defined by a success probability \(q\) and a dispersion parameter \(r\). The mean is given by \(qr/(1-q)\). It relates to the geometric distribution by setting \(r=1\) and to the Poisson distribution by letting \(r\rightarrow\infty\). The probabilities of establishment for the continuous-production model and the Poisson-distributed burst size model represent the two extremes of negative-binomially distributed burst size models with dispersion parameter \(r\in(1,\infty)\). This holds because the establishment probability can be computed by the probability generating function (Haccou et al., 2005) which is continuous and monotone in the dispersion parameter \(r\).
\[g(z)=\left(\frac{1-q}{1-qz}\right)^{r},\] (S5)
### Establishment probability
We compute the establishment probability of the virus in the burst size model. A key ingredient is the offspring distribution of a single virus particle. The offspring distribution is given by a zero-inflated Poisson distribution:
\[\mathbb{P}(0\text{ infectious virus offspring})=\underbrace{\frac{c}{c+ \beta T}}_{\text{no cell infected infected infected cell with 0 virions produced}},\] (S6) \[\mathbb{P}(j\text{ infectious virus offspring})=\frac{\beta T}{c+\beta T }\frac{(\eta N)^{j}}{j!}e^{-\eta N},\quad\text{for}\,j\in\{1,2,3,...\}.\]
Note, that we are only considering infectious virus particles here because non-infectious virus particles do not affect the future virus dynamics.
The life cycle of a virus (conditioned on infecting a cell) is given by a three step process: cell infection, eclipse phase and virus production within an infected cell. Ignoring this time delay which is irrelevant if we just consider the establishment probability, the virus population can be modeled by a discrete time branching process. At each time, all infectious virions alive at the time step before produce a random number of (infectious) virions according to the offspring distribution given in eq. (S6).
The extinction probability of a time-discrete branching process, when starting with one infectious virus particle, is given by the non-trivial fixed point of the probability generating function of the offspring distribution, i.e. the fixed point in the interval \(\)(Haccou et al., 2005).
\[g(z)=\mathbb{E}[z^{\eta N}]=\frac{c}{c+\beta T}+\frac{\beta T}{c+\beta T}e^{ \eta N(z-1)},\] (S7)
The fixed point of this function is given as
\[z^{*}=\frac{c}{c+\beta T}-\frac{W\left(-\eta N\exp\left(-\eta N\frac{\beta T}{ c+\beta T}\right)\right)}{\eta N},\] (S8)
It is defined for \(x\geq-\exp(-1)\). For values below this threshold, we need to solve eq. (S7) numerically. In fact, when plotting the establishment probability in Fig. S1 below, we solve eq. (S7) numerically because the approximation of the Lambert-W function \(W(x)\) is inaccurate for negative \(x\), especially when close to \(-\exp(-1)\).
The establishment probability, denoted \(\varphi\), is then given by
\[\mathbb{P}(\text{virus survives})=\varphi=1-\min(1,z^{*})^{V_{I}},\] (S9)
For alternative derivations of this result see also Pearson et al. and Conway et al..
## S3 Comparison of the continuous-production and burst model
We compare the establishment probability from the burst model described above with that obtained in the continuous-production model. Redrawing the first row of from the main text and comparing it with the corresponding graphs obtained from the burst model, we do not see any qualitative difference between the two models, cf. Fig. S1. As outlined in Section S2, the two studied models can be seen as the extreme values of a model continuum. By varying the dispersal parameter \(r\) of the negative binomial distribution, one can explore the entire continuum between the geometrically distributed burst size (which is equivalent to the continuous-production model) and the Poisson-distributed burst size model. Therefore, it seems safe to say that the exact mechanism by which we implement virus production in the model will only result in (minor) quantitative differences on the probability of virus establishment.
\begin{tabular}{c||c|c|c|c}
## Parameter set** & \(\eta p\) [\(d^{-1}\)] & \(T_{0}\) **[cells]** & \(\eta N\) **[virtons]** & \(R_{0}\) **[cells]
\\ \hline Low burst size (LowN) & 11.2 & \(4\times 10^{4}\) & 18.8 & 7.69 \\ High burst size (HighN) & 112 & \(4\times 10^{3}\) & 188 & 7.69 \\ \end{tabular}
Table S1: **Model parameters used in the main text and for the simulations in Fig. S1.** The remaining parameters are not changed between the simulations and are set to: \(k=5\ d^{-1}\), \(\delta=0.595\ d^{-1}\), \(c=10\ d^{-1}\), \(\beta=c\delta R_{0}/(T_{0}(\eta p-\delta R_{0}))\ d^{-1}\), \(\eta=0.001\).
Figure S1: **Comparison of establishment probabilities in the continuous-production and burst model.** The first row is the same as the first row in in the main text. The second row corresponds to the burst model. Theoretical approximations of the establishment probability for the burst model are obtained from Eq. (S9) adapted to the different scenarios.
## S4 Establishment probability when starting with a single infected cell
In this section, we investigate how the establishment probability changes if treatment is started when there is already an infected cell within the host. This situation might be more realistic to post-exposure treatment where infectious virus from the initial inoculum might have already infected a target cell (if the virus was not cleared). Instead of starting with a viral inoculum, we thus need to consider the situation where an infectious cell is already producing virus (but has not yet produced an infectious virus particle). The reasoning for computing the establishment probability is then as follows: we combine the establishment probability with initially \(j\) infectious virus particles with the probability for this infected cell to produce \(j\) infectious virus particles. As we have seen in Section S1.1 the number of infectious virus particles produced by an infectious cell is geometrically distributed with success parameter \(\delta/(\delta+\eta p)\).
\[\begin{split}\psi&=\sum_{j=1}^{\infty}\underbrace{ \left(\frac{\eta p}{\eta p+\delta}\right)^{j}\left(\frac{\delta}{\eta p+\delta }\right)}_{j\text{ infectious virus particles}}\underbrace{\left(1-(1-\varphi)^{j} \right)}_{\text{est. prob. for $j$ inf. virions}}\\ &=\left(\frac{\delta}{\eta p+\delta}\right)\sum_{j=1}^{\infty} \left(\frac{\eta p}{\eta p+\delta}\right)^{j}\left(1-\left(1-\frac{R_{0}-1}{ \eta N}\right)^{j}\right)\\ &=\frac{p(R_{0}-1)}{\delta N+p(R_{0}-1)}\\ &=1-\frac{1}{R_{0}}\,.\end{split}\] (S10)
This result has also been derived in Duwal et al. for a similar model in the context of HIV prophylaxis.
In our high burst size parameter set, there is no visible difference between treatment with a drug reducing productivity \(p\) and a drug reducing viral infectivity \(\beta\) (Fig. S2b). However, for the low burst size parameter set, in contrast to what we found in the main text when initializing the system with a viral inoculum, now drugs reducing the infectivity \(p\) (blue) stronger reduce the establishment probability than drugs reducing the infectivity \(\beta\) (orange), cf. Fig. S2a. This is explained by the order in which the drugs act: while a drug reducing viral production can immediately lower the chances for a further virus propagation, drugs reducing infectivity need to 'wait' for their targets, the extra-cellular virus, to arrive.
Figure S2: **Establishment probability when starting with a single infected cell.** We compare the theoretical prediction (solid lines) of Eq. (S10), adjusted for an antiviral drug affecting either virus productivity or virus infectivity, with stochastic simulations in the (a) LowN and (b) HighN parameter set. In the theoretical derivation of the results, target cells are fixed to their initial values. In the stochastic simulations, this number is allowed to decrease after cell infection. Averages of 10,000 realizations are depicted as dots. In contrast to the finding in the main text, in the LowN parameter set drugs reducing viral production \(p\) reduce the establishment probability stronger than antivirals reducing infectivity \(\beta\). This difference becomes negligible in the HighN parameter set.
## S5 Combination therapy in the HighN parameter set
We investigate the effect of combination therapy in the high burst size parameter set (Table S1). We find that the overall shape of the curves do not change compared to the LowN parameter set. A higher burst size decreases the establishment probability of the virus. If we compare Fig. S3(b) with in the main text, we see that a ten-fold increase of the initial inoculum in the HighN parameter set (\(V_{0}=10\)) gives similar quantitative results as the LowN parameter set with \(V_{0}=1\). This can be attributed to our ten-fold increase of the burst size when deriving the HighN parameter set from the LowN parameter set.
## S6 Time to detectable viral load
In this section, we study the mean time to reach a certain amount of viral load at the infection site within the host. We approximate this time using a mixture of deterministic and stochastic arguments. Classical branching processes typically have two possible outcomes: either the process goes extinct or grows indefinitely (Haccou et al., 2005). The deterministic model is captured by the mean of such a branching process, i.e. it takes into account both possible outcomes. Therefore, if we condition the branching process on survival, the deterministic model will typically underestimate the actual size of the corresponding branching process (Desai and Fisher, 2007). One can correct this error by rescaling the deterministic process by the probability of survival. In our specific setting this means that the total number of virus particles at any time \(t\), \(V(t)=V_{I}(t)+V_{NI}(t)\), can be estimated as follows:
\[\begin{array}{l}\mathbb{E}[V(t)]=\varphi(t)\mathbb{E}[V(t);V(t)>0]+(1-\varphi (t))\underbrace{\mathbb{E}[V(t);V(t)=0]}_{=0}\\ \Longleftrightarrow\ \ \mathbb{E}[V(t);V(t)>0]=\frac{\mathbb{E}[V(t)]}{\varphi(t)}, \end{array}\] (S11)
To compute the time for the viral load to reach a certain threshold we set \(\varphi(t)=\varphi\). In other words, we approximate the survival of the branching process until time \(t\) by the total establishment probability expressed in eq. in the main text. This is a good approximation if the 'typical' time \(t\) to reach the threshold is large enough, so that \(\varphi(t)\) is already close to the limit survival probability \(\varphi\). The other term on the right-hand side in eq. (S11), the mean of the stochastic process \(\mathbb{E}[V(t)]\), can be approximated by the deterministic model of the within-host model defined in eq. in the main text.
As explained in the main text, we set the threshold viral load \(2,000\) virions (in the main text). The mean time to reach this threshold value is then approximated by the time when the size \(2,000\times\varphi\) is reached in the deterministic model.
### Growth rate of the viral population to leading order
The exponential growth rate of the deterministic model described in eq. in the main text is given by the leading eigenvalue of the system when evaluated at the origin, i.e. at zero virions Bonhoeffer et al.. For efficacies close to the critical efficacy, the eigenvalue is small and can therefore be approximated by the root of a linear equation instead of a higher order polynomial. This approximation yields \(\frac{R_{0}-1}{\frac{1}{c+\beta P_{0}}+\frac{1}{k}+\frac{1}{\beta}}\) as the leading eigenvalue. A _Mathematica_ notebook showing this calculation is deposited at: gitlab.com/pczuppon/virus_establishment.
### Explaining the shape of the curves in of the main text
In this section, we provide more detailed explanations about the shapes of the establishment time curves depending on the mode of action of the drug. Throughout this discussion, it isimportant to keep in mind that for the average establishment times, only trajectories that result in establishment are taken into account. To ease the discussion, Fig. S4 shows from the main text.
Treatment that targets the virus infectivity \(\beta\) does not increase the establishment time because these drugs do not affect the virus dynamics itself. Conditioned on virus establishment, the initially present virus particle will infect a target cell relatively quickly, i.e., on a similar time scale than without treatment, and then follow the same dynamics as without treatment. Since the burst size largely exceeds the detection threshold, in our model just two infected cells are sufficient to reach this threshold. Therefore, the establishment time remains largely unaffected by drugs targeting the infectivity \(\beta\).
For drugs increasing the infected cell death rate \(\delta\), the trajectories that contribute to the results in Fig. S4 are the ones that produced a large number of virus particles from a single cell in a short time. This is because of the strongly increased cell death rate for large values of efficacy \(\varepsilon_{\delta}\). Therefore, a surviving virus trajectory needs to reach large numbers of virus particles in a short time to avoid extinction. This is different for a reduced viral production \(p\) where the infected cell death rate is unaffected. Therefore, it is not necessary for a surviving virus trajectory to reach high viral loads very quickly, even though this is of course possible which is reflected by the large 90% confidence interval. This is visualized in Fig. S4, panel B: green trajectories correspond to drugs affecting the cell death rate and blue trajectories correspond to drugs reducing viral production.
Lastly, increasing the viral clearance rate \(c\) by prophylactic treatment increases the establishment time with increasing efficacy, but not as much as treatment with drugs that reduce viral production \(p\). The reason here is that clearance acts just after the viral production, i.e., there is time passing between the production of a virus particle and its clearance. Hence, reducing virus production has a stronger effect on the establishment time than an increase of viral clearance \(c\) which acts later in the viral life cycle.
## S7 Parameter estimation
Patient data from Young et al. were fitted using the set of differential equations presented in eq. in the main text. To ensure identifiability of critical parameters of the viral dynamics, i.e. the basic reproductive number \(R_{0}\), the loss rate of infected cells \(\delta\) and the viral production \(p\), the remaining parameters \(c\), \(k\) and \(V_{0}\) were fixed. Viral clearance \(c\) was fixed to \(10\) day\({}^{-1}\). For the eclipse phase \(k\) we chose \(5\) day\({}^{-1}\) and the initial inoculum \(V_{0}\) was set to \(1/30\) copies.mL\({}^{-1}\) (see Goncalves et al. for further details). Parameters were estimated in a non-linear mixed effect model using the SAEM algorithm implemented in Monolix (www.lixoft.com). The best fit using all available patient data resulted in the parameter values \(R_{0}=7.69\), \(\delta=0.595\) and \(p=11,200\), the principal data set used in the main text (LowN parameter set).
### Parameter estimates for individuals plotted in in the main text
Applying this method to data from four single patients in Young et al., we obtain the best parameter set for each individual. These individual parameter sets were used to plot the deterministic curves in from the main text. The exact parameter values are given in Table S2.
Sensitivity analysis with respect to variations in the fraction of infectious virus particles \(\eta\)
We evaluate how different choices of \(\eta\), the fraction of infectious virus among all produced virus particles, affect the estimates of the within-host reproductive number \(R_{0}\) and the burst size \(\eta\). In the main text, we have used the parameter estimate with \(\eta=10^{-3}\) which resulted in \(R_{0}=7.69\) and \(N=18,823\). For a larger fraction of infectious virus particles, \(\eta=10^{-2}\), we find \(R_{0}=5.3\) and \(N=3,303\); for a smaller fraction of infectious virus particles, \(\eta=10^{-4}\), we obtain \(R_{0}=9.2\) and \(N=349,367\). While the within-host reproductive number \(R_{0}\) does not vary too much between the different choices of \(\eta\), the burst size \(N\) shows large variation. This has no effect on our results on the establishment of a SARS-CoV-2 infection because the burst size always enters in the form of a product with \(\eta\). In all the different scenarios above, the product \(\eta\times N\) varies between \(18\) for \(\eta=10^{-3}\) and \(35\) for \(\eta=10^{-4}\).
Overall, the differences in estimates for \(R_{0}\) will affect the precise estimate of the critical efficacy and differences in the estimate for \(N\) translate to differences in the quantitative valuesof the establishment probability curves below the critical efficacy. The predictions on the detection and extinction time strongly depend on the overall burst size \(N\) so that these will vary considerably depending on the choice of \(\eta\).
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093484_file02 | ## Appendix, Berkson's Bias and Residual Confounding
This appendix addresses topics of Berkson's bias and residual confounding. To do so, it includes analyses of weekday vs. weekend fever rates and fever rates in a large U.S. study of the general (non-medical) population (_n_=6,535), which may be of independent interest to some readers.
## Background
In this study, the analyzed body temperatures were taken from patients presenting to emergency departments. Consequently, the morning and evening temperatures come from different groups of patients--namely, from patients who went to emergency departments in the morning and from those who went to emergency departments in the evening. This raises the possibility that the differences between the observed morning and evening fever rates do not result from differences in the actual rates of fever at these times, but instead result from other differences between the patients seen during mornings and evenings.
In the main text, we used a multivariable logistic regression approach to control for time-of-day differences in 12 variables. This controlling produced almost no change in the fever rates, which substantially raises our confidence that the findings do not result from time-of-day differences in the case mix of patients seen at emergency departments. However, it remains possible that the controlling was not sufficient to address confounding or that the findings are affected by selection bias in the form of Berkson's bias--possibilities addressed in this appendix.
There are several names for Berkson's bias, including Berkson's fallacy, Berkson's paradox, Berksonian bias, collider selection bias, and collider stratification bias.\({}^{1,2}\) Berkson's bias may alter the estimated relationship between an exposure and outcome when a study is limited to apatient group, and when the exposure and outcome affect membership in that group. For the current study, the bias could apply because the study is limited to patients presenting to emergency departments (patient group), and because both time of day (exposure) and body temperature (outcome) can affect the decision to go to an emergency department. Explained in common language, Berkson's bias could be expected to arise in the following way: If it is harder to go to the emergency department at some times of day than others, a more substantial collection of symptoms may be necessary to induce an emergency department visit at these times. Since the presence of fever may make an individual's overall extent of symptoms more substantial, this could result in an inverse association between convenient times of day and fever rates, unrelated to the rhythms of body temperature in disease.
For technical discussion of Berkson's bias, we refer the reader to articles by Westreich and Snoep et al. As these show, an important feature of Berkson's bias is that it is not eliminated by using multivariable regression to control for confounders. Instead, it can be addressed by considering the underlying logic of the situation, through sensitivity analyses, and by analyzing a general population (nonmedical) dataset, and by referring to previous research. These points are also relevant to residual confounding. We address them below.
### Underlying logic
In our study, fever rates are higher at the more convenient times of day (after work and during the evening; **Figure 1, Supplementary Figure S1**). This is contrary to the effect we generally expect from Berkson's bias, but is consistent with the circadian rhythm of body temperature. Considering the underlying logic in this way suggests that, if present, Berkson's bias would be likely to dampen the size of the morning-evening difference, rather than inflate it.
#### Sensitivity analyses
We compared fever rates during weekdays and weekends as a check on the potential effects of Berkson's bias and, more generally, the effects of differences between weekday and weekend schedules on the observed fever rates. Such effects could arise, for example, since the decision to go to the emergency department can be affected by work and schooling hours, and by the hours and days that alternative sources of care are open (such as primary care physicians' offices). Work shifts, school times, and alternative care availability are the main mechanisms through which we anticipate Berkson's bias and residual confounding could occur during daytime hours, and we therefore think the weekday vs. weekend comparison should be a revealing assessment for both.
We found that the time of day variation in fever rates was similar on weekdays and weekends, as shown in Figure A below. The similarity between weekday and weekend results is contrary to the anticipated mechanisms of Berkson's bias and residual confounding, but matches with the physiological consistency that is expected for the circadian rhythm of body temperature.
Our previous research also includes comparisons of weekend and weekday fever rates for other fever definitions, also with similar results.3
## Appendix on Berkson's bias, Figure A. Time-of-day variation in the rate of fever (temperature \(\geq\)100.4\({}^{\text{o}}\)F, \(\geq\)38.0\({}^{\text{o}}\)C), comparing weekdays and weekends.
The time-of-day cycle of fever rates is similar during weekdays and weekends, suggesting that the cycle of fever rates is not a consequence of daily schedule changes or the availability of alternative sources of care. Curves are from logistic regressions using a cyclic cubic spline term with knots placed at quintiles of the recorded times of day and midnight. To illustrate the correspondence between the data and the curves, points are also shown with the average time and fever rate for every 20% segment of the recorded times of day. As in the previous figures, national study results are nationally representative of adult visits to US emergency departments. Confidence bands are 95% (pointwise).
As a further check for Berkson's bias, we analyzed body temperatures from a large general population (non-medical) study of the United States, the National Health and Nutrition Examination Survey (NHANES) I. Analyzing general population body temperatures is also useful to examine the generalizability of our emergency department findings.
_Methods:_ NHANES I was performed in 1971-1975 to evaluate the health of the general US population. Despite the age of this study, it appears to be the largest collection of general population body temperatures that is currently available. Perhaps because of this, NHANES I body temperatures have been the subject of renewed interest, including in a prominent study by Protsiv et al. Clinical examination data are available from 23,808 persons age \(\leq\)75. Time of day was recorded during clinician-performed blood pressure assessments that were given to 6,877 adults, all of whom were age 25-75. Of the adults with time of day records, 339 were missing body temperature measurements, 2 had unrealistically low body temperatures indicating measurement error (\(<\)95.0\({}^{\circ}\)F, \(<\)35.0\({}^{\circ}\)C), and 1 was missing information on obesity status. We excluded these individuals and analyzed body temperatures for the remaining 6,535 persons.
Analyses of NHANES I can provide nationally representative findings by accounting for the survey's design. However, because temperatures and times were only available for a subset of individuals, we chose not to account for the survey design in the analyses, meaning that the results are not nationally representative estimates, but should instead be interpreted as coming from a cohort study of 6,535 persons.
Body temperatures were measured by a clinician using oral mercury thermometers. Because of the non-medical population under study, high temperatures were much rarer than in the emergency department data. Of the 6,535 analyzed individuals, 1 had a temperature \(\geq\)100.4\({}^{\circ}\)F (\(\geq\)38.0\({}^{\circ}\)C), 6 had a body temperature \(\geq\)100.0\({}^{\circ}\)F (\(\geq\)37.8\({}^{\circ}\)C) and 30 had a body temperature \(\geq\)99.5\({}^{\circ}\)F (\(\geq\)37.5\({}^{\circ}\)C). The lack of temperatures \(\geq\)100.4\({}^{\circ}\)F (\(\geq\)38.0\({}^{\circ}\)C) prevented analyses of this fever threshold, and analyses were therefore restricted to \(\geq\)100.0\({}^{\circ}\)F (\(\geq\)37.8\({}^{\circ}\)C) and \(\geq\)99.5\({}^{\circ}\)F (\(\geq\)37.5\({}^{\circ}\)C).
The examinations were performed from morning to evening, with 95% of all times of day falling between 9:05 AM and 9:20 PM. Older individuals were somewhat less common at evening examinations, and multivariate adjustment was therefore performed, following the same approach used for the NHAMCS national study of emergency department data. The following covariates were included in the multivariate adjustment: gender (coded as male or female in NHANES I), age (analyzed a continuous variable using a spline with knots at ages 35, 45, 55, and 65), race (coded as black, white, or other in NHANES I), and obesity (coded as present or absent in NHANES I).
_Results:_ As shown in Figure B, fever rates increased from morning (before noon) to evening (after 6 PM) for both investigated fever definitions. Multivariate-adjusted analyses continued to show increased fever rates from the morning to the evening. For the \(\geq\)99.5\({}^{\circ}\)F (\(\geq\)37.5\({}^{\circ}\)C) fever definition, the morning-to-evening fever risk ratio was 0.23 (95% CI 0.09-0.64) in the unadjusted analysis and 0.24 (95% CI 0.09-0.67 in the adjusted analysis). For the \(\geq\)100.0\({}^{\circ}\)F (\(\geq\)37.8\({}^{\circ}\)C) fever definition, the morning-to-evening fever risk ratio was 0.00 (95% CI 0.00-0.86 ) in the unadjusted analysis and was statistically undefined in the adjusted analysis because no fevers in this range occurred during mornings.
_Discussion:_ Analysis of body temperatures from the general population continued to show increased fever rates from morning to evening, providing further support for a physiological origin of this morning-evening difference, rather than the alternative that it results from Berkson's bias.
However, there are several limitations to the general population results, including the rarity of fever-range temperatures in the studied cohort and the lack of overnight temperatures. Additionally, it is not clear whether NHANES I fever rates accurately estimate fever rates in the general population, or if individuals with fever were predisposed to not show up to their NHANES I examinations because they were sick. Yet, even if the latter possibility is true, it would be expected to lead to a reverse of the effects of Berkson's bias for emergency departments (where fever increases the chance of presentation, rather than decreasing it), meaning that the observation of morning-evening fever rate increases in both the general population and emergency department studies continues to support a physiological origin to this pattern.
In summary, findings from a general population cohort are consistent with morning-evening increases in fever rates that are physiological, rather than an artifact of Berkson's bias. Results also show that the morning-evening increases in fever rates occur outside of medical populations.
## Appendix on Berkson's bias, Figure B. Increasing fever rates by time of day in the general population study.
When analyzing a large (\(n\)=6,535) general (non-medical) population sample, the rate of fever-range temperatures continued to rise from morning to evening. This supports a physiological origin for the morning-evening difference in fever-range temperatures, rather than the alternative that Berkson's bias explains the morning-evening difference. However, there were too few fevers \(\geq\)100.4\({}^{\circ}\)F (\(\geq\)38.0\({}^{\circ}\)C; \(n\)=1) to be analyzed by time of day in the general population study, and the general population study also did not include post-midnight temperature measurements. Confidence intervals are 95%. The multivariable analysis adjusts for age, sex, race, and obesity status, but does not differ meaningfully from the unadjusted results.
### Previous research
In previous studies of the relationship between the circadian rhythm and fever, longitudinal data were collected on groups of hospital inpatients and healthy young men with experimentally induced fevers. Because of the longitudinal data collection in these studies, their results are not subject to Berkson's bias or confounding for morning-evening comparisons. Each study also showed a rise in fever-range temperatures from morning to evening, consistent with a physiological effect, though the sample sizes were not large enough to reliably evaluate the degree of morning-evening differences in those studies.
Drawing on previous research, numeric estimation also suggests that circadian physiology can cause fever-range temperatures (\(\geq\)100.4\({}^{\circ}\)F, \(\geq\)38.0\({}^{\circ}\)C) to be half as common in the morning as in the evening--consistent with the morning-evening change observed in our study, without involving any Berkson's bias or residual confounding. The estimation proceeds as follows: Healthy body temperatures reportedly change an average of 0.9\({}^{\circ}\)F (0.5\({}^{\circ}\)C) from the morning low to the evening high as part of the physiology of the circadian rhythm. Additionally, the morning-evening temperature change in febrile disease is usually at least as large or larger than observed in health. In our Boston study, of all the body temperatures that were in the fever range in the evening (6 PM--midnight), 44% were at least 0.9\({}^{\circ}\)F above the fever threshold, and therefore would stay in the fever range in the morning if they reduced the average circadian amount. Similarly, in the national emergency department study, 48% of evening fever-range temperatures were at least 0.9\({}^{\circ}\)F above the fever threshold, and therefore would stay in the fever range in the morning if they reduced the average amount. So in both cases, estimation suggeststhat fever-range temperatures can be half as common in the morning as in the evening owing to circadian physiology alone, without any biases.
To examine the dependence of these estimates on the circadian temperature change, we also investigated average circadian changes of 0.5\({}^{\circ}\)F and 1.5\({}^{\circ}\)F, instead of 0.9\({}^{\circ}\)F. These alternative circadian changes produced morning-vs-evening fever rate ratios in the range of 0.34-0.72, which continue to be consistent with the morning-evening fever rate changes observed in our results, without involving potential biases.
### Summary
In this appendix, the potential consequences of Berkson's bias and residual confounding were examined through sensitivity analyses, analyses of a general population dataset, and consideration of previous research. Overall, the results are consistent with large morning-evening increases in fever rates that are physiological and not artifacts of Berkson's bias or residual confounding.
## Appendix, COVID-19 Fevers
This appendix provides an overview of fevers in COVID-19, including sections on the occurrence of fever, thresholds used for fever, and time-of-day variation in fever. The included summaries of the literature were last updated on September 21, 2020.
## Occurrence of fever in COVID-19
Fever is thought to be the most common COVID-19 symptom, and first symptoms often include fever. Currently, the amount of evidence on COVID-19 fever rates differs substantially by patient group.
The most evidence on COVID-19 fever rates is available for hospitalized patients, who generally have high rates of fever: 88.7%, including 43.8% on admission; 94.3%, including 87.1% at illness onset; 98.6% at onset; 30.7% on triage or admission; 83%, including 26% on admission; about 89% of symptomatic adult cases; 80.4% of severe and 82.4% of non-severe/common cases at onset; and 85.0% with fever or chills on admission. Fevers in hospitalized patients also present on many days (median fever days per patient: 9 in inpatients without ICU stays, 31 in inpatients with ICU stays, and 12 in surviving inpatients), which would allow multiple opportunities for screening detection if observations are similar outside the hospital setting (which is unknown). Examining the temperatures attained by febrile patients hospitalized with COVID-19 suggests that overall they are not unusually high, and do not stand out relative to the temperatures attained in common diseases like seasonal influenza.
Less evidence is available for residents of skilled nursing and assisted living facilities. In studies of skilled nursing facilities, fevers were noted in 39% of residents with confirmed COVID-19, 43% of residents with confirmed COVID-19, and 53% of those under investigation for COVID-19. The lower fever rates may result from older individuals' diminished ability to mount febrile responses.
Limited evidence is also available for the general population of patients with COVID-19 who have not been hospitalized and are not nursing facility residents. However, studies that have tracked new cases suggest fairly high rates of fever in this group, including reports of fever in 71% of contact-traced cases; 75.0% of healthcare personnel, including 41.7% at first onset; 55.4% of healthcare workers according to self-report and 85.0% of healthcare workers defined by temperature \(\geq\)37.5\({}^{\circ}\)C; at onset, 53.3% of index cases and 56.3% of household members they infected; self-reported by 57.5% of patients at times of positive COVID-19 tests; and self-reported by 48.7% of healthcare workers and 43.7% of others at times of positive COVID-19 tests. Additionally, in CDC analyses, fever was reported for 68% of healthcare personnel with COVID-19 and about 73% of symptomatic non-hospitalized adults.
Overall, reports to date show fever rates that are high during COVID-19's clinical course and intermediate at first onset. Our results on the daily cycle of fever rates suggest that some onset research could underestimate fever rates by using morning temperatures, but we cannot tell which studies are affected because none report temperature measurement times.
An added complication is that, in populations with sufficiently low COVID-19 prevalence,1 the number of false-positive test results can approach or exceed the number of true-positive test results, leaving open the possibility that false-positive cases may be confused for asymptomatic cases.35 If this is occurring, it would artificially increase the proportions of COVID-19 cases believed to be asymptomatic (and afebrile) in data from low-prevalence settings. On the other hand, asymptomatic cases are especially likely to go untested in many contexts, creating a contravening bias that could lead to underestimation of the proportion of COVID-19 cases that are afebrile. The competing biases make the overall fever rate in COVID-19 somewhat unclear, despite substantial study.
Footnote 1: Or very high rates of testing, such as the frequent retesting that is sometimes given to healthcare workers.
#### Temperature thresholds used for COVID-19
Several temperature thresholds have been used to define fever for COVID-19, such as >=100.4degF (>=38.0degC), >=100.0degF (>=37.8degC), and >=99.5degF (>=37.5degC). The large range of fever rates reported by previous studies of COVID-19 may be partially attributable to the choice of different fever thresholds in different studies. However, an added complication is that different thermometer sites (e.g., oral, temporal, tympanic, axillary, or rectal) have also been used by different studies, and that some of these sites generally attain lower temperatures in fever than do others.36 In particular, several studies using low fever thresholds have used axillary thermometers,25 which tend to show the lowest temperatures during fever. This complication leaves the overall relationship between temperature thresholds and COVID-19 fever rates unclear.
No information is currently available on an optimal fever threshold for COVID-19, overall or by thermometer site.
#### Time-of-day variation of fever in COVID-19
To our knowledge, no study has examined the time-of-day variation of fever in COVID-19. Further, we were unable to find any study of the time-of-day variation of fever in the related disease Severe Acute Respiratory Syndrome (SARS). However, in most febrile diseases, body temperature follows an exaggerated version of the healthy circadian rhythm, which reaches its minimum in the morning and its maximum in the late afternoon or evening. (In our study, this pattern of fever rates occurred during both the periods of high influenza activity and the remaining periods.) It remains to be seen whether body temperatures follow this usual pattern in COVID-19, or whether COVID-19 is an exceptional case.
If COVID-19 is an exceptional case, it is possible that its temperature low point may not occur during mornings. In this case, the solutions outlined in our main text may not be useful for COVID-19 prevention, though twice-daily screening could still mitigate the detection problems that are posed by time-of-day variation in fever rates, so long as at least one screening does not occur at the time of temperature low points.
#### Recommendations for future research
Overall, we hope that our research encourages study of fever's course in COVID-19, which could help improve screening practices, such as by identifying optimum times of day for screening. For reasons of practicality, an advantageous time for morning measurements may be directly before leaving for work or school. Based on the physiology of the circadian cycle, an advantageous time for evening temperature measurements could be directly before dinner, which is both near the circadian highpoint and precedes the small metabolism-associated increases in body temperature that follow dinner (and do not result from fever). Before-dinner measurement is also generally consistent with the fever rate highpoints in our analyses of general and influenza-caused fevers.
When planning future COVID-19 fever research, we recommend that investigators keep the following potential obstacles in mind: Inpatients with COVID-19 may not show a daily cycle of fever rates, or may show a distorted cycle. This is because circadian rhythms can be severely disrupted by poor sleep and other stressors of being an inpatient. Similarly, night workers may show a distorted or reversed cycle. Observed fever rates can be affected by Berkson's biases (**Appendix, Berskson's bias**). In populations with low COVID-19 prevalence or very high testing rates, many or most of the apparently asymptomatic and afebrile cases may be false positives, as discussed above. Lowering the fever threshold in the morning may help to compensate for the daily cycle of fever rates, but could adversely affect screenings for individuals whose circadian rhythms do not follow the usual pattern of a morning low and evening high, such as some inpatients and night workers.
## Appendix, Screening and Transmission
This appendix uses simple examples to explain how fever and other symptom screenings can confer benefits if they can modestly reduce disease transmission rates during outbreaks, following similar arguments that have been applied for public use of face masks.
Temperature screenings are used for COVID-19 because measurements are simple enough to be performed by non-clinicians, because fever is among the most common and earliest symptoms, because many or most symptomatic people appear not to self isolate until they receive positive test results, because symptomatic health care personnel have often kept working, and because false-negative test results are common, potentially resulting in individuals with symptomatic COVID-19 who continue to participate in work and daily activities because they think they do not have COVID-19. Temperature screenings have also been considered for future pandemic influenza events because fever is a common and early symptom of influenza. However, an important limitation to fever and other symptom screenings is that they cannot detect nonfebrile, asymptomatic, or presymptomatic cases, which are thought to occur substantially for both COVID-19 and influenza.
Despite symptom screenings' inability to detect some cases, they can still confer benefits that grow considerably in time if they are able to reduce disease transmission rates. For example, suppose that screening only modestly improves case detection and isolation, resulting in an average reduction of 15% in the number of people that each infected individual transmits theirdisease to.+ Then, on average, an infected individual would infect 15% fewer others, the people who are nevertheless infected by this individual would infect 15% fewer others, the people who are nevertheless infected by _these_ individuals would infect 15% fewer others, and so on, with the benefits of screening compounding at each generation of disease transmission. The consequence is that at the first, second, third, and fourth generations of transmission in a new outbreak, there would be roughly 85%, 72.3%, 61.4%, and 52.2% as many new cases as would otherwise occur (=85%"). In this way, over the span of only a handful of disease transmission generations, the modest 15% reduction in disease transmission translates into the large benefit of having only 52.2% as many new cases as would occur without screening.
Footnote †: In other words, this is a reduction of 15% in the disease’s \(R\) effective.
The growth of benefits is also why addressing screening failure points, like low morning fever rates, can be more beneficial than intuition may suggest: For example, if addressing this issue were to change the effect on transmission from a 15% reduction to a 25% reduction, then at the fourth generation of a new outbreak, there would be roughly 31.6% as many new case as would occur without screening, rather than 52.2%.
Importantly, the growth of benefits eventually stops following this exponential pattern as the growth of the outbreak stops being exponential itself. However, the benefits slow outbreaks, allowing more time to try case tracking and other limited countermeasures before closures and lockdowns become the only options for stopping extensive disease spread.
In previous studies, similar reasoning has been pursued with greater thoroughness to explain how large benefits can accompany other imperfect, partial measures of blocking disease transmission, in particular including public use of cloth and procedure face masks to reduce the spread of COVID-19. However, we caution that no similar analyses of workplace and school fever screening have been published to date.
## Appendix Methods
This appendix describes additional methods.
## Datasets and measurements
We performed the Boston study at the Beth Israel Deaconess Medical Center Emergency Department (September 2009-March 2012) using temporal artery thermometers connected to automatic data-loggers that recorded the measured temperatures and times. The national study was performed by the US Centers for Disease Control and Prevention as the emergency department components of the year 2003-2010 National Hospital Ambulatory Medical Care Surveys (NHAMCS), which are multi-stage probability sample surveys that provide nationally representative data on hospital emergency and outpatient visits, including visit records from December 2002 to December 2010. NHAMCS collected case records for every _n_th visit following a random start, with the mode of thermometry left to the discretion of participating clinicians and institutions.
For analyses of the Boston study, sample sizes were determined by the study duration. For analyses of the national study, sample sizes were determined by the years chosen for investigation. Years were selected to include a long period during which the survey design and the recorded variables of interest remained consistent enough to analyze together. Years were also chosen to provide some results predating the widespread use of temporal artery thermometers, to demonstrate that time-of-day variations in fever rates were also present beforehand (see original publication).
Please see the original publication that this research letter builds on for further details on patient demographics, dataset characteristics, measurement methods, and inclusion and exclusion choices. The original publication also includes sensitivity analyses that demonstrate robustness of study findings to changes in the exclusion criteria, and to the use of arrival times as substitutes for measurement times in the national study.
### Statistical analyses of the national study
We accounted for the national study's multistage design to obtain nationally representative findings. For the national study, time-of-day case mix differences in age (years, analyzed with spline), urgency/immediacy of case (4 levels and unknown), pain (4 levels and unknown), sex (male or female), race (black, white, or other), Hispanic or Latino ancestry (yes or no), hospital admission (yes or no), test ordering (yes, no, or unknown), procedure administration (yes, no, or unknown), medication ordering (yes, no, or unknown), ambulance arrival (yes, no, or unknown), and expected payment source (7 categories and unknown) were excluded as responsible factors for the time-of-day fever rate differences using multivariable logistic regression and average marginal predictions. Additional variables and categories for gender, race, and ethnicity were not available for some or all study years, and were therefore not analyzed. Additionally, for variables such as urgency/immediacy to be seen and degree of pain, some levels with more detail were merged to obtain consistent categories across study years.
As discussed in the original study, time-of-day variation in the studied characteristics was modest, which helps to explain why the adjusted and unadjusted results were broadly similar.
Cardiovascular events are known to vary by time of day, generally peaking in morning hours. However, the incidence of cardiovascular events was too small to meaningfully affect the time-of-day variation in fever rates (for example, cardiac arrest accounts for 0.17% of emergency department presentations). We therefore decided it was not necessary to control for cardiovascular events in the multivariate analyses.
Anonymity requirements prevented linkage of the Boston temperatures to patient characteristics, thereby preventing multivariate-adjusted analyses of the Boston data.
## Statistical analyses with time of day as a continuous variable
In some appendix figures, time of day was evaluated as a continuous variable instead of being binned (**Supplementary Figures S1, S2, A**). These analyses were performed using logistic regressions with cyclic cubic splines. They account for the national study's multistage design, though national representativeness may not be present in some results from the year-stratified analyses (**Supplementary Figure S2**) because some year-by-outbreak period strata include case records sampled from relatively few hospitals.
Evaluating time as a continuous variable helps to address the arbitrariness of choosing bin boundaries in binned analyses, as well as the possible sensitivity of results to choices of bin boundaries. However, spline results can still be somewhat sensitive to the choices of spline types and parameters, such as knot locations. Additionally, we caution that it is difficult to make inferences about the exact times of the daily minimum and maximum fever rates from the spline fits, owing to statistical uncertainties in these quantities and their potential sensitivity to choices of spline types and parameters, even in large datasets such as used for this study.
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095448_file02 | ## Figure S2. Global accumulation of genomic mutations of SARS-CoV-2.
Accumulation of genomic mutations of SARS-CoV-2 over time around the globe. Each data-point is represented as a bead, whereby each bead corresponds to a specific set of virus mutations (mutation haplotype). Beads and bead sequences are color-coded, according to the country where the virus sample was isolated from (bottom left). The 'beads-on-a-string' plots link successions of viral mutations, i.e. mutation haplotypes that acquired additional mutations over time. Phylogeny trees for such mutations are presented, that draw distinct evolutionary branches of SARS-CoV-2 over calendar dates (bottom) (nextstrain.org/ncov/). Larger beads indicate mutations identified in the indicated country. UK: bright yellow; Australia: blue; Canada: red. Rectangles enclose mutations evolutionary branches by country.
Accumulation of genomic mutations of SARS-CoV-2 over time in Europe. Each data-point is represented as a bead, whereby each bead corresponds to a specific set of virus mutations (mutation haplotype). Beads and bead sequences are color-coded, according to the country where the virus sample was isolated from (upper left). The 'beads-on-a-string' plots link successions of viral mutations, i.e. mutation haplotypes that acquired additional mutations over time. Phylogeny trees for such mutations are presented, that draw distinct evolutionary branches of SARS-CoV-2 over calendar dates (bottom) (nextstrain.org/ncov/europe?branchLabel=aa).
Accumulation of genomic mutations of SARS-CoV-2 over time in Spain is shown as strings of dark-yellow large dots. Each data-point is represented as a bead, whereby each bead corresponds to a specific set of virus mutations (mutation haplotype). The 'beads-on-a-string' plots link successions of viral mutations, i.e. mutation haplotypes that acquired additional mutations over time. Phylogeny trees for such mutations are presented, that draw distinct evolutionary branches of SARS-CoV-2 (nextstrain.org/ncov/europe?branchLabel=aa). Dark-yellow rectangles enclose successions of viral mutations in Spain in each phylogenetic branch.
The number of accumulated mutations in individual viral isolates is indicated at the bottom.
Color codes by country are shown in the upper left.
Accumulation of genomic mutations of SARS-CoV-2 over time in Italy is shown as strings of yellow large dots. Each data-point is represented as a bead, whereby each bead corresponds to a specific set of virus mutations (mutation haplotype). The 'beads-on-a-string' plots link successions of viral mutations, i.e. mutation haplotypes that acquired additional mutations over time. Phylogeny trees for such mutations are presented, that draw distinct evolutionary branches of SARS-CoV-2 (nextstrain.org/ncov/europe?branchLabel=aa). Yellow rectangles enclose successions of viral mutations in Italy in each phylogenetic branch.
The number of accumulated mutations in individual viral isolates is indicated at the bottom.
Color codes by country are shown in the upper left.
Accumulation of genomic mutations of SARS-CoV-2 over time in Sweden is shown as strings of red large dots. Each data-point is represented as a bead, whereby each bead corresponds to a specific set of virus mutations (mutation haplotype). The 'beads-on-a-string' plots link successions of viral mutations, i.e. mutation haplotypes that acquired additional mutations over time. Phylogeny trees for such mutations are presented, that draw distinct evolutionary branches of SARS-CoV-2 (nextstrain.org/ncov/europe?branchLabel=aa). Red rectangles enclose successions of viral mutations in Sweden in each phylogenetic branch.
The number of accumulated mutations in individual viral isolates is indicated at the bottom.
Color codes by country are shown in the upper left.
Accumulation of genomic mutations of SARS-CoV-2 over time in The Netherlands is shown as strings of bright-green large dots. Each data-point is represented as a bead, whereby each bead corresponds to a specific set of virus mutations (mutation haplotype). The 'beads-on-a-string' plots link successions of viral mutations, i.e. mutation haplotypes that acquired additional mutations over time. Phylogeny trees for such mutations are presented, that draw distinct evolutionary branches of SARS-CoV-2 (nextstrain.org/ncov/europe?branchLabel=aa). Bright-green rectangles enclose successions of viral mutations in The Netherlands in each phylogenetic branch. The number of accumulated mutations in individual viral isolates is indicated at the bottom. Color codes by country are shown in the upper left.
Accumulation of genomic mutations of SARS-CoV-2 over time in Belgium is shown as strings of light-green large dots. Each data-point is represented as a bead, whereby each bead corresponds to a specific set of virus mutations (mutation haplotype). The 'beads-on-a-string' plots link successions of viral mutations, i.e. mutation haplotypes that acquired additional mutations over time. Phylogeny trees for such mutations are presented, that draw distinct evolutionary branches of SARS-CoV-2 (nextstrain.org/ncov/europe?branchLabel=aa). Light-green rectangles enclose successions of viral mutations in Belgium in each phylogenetic branch.
The number of accumulated mutations in individual viral isolates is indicated at the bottom.
Color codes by country are shown in the upper left.
## Figure S9. Genomic mutations of SARS-CoV-2 - France.
Accumulation of genomic mutations of SARS-CoV-2 over time in France is shown as strings of deep-green large dots. Each data-point is represented as a bead, whereby each bead corresponds to a specific set of virus mutations (mutation haplotype). The 'beads-on-a-string' plots link successions of viral mutations, i.e. mutation haplotypes that acquired additional mutations over time. Phylogeny trees for such mutations are presented, that draw distinct evolutionary branches of SARS-CoV-2 (nextstrain.org/ncov/europe?branchLabel=aa). Deep-green rectangles enclose successions of viral mutations in France in each phylogenetic branch.
The number of accumulated mutations in individual viral isolates is indicated at the bottom.
Color codes by country are shown in the upper left.
## Figure S10. Progression of COVID-19 over Italy - Northern Provinces *.
*: Case incidence in the indicated municipalities is plotted versus time (days, from March 3 to March 27, 2020).
For comparison purposes, all graphs were normalized versus the highest number of cases per province. COVID-19 doubling times were computed on non-normalized, absolute numbers of infection cases.
Graphs are in alphabetical order by province name.
## Figure S11. Progression of COVID-19 over Italy - Central & Southern Provinces*.
Central
## Figure S12. Progression of COVID-19 over Italy - global data by region*.
Koppen-Geiger climate classification map. Compounded data of COVID-19 spreading in individual Italy's regions versus time (days, from March 3 to March 27, 2020) are overlaid over the country's climate areas. (_insets_) Dark gray dots: SARS-CoV-2-positive cases; brown dots: hospitalized cases; green dots: intensive-care unit cases; orange dots: recovered cases. (_bottom_) color codes for climate areas classification.
## Figure S13. Progression of COVID-19 over Spain*.
## Figure S14. Progression of COVID-19 over Norway*.
## Figure S15. Progression of COVID-19 over Finland*.
## Figure S16. Progression of COVID-19 over Sweden*.
## Figure S17. Progression of COVID-19 over France, Germany and UK*.
## Supplemental online Table 1
COVID-19 spreading in Central and South America.
*: cases were recorded from March 1 to March 23, 2020.
## Supplemental online Table 3
COVID-19 doubling time by province *.
\begin{tabular}{|l|r|l|} \hline & **Doubling** & **Geographical** \\ \hline AGRIGENTO & 6,67 & South \\ ALE5SANDRIA & 5,55 & North \\ ANCONA & 6,84 & Center \\ AOSTA & 6,29 & North \\ AREZZO & 5,86 & Center \\ ASCOLPICENO & 5,19 & Center \\ ASTI & 5,41 & North \\ AVELLINO & 6,06 & South \\ BARI & 4,90 & South \\ BAT & 3,97 & South \\ BELLUNO & 6,10 & North \\ BENEVENTO & 6,25 & South \\ BERGAMO & 9,65 & North \\ BELLA & 5,17 & North \\ BOLOGNA & 4,97 & North \\ BOLZANO & 6,12 & North \\ BRESCIA & 8,00 & North \\ BRINDISI & 7,54 & South \\ CAGLIARI & 6,55 & South \\ CATALNISSETTA & 4,50 & South \\ CAMPOBASSO & 6,33 & Center \\ CASERTA & 6,40 & South \\ CATANIA & 5,73 & South \\ CATANZARO & 6,21 & South \\ CHIETI & 5,64 & Center \\ COMO & 5,64 & North \\ COSEN2A & 4,10 & South \\ CREMONA & 10,94 & North \\ CROTONE & 6,22 & South \\ CUNEO & 5,01 & North \\ ENNA & 1,95 & South \\ FERMO & 5,00 & Center \\ FERRARA & 5,00 & North \\ FIRENGE & 5,89 & Center \\ FOGGA & 5,84 & South \\ FORLICESENA & 6,00 & North \\ FROSINONE & 4,86 & Center \\ GENOVA & 6,88 & North \\ GORIZIA & 4,69 & North \\ GROSSETO & 6,74 & Center \\ IMPERIAL & 7,50 & North \\ ISERNIA & 6,67 & Center \\ LAGUILA & 4,50 & Center \\ LASPEZIA & 7,81 & North \\ LATINA & 5,17 & Center \\ LECCE & 5,35 & South \\ LECCO & 5,95 & North \\ LIVORNO & 5,50 & Center \\ LODI & 15,60 & North \\ LUCCA & 6,48 & Center \\ MACERATA & 5,60 & Center \\ MANTOVA & 6,39 & North \\ MASSACARARA & 7,33 & Center \\ MATERA & 2,00 & South \\ MESSINA & 3,60 & South \\ MILANO & 6,38 & North \\ MODENA & 5,00 & North \\ MONZARIANZA & 5,07 & North \\ NAPOL & 6,45 & South \\ \hline \end{tabular}
NOVARA & 5,33 North NUORO & 14,33 South ORISTANO & 5,50 South PADOVA & 7,63 North PALERMO & 2,74 South PABRAMA & 6,12 North PAVIA & 9,15 North PERUGIA & 5,42 Center PESARO & 9,81 Center PECSARA & 6,27 Center PIACENZA & 9,20 North PISA & 5,63 Center PISTOIA & 6,78 Center PORDENONE & 4,18 North POTENZA & 5,62 South PRATO & 5,21 Center RAGUSA & 0,85 South RAVENNA & 5,70 North REGGIOEMILIA & 4,90 North RIETI & 4,75 Center RIMINI & 7,07 North ROMA & 5,53 Center ROFIGO & 6,45 North SALERNO & 5,22 South SASSARI & 5,70 South SAVONA & 7,81 North SIFNA & 5,63 Center SILRAACUSA & 6,20 South SONDRIO & 6,16 North TARANTO & 5,50 South TERNAMO & 4,31 Center TERNI & 6,25 Center TORINO & 5,29 North TRAPANI & 5,50 South TRENTO & 5,26 North TRENTO & 7,03 North TRIESTE & 7,83 North UDINE & 6,59 North VARESE & 8,00 North VERBANOCUSIOOSSOLA & 5,35 North VERCELU & 5,68 North VERONA & 6,57 North VIBOVALENITA & 3,83 South VICENZA & 6,39 North VITERBO & 5,15 Center & *: The COVID-19 doubling time was computed on province-base
## Supplemental online Table 4
COVID-19 spreading in Scandinavia by county *.
\begin{tabular}{|l|c|c|c|} \hline
## Sweden** & & & **Norway** \\ \hline & & & \\ & & & **Doubling** \\ & **Doubling time** & & **time
\\ \hline DALARNA & 7,17 & AGDER & 13,06 \\ \hline GAVLEBORG & 8,25 & INNLLANDET & 11,70 \\ HALLAND & 12,00 & MOREOGROSMDAL & 13,61 \\ JONKOPING & 7,91 & NORDAND & 10,17 \\ OREBRO & 6,86 & OSLO & 11,64 \\ OSTERGOTLAND & 8,70 & ROGALAND & 17,29 \\ SKANE & 23,92 & TROMSOGF & 11,98 \\ SODERMANLAND & 8,62 & TRONDELAG & 12,96 \\ STOCKHOLM & 9,64 & VESTFOLDOGT & 12,86 \\ UPPSALA & 8,19 & VESTLAND & 14,27 \\ VASTERBOTTEN & 6,79 & VIKE & 12,88 \\ VASTMANDLAND & 6,13 & & \\ VASTRAGOTALAND & 8,00 & & \\ \hline \end{tabular}
*: Landmark dates were the 9th of April for Sweden and the 7th of April for Norway.
## Supplemental online Table 5
COVID-19 cumulative incidence by date in France.
\begin{tabular}{c c} & TOTAL \\ DATE & CASES \\
\end{tabular}
## Supplemental online Table 6
COVID-19 cumulative incidence by date in Germany.
\begin{tabular}{c c} & TOTAL \\ DATE & CASES \\
\end{tabular}
## Supplemental online Table 7.
COVID-19 cumulative incidence by date in UK.
\begin{tabular}{c c} & TOTAL \\ DATE & CASES \\
\end{tabular}
21/03/20 5018
22/03/20 5683
23/03/20 6650
24/03/20 8077
25/03/20 9529
26/03/20 11658
27/03/20 14548
28/03/20 17104
29/03/20 19606
30/03/20 22271
31/03/20 25521
01/04/20 30088
02/04/20 34610
03/04/20 39282
04/04/20 43282
05/04/20 49481
06/04/20 53624
07/04/20 57512
08/04/20 63377
09/04/20 68052 |
098509_file02 | #1, 5 and 8, the DCS operated at 2 Hz. In all other patients the device operating software was updated, and FDNIRS-DCS was run at 10 Hz. Crosstalk between the DCS and FDNIRS components is eliminated by optical filters in front of the detectors. To comply with the American National Standards Institute's standards (ANSI), the DCS laser power was set at below 34 mW, the FDNIRS laser power between 2-3 mW, and the light at the probe was diffused over an area \(>\) 1mm. Measurements in patient #2 were done with a DCS-only device with the same design and laser as the DCS portion of the MetaOx system, but with only 4 photon-counting modules, as used in a study by Selb et al.
### Probe
Light sources and detectors from the device were connected via fiber optics to a soft rubbery 3D printed probe attached to the patient's head. All the fibers at the probe end were terminated with prisms to allow for a low probe profile. For light transmission to the patient, we used a single fiber cable that included the fiber bundle from the FDNIRS lasers and a 200 mm multimode fiber from the DCS laser. One single mode fiber located at 5 mm from the source collected the short separation DCS light. 4 fiber bundles at 2, 2.5, 3 and 3.5 cm distances from the source collected photons back to the FD-NIRS detectors. Some of these bundles also included DCS single mode detection fibers for a colocalized acquisition (in Manuscript).
### FDNIRS Data Analysis
We used custom MATLAB code for all data analysis. In preprocessing, we smoothed the 10 Hz FDNIRS AC and phase shift using a 50-point averaging window, down-sampling to 0.2 Hz. The FDNIRS data had interference from the hospital oximeter and affected data were removed during preprocessing. In two patients the interference was particularly strong, hence we had to discard large sections of the raw data and only recovered discontinuous SO\({}_{2}\) measurements. The hospital INVOS cerebral oximeter employs 730 nm and 810 nm LEDs switched on and off at \(<\) 30 Hz, while our FDNIRS employs 8 wavelengths turned on in sequence at 10 Hz per cycle. The light cross-talk of the two devices results in spurious peaks in the FDNIRS signal, which appear at different wavelengths and different times throughout the data collection. By using Fourier analysis, we found and discarded contaminated data segments, typically lasting less than 1 minute. We also interpolated across the discarded periods to obtain continuous time traces. The raw signal for oneof these patients is shown in In patients #4 and #12, our probe was so close to the hospital oximeter's probe and the interference was so strong that we could not recover a continuous signal, but rather only segments.
After preprocessing the raw data, we used the frequency domain multi-distance method to compute the optical properties of the measured tissue with a minimum of 5 out of the 8 wavelengths. At each wavelength, the AC and phase shift slopes versus distance were used to quantify the absorption and scattering coefficients, \(\upmu_{\text{a}}\) and \(\upmu_{\text{s}}{}^{\prime}\), respectively. After calculating \(\upmu_{\text{a}}\) and \(\upmu_{\text{s}}{}^{\prime}\) at all wavelengths, we computed the oxy, deoxy and total hemoglobin concentrations, as well as the hemoglobin oxygen saturation (SO\({}_{2}\)) assuming a water fraction in tissue of 0.75.
## DCS Analysis
Interference of the INVOS with the FDNIRS raw phase data on patient #6. The figure shows the phase signal at 3 wavelengths for one detector with no preprocessing. The small jumps in the raw signal are due to the repetitive interference caused by the 30 Hz light modulation of the INVOS oximeter. Each jump is roughly 30-50 seconds wide.
FDNIRS phase data from patient #12, one of the two patients where the interference was so strong and overlapping at different wavelengths that we could only recover sections of FDNIRS data. Each interference section is ~7 minutes wide, making potential interpolation infeasible. For these patients, rather than linearly interpolating, we removed interference sections leaving gaps in the data before further analysis.
During preprocessing, the DCS intensity autocorrelation functions (g2) were smoothed using a 10-point averaging window for patients #1, 5 and 8 (acquired at 2 Hz), and a 50-point window for all other patients (acquired at 10 Hz) to achieve a final sampling rate of 0.2 Hz in all patients. We further smoothed the g2 with a 5-point moving average to improve signal to noise ratio.
We analyze the DCS data using the semi-infinite medium boundary condition for correlation diffusion equation. In all subjects we report BFi at 25 mm separation except for patient #12, for which we only had the measure at 30 mm. Optical properties at 850 nm are needed to calculate blood flow index (BFi). For 6 patients (#2-4, 6-7, 9-10) we used the optical properties measured with the FDNIRS by extrapolating absorption and reduced scattering spectra at 850 nm. For all the other patients, since we did not have FDNIRS measurements, we used average optical properties measured in the above patients, specifically, we used \(\mu_{\text{a}}=0.12\) and \(\mu_{\text{s}}{}^{\prime}=8.94\). In the 6 subjects with measured optical properties we also calculated BFi using fixed optical properties and confirmed that there were no significant changes in the estimated flow relative changes.
## Quantification of CBFi changes with circulatory arrests
We quantified the CBFi at CAs by calculating the average BFi changes during the CA period with respect to that of a pre-CA period for each patient. The duration of the pre-CA period was defined manually as a 1- to 10- minute window immediately before the CA onset during which BFi, SO2 and systemic physiology were stable. The CBFi changes during HCA were calculated by averaging BFi from 90 seconds after CA start until the stop time. The 90-second delay was used to discard any artifacts at the beginning of the procedure. We measured the CBFi overshoot at reperfusion times by averaging the values at the highest reperfusion peaks (there were multiple peaks in some cases where the surgeon asked to have the pump started and stopped several times) and comparing them to the settled CBFi value, found by averaging a several-minute window after the overshoot.
## Quantification of SO2 changes through circulatory arrests
For the patients with FDNIRS measurements, we quantified SO2 drops by averaging one-minute pre-CA and the one-minute right before reperfusion.
## Quantification of cerebral metabolic rate of oxygen and its relationship with temperature
To calculate oxygen consumption, we used the equation: \(CMRO_{2i}=\frac{HGB}{MW_{Hb}}*CBF_{i}(SaO_{2}-SO_{2})\), where HGB is the patient's hemoglobin concentration in the blood (units g/dL) and MWHb is the molecular weight of hemoglobin (65,400 g/Mol). HGB was collected at 30-minute intervals by the clinical team, and we linearly interpolated over the points to get a continuous variable.
|
098970_file03 | #### a.1.1 Overview
The modelling of the spread of the disease is based on the interplay of four modules.
1. Population. Altogether the agent-based COVID-19 model is based on the Generic Population Concept (GEPOC, see), a generic stochastic agent-based population model of Austria, that validly depicts the current demographic as well as regional structure of the population on a microscopic level. The flexibility of this population model makes it possible to modify and extend it by almost arbitrary modules for simulation of population-focused research problems.
2. Contacts. In order to develop a basis for infectious contacts, we modified and adapted a contact model previously used for simulation of influenza spread. This model uses a distinction of contacts in different locations (households, schools, workplaces, leisure time) and is based on the POLYMOD study, a large survey for tracking social contact behaviour relevant to the spread of infectious diseases.
3. Disease. We implemented a module for the course of the disease that depicts the current pathway of COVID-19 patients starting from infection to recovery or death and linked it with the prior two modules.
4. Policies. Finally, we added a module for implementation of interventions, ranging from contact-reduction policies, hygienic measures and, in particular, contact tracing. This module is implemented in form of a timeline of events.
#### a.1.1 Purpose
The agent-based COVID-19 model aims to give ideas about the potential impact of certain policies and their combination on the spread of the disease, thus helping decision makers to correctly choose between possible policies by comparing the model outcomes with other important factors such as socioeconomic ones. In order to fulfil this target, it is relevant that the agent-based COVID-19 model validly depicts the current and near future distribution and state of disease progression of infected people and their forecasts.
In the following overview of the model, we will not state any parameter values to focus on the model concept. A full collection of model parameters including values, sources and justifications is found in Section A1.3.3.
#### a.1.2 Entities and State Variables
Each person-agent is a model for one inhabitant of the observed country/region. We describe state variables of a person-agent sorted by the corresponding module.
Population. Each person-agent contains the population specific state variables _sex_, _date of birth_ (\(\cong\) age) and _location_. The latter defines the person-agent's residence in form of latitude and longitude and uniquely maps to the agent's municipality, district and federal state.
Contacts. The person-agent features a couple of contact network specific properties. These include a _household_ and might include a _workplace_ or a _school_. We summarise these as so-called _locations_ which stand for network nodes via which the person-agent has contacts with other agents. Assignment of person-agents to _locations_ is based on distance of the agent's residence to the position of the _location_. Each day, an agent has a certain number of contacts within each of the _locations_, which essentially leads to spread of the disease. Tomodel contacts apart from these places, every person-agent has an additional amount of leisure time contacts, which are sampled randomly based on a spatially-dependent distribution. The contact network is schematically displayed in Figure A1.
Disease. In order to model the spread of the disease each person-agent has a couple of health states that display the current status of the agent. The parameter necessary for the simulation dynamics are _susceptible_, _infected_, _infectious_, _confirmed_, _hospitalised_,_quarantined_ and _critical_. These states can either be true or false, and multiple of them can be true at a time. They stand for certain points within the patient pathway of an infected person and enable or disable, respectively, certain person-agent actions. The meaning of these attributes is usually self-explanatory: for example an agent with attribute _confirmed=true_ indicates that the agent has been detected by by a SARS-CoV-2 test. To make generation of simulation output easier, we sometimes make use of derived parameters such as _severe_ (=_hospitalized_\(\wedge\)\(-\)_critical_) or _undetected_ (=_infected_\(\wedge\)\(-\)_confirmed_). More on the influence of these state variables and how they change is described in Section A1.1.4.
Policies. Policies apply either to _locations_ or to person-agent-behaviour directly and require additional agent properties. All _locations_ except for households are defined _open_ or _closed_ which marks whether this place is available for having contacts. For person-agents the variable _quarantined_ is applied to mark agents isolated not only via a positive test but also due to tracing measures.
For the sake of simplicity of speech we furthermore address mentioned parameters as attributes for the corresponding agents. I.e. an agent with _infectious_ set to true will be denoted as "_infectious_ agent".
#### a1.1.3 Scales
Unlike other agent-based models it is not possible to validly run the model with a smaller number of agents (e.g. one agent represents 10 or 100 persons in reality) as certain contact-network parameters do not scale this way (average school size,\(\ldots\)). Consequently, one simulation run always uses agents according to the size and structure of the full population.
#### a1.1.4 Process Overview and Scheduling
Like the underlying population model, the agent-based COVID-19 model can be interpreted as a hybrid between a time-discrete and a time-continuous (i.e. event-updated) agent-based model:
The overall simulation updates itself in daily time steps, wherein each step is split into three phases. In the first phase each agent is called once to plan what it aims to do in the course of this time step. In the second phase, each agent is, again, called once to execute all planned actions for this time step in the defined order. In the third step, a recorder-agent keeps track of all aggregated state variables.
On the microscopic scope, each person-agent is equipped with its own small discrete event simulator. In the mentioned planning phase, each agent schedules certain events for the future which may, but not necessarily must, be scheduled within the current global time step. In the second phase, the agent executes all events that are scheduled for the currently observed time interval, but leaves all events that exceed this scope untouched.
This strategy comes with the following benefits:
* In contrast to solely event-based ABMs, the event queue is distributed among all agents which massively increases the speed for sorting (a solely event-based ABM with millions of complex agents would not be executable is feasible time).
* Moreover, in contrast to solely event-based ABMs, usage of daily transition probabilities/rates instead of transition times is possible as well.
* In contrast to solely time-discrete ABMs, agents can operate beyond the scope of time steps and sample continuous time-intervals for their state-transitions.
We shortly describe all actions that are scheduled and executed by one person-agent within one time step sorted by the specified module.
Population. As briefly described in, agents trigger birth and death events always via time- and age-dependent probabilities that apply for the observed time step (i.e. the observed day). If one of these events triggers, the agent samples a random time instant within the current time step and schedules the event. Note that in contrast to the basic population model, immigration and emigration events are disabled in the agent-based COVID-19 model due to closed borders in reality.
Contacts. Also contact specific events are scheduled and executed within the scope of only one time step: First of all, the agent schedules a contact event with every other member of its _household_. Moreover, if such a location is present in the contact network, a certain number of _workplace_ or _school_ contacts, respectively, are scheduled and corresponding partners drawn randomly from the assigned location. Finally, a certain number of _leisure time_ contacts are sampled and partners are drawn based on an origin-destination matrix on municipality resolution. The latter has been gathered from mobile data (see Tables A2-A3).
As mentioned, some states limit the agents' capabilities of interaction. In specific, _quarantined_ agents have no random leisure time contacts and no contacts at _work_ or _school_. Furthermore, _hospitalised_ agents do not even contact their household members.
Anyway, planned contacts are always scheduled for the beginning of the new time-step. Hence, interaction between agents is actually limited to the discrete time steps of the simulation. This guarantees, that the states of both involved agents do not differ between the time of the planning of the event and its execution.
Disease. First of all, it is important to mention that the model is not parametrised by a reproduction number \(R_{0}\) or \(R_{eff}\), but by a contact-specific probability for a transmission in case of a contact. Nevertheless, the agent-based model provides the opportunity to generate estimates for \(R_{0}\) and \(R_{eff}\) by its original definition: the average number of secondary infections of an infected agent. Hence, what comes as model input for many traditional SIR models becomes a model output for the agent-based COVID-19 model.
In case of a contact, _infectious_ agents spread the disease to _susceptible_ agents with a certain _infection probability_ which triggers the start of the newly-infected agent's patient-pathway. This pathway describes the different states and stations an agent passes while suffering from the COVID-19 disease and can be interpreted as a sequence of events of which each triggers the next one after a certain sampled duration.
We show this infection strategy in a state chart in Figure A2 and describe how to interpret this figure by explaining the initial steps in the pathway in more detail: As soon as a person-agent becomes infected, its _infected_ state is set to _true_, its _susceptible_ variable is set to _false_ and a _latency period_ is sampled according to a specific distribution. The corresponding "Infectious" event is scheduled for the sampled time instant in the future. As soon as this "Infectious" event is executed, the _infectious_ parameter is set to _true_ and a random number decides about whether the person will develop symptoms or not. This point marks the first branch in the patient's pathway and whether the "Symptoms Onset" event or the "Unconfirmed Disease" Event is scheduled. The prior would be planned after a sampled time span corresponding to the difference between latency and incubation time, the latter would be triggered instantaneously. All other elements of the pathway follow analogously. The branches are evaluated with age-class-dependent probabilities (see Section A1.3.3).
In most cases (i.e. if the agent does not die for any other non-COVID related reason - see Population module), the final state of every agent's disease pathway is the _Recovery/Removal_ event with either sets the agent _resistant_, or renders it deceased with a certain death-by-COVID probability that depends on the agent's disease severity. Consequently, the model differs between COVID-caused and COVID-affected deaths.
Policies. Every policy is modelled as a global event occurring before the planning phase of any of the simulation time steps. Policies are timed-events that are fed into the model as an event-timeline (see Figure A3). The elements of this timeline may include real policies like closure or opening of locations, start of tracing (for a full list, see Table A7), but may also contain incidents that change the model behaviour but are not directly related to policies, such as raising hygiene awareness or distancing. The most outstanding feature of the model is clearly its ability to model contact tracing policies, since agents are aware of all other agents with which they had contacts. Using simple housekeeping arrays, these can be logged for a certain period of time and used for detection and isolation of contact partners.
Figure A2: State chart of the patient pathway of a person-agent in the agent-based COVID-19 model. Only those state variables that are changed by the corresponding event are labelled, all others remain at the current value. The initial state of all infection-specific state variables is _false_, except from _susceptible_ which is initially _true_.
### Design Concept
#### a.1.2 Basic Principles.
Increasing the level of detail from a standard epidemiological model for simulation of disease waves to a model that is capable of dealing with various different policies is a huge step with respect to model complexity. It excludes the use of macroscopic strategies and requires modelling of a contact network and contact behaviour. Consequently a detailed demography, spatial components and stochasticity need to be introduced to the model which come with a huge number of additional parameters and parameter values.
Hence, we were very careful that the agent-based model is designed as simple as possible yet tracking the most important features for evaluation of certain policies. Hereby, many details within the pathway of an infected person and, in particular, lots of details within the personal daily routine are simplified to avoid indeterminable model parameters and unpredictable model dynamics.
#### a.1.2 Emergence.
In addition to the classic emergence of nonlinear epidemiological effects, analysis of the effects of interaction between different measures is one of the key objectives of the model. For example, seemingly unconnected policies like _school closure_ and _contact reduction for the 65+_ might lead to unexpected effects when applied simultaneously. More generally speaking, the model displays that the individual effects of applied policies do not add up linearly.
#### a1.2.3 Sensing.
Agents' perception of reality is one of the key problems of modelling COVID-19 as no agent is actually aware of its own disease and, more importantly, infectiousness until symptoms occur. Therefore, agent parameters can be distinguished into two sets: the ones the agent is aware of (e.g. _critical_, _hospitalised_), and the ones it is not (e.g. _infected_, _infectious_).
Interestingly, besides the individual perception of agents and the perception of an omniscient observer, there is also a third level of perception included into the model: the perception of the general public. While an individual agent knows about its symptoms, the public is not yet aware of this additional infected case, until the person-agent has reacted on the disease, has had itself tested and eventually becomes _confirmed_.
Consequently, the levels of perception can be sorted with regards to their amount of knowledge:
\[\text{omniscient observer}>\text{person-agent}>\text{general public}.\]
#### a1.2.4 Interaction.
Interaction between agents only occurs in form of contacts at _locations_ or _leisure time_. The features provided by the underlying population model make it possible to investigate contacts on a very local level. As described before, _leisure time_ contacts are weighted by their regionality, but also _school_ and _workplace_ contacts depict locality: Using specified latitude and longitude for locations, it is possible to assign person-agents with distance-dependent probabilities (see Section A1.3.1). Consequently, interactions between agents follow a spatially-continuous locally-biased contact network.
#### a1.2.5 Stochasticity.
Basically all model processes, including the initialisation, contain sampling of random numbers. Therefore, Monte Carlo simulation is applied, results of runs are averaged and also their variability is assessed (see Section A3).
#### a1.2.6 Observation.
Inspired by, a recorder-agent takes care about tracking and aggregating the current status of the simulation. At the end of each global time step, all person-agents report to the recorder-agent which furthermore keeps track of all necessary aggregated model outputs. This includes for example _confirmed active cases_, _confirmed cumulative cases_, _hospitalised agents_, _undetected agents_, _pre-symptomatic agents_, _recovered agents_, _agents in a certain hospital_, or _average-number of contacts per infectious agent_. If required, numbers can also be tracked with respect to age, sex, regional level and/or location.
### Details
Clearly, Section A1.1 could only outline the basic concepts of the model and left a lot of technical and modelling details necessary for a reproducible model definition open. In particular, this refers to the highly non-trivial initialisation process of the model. Hereby, two problems occur that require completely different approaches. The first problem considers the generation of the person-agents, locations and hospitals in the first place. The second problem deals with the initialisation of the status quo of the distribution of the disease states of the agents for the specified initial date.
#### a1.3.1 Initialisation of Person-agents, Locations and Hospitals.
A lot of problems that deal with the sampling of the initial population have already been solved in the original GEPOC model. In particular this refers to the Delaunay-triangulation-based sampling method for locations. We apply this method to merge information from the national statistics institute and the global human settlement layer. Consequently, besides initialisation of the disease states which is described in the next section, only new methods for location- and hospital-generation had to be implemented.
Schools are initialised based on known distributions w.r.t. average school size and number of pupils in total. A _school-sampler_ iteratively generates schools with a random size/capacity (truncated normal distribution) until the sum of all capacities matches the known number of pupils in reality. Each school is furthermore sampled a position (latitude and longitude) analogous to the sampling for person-locations (see). In a second step, schools are "filled" with person agents. Hereby, model agents with age between 6 and 18 are assigned to a school based on a locally biased distribution. This is done with probabilities \(p_{m}^{s},p_{d}^{s},p_{f}^{s}\) and \(p_{a}^{s}\) for assigning the school in the same municipality, district, federal-state and country as the agent's residence.
Clearly, the number of model agents in this age group is larger than the number of known pupils. Consequently, we force distribution of all 6 to 14 year old agents, and distribute as many 15 to 18 year old agents as possible. All remaining 15 to 18 year old agents are considered to be working.
Workplaces1 are initialised analogously to schools. A _workplace-sampler_ iteratively generates workplaces with size/capacity according to a discrete distribution (see Tables A2-A3). The sampler stops generating if the sum of all capacities matches \((a+b)(1-\alpha)-c\), whereas \(a\) denotes all model agents between 19 and 64, \(b\) denotes all agents between 15 and 18 that have not been yet assigned a school, \(c\) denotes the total number of care-home workers in Austria, and \(\alpha\) denotes the current unemployment rate. Location sampling and "filling" works analogously to the _school-sampler_ with different probabilities (commuter data).
Footnote 1: Workplaces should not be confused with total companies. They rather represent the different teams where the members are in regular contact with each other.
Care-homes are generated with a fixed size and providing space for a fixed number of inhabitants and workers (\(=c\), see above). Workers and inhabitants are assigned based on the same distribution as workplaces, although assigning inhabitants actually transfers theirs residence to the sampled place of the _care-home_.
Hospitals are generated based on publicly available data. This includes capacities (beds, intensive-care units) as well as their location (latitude and longitude).
#### a1.3.2 Initialisation of the Disease State
The spread of SARS-CoV-2 displays probably better than any other system, that the most dangerous enemy is the invisible one. While confirmed infected persons are detected and well known, they hardly contribute to the spread of the disease - they are already isolated properly, and most infections occur even before the onset of symptoms.
Consequently, it is not possible to simply "start" the simulation with a certain number of confirmed cases, acquired for example from official internet sources. Valid values for pre-symptomatic (e.g. persons within latency and incubation period) and asymptomatic persons need to be acquired as well - yet, this number is hardly measurable in reality.
In order to solve this problem, a three stage concept, henceforth denoted as initialisation phase, was designed to generate a feasible initial state for a certain time \(t_{0}\):
1. **Initialise-Simulation.** The agent-based COVID-19 model is set up with a small number of initially infected agents (40 was found to be the most stable and useful option). This number corresponds to an estimated count of initial infection clusters in the country, but actually hardly influences the outcome. Furthermore, the agent-based simulation is run and interrupted by a state event, namely if the cumulative number of _confirmed agents_ in the model is greater or equal to a specific value \(C(t_{-1})\). Hereby, \(t_{-1}\) refers to a self chosen point in time and \(C(t_{-1})\) to the reported number of positive tests in reality until \(t_{-1}\). Hereby \(t_{-1}\) must be chosen properly so that the reported number of positive tests is large enough to be representative yet before implementation of any policies. As soon as the simulation is interrupted by the state-event, the timelines of simulation and reality are synced: \(t_{-1}\) in reality becomes \(t_{-1}\) in the simulation. The initialise-simulation is continued, considering all policies that have been implemented in reality, until, finally, \(t_{0}\) is reached. Properly calibrated by a calibration routine (see Section A1.3.4), the initialise-simulation contains approximately the same cumulative number of _confirmed agents_ as the corresponding reported number in the real system. The initialise-simulation is finished by exporting parts of the final state of the simulation. This refers to all households that contain either infected or recovered agents which are finally written into a file. Hereby, an initial population is generated that contains not only a valid approximation of the confirmed cases, but also a valid estimate for the unknown pre-symptomatic and asymptomatic persons, a correct distribution of their future planned events and a correct household distribution as well.
2. **Fine Tuning.** Even with best calibration routines (see Section A1.3.4) it is not possible to perfectly match the model output with the status quo in reality, in particular w.r.t. regional distribution. Therefore, a bootstrapping algorithm was implemented that corrects the small differences between the initialise-simulation output and the real data (confirmed cases, hospitalisation, intensive-care units and recoveries per region) to make sure, that the initial state of the actual simulation matches the current state precisely. This step can be omitted, if matching the current state precisely is not required.
3. **Load Households.** Finally, the actual simulation is initialised with the previously recorded and fine-tuned agents from the initialise-simulation. To be precise, this process does not only include agents themselves, but also the _households_ these agents live in. Hereby, the fundamental network structure from the initialise-simulation can be maintained.
#### a1.3.3 Parametrisation
With respect to parametrisation, we will distinguish between model input and model parameters.
Classical model parameters specify scalar or array-typed model variables that are initialised at the beginning of the simulation and, if not changed by certain model events, keep their value for the entire simulation time. Examples are the infection probability of the disease, the age-dependent death rate of the population, or the distribution parameters of the recovery time.
In contrast to model parameters, the model input consists of an event-timeline that describes at which point in time a certain incident changes the behaviour of the model. This incident usually refers to the introduction of a policy, e.g. closure of schools or start of tracing, but may also refer to instantaneous changes of model parameters which are related but cannot be directly attributed to policies, e.g. the increase of compliance among the population to increase hygiene.
In the following, we state lists of used parameters and parameter-values including corresponding sources and/or justifications. They are found in Tables A1 to A6. Table A7 states a list of possible event-timeline elements that can pose as the model's input.
#### a1.3.4 Calibration
Clearly, there is no valid data available for direct parametrisation of the _infection probability_ in case of a direct contact. First of all, this parameter is hardly measurable in reality and moreover strongly depends on the definition of "contact". Consequently, this parameter needs to be fitted in the course of a calibration loop.
The calibration experiment is set up as follows:
* We vary the parameter _infection probability_ using a bisection algorithm.
* For each parameter value, the simulation, parametrised without any policies, is executed ten times (Monte Carlo simulation) and the results are averaged.
* The average time-series for the _cumulative confirmed cases_ is observed and cropped to the beginning upswing of the epidemic curve, to be specific, all values between 200 and 3200. In this interval the growth of the curve can be considered as exponential.
* The cropped time-series is compared with the corresponding time-series of real measured data in Austria, specifically the confirmed numbers between March \(10^{\text{th}}\) and \(20^{\text{th}}\) 2020 (source EMS system,).
* Both time-series are compared w.r.t. the average doubling time of the confirmed cases. The difference between the doubling times is taken as the calibration error for the bisection algorithm.
Note: As the sample standard deviation of each observable of the runs has been observed to be at most a fifth of the sample mean, the iteration number of nine for the Monte Carlo simulation has been considered to be sufficient for calibration purposes w.r.t. the ideas in.
After calibrating the infection probability parameter, also the parameters of the input timeline of the initialisation-simulation needs to be calibrated to the policies applied in the real system. This is done iteratively using a bisection algorithm as well. For example, the Austrian government introduced lockdown policies on March \(17^{\text{th}}\) and started with the first reopening steps on April \(16^{\text{th}}\). Consequently, this time-period was used to calibrate the unknown _leisure-time contact reduction_ parameters in the lockdown-related policy events.
## Appendix A2 Model Implementation
Simulation of agent-based models like the agent-based COVID-19 model is a huge challenge with respect to computational performance. As the model cannot be scaled down, almost 9 Million interacting agents need to be included into the model in order to simulate the spread of the disease in Austria.
These high demands exclude most of the available libraries and software for agent-based modelling including AnyLogic, NetLogo, MESA, JADE or Repast Simphony. Most of these simulators cannot be used as their generic features for creating live visual output generates too much overheads.
Consequently, we decided to use our own agent-based simulation environment ABT (Agent-Based template, see), developed in 2019 by dwh GmbH in cooperation with TU Wien. The environment is implemented in JAVA and specifically designed for supporting reproducible simulation of large-scale agent-based systems.
The next section contains more technical details about the implementation.
## Appendix A3 Technical Implementation Details
The implementation of the agent-based COVID-19 model uses JAVA 11 and applies the _UniformRandomProvider_ random number generator (RNG) by Apache Commons. This RNG implements a 64 bit version of the Mersenne Twister and exceeds the standard RNG of JAVA, a simple Linear Congruential Generator, in both performance and quality.
The simulation itself is always executed in a Monte Carlo setting and several runs with different RNG seeds are averaged. Due to the huge number of agents, a Law-of-Large-Numbers-effect can be observed (similar to Chapter 5.2), and the standard deviation of the model output is always comparably small. Consequently, Monte Carlo replication numbers of 10 to 20 are usually enough to estimate the mean sufficiently well (we apply the algorithms from).
## Appendix A4 Detailed Scenario Definition
In order to give a reproducible definition of scenarios, we explain the used event-timelines in detail in tables A8 and A9. The prior shows the calibrated timeline of initialization phase, the latter displays the timeline of the baseline scenarios.
This event-timeline was calibrated extending the ideas from Section A1.3.4
\begin{table}
\begin{tabular}{p{56.9pt}|p{113.8pt}|p{113.8pt}|p{113.8pt}} date & policy event & interpretation & parameters \\ \hline Mar.10 & reduction of leisure time contacts & Due to the raising anxiety and awareness among the population resulting from the medial coverage, we assume that many Australians have already minimized their contact behavior before introduction of the policies. & A simulated leisure time contact is refused by an agent with probability 0.16. \\ \hline Mar.10 & increased hygiene and distancing in _leisure time_ & Increasing awareness leads to increased hygiene among the population. & _Leisure time transmission probability_ is reduced by 50\%. \\ \hline Mar.14 & closing of _schools_ and _workplaces_ & Although closure of schools and workplaces was announced for March 16\({}^{\text{th}}\), a Monday, the policy is actually active already two days earlier, as all schools and most workplaces are closed during the weekend anyway. & All _schools_ and 50\% of the _workplaces_ are disabled for contacts. \\ \hline Mar.14 & increased hygiene and distancing at _workplaces_ & Due to increasing hygiene and distancing at _workplaces_ & _Workplace transmission probability_ is reduced by 50\%. \\ \hline Mar.14 & reduced contact frequency at _workplaces_ & Due to increased use of home-office, also the total number of contacts at work per day is reduced. & The average number of _workplace contacts per day_ is reduced by 50\%. \\ \hline Mar.16 & reduction of leisure time contacts & Due to massive restriction of mobility, leisure time contacts of people are heavily reduced. & A simulated leisure time contact is refused by an agent with probability 0.7. \\ \end{tabular}
\end{table}
Table A8: Initialization phase definition: model policies introduced to fit the current lockdown time-series in Austria
|
102129_file02 | ## PROTOCOL OF THE TARGET TRIALS Eligibility criteria
The trials would enrol healthy men and non-pregnant women aged 45-69 years old, from primary care practices in England registered between 1998 and 2016 who had not undergone bariatric surgery in the past and without any prevalent cardiovascular disease, diabetes, cancer (apart from non-melanoma skin cancer), severe mental diseases (acute stress, phobia, anxiety, schizophrenia, depression, bipolar disorder or affective disorder), major inflammatory diseases (systemic lupus erythematosus, rheumatoid arthritis, gout and ulcerative colitis), Parkinson's disease, multiple sclerosis, renal disease and renal failure at baseline. Moreover, individuals who either die or develop one of the aforementioned chronic diseases or the outcome or women who become pregnant during the 1st year of the hypothetical interventions, would be excluded from the trials. The trials would be conducted separately among normal weight, overweight and obese individuals (see Table 1 and Figure 1). We would additionally consider these trials, stratified by sex (males and females) and age (<60 & >=60 years old).
## Treatment strategies
Individuals in the trials would be randomly assigned to the following two-year hypothetical weight change interventionsa) lose \(\geq\)3% & \(<\)20% of their weight each year or undergo bariatric surgery
b) maintain their weight, defined as weight change \(>\)-3% & \(<\)3% of bodyweight each year
Under all three strategies, individuals would be allowed to deviate from their assigned weight change intervention after 2 years. From these trials, we considered women who became pregnant and individuals who developed chronic diseases during the 2nd year of follow up as a clinically allowable reason for deviating from assigned intervention; thus, these individuals will be allowed to deviate from their assigned intervention in the 2nd year. The chronic diseases considered as clinically allowable conditions to deviate from the intervention in these trials would be the following; diabetes, cancer (apart from non-melanoma skin cancer), dementia, severe mental diseases (acute stress, phobia, anxiety, depression, schizophrenia, bipolar disorder and affective disorder), chronic kidney disease, chronic obstructive pulmonary disease, HIV, major inflammatory diseases(systemic lupus erythematosus, rheumatoid arthritis, gout, and inflammatory bowel disease), Parkinson's disease, multiple sclerosis and renal failure. When diabetes or non-melanoma skin cancer were the outcomes of interest (positive and negative control outcomes), we also considered CVD as a clinically allowable condition for deviating from the initial intervention. For more details, see table 1.
## Treatment assignment
Individuals would be randomly assigned to a treatment strategy at baseline
## Follow-up
Follow-up would start at randomization and would end at diagnosis of a cardiovascular event, death, loss to follow-up, 7 years after baseline, or 31st June 2016, whichever occurs first.
## Endpoints
Primary endpoint;Composite CVD outcome (CVD death, non-fatal Myocardial infarction, non-fatal stroke, hospitalisation from coronary heart disease and heart failure)
Secondary endpoints;
a) Composite CHD outcome (CHD death, non-fatal Myocardial infarction, hospitalisation from coronary heart disease)
b) fatal and non-fatal Myocardial infarction,
c) fatal and non-fatal stroke,
d) heart failure
e) CVD deaths
it is expected that weight loss reduces and weight gain increases the risk of diabetes)
it is expected that no effect of weight loss or gain on non-melanoma skin cancer)
## Causal contrasts
Per-protocol effect, defined as the effect of adhering to the assigned intervention for two years
## Analysis plan
_i. Data structure_: Follow-up would be divided into one year periods in which the weight change intervention per year was recorded, along with information on confounders, CVD outcome (1:yes, 0:no), death (1:yes, 0:no) and loss to follow-up (1:yes, 0:no) recorded during each year.
_ii. Outcome regression:_ Pooled logistic regression model would be used to estimate the hazard ratios of the hypothetical interventions and the cumulative incidence risk curves of each intervention.
_iii. Emulating randomisation at baseline:_ Individuals would be randomised at baseline_iv. Dealing with non-adherence to intervention:_. Inverse probability of treatment weights (IPTW) would be used to adjust for time-fixed and time-dependent confounders. In IPTW, each observation would be weighted by the inverse of the probability of an individual having received his/her observed weight change intervention during the 2\({}^{\text{nd}}\) year, given his/her past intervention and prognostic factors history. To calculate the denominator of the IPTW, we would use multinomial logistic regression models for the observed weight change intervention (i.e. weight loss, maintenance and gain) during the 2\({}^{\text{nd}}\) year, in which we would include the determinants of the observed intervention at the 2\({}^{\text{nd}}\) year, i.e. prognostic factors measured before baseline, during the 1\({}^{\text{st}}\) year (as described above) and during the 2\({}^{\text{nd}}\) year of these interventions, along with the observed weight change intervention during the 1\({}^{\text{st}}\) year. The IPTW remained constant after the second year, because we would be interested in the effect of a weight change strategy sustained over 2 years only. After calculating the IPTW for the received intervention in the second year, individuals would be then censored during the second year, if they deviated from their assigned intervention. For those individuals who would develop a chronic disease other than CVD during the 2\({}^{\text{nd}}\) year (and thus were free to deviate in the 2\({}^{\text{nd}}\) year as well from their assigned intervention), they would be assigned the weight of 1 across all time points. We remark that we would use the non-stabilised weights, because the regime of the trials was dynamic (i.e. we had specified clinically allowable reasons after which individuals were free to deviate from their initial strategy)
_v. Dealing with loss to follow-up:_ Additional adjustment for pre- and post-randomisation prognostic factors of loss to follow-up would also be used through inverse probability of censoring weighting (IPCW), to estimate the effect of the interventions, had the participants remained uncensored during the follow-up. These analyses would be thus valid under missing at random, given the covariates used to model the censoring mechanism.
_vi. Final calculation of IP weights_: IPTW and IPCW would be multiplied at each time point. The final weight for each individual for a specific time would be taken as the product of his/her weights up until that time point. We would truncate weights \(>\)15 (which were higher than the 99\({}^{\rm th}\) percentile of weights) and would set it to 15.
_vii. Risk curves_: We would additionally estimate absolute risks for CVD, CHD and diabetes by fitting the pooled logistic models that were mentioned above, including product terms between treatment and follow-up time (time, squared time and cubic time) to allow for time varying effects. The estimated parameters would be then used to calculate the cumulative incidence of CVD, CHD and diabetes (see details in the Appendix - section 3).
_viii. Variance estimators:_ We would use robust variance estimators to calculate 95% CI for the hazard ratio estimates, and we would use non-parametric bootstrapping from 500 samples to obtain percentile-based 95% CI for the cumulative incidence estimates.
## PROTOCOL OF THE EMULATED TRIALS
## Eligibility criteria
Same as for the target trials plus we additionally excluded individuals with an excess number of bodyweight measurements or clinical consultations in the 1\({}^{\rm st}\) year (defined as \(\geq\)6 bodyweight measurements or with \(\geq\)12 primary care consultations), under the assumption that these individuals would be too unhealthy to participate in the study.
## Treatment strategies
Same as for the target trials plus we excused individuals from following their assigned intervention if they have \(\geq\)12 clinical consultations or measured their bodyweight \(\geq\)6 times per year in the primary care\({}^{\ddagger}\) during the 2\({}^{\rm nd}\) year.
_Treatment assignment_Patients are classified into one of three weight change groups (maintenance, loss, or gain) based on their observed weight status. Randomization is emulated via adjustment for baseline covariates.
## Follow-up
Same as for the target trials
## Endpoints
Same as for the target trials
## Causal contrasts
Observational analog of the per-protocol effects
## Analysis plan
Same as for the target trial, the only difference is that individuals are not randomised at enrolment. To emulate randomization at baseline, we adjusted for: age (in years), sex (men/women), BMI (in kg/m\({}^{2}\)), prevalence of hypertension (yes/no), record of high LDL levels (before baseline; yes/no), use of diuretics (before baseline; yes/no); family history of CVD (yes/no); hypertension (during the 1st year, yes/no); high LDL levels (during the 1st year; yes/no), use of diuretics (during the 1st year); smoking status (during the 1st year; never/former/ current), number of weight measurements (during the 1st year; 1 meas./ 2 meas./ 3-5 meas.), number of clinical consultations (during the 1st year; 1-2 consultations, 3-5 consultations, 6-8 consultations, 9-11 consultations) and region (in categories; London/ South West/ South Central/ South East/ East/ West Midlands/ Central North and North West)
## Section 3: Details on the statistical analysis
### Disease models
To estimate the hazard ratios in all analyses, we used pooled logistic regression models. In these models, we use the following notation; \(t\) is the follow-up time (in years), \(A_{t,wl}\) denotes the value of the "weight loss intervention" between t and t+1, \(A_{t,wm}\) denotes the value of the "weight maintenance intervention" between t and t+1, \(A_{0,wg}\) and \(A_{t,wg}\) indicates the value of the "weight gain intervention" between t and t+1, \(\boldsymbol{L_{t}}\) indicates a vector of covariates (number of weight measurements [categorical; 1: 1 meas, 2:2 meas., 3: 3-5 meas), number of clinical consultations (ordered; 1: 1-2 clinical cons., 2: 3-5 clinical cons., 3: 6-8 clinical cons, 4: 9-11 clinical cons), record of hypertension, record of high LDL measurement, use of diuretics] measured between t and t+1. Of note, \(\boldsymbol{L_{0}}\) (i.e. baseline confounders) additionally contains information on age (at baseline), sex, region, BMI (in kg/m\({}^{2}\) at baseline), prevalence of hypertension (at baseline - criteria; systolic blood pressure\(>\)140mmol/Hg or diastolic blood pressure\(>\)90mmol/Hg), record of high LDL measurement (before baseline), use of diuretics (before baseline), apart from the information of number of weight measurements, number of clinical consultations, record of hypertension, high LDL measurement and use of diuretics that occurred during the 1st year (i.e. between t=0 and t=1). Moreover, \(D_{t}\) indicates the values of the CVD outcome between t and t+1 and \(C_{t}\) denotes whether an individual was censoredbetween t and t+1. The over-bars represent the previous history of a variable from the beginning of follow-up and the superscript \(T\) indicates a transpose of a vector of parameters. Throughout our analyses, we censored the person-time when someone discontinued his/her initial treatment assignment, because we were interested in the per-protocol effect of our "interventions". That is, we fit the model:
\[logit[pr\left(D_{t+1}=1\big{|}A_{0},L_{0},\overline{D}_{t}=0,\overline{C}_{t+1} =0\right)]=\beta_{0,t}+\beta_{1}A_{0,wl}+\beta_{2}A_{0,wg}+\beta_{3}{}^{T} \boldsymbol{L_{0}}\] (S.1)
Moreover, \(\beta_{1}\) and \(\beta_{2}\) corresponds to the log hazard ratios for the weight loss and weight gain "interventions" respectively (compared to the weight maintenance "intervention").
#### Models for IP weights
We were interested in the per-protocol effect of our "trails", so we weighted our disease models with the inverse probability of treatment weights (IPTW). The IPTW correspond to the reciprocal of the probability that an individual adhered his/her observed weight change intervention given his past treatment and pre and post baseline prognostic factors history. We used the unstabilised version of IPTW because the regime of our trials was dynamic (if people were not healthy at year 1, they were free to deviate from their allocated intervention).
During the 1st year, individuals adhered to the initial intervention they were allocated (by default in our observational analog of the target trial), so the IPTW during the 1st year was 1 for all individuals (i.e. the probability that an individual adhered his/her observed weight change intervention was 1, the same for the inverse of this probability). For the 2\({}^{\text{nd}}\) year (i.e. year 1), we calculated the IPTW as follows.
The unstabilized inverse probability weights for each patient at year 1 (i.e.
\[IPTW_{1}=\frac{1}{f(A_{1}|A_{0},L_{0},L_{1},\overline{D_{1}}=0\ )}\]
As described elsewhere, we fit the multinomial logistic model
\[logit[pr\left(A_{1}=j\big{|}A_{0},L_{0},L_{1},\overline{D}_{1}=0\right)]=\varphi _{0}+\varphi_{1}A_{0}+\varphi_{2}^{T}L_{0}+\ \varphi_{3}^{T}L_{1}\] (S.2)
To be consistent with the notation, we used previously in the outcome regression model,
\[\text{if}\ A_{1}=1\Rightarrow A_{1,wl}=1,A_{1,wm}=0,A_{1,wg}=0\]
\[\text{if}\ A_{1}=2\Rightarrow A_{1,wl}=0,A_{1,wm}=1,A_{1,wg}=0\]
\[\text{if}\ A_{1}=3\Rightarrow A_{1,wl}=0,A_{1,wm}=0,A_{1,wg}=1\]
If the participants develop a severe disease at year 1, then the participants are free to deviate from their intervention. These individuals will not be used in model (S.2), i.e. only healthy individuals contribute in the calculation of the probability of adhering to their intervention in year 1 [\(f(A_{1}|A_{0},L_{0},L_{1},\overline{D}_{1}=0\ )\)], and will have IPTW=1. Of note, we run this model before excluding the individuals who did not adhere to their allocated intervention during the 2\({}^{\text{nd}}\) year.
Moreover, from year 2 onwards, participants were free to deviate from their hypothetical weight change intervention, so the weights remained constant till the end of their follow-up.
We also took into consideration the potential bias due to loss to follow-up, by calculating the effect of an intervention, had the participants remained uncensored. Toimplement that, we additionally multiply IPTW calculated from (S.2) with the reciprocal of the probability of remaining uncensored
More specifically, we calculate the inverse of the probability of remaining uncensored at each time point
\[IPCW_{t}=\prod_{k=0}^{t}\frac{1}{f(C_{k+1}=0|A_{k},\overline{L_{k}},\overline{C _{k}}=0,\overline{D_{k+1}}=0)}\]
by running the pooled logistic regression
\[logit[pr\ (C_{t+1}=1|A_{t},\overline{L_{t}},C_{t}=0,\overline{D_{t+1}}=0)]=d_{0, t}+d_{1}A_{t,wl}+d_{2}A_{t,wg}+\ d_{3}{}^{T}\boldsymbol{L_{0}}+\ d_{4}{}^{T} \boldsymbol{L_{t}}\] (S.4)
Then we calculate \(f(C_{k+1}=0|A_{k},\overline{L_{k}},\overline{C_{k}}=0,\overline{D_{k+1}}=0)\)\(=\)1- \(f(C_{k+1}=1|A_{k},\overline{L_{k}},\overline{C_{k}}=0,\overline{D_{k+1}}=0)\) at each time point and finally we multiply these probabilities through all time points, to estimate \(\prod_{k=0}^{t}f(C_{k+1}=0|A_{k},\overline{L_{k}},\overline{C_{k}}=0,\overline {D_{k+1}}=0)\). Then the \(IPCW_{t}\) is the reciprocal of this probability in each time point.
For IPCW, we used smoking status only for the 1\({}^{\text{st}}\) year (i.e. in the vector \(L_{0}\)). We didn't use information from smoking status in the vector \(L_{k}\), with k\(\geq\)1, from follow-up, due to near positivity violations.
Participant ID=1 was allocated in the weight loss arm (she lost \(\geq\)3% of her bodyweight at year 0 and year 1). She was censored at 7/8/2004, during the 3\({}^{\text{rd}}\) year, so this was recorded in her year 2 raw in C\({}^{\text{t}}\) and in her year 1 in C\({}^{\text{t+1}}\). We subsequently delete any observations from this participant from time 2 onwards (orange line).
Participant ID=2 was allocated in the weight maintenance arm (her bodyweight change was \(<\)3 % at year 0 and year 1). She remained in the weight maintenance arm from year 2 onwards, even if she has no other measures of bodyweight, as after the completion of 2 years, people are free to deviate from their intervention. She developed the CVD outcome during the 7\({}^{\text{th}}\) year (10/11/2007).
Participant ID=3 was allocated in the weight loss arm (she lost \(\geq\)3% of her bodyweight at year 0). She developed cancer (which is included in the set of the severe chronic diseases described in the paper, so she was free to deviate from her intervention) during the 2\({}^{\text{nd}}\) year of follow-up, at 11/12/2007. Even if at time 1 (i.e. during the second year) she gained weight, he remained in the weight reduction arm. Her IPTW is 1 (because she developed cancer at year 1). She was censored during her 3\({}^{\text{rd}}\) year, so we subsequently deleted any observations from this participant from time 2 onwards.
After calculating the IPTW from (S.2), we fitted a (weighted) pooled logistic regression model as the one described in the beginning of section 1 in (S.1), with the only difference being that we add product terms with a linear, a quadratic and a cubic term for time t in the variables for weight loss and weight gain "intervention" at baseline.
\[logit[pr\left(D_{t+1}=1\big{|}A_{0},L_{0},\overline{D}_{t}=0,\overline{C}_{t+1} =0\right)]=\]
\[=c_{0,t}+c_{1}A_{0,wl}+c_{2}A_{0,wg}+c_{3}A_{0,wl}*t+c_{4}A_{0,wg}*t+c_{5}A_{0,wl }*t^{2}+c_{6}A_{0,wg}*t^{2}+\]
\[c_{7}{}^{T}L_{0}\hskip 42.679134pt\text{(S.3)}\]
Then, we created a dataset with all the time points under each "treatment", by copying each subject 3 times (one copy for every arm). We predicted the probability of the events from the (S.3) at each time point t and then we calculated probabilities that the participants remained free from the CVDs [S(t)=1-pr(D(t)=1)] for each person each year under all 3 "interventions". We then multiplied these probabilities (i.e. of remaining free from the outcome) through time t. Finally, we averaged the adjusted time-to-event curves over all subjects, so we obtained marginal time-to-event curves under each "intervention". Finally, we calculate the risk at each time point, by subtracting the marginal time-to-event probabilities from one.
#### Sensitivity analyses
#### 3.1.1 Including physical activity, index of multiple deprivation or ethnicity
We implement complete case analyses, requiring from all individuals to have measurements of physical activity or ethnicity at baseline. We assume in the calculation of the time "windows" of physical activity and smoking status that the last observation carries forward for at most 4 years.
#### 3.1.2 Impact of pre-clinical diseases
To take into consideration the impact of potential bias due to preclinical diseases, we assume that a chronic disease occurred one, two or three years before it was recorded during the follow-up time and we check whether our results remain the same in this sensitivity analysis.
## Section 4
**Extra results**Figure S1: Estimated hazard ratios for non-melanoma skin cancer (i.e.
Figure S2: Percentage of individuals who developed a chronic disease (other than CVD) in the 2nd, 3rd and 4th year, by hypothetical interventions, BMI group
Figure S3: Hazard ratios of the per-protocol analysis emulated (two-year) interventions on cardiovascular diseases in normal weight individuals, using pooled logistic regression, by age group and sex
Figure S4: Hazard ratios of the per-protocol effect of the emulated interventions on the composite CVD outcome in normal weight, overweight and obese individuals.
Figure S5: Hazard ratios of the emulated interventions on cardiovascular diseases in overweight individuals, using pooled logistic regression after assuming that a set of chronic diseases1 occurred two years prior to the recorded date
Figure S6: Hazard ratios of the per-protocol analysis emulated (two-year) interventions on cardiovascular diseases in overweight individuals, using pooled logistic regression, by age group and sex
Figure S6: Hazard ratios of the per-protocol analysis emulated (two-year) interventions on cardiovascular diseases in overweight individuals, using pooled logistic regression, by age group and sex
Figure S7: Hazard ratios of the per-protocol analysis emulated (two-year) interventions on cardiovascular diseases in obese individuals, using pooled logistic regression, by age group and sex
## Section 5 - Codelists used for the outcome definition
## 1) Primary outcome: Composite CVD
The primary outcome (composite CVD) consists of
i.
stable angina (hospitalization),
unstable angina (hospitalization),
other CHD (hospitalization),
v.
CVD deaths
i.
a. Self-reported from primary care (CPRD)
b.
I252
I21
Acute myocardial infarction
I22
Subsequent myocardial infarction
I23
Certain current complications following acute myocardial infarction
I241
Dressler's syndrome
c.
K50.2
Percutaneous transluminal coronary thrombolysis using streptokinase
K50.3
Percutaneous transluminal injection of therapeutic substance into coronary artery NEC.
d.
I21
Acute myocardial infarction
I22
Subsequent myocardial infarction
I23
Certain current complications following acute myocardial infarction
## i.**: **Stable Angina (hospitalization)
## a.
I201
Angina pectoris with documented spasm
I208
Other forms of angina pectoris
I209
Angina pectoris, unspecified
## b. OPSC codes from Hospital Episodes Statistics (HES)
\begin{tabular}{l l} OPCS code & Interpretation \\ K40 & Saphenous vein graft replacement of coronary artery \\ K40.1 & Saphenous vein graft replacement of one coronary artery \\ K40.2 & Saphenous vein graft replacement of two coronary arteries \\ K40.3 & Saphenous vein graft replacement of three coronary arteries \\ K40.4 & Saphenous vein graft replacement of four or more coronary arteries \\ K40.8 & Other specified saphenous vein graft replacement of coronary artery \\ K40.9 & Unspecified saphenous vein graft replacement of coronary artery \\ K41 & Other autograft replacement of coronary artery \\ K41.1 & Autograft replacement of one coronary artery NEC \\ K41.2 & Autograft replacement of two coronary arteries NEC \\ K41.3 & Autograft replacement of three coronary arteries NEC \\ K41.4 & Autograft replacement of four or more coronary arteries NEC \\ \end{tabular}
* **Unsable Angina (hospitalization)** _a.
* I240 Coronary thrombosis not resulting in myocardial infarction
* I248 Other forms of acute ischaemic heart disease
* Acute ischaemic heart disease, unspecified
* Unstable angina
* **Other CHD (hospitalization)** _a.
* I250 Atherosclerotic cardiovascular disease, so described
* I251 Atherosclerotic heart disease
* I253 Aneurysm of heart
* I254 Coronary artery aneurysm
* I255 Ischaemic cardiomyopathy
* I256 Silent myocardial ischaemia
* I258 Other forms of chronic ischaemic heart disease
* Chronic ischaemic heart disease, unspecified
* ICD-10 codes from ONS
* ONS ICD10 Interpretation
* I20 Angina pectoris
* I21 Acute myocardial infarction
* I22 Subsequent myocardial infarction
* I23 Certain current complications following acute myocardial infarction
* I24 Other acute ischaemic heart diseases
* Chronic ischaemic heart disease
* ICD-9 codes from ONS
## v.**: **Heart failure (hospitalization)
## a.
150.0 Congestive heart failure
150.1 Left ventricular heart failure
150.9 Heart failure, unspecified
111.0 Hypertensive heart disease with (congestive) heart failure
113.0 Hypertensive heart and renal disease with (congestive) heart failure
132.2 Hypertensive heart and renal disease with both (congestive) heart failure and renal failure
b.
150.0 Congestive heart failure
150.1 Left ventricular heart failure
150.9 Heart failure, unspecified
111.0 Hypertensive heart disease with (congestive) heart failure
113.0 Hypertensive heart and renal disease with (congestive) heart failure
113.2 Hypertensive heart and renal disease with both (congestive) heart failure
113.2 Hypertensive heart and renal disease with both (congestive) heart failure and renal failure
c.
428 Congestive heart failure, unspecified428.1 Left heart failure
428.9 Heart failure, unspecified
## vi.**: **Stroke
## a. Self-reported from primary care (CPRD)
## b.
I690 Sequelae of subarachnoid haemorrhage
I61 Intracerebral haemorrhage
I60 Subarachnoid haemorrhage
I620 Subdural haemorrhage (acute)(nontraumatic)
I621 Nontraumatic extradural haemorrhage
I629 Intracranial haemorrhage (nontraumatic), unspecified
I693 Sequelae of cerebral infarction
I63 Cerebral infarction
I690 Sequelae of subarachnoid haemorrhage
I61 Intracerebral haemorrhage
I60 Subarachnoid haemorrhage (acute)(nontraumatic)
I621 Nontraumatic extradural haemorrhage
I629 Intracranial haemorrhage (nontraumatic), unspecified
I691 Sequelae of intracerebral haemorrhage
I692 Sequelae of other nontraumatic intracranial haemorrhage
I694 Sequelae of stroke, not specified as haemorrhage or infarction
I698 Sequelae of other and unspecified cerebrovascular diseases
G463 Brain stem stroke syndrome
G464 Cerebellar stroke syndrome
G465 Pure motor lacunar syndrome
G466 Pure sensory lacunar syndrome
G467 Other lacunar syndromes
I64 Stroke, not specified as haemorrhage or infarction _ICD-10 codes from ONS_
ONS ICD10 code Interpretation
1690
Sequelae of subarachnoid haemorrhage
161
Intracerebral haemorrhage
160
Subarachnoid haemorrhage
1620
Subdural haemorrhage (acute)(nontraumatic)
1621
Nontraumatic extradural haemorrhage
1629
Intracranial haemorrhage (nontraumatic), unspecified
1693
Sequelae of cerebral infarction
163
Cerebral infarction
1690
Sequelae of subarachnoid haemorrhage
161
Intracerebral haemorrhage
160
Subarachnoid haemorrhage (acute)(nontraumatic)
1621
Nontraumatic extradural haemorrhage
1629
Intracranial haemorrhage (nontraumatic), unspecified
1694
Sequelae of stroke, not specified as haemorrhage or infarction
1698
Sequelae of other and unspecified cerebrovascular diseases
164
Stroke, not specified as haemorrhage or infarction
1672
Cerebral atherosclerosis
1679
Cerebrovascular disease, unspecified ICD-9 codes from ONS
ICD9 code Interpretation
431 intracerebral hemorrhage
430 Subarachnoid hemorrhage
4321 Other and unspecified intracranial hemorrhage ; Subdural hemorrhage
4320 Other and unspecified intracranial hemorrhage ; Nontraumatic extradural hemorrhage
4329 Other and unspecified intracranial hemorrhage ; Unspecified intracranial hemorrhage
433 Occlusion and stenosis of precerebral arteries
434 Occlusion of cerebral arteries
431 Intracerebral hemorrhage
430 Subarachnoid hemorrhage
4321 Other and unspecified intracranial hemorrhage ; Subdural hemorrhage
4320 Other and unspecified intracranial hemorrhage ; Nontraumatic extradural hemorrhage
4329 Other and unspecified intracranial hemorrhage ; Unspecified intracranial hemorrhage
436 Acute, but ill-defined, cerebrovascular disease
4370 Other and ill-defined cerebrovascular disease ; Cerebral atherosclerosis
4379 Other and ill-defined cerebrovascular disease ; Unspecified
## vii.
1.
## 2) Secondary outcome: Composite CHD
## Composite CHD consists of
## i.
## ii. stable angina (hospitalization),
## iii. unstable angina (hospitalization),
**iv. other CHD (hospitalization),** |
111245_file07 | ## Supplementary Correlation between IgG positivity and number of symptoms.****a**, **b**, Distribution of the IgG equivocal population (IgG 12-15 AU/mL) (**a**) and IgG truly positive population (IgG>15 AU/mL) (**b
Both populations follow a sigmoidal, four parameter logistic curve whereby X is the number of symptoms. Distribution R\({}^{2}\) numbers are reported to demonstrate the fitness of the curve.
## Supplementary Association between site and IgG positivity.
Odds-ratio calculated with multilevel logistic analysis.
## Supplementary Distribution of the IgG positive population (IgGz12 AU/mL) according to smoke.
Odds ratio calculated with multilevel logistic analysis (OR=0.45; 95%CI 0.34-0.60, \(p\)<0.0001).
## Supplementary ROC analysis of relationship between IgG positivity and symptoms.
Logistic model.
Supplementary Association between role and IgG plasma levels. Odds-ratio calculated with logistic regression applied to ordinal data.
## Supplementary Association between smoking and IgG plasma levels.
## a**, Distribution of the IgG positive population (IgGz12 AU/mL) as plasma levels divided by smoking habit (yes or no). \(p\)-value was calculated using Kruskal-Wallis test; **b
Odds-ratio calculated with logistic regression applied to ordinal data. LR test for global null hypothesis, p=0.207.
## Supplementary IgG plasma level distribution in the positive population (IgG = 12 AU/mL) versus symptoms across all and the two major sites, ICH and Gavazzeni.
The areas under the curve are respectively: 571 All, 550 ICH, 522 Gavazzeni. Below each graph is reported the corresponding ROC curve. All of them show 100% of sensitivity and specificity.
Supplementary Table 3 Sensitivity, specificity and positive Likelihood ratio of symptoms
\begin{tabular}{|l|c c c c c c|} \hline
## Symptoms** & **True pos** & **False pos** & **True neg** & **False neg** & **LR pos** & **LR neg
\\ \hline Fever & 40.9\% & 8.2\% & 91.8\% & 59.1\% & 5.01 & 1.55 \\ \hline Low-grade Fever & 78.0\% & 9.0\% & 91.0\% & 78.0\% & 8.63 & 1.17 \\ \hline Cough & 38.0\% & 20.6\% & 79.4\% & 62.0\% & 1.85 & 1.28 \\ \hline Sore Throat/Runny nose & 43.4\% & 30.9\% & 69.1\% & 56.6\% & 1.40 & 1.22 \\ \hline Muscle pain & 52.2\% & 21.8\% & 78.2\% & 62.0\% & 2.39 & 1.26 \\ \hline Asthenia & 44.7\% & 14.8\% & 85.2\% & 55.3\% & 3.01 & 1.54 \\ \hline Anosmia/Dysgeusia & 48.6\% & 3.3\% & 96.7\% & 51.4\% & 14.75 & 1.88 \\ \hline Gastrointestinal disorders & 32.5\% & 18.8\% & 81.2\% & 67.5\% & 1.73 & 1.20 \\ \hline Conjunctivis & 16.3\% & 9.2\% & 90.8\% & 83.7\% & 1.77 & 1.08 \\ \hline Dyspnea & 16.8\% & 4.9\% & 95.1\% & 83.2\% & 3.41 & 1.14 \\ \hline Chest pain & 18.0\% & 6.6\% & 93.4\% & 82.0\% & 2.74 & 1.14 \\ \hline Tachycardia & 15.7\% & 10.1\% & 89.9\% & 84.3\% & 1.55 & 1.07 \\ \hline Pneumonia & 5.5\% & 0.1\% & 99.9\% & 94.5\% & 38.39 & 1.06 \\ \hline Other symptoms & 6.9\% & 3.5\% & 96.5\% & 93.1\% & 1.97 & 1.04 \\ \hline Fever \& Anosmia/Dysgeusia & 25.6\% & 0.9\% & 99.1\% & 74.4\% & 28.61 & 1.33 \\ \hline \end{tabular}
Supplementary Table 4b: Summary measures of association of comorbidity with IgG positivity
\begin{tabular}{|l||r|r|r|r|} \hline Comorbidity & Odds ratio & \multicolumn{2}{c|}{95\% CI} & \multicolumn{1}{c|}{P value} \\ \hline COPD & 3.17 & 0.79 & 12.71 & 0.1034 \\ Asthma & 0.91 & 0.59 & 1.41 & 0.6664 \\ \hline Dyslipidemia/High Cholesterolemia & 0.94 & 0.64 & 1.39 & 0.7661 \\ \hline Active NPL & NM & NM & NM & NM \\ History of NPL & 0.98 & 0.52 & 1.82 & 0.9398 \\ Chronic heart failure & NM & NM & NM & NM \\ Hypertension & 1.13 & 0.76 & 1.67 & 0.5401 \\ History of CHD & 0.52 & 0.06 & 4.30 & 0.5452 \\ Atrial Fibrillation & 1.29 & 0.39 & 4.26 & 0.6712 \\ History of TIA/Stroke & 0.97 & 0.11 & 8.41 & 0.9757 \\ Steatosis/Cyrrhosis & 0.81 & 0.16 & 3.99 & 0.7972 \\ Other hepatic diseases & 0.47 & 0.10 & 2.24 & 0.3456 \\ Chronic kidney failure & 0.50 & 0.05 & 4.93 & 0.5493 \\ Rheumatoid arthritis & 1.92 & 0.91 & 4.04 & 0.0858 \\ Other Immune system diseases & 1.08 & 0.72 & 1.64 & 0.7013 \\ Diabetes & 0.19 & 0.02 & 1.42 & 0.1055 \\ Gouet & NM & NM & NM & NM \\ Other comorbidities & 0.65 & 0.44 & 0.95 & 0.0274 \\ Number of comorbidities & 0.92 & 0.80 & 1.06 & 0.2414 \\ \hline Multilevel logistic analysis, considering subjects nested in the hospital site. Adjusted for role, age (cut off = 60 years), gender, BMI, smoking habits. & NM = not measurable & & \\ \hline \end{tabular}
\begin{tabular}{l|r|r|r|r|r|r|} Instruments technician & 17 & 31.90 & 23.80 & 48.70 & 16.20 & 63.10 \\ \hline Staff & 17 & 31.90 & 23.80 & 48.70 & 16.20 & 63.10 \\ \hline Other & 179 & 31.20 & 20.30 & 56.10 & 12.10 & 265.00 \\ \hline
## Total
& 522 & 31.20 & 18.60 & 54.80 & 12.10 & 778.00 \\ \hline \end{tabular}
Kruskal Wallis test statistic for categorical variable; Cuzick's test for trend for ordinal variables.
Supplementary Table 7 Medians and percentiles of IgG plasma levels in relation to symptoms
\begin{tabular}{|l|c|c|c|c|c|c|} \hline \hline & \multicolumn{6}{c|}{**Positivity \(\pm\)12AU/mL**} \\ \cline{2-7} & **N** & **Median** & **25deg**centile** & **75deg**centile** & **Min** & **Max** & **P value\({}^{*}\)** \\ \hline
## Pneumonia
& & & & & & \textless{}0.0001 \\ \hline No & 493 & 29.80 & 18.30 & 50.20 & 12.10 & 778.00 & \\ \hline Yes & 29 & 76.10 & 58.80 & 105.00 & 12.10 & 178.00 & \\ \hline
## Others
& & & & & & 0.1722 \\ \hline No & 486 & 30.40 & 18.50 & 52.60 & 12.10 & 778.00 & \\ \hline Yes & 36 & 39.65 & 21.75 & 58.50 & 12.10 & 174.00 & \\ \hline
## Number of symptoms
& & & & & & 0.014 \\ \hline
0 symptoms & 62 & 26.30 & 18.60 & 39.70 & 12.10 & 257.00 & \\ \hline
1 symptoms & 56 & 23.25 & 17.60 & 34.50 & 12.20 & 778.00 & \\ \hline
2 symptoms & 65 & 33.10 & 16.10 & 56.60 & 12.30 & 160.00 & \\ \hline
3 symptoms & 61 & 26.80 & 18.00 & 45.40 & 12.80 & 128.00 & \\ \hline
4 symptoms & 55 & 27.80 & 19.50 & 60.50 & 12.20 & 265.00 & \\ \hline
5 or more symptoms & 223 & 36.60 & 21.60 & 61.40 & 12.10 & 178.00 & \\ \hline
## Fever and Anosmia/Dysgeusia
& & & & & & \textless{}0.0001 \\ \hline No & 189 & 26.10 & 16.10 & 48.70 & 12.10 & 778.00 & \\ \hline Fever & 119 & 28.80 & 19.20 & 44.20 & 12.20 & 170.00 & \\ \hline Anosmia/Dysgeusia & 80 & 32.95 & 21.25 & 57.85 & 12.30 & 174.00 & \\ \hline Fever and Anosmia/Dysgeusia & 134 & 39.10 & 23.80 & 63.60 & 12.10 & 265.00 & \\ \hline
## Total
& 522 & 31.20 & 18.60 & 54.80 & 12.10 & 778.00 & \\ \hline \hline \end{tabular}
Kruskal Wallis test statistic for categorical variable, Cuzick's test for trend for ordinal variables
\begin{tabular}{l|c|c|c|c|c|c|c|c} \hline \hline & \multicolumn{8}{c}{**Positivity \(\pm\)12AU/mL**} & \multicolumn{1}{c}{**P value\({}^{*}\)**} \\ \cline{2-9} & **N** & **Median** & **25\({}^{*}\)centile** & **75\({}^{*}\)centile** & **Min** & **Max** & \\ \hline
## Chronic kidney failure
& & & & & & & 0.1197 \\ No & 521 & 31.20 & 18.60 & 53.90 & 12.10 & 778.00 & \\ Yes & 1 & 110.00 & 110.00 & 110.00 & 110.00 & 110.00 & \\ \hline
## Rheumatoid arthritis
& & & & & & & 0.2702 \\ \hline No & 510 & 31.20 & 19.20 & 55.40 & 12.10 & 778.00 & \\ \hline Yes & 12 & 31.70 & 14.60 & 41.70 & 13.90 & 56.10 & \\ \hline
## Other immune disorders
& & & & & & & 0.7754 \\ No & 483 & 31.10 & 18.50 & 55.40 & 12.10 & 778.00 & \\ \hline Yes & 39 & 34.30 & 20.00 & 50.10 & 13.50 & 147.00 & \\ \hline
## Diabetes mellitus
& & & & & & & 0.0938 \\ No & 521 & 31.20 & 18.60 & 53.90 & 12.10 & 778.00 & \\ \hline Yes & 1 & 167.00 & 167.00 & 167.00 & 167.00 & 167.00 & \\ \hline
## Gout
& & & & & & & na \\ No & 522 & 31.20 & 18.60 & 54.80 & 12.10 & 778.00 & \\ Yes & 0 &. &. &. & & & \\ \hline
## Other comorbidities
& & & & & & & 0.0082 \\ No & 482 & 29.85 & 18.40 & 52.00 & 12.10 & 778.00 & \\ \hline Yes & 40 & 44.85 & 26.05 & 76.15 & 12.10 & 139.00 & \\ \hline
## Number of comorbidities
& & & & & & & 0.2895 \\ \hline
0 comorbidity & 345 & 29.10 & 18.50 & 52.00 & 12.20 & 778.00 & \\ \hline
1 comorbidity & 133 & 33.40 & 19.70 & 56.20 & 12.10 & 178.00 & \\ \hline
2 comorbidities & 29 & 30.20 & 15.70 & 48.90 & 12.30 & 169.00 & \\ \hline
3 comorbidities & 11 & 50.10 & 33.10 & 65.20 & 15.50 & 107.00 & \\ \hline
4 or more comorbidities & 4 & 38.25 & 19.95 & 83.05 & 19.50 & 110.00 & \\ \hline
## Total
& 522 & 31.20 & 18.60 & 54.80 & 12.10 & 778.00 & \\ \hline \hline \end{tabular}
Kruskal Wallis test statistic for categorical variable, Cuzick's test for trend for ordinal variablesSupplementary Table 9 Medians and percentiles of IgG plasma levels in relation to vaccinations
\begin{tabular}{|l|c|c|c|c|c|c|c|} \hline & \multicolumn{6}{c|}{**Positivity \(\pm\)12AU/mL**} & \multicolumn{1}{c|}{**P value\({}^{*}\)**} \\ \cline{2-7} & **N** & **Median** & **25\({}^{*}\)**centile** & **75\({}^{*}\)**centile** & **Min** & **Max** & \\ \hline
## 2019/2020 Flu vaccine
& & & & & & & 0.5250 \\ \hline No & 360 & 31.25 & 19.25 & 55.65 & 12.10 & 778.00 & \\ \hline Yes & 162 & 30.50 & 18.50 & 51.10 & 12.20 & 160.00 & \\ \hline
## Antipneumococcus
& & & & & & 0.0299 \\ \hline No & 500 & 31.70 & 19.50 & 55.65 & 12.10 & 778.00 & \\ \hline Yes & 22 & 24.70 & 15.00 & 29.40 & 12.20 & 139.00 & \\ \hline
## Anti-Tubercolor
& & & & & & 0.6550 \\ \hline No & 476 & 31.25 & 19.10 & 53.85 & 12.10 & 778.00 & \\ \hline Yes & 46 & 29.25 & 18.00 & 56.30 & 12.10 & 133.00 & \\ \hline
## Other Vaccinations
& & & & & & 0.9761 \\ \hline No & 488 & 31.15 & 18.50 & 53.25 & 12.10 & 778.00 & \\ \hline Yes & 34 & 32.10 & 20.30 & 58.80 & 12.20 & 96.60 & \\ \hline
## Number of vaccinations
& & & & & & 0.5928 \\ \hline
0 vaccination & 303 & 31.50 & 19.50 & 55.30 & 12.10 & 778.00 & \\ \hline
1 vaccination & 180 & 30.30 & 18.55 & 53.40 & 12.10 & 160.00 & \\ \hline
2 vaccinations & 33 & 31.60 & 14.10 & 56.60 & 12.20 & 139.00 & \\ \hline
3 or more vaccinations & 6 & 26.65 & 18.40 & 29.40 & 13.40 & 45.40 & \\ \hline
## Total
& 522 & 31.20 & 18.60 & 54.80 & 12.10 & 778.00 & \\ \hline \end{tabular}
Kruskal Wallis test statistic for categorical variable, Cuzick's test for trend for ordinal variables
## Supplementary Data S1. Questionnaire.
## Questionario anamnestico di arruolamento
## Caratteristiche Socio-Demografiche
Nome
Cognome
Data di nascita
Codice fiscale
E-mail
Genere
Peso
Altezza
Fumo sigaretta (n./die)
## Lavoro
Dove laviori?
\(\bullet\) Humanitas Rozzano (ICH)
\(\bullet\) Humanitas San Pio X
\(\bullet\) Humanitas Gavazzeni
\(\bullet\) Humanitas Mater Domini (HMD)
\(\bullet\) Humanitas University (HU)
\(\bullet\) Humanitas Medical Care (HMD)
Che ruolo ha in ospedale?
\(\bullet\) Medico
\(\bullet\) Chirurgo
\(\bullet\) Anestesista
\(\bullet\) Infermiere
\(\bullet\) OSS
\(\bullet\) Tecnico di Radiologia
\(\bullet\) Tecnico di Laboratorio
\(\bullet\) Biology
\(\bullet\) Fisioterapista
\(\bullet\) PARC
\(\bullet\) Staff
\(\bullet\) Personale Ricerca
\(\bullet\) Studente
\(\bullet\) Servizio Trasporto
\(\bullet\) Servizio Pulizie
\(\bullet\) AltroIn media nelle ultime settimane quante volte sei uscito di casa non per motivi di lavoro durante la settimana? [N.]
Negli ultimi mesi hai lavorato da casa [SI/NO]
Se si, per quanti gg/settimana
## ANAMENESI PATOLOGICA PROSSIMA- SINTOMATOLOGIA RIFERITA
Nel periodo dal 1\({}^{\circ}\) Febbraio 2020 ad oggi, ha o ha avuto uno o piu dei seguenti sintomi?
\(\bullet\) Febbre, con temperatura superiore ai 37,5\({}^{\circ}\)C
\(\bullet\) Febbricola, temperatura inferiore o uguale 37,5\({}^{\circ}\)C per almeno tre giorni consecutivi
\(\bullet\) Tosse
\(\bullet\) Mal di gola e/o raffreddore
\(\bullet\) Mal di testa
\(\bullet\) Dolori muscolo-articolari
\(\bullet\) Astenia
\(\bullet\) Perdita di gusto e/o olfatto
\(\bullet\) Disturbi gastrointestinali (diarrea, nausea, vomito)
\(\bullet\) Congiuntivite (occhi arrossati)
\(\bullet\) Difficolta respiratoria/dispnea (senso di affanno a riposo)
\(\bullet\) Dolore al petto (dolore allo sterno)
\(\bullet\) Tachicardia/Palpitazioni
\(\bullet\) Polmonite
## ANAMENESI PATOLOGICA REMOTA - ComORBIDITA
Soffre cronicamente o le sono state diagnosticate una o piu di queste condizioni?
\(\bullet\) Broncopneumopatia Cronico Ostruttiva
\(\bullet\) Asma
\(\bullet\) Dislipidemia (colesterolo o trigliceridi alti) [SI/NO]
\(\bullet\) Neoplasie attive
\(\bullet\) Neoplasie pregresse
\(\bullet\) Ipertensione
\(\bullet\) Scompenso cardiaco cronico
\(\bullet\) Coronaropatie pregresse
\(\bullet\) Fibrillazione atriale
\(\bullet\) Pregresso lctus/TIA cerebrale
\(\bullet\) Insufficienza renale cronica
\(\bullet\) Steatosi/Cirrosi
\(\bullet\) Altre malattie epatiche (ad es.
\(\bullet\) Altre malattie del sistema immunitario (ad es.
\(\bullet\) Gotta
\(\bullet\) Demenze
## ALTE CONDIZION DA SEGNALARE
\(\bullet\) Interventi chirurgici nell'ultimo anno in anesthesia generale \(\bullet\) Trapianti
\(\bullet\) Allergie
\(\bullet\) Gravidanza
\(\bullet\) Immunosuppressione/ Trattamenti immunosuppressivi
## VaccinaZIONI
Antinfluenzale nell' autumno/inverno 2019/2020 [SI/NO]
Antipneumococcica [SI/NO]
Anti-Tuberculace [SI/NO]
## Esposizione COVID-19
Negli ultimi 3 mesi e entrato/a in stretto contatto (contatto diretto a meno di 2 metri di distanza, o in ambiente chiuso come casa, sede di lavoro, mezzo di trasporto) con **casi accertati** o sospetti di COVID-19?
Se si, chi era?
Collega
Paziente
Familiarare
Altro_specifcare |
115915_file02 | ### Robustness of the model with respect to the definition of the infectiousness probability
We consider here another infectiousness curve that has been derived in the recent literature by He et al.. We follow here the author-correction version, that followed a critic and correction suggestion on the first version.
We show that, although this curve is different from the curve \(\omega\) that we use in this paper, the predictions of the model do not change significantly, showing their robustness with respect to changes in the infectiousness curve.
In the cited works the infectiousness is defined by means of two probability density functions (PDFs): The incubation time \(g(t)\) (probability of symptom onset as a function of the time \(t\) since infection), and the infectiousness probability \(f(t)\), which is a function of the time \(t\) elapsed since the symptom onset (\(t\) can take negative values because of pre
\begin{table}
\begin{tabular}{|c|c|c|c|c|} \hline \(R_{0}\) & 3.0 & 2.0 & 1.5 & 1.2 \\ \hline \(r_{R_{0}}\) & 1.0 & 0.53 & 0.39 & 0.26 \\ \hline \end{tabular}
\end{table}
Table 5: In the first row the desired values of \(R_{0}\) are reported, while the second row shows the corresponding values of the reduction factor \(r_{R_{0}}\) needed to obtain them, with a scaling factor \(p_{R_{0}}=60\).
Left and central panels: Growth or decrease rate of the number of newly infected individuals for each policy, assuming respectively that the dependence of infectiousness from duration and proximity follows the pink curves and the blues curves of Supplementary The reducing factor \(r_{R_{0}}\) is set to have \(R_{0}=1.5\) and we assume 40% app adoption. All the points have been obtained as mean values over \(n=200\) simulations and the error bars represent the standard error.
symptomatic infectiousness). In more details, the function \(g\) is in turn taken from Li et al., and it is a lognormal distribution with mean \(1.434065\) and std \(0.6612\). The function \(f\) is instead estimated by He et al.: it is assumed to be a gamma distribution, and via a max-likelihood approach it is estimated to have shape \(20.516508\) and scale \(1.592124\), and to be shifted by an offset \(12.272481\).
From these \(g,f\), we can reconstruct a PDF \(\omega_{\mathrm{He}}(\tau)\) to be used in our model. This can be done simply by sampling two values from \(g\) and \(f\) and adding them (the total time from infection to secondary infection is simply split into two intervals separated by the time of symptoms onset).
\[\omega_{\mathrm{He}}(\tau)=\int_{-\infty}^{\infty}f(\tau-t)g(t)dt,\]
The discretized convolution is also shown in Supplementary Fig. 3b, and it coincides indeed with the numerical values of \(\omega_{\mathrm{He}}\).
Observe that this distribution assigns a positive probability (\(6.01\%\), see below) also to infectiousness at negative times (i.e. an individual may infect another one before being itself infected). We assume that this is due to the fact that the two distributions \(f\) and \(g\) are estimated from two different populations, and thus statistical errors may be present. For our aims this is not a limitation, as it just mean that the (cumulative) probability of infection at zero is strictly positive.
Supplementary shows also the PDF \(\omega\) that we used in the paper. Both distributions peak roughly at the same time (\(\omega\) at 5 days, while \(\omega_{\mathrm{He}}\) at 4 days). On the other hand, \(\omega_{\mathrm{He}}\) has a wider support and a larger right tail, meaning that it models a non negligible probability of secondary infection also several days after the infection of the spreader.
To have an analytical expression of \(\omega_{\mathrm{He}}\) we try to fit shifted lognormal, gamma, and Weibull distributions to \(\omega_{\mathrm{He}}\) by least-squares minimization over the PDF obtained by convolution. The best results are obtained with a gamma distribution with density \(h(\tau)=\frac{p_{1}^{2}}{\Gamma(p_{1})}\tau^{p_{1}-1}e^{-p_{2}\tau}\) with parameters \(p_{1}=5.73\), \(p_{2}=0.55\), and shifted by \(4.67\), which is plotted in Supplementary This allows also to derive an explicit cumulative density function \(\mathrm{CDF}_{\mathrm{He}}\) of \(\omega_{\mathrm{He}}\), which gives an estimate of \(\mathrm{CDF}_{\mathrm{He}}=0.0601\) (the fraction of negative-time infections).
We can now use this modified infectiousness \(\omega_{\mathrm{He}}\) in our model and compare the results with the ones of of the main text. First, we estimate again the reduction parameter defining \(\omega_{\mathrm{data}}\) (see Section of the main text), and we get \(r_{R_{0}}=0.35\).
Using this functional form of \(\omega_{\mathrm{He}}\) in the model, we obtain the results of Supplementary (see central panel in of the main text for the corresponding results with \(\omega\)). It is clear that the difference is quite limited since only Policy 1 and Policy 2 for \(\varepsilon_{I}=0.8\) move from being ineffective (Fig. 5, main text) to being effective. We can thus conclude that no significant change in our conclusions would be introduced by adopting this alternative infectiousness function in place of the current one. In particular, the predictions using \(\omega\) appear to be less optimistic in the prediction of the policies' effectiveness, since they estimate that not all policies are successful for \(\varepsilon_{I}=0.8\).
**Tracing policy efficiency for alternative infectiousness.** Growth or decrease rate of the number of newly infected individuals using the modified infectiousness curve \(\omega_{\text{He}}\). The points correspond to the parameter pairs such that \(\varepsilon_{I}\) is an input and \(\varepsilon_{T}\) an output of the simulations on real contact data, for the policies of Here \(R_{0}=1.5\) with \(40\%\) app adoption. All the points have been obtained as mean values over \(n=200\) simulations and the error bars represent the standard error.
|
119057_file02 | #### ii.1.2 Population structure and contact patterns
The annual population size by age in each year from the pre-PCV7 to the post-PCV13 period was obtained from census data and the estimated demographic changes out to 2030 from the Office of National Statistics. The contact pattern within and between age groups was derived from the POLYMOD survey conducted in the UK in 2006 supplemented by an additional contact survey among infants under one year.
#### ii.1.3 PCV coverage data
Vaccine coverage by dose, monthly birth cohort and calendar month in the PCV7 catch-up and the routine 2+1 PCV7 programme up to 2008 was obtained from the General Practice Research databaseas previously described. Thereafter, coverage for the second priming dose and the booster dose was obtained from annual national coverage data.
#### Model structure
#### ii.1.1 Model population
The population in the model is divided into 100 annual age cohorts (0, 1, 2, 3,..., 99). Each annual age-cohort is divided into 48 equal-sized age-cohorts (in total 4,800 age-cohorts in the total population in the model).
#### ii.1.2 Transition between model compartments
In the absence of vaccination individuals are born susceptible (S) to pneumococcal carriage and become infected (I) with a VT1, VT2 or NVT serotype as determined by the serogroup-specific force of infection. An episode of carriage does not result in protection against subsequent carriage of any serotype (i.e. SIS model structure). Invasive disease is assumed to occur at the time of carriage acquisition whereas transmission can occur at any time during the carriage episode. Individuals clear their infection with age-dependent clearance rates as estimated previously and become susceptible again. Individuals already carrying a serotype from one of the three groupings will have some degree of protection against infections from another serotype grouping according to the level of competition between the three serotype groupings. These competition parameters determine the extent of serotype replacement in carriage (and therefore in IPD) when vaccine serotypes decline post-PCV introduction.
[https://doi.org/10.1371/journal.pmed.1002845.g002](https://doi.org/10.1371/journal.pmed.1002845.g002).
#### ii.1.3 Vaccine efficacy parameters
Within the vaccine protected group, two doses in the first year of life or one dose after 12 months of age are assumed to confer the maximum degree of protection that can be obtained from PCV7 or PCV13 against carriage acquisition of the respective serotype grouping (termed full protection). A single dose in the first year of life is assumed to provide half the maximum protection (termed partial protection). Protection wanes exponentially with fully protected individuals moving back to the partially protected group and then back to the fully susceptible group. For the base case the average duration of protection for both full and partial protection is set at 5 years.
Vaccine efficacy against IPD given carriage of a vaccine serotype for fully protected individuals is assumed to be 100% at the time of vaccination and to wane with the same average duration as for the full and partial protection respectively against carriage.
[https://doi.org/10.1371/journal.pmed.1002845.q003](https://doi.org/10.1371/journal.pmed.1002845.q003).
The propensity to develop invasive disease upon carriage acquisition within each age group will be determined by the overall case-carrier ratio (CCR) of serotypes comprising the VT1, VT2 and NVT groupings ([https://doi.org/10.1371/journal.pmed.1002845.q006](https://doi.org/10.1371/journal.pmed.1002845.q006)) and is derived from the ratio of IPD cases: incident carriage infections within each serotype grouping in each age group.
#### Model parameter estimation
The model fitting process consists of a static pre-vaccination equilibrium component and post-vaccination dynamic component. By fitting the model to the given datasets, we estimate 26 model parameters: competition parameters for six age groups and three serotype groupings, the two vaccine efficacies against carriage acquisition of VT1 and VT2 serotypes and an additional parameter that allows for an increase in the case carrier ratio of the serotypes in the NVT group after 2013/14 when the rate of serotype replacement suddenly increased. This last parameter is allowed to vary between each of the six age groups generating in total 26 parameters.
[https://journals.plos.org/plosmedicine/article/figure?id=10.1371/journal.pmed.1002845.t001](https://journals.plos.org/plosmedicine/article/figure?id=10.1371/journal.pmed.1002845.t001).
As described in Choi et al the force of infection and clearance parameters that determine the rate of acquisition and termination of a new carriage episode for the VT1, VT2 and NVT groups were estimated by fitting a static model to the pre-vaccination carriage data. The competition parameters that determine the extent to which carriage of serotypes in one group protects against acquisition of serotypes in another group were estimated by fitting a post-vaccination model to the changes in serotype grouping after the introduction of PCV7 and PCV13 from 2005/6 to 2015/16.
The uncertainty intervals were generated from 500 randomly selected sets of model parameters that generated outputs within +-0.3 of the set that gave the maximum likelihood value obtained using the Nelder-Mead Downhill Simplex method when compared with the post-PCV IPD data.
[https://journals.plos.org/plosmedicine/article/figure?id=10.1371/journal.pmed.1002845.t002](https://journals.plos.org/plosmedicine/article/figure?id=10.1371/journal.pmed.1002845.t002).
VECVT1 (Vaccine efficacy against acquiring VT1 carriage) and VEcVT2 (Vaccine efficacy against acquiring VT2 carriage) were estimated at 0.55 (0.53, 0.57) and 0.30 (0.26, 0.36) respectively (minimum and maximum).
#### Long-term simulations
Using the 500 parameter sets obtained for the uncertainty boundary the model simulated various scenarios to investigate the potential impact of two lockdowns occurred during the COVID-19 pandemic until 2030/31, the furthest year for which there are population age-structure predictions.
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120964_file02 | ## Figure 6/S2.
This figure shows all nine of the PLV scalp maps generated by sliding windows of 200ms, overlapped by 50%. Thus, the PLV windows reported in the main text were selected from this set of nine, i.e. windows 1, 3, 5, 7, 9.
## 3 Stimulus-locking analyses
Phase-lockingAs shown in Figure 3, we used EEGLAB to generate pre-stimulus alpha (10 Hz) phase-aligned event-related potentials images at electrode Pz, for randomly-selected correct inhibition or response trials, separately for the two TOVA conditions (H1 and H2). For the control group a moving-window smoothing of 100 trials was applied; and, as above, smoothing for ADHD was adjusted to 300 (H1) and 260 (H2). Thecenter for phase alignment was set at 80 ms before stimulus onset.
## Figure 7/S3.
Stacked correct-trial amplitudes, aligned to the pre-stimulus (-80 ms) alpha (10 Hz) phase, shown separately for the first and second halves of TOVA (H1 and H2) for both groups. Amplitude from -10.9 to 10.9 \(\mu V\) is colour-coded to blue and red, respectively. The control group shows higher amplitudes in all stimulus-locked waves, i.e. phase-resetting reaction is enhanced compared to ADHD group.
## Inter-Trial Coherence
EEGLAB was used to compute 10 Hz alpha Inter-Trial Coherence (ITC) at Pz, separately for the two TOVA conditions (H1 and H2) and two groups, shown in EEGLAB computes statistical significance of the ITC via permutation testing of single-trial spectral estimates across latencies (Delorme & Makeig, 2004).
## Figure 8/S4.
Inter-trial coherence calculated for both groups and both TOVA conditions - all four ITC curves show peak around 200ms and smaller harmonic peaks, especially at 400. Wider lines show when ITC was significantly above chance level (the level of ITC which is significant depends on the sample, so no horizontal indicator is drawn).
## Top row
## 2nd row
ADHD group condition H1 v H2 - a small reduction from H1 to H2 is seen.
## 3rd row**: control H1 v ADHD H1 - substantial peak differences are seen at 200 (\(\sim\)40%) & 400 (\(\sim\)120%) ms. **4th row
Control v ADHD comparisons also show that ADHD ITC is more dispersed, i.e. having weaker phase-locking to targets.
## 4 Descriptive Statistics and Analysis Results
## Table A1.
The final number of participants and trials per participant used for statistical EEG analyses, split by group.
\begin{tabular}{c c c c c} \hline & TOVA condition & Number of participants & EEG trials \\ & or time segment & & & per participant \\ \cline{3-4} & & ADHD & Control & \\ \hline Correct inhibition & H1-H2 & 42 & 15 & 108 \\ Correct response & H1-H2 & 40 & 14 & 108 \\ All correct trials & H1 & 45 & 15 & 102 \\ Continuous EEG & H2 & 39 & 15 & 102 \\ & segments 1-3 & 49 & 18 & - \\ \hline \hline \end{tabular}
## Table A2.
Descriptive statistics of key standardised behavioural variables.
\begin{tabular}{c c c c c c c c} \hline & & & ADHD & & & Control & \\ \cline{3-8} Source & Time & Mean & SD & 95\% CI & Mean & SD & 95\% CI \\ \hline RT variability & H1 & 89.02 & 28.32 & 80.88-97.15 & 100.19 & 17.57 & 91.45-108.92 \\ & H2 & 86.99 & 30.12 & 78.34-95.65 & 101.36 & 16.13 & 93.34-109.39 \\ & H1 & 109.42 & 12.18 & 105.92-112.92 & 115.16 & 10.46 & 109.95-120.36 \\ Mean RT & H2 & 109.04 & 14.82 & 104.78-113.30 & 111.21 & 9.70 & 106.38-116.02 \\ Commission errors & H1 & 98.90 & 10.83 & 95.79-102.01 & 104.56 & 6.58 & 101.29-107.83 \\ & H2 & 83.08 & 25.11 & 75.87-90.30 & 91.26 & 20.36 & 81.14-101.38 \\ & H1 & 99.26 & 5.41 & 97.71-100.81 & 100.61 & 5.18 & 98.04-103.19 \\ & H2 & 75.95 & 55.29 & 60.07-91.83 & 90.70 & 27.68 & 76.94-104.47 \\ & H1 & 92.18 & 16.88 & 87.33-97.03 & 102.20 & 17.68 & 93.41-110.99 \\ d’ & H2 & 78.07 & 28.02 & 70.02-86.12 & 82.43 & 29.19 & 67.91-96.95 \\ \hline \hline \end{tabular}
_Note._ Scores \(>\) 85 are within or above normal limits, scores 80-85 indicate borderline ADHD, scores \(<\) 80 indicate performance that is not within normal limits.
\begin{table}
\begin{tabular}{c c c c c c c} \hline Group & Measure & df & Error df & \(F\) & \(p\)\(<\) & \(\eta^{2}\) \\ \hline \multirow{4}{*}{ADHD} & RT variability & 1 & 48 &.26 &.610 &.005 \\ & RT mean & 1 & 48 &.15 &.702 &.003 \\ & Commission errors & 1 & 48 & 26.08 &.0005*** &.352 \\ & Omission errors & 1 & 48 & 11.15 &.002** &.189 \\ & d’ & 1 & 48 & 20.16 &.0005*** &.296 \\ \hline \multirow{4}{*}{Control} & RT variability & 1 & 17 &.10 &.752 &.006 \\ & RT mean & 1 & 17 & 3.83 &.067 &.184 \\ \cline{1-1} & Commission errors & 1 & 17 & 11.58 &.003** &.405 \\ \cline{1-1} & Omission errors & 1 & 17 & 2.31 &.147 &.120 \\ \cline{1-1} & d’ & 1 & 17 & 8.67 &.009* &.338 \\ \hline \end{tabular} _Note. *_ significant at p\(<\).05, ** p\(<\).005, *** p\(<\).0005, Bonferroni adjusted for multiple comparisons.
\end{table}
Table A3: Main effect of group (MANOVA) and simple effects of group (separate ANOVAs) on each TOVA standardised variable, split by test halves.
\begin{table}
\begin{tabular}{c c c c c c c} \hline Source & Time & df & Error df & \(F\) & \(p\)i & \(\eta^{2}\) \\ \hline \multirow{2}{*}{Group (main effect)} & H1 & 5 & 62 & 1.45 &.218 &.105 \\ & H2 & 5 & 62 & 1.26 &.294 &.092 \\ & H1 & 1 & 68 & 2.71 &.104 &.039 \\ & H2 & 1 & 68 & 4.52 &.037* &.064 \\ & H1 & 1 & 68 & 2.55 &.115 &.037 \\ & H2 & 1 & 67 &.055 &.815 &.001 \\ Commission errors & H1 & 1 & 67 & 4.12 &.046* &.059 \\ & H2 & 1 & 68 & 1.68 &.119 &.025 \\ & H1 & 1 & 67 &.95 &.333 &.014 \\ & H2 & 1 & 67 & 1.18 &.282 &.017 \\ d’ & H1 & 1 & 68 & 5.30 &.024* &.074 \\ & H2 & 1 & 68 &.68 &.412 &.010 \\ \hline \end{tabular} _Note. *_ significant at \(p\)\(<\).05, Bonferroni adjusted for multiple comparisons.
\end{table}
Table A4: Simple effects of TOVA condition on standardised scores in each group.
## Table A5.
Effect of time segment on frontal (F3, F4, Fz) and parietal (P3, P4, Pz) alpha (8-12 Hz) power.
\begin{tabular}{c c c c c c c c c} \hline \hline & & & & & & & & Pairwise comparisons \\ Electrodes & Measure & df & Error df & \(F\) & _p\(<\)_ & \(\eta^{2}\) & 1\(<\)2 & 1\(<\)3 & 2\(<\)3 \\ \hline & 8 Hz & 1.32 & 85.56 & 9.91 &.001** &.132 & ** & ** & ns \\ Frontal & 9 Hz & 1.36 & 88.54 & 22.05 &.0005*** &.253 & ** & *** & *** \\ (F3, F4, Fz) & 10 Hz & 1.72 & 111.67 & 29.64 &.0005*** &.313 & *** & *** & *** \\ & 11 Hz & 1.71 & 111.38 & 38.30 &.0005*** &.371 & *** & *** & *** \\ & 12 Hz & 1.59 & 103.41 & 30.37 &.0005*** &.318 & *** & *** & *** \\ \hline & 8 Hz & 1.40 & 90.91 & 7.39 &.003** &.102 & * & * & ns \\ & 9 Hz & 1.50 & 96.58 & 18.14 &.0005*** &.218 & *** & *** & * \\ Parietal (P3, P4, Pz) & 10 Hz & 1.50 & 97.49 & 23.20 &.0005*** &.263 & *** & *** & ** \\ & 11 Hz & 1.59 & 103.57 & 25.98 &.0005*** &.286 & *** & *** & ** \\ & 12 Hz & 1.52 & 98.48 & 27.94 &.0005*** &.301 & *** & *** & *** \\ \hline \hline _Note._* significant at p\(<\).05, ** p\(<\).005, *** p\(<\).0005. Degrees of freedom are Greenhouse-Geisser adjusted for violations of sphericity. Time segments in the pairwise comparisons are \(1\) = first 5 minutes of TOVA (infrequent mode), \(2\) = middle 5 minutes (both infrequent and frequent mode), \(3\) = last 5 minutes (frequent mode).
## Table A6.
Effect of TOVA condition on parieto-occipital pre-stimulus alpha (8-12 Hz) power.
\begin{tabular}{c c c c c c c} \hline \hline Measure & df & Error df & \(F\) & _p\(<\)_ & \(\eta^{2}\) & Comparisons \\ \hline
8 Hz & 1 & 51 & 2.96 &.092 &.055 & H1\(<\)H2 n.s. \\
9 Hz & 1 & 51 & 4.28 &.044* &.077 & H1\(<\)H2* \\
10 Hz & 1 & 51 & 9.27 &.004** &.154 & H1\(<\)H2* \\
11 Hz & 1 & 51 & 8.08 &.006* &.137 & H1\(<\)H2* \\
12 Hz & 1 & 51 & 13.27 &.001** &.206 & H1\(<\)H2** \\ \hline \hline \end{tabular}
_Note._ Bonferroni adjusted for multiple comparisons: * significant at p\(<\).05, ** p\(<\).005.
** p\(<\).0005. |
121145_file02 | ### Determining the observed time period
Fitting the model to the available data requires to determine the duration of the observed period for each household, which is used in the simulations providing the likelihood calculations below. We restrict the observed time period as follows:
1. To set the start date of the observed period in a given household, we first identify the earliest indication of infection in the household, which is either onset of symptoms of a positive case or a first positive test. While testing a household was prompted by reporting of symptoms, in \(\sim\) 10% of the households, the earliest indication was a positive test, which could be attributed either to missing reports of symptoms or to cases in which the symptomatic individual who prompted the initial testing was found to be negative (our data set does not include reports of symptoms for negative cases). In addition, in cases in which the reported symptoms onset was over four weeks prior to the first test, the onset date of symptoms was discarded (12 cases).
2. If the earliest indication is an onset of symptoms, then the start date is set to be five days prior to this onset (the mean incubation period). Otherwise the start date is set as 10 days prior to the first date of a positive test (the mean time from infection to detection, during March-April 2020, as estimated from Israeli epidemiological investigation data, see Figure S2 below). This determination of the initial date reflects the approximate timing of infection of the index case.
3. The end date of the observed period was set as the latest date on which some household member was tested positive for the first time.
### Determining the age group of the index case
The reported onset dates of symptoms and test dates were also used to discern the index case in each household. Positive household members whose first indicative date (onset of symptoms or first positive test) was five or less days from the earliest indicative date of all positive household members were considered suspected index cases with equal probability. Thus, for example, if there were three positive household members whose first indicative date was within five days of the first indicative date in the household, each of the three were given a probability of being an index case of 1/3 (and the rest of the household were given probability 0). For each household, the probability that the index case is an adult (child) was obtained by summing the probability of being an index case for all the adults (children) in that household. See in the main text for examples of the determination of the observed period and the suspected index cases in two households, using the above criteria. TableS1 presents the number of households with a given probability assigned for the index case to be an adult. Note that in most cases this probability is either 1 or 0.
### The likelihood function
Assume that we have information on a set of households indexed by \(h\). For each household we have the data:
\[(N_{a}(h),N_{c}(h),\rho(h),I_{a}(h),I_{c}(h),D(h)),\]
The variables \(I_{a}(h)\) and \(I_{c}(h)\) stand for the number of adults and of children who were infected, while \(D(h)\) is the duration of the observed outbreak, determined as described in the main text.
Consider a household \(h\), and assume that the index case \(i\) is of type \(ind(h)\) (where \(ind=a\) for an adult or \(ind=c\) for a child index case).
\[P_{h}(I_{a},I_{c}\mid ind,\beta)\]
In order to compute \(P_{h}\) we run \(S=1000\) realizations of the simulation of the household model, for a household with \(N_{a}(h)\) adults, \(N_{c}(h)\) children and with index case of type \(ind\), with the parameters \(\beta\)for a duration of \(D(h)\) days. We generate a table of the fraction of the simulations in which each of the possible outcomes was obtained, thus obtaining estimates for the above probabilities.
Given the actual outcome \((I_{a}(h),I_{c}(h))\) in a household the likelihood corresponding to this household, taking into account the uncertainty regarding the identity of the index case, is
\[L_{h}\left(\beta\right)=\rho(h)P(I_{a}(h),I_{c}(h)\mid a,\beta)+(1-\rho(h))P(I_ {a}(h),I_{c}(h)\mid c,\beta).\]
The likelihood corresponding to the entire data set is given by the product of the likelihoods corresponding to each of the households:
\[L(\beta)=\prod_{h}L_{h}(\beta),\]
and the corresponding log-likelihood is
\[LL(\beta)=\sum_{h}\log L_{h}(\beta).\]
To estimate the parameters \(\beta\) we maximize \(LL(\beta)\) over the parameters \(\beta\). Specifically, we consider the special structure of the \(\beta\) matrix given by.
## 3 Comparison with an alternative model
We compared our model with an alternative, naive model fit to the data. We considered a simpler model in which in each household, all the infected members were infected by the index case, with no secondary infections within the household. We assume that in a household with an adult index case, the probability that a child will be infected is \(p_{ca}\) and the probability that an adult will be infected is \(p_{aa}\). Similarly, in a household with a child index case, the probability that a child will be infected is \(p_{cc}\) and the probability that an adult will be infected is \(p_{ac}\). In this simple model, in a household with \(N_{a}\) adults and \(N_{c}\) children and an adult index case, the number of children infected in the household will be binomially distributed with \(n=N_{c}\), \(p=p_{ca}\), and the number of adults infected (excluding the index case) will be binomially distributed with \(n=N_{a}-1\) and \(p=p_{aa}\), and similarly for a household with a child index case. We therefore refer to this model as the binomial model. The parameters in this binomial model are easily estimated as the ratio of the number of individuals infected to the number of individuals at risk.
\[\hat{p}_{aa}=0.45,\quad\hat{p}_{ca}=0.24,\quad\hat{p}_{ac}=0.49,\quad\hat{p}_{ cc}=0.31.\]
Figure S3 suggests that the dynamic model fits the data considerably better than the naive binomial alternative. Note that the dynamic model has 3 parameters compared to 4 of the binomial, hence is a more parsimonious model.
Bootstrap simulations
In order to obtain parametric bootstrap confidence intervals for the ML parameter estimates we ran 1000 simulations of the dynamic model using the ML parameter estimates and employing the exact same households as in the Bnei-Brak data, and generated the number of infected children and adults in each household. We then re-estimated the parameters for these simulated data sets. The results are shown in Figure S4. The obtained 95% confidence intervals are \([0.35-0.45]\) for \(\beta_{aa}\), \([0.30-0.40]\) for \(\gamma\) and \([0.55-0.90]\) for \(\delta\).
## 5 Sensitivity analysis
Sensitivity analysis was performed to examine the stability of the results to variations in the assumptions made when fitting the data.
### Sensitivity to observed epidemic duration
We examined the sensitivity to variations in the observed epidemic time-period of the households in the data. We modified the duration of the observed epidemic in each household in the data set as follows: If a household's first indicative date was some member's symptom onset date, then instead of using the mean incubation time to determine the start time of the epidemic, we sampled an incubation period from the incubation time distribution in the general COVID-19 cases data in Israel. If a household's first indicative date was some member's first test date, then instead of using the mean detection time to determine the start time of the epidemic, we sampled an detection period from the detection time distribution in the general COVID-19 cases data in Israel. We refitted the model to this data set to estimate the model parameters. This was repeated 100 times. The results of this test are shown in Figure S5. Blue color indicates the ML parameter estimates obtained using the duration set as in the main text. In most cases the inferred parameter values were identical or very similar to the original estimates, demonstrating small sensitivity of the results to the exact number of days the epidemic was observed in each household.
### Sensitivity to uncertainty regarding the index case age-group
We examined the sensitivity of the results to the fact that in some cases the age-group to which the index case belongs is uncertain. In cases where the index case age-group was not certain (in 75 of the 637 households - see Table S1), we randomly selected an age-group for the index case according to the probability of the index case being in each of the age-groups (as described in the Methods section). The model parameters were re-estimated by fitting the model to this data set. This was repeated 100 times. The results of this test are shown in Figure S6. Blue color indicates the ML parameter estimates obtained using the original data set. In most cases the inferred parameter values were identical or very similar to the original estimates, demonstrating small sensitivity of the results to the uncertainty regarding the index case age-group.
### Sensitivity to the mean generation-time
This analysis is aimed for testing the sensitivity of the estimation results to the mean of the generation-time distribution. Recall that in the main text the results were obtained using a generation-time distribution with a mean value of 4.5. Here, we generated 100 simulated data sets with the exact household types as in the Bnei-Brak data set, while employing the ML parameter estimates and a generation-time distribution with mean of 4 days. Then we fitted a model to this data set assuming a mean generation time of 4.5 days, as used in Section Results of the main text. The results are presented in the top row of Figure S7. It shows that the obtained estimates are not too sensitive to these deviations from the actual mean generation time. We repeated this type of analysis, now generating 100 data sets with a mean generation time of 5 days, and fitting again a model to this data set assuming a mean generation time of 4.5 days. The results are presented in the bottom row of Figure S6 and here as well, the estimates are not too sensitive to such deviations.
Figure S7: Results for data sets with mean generation-time of 4 days (top row) and mean generation-time of 5 days (bottom row). \(\beta_{aa}\) - the transmission parameter among adults, \(\gamma\) - relative susceptability of children, \(\delta\) - relative infectivity of children.
Positive rates per 10,000 in different age groups
Figure S8 shows the positive rates per 10,000 in different age groups through time. Since the re-opening of schools on September 1st the infection rates in children aged 15-19 has more than doubled, and seem to have triggered growing infection rates in other age groups as well.
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122358_file03 | ## 4 Additional Calculations and Application to Serology Studies
The studies in New York and Chelsea provided only positive testing rates, not prevalence estimates. The positive testing rate is not the same as the prevalence. We conduct sensitivity analyses after including initial calculations. Results were generally similar. Often the estimated prevalence (and PPV) was slightly lower than the seropositivity rate.
First, we break down the probability of testing positive in equation.
\[P(T=1) = P(T=1\cap D=1)+P(T=1\cap D=0)\] \[= P(T=1|D=1)P(D=1)+P(T=1|D=0)P(D=0)\] \[= P(T=1|D=1)P(D=1)+[1-P(T=0|D=0)][1-P(D=1)]\] \[= p*sensitivity+(1-p)*(1-specificity)\] \[= p*(sensitivity+specificity-1)+(1-specificity)\]
The proportion testing positive in a seroprevalence study can be used to estimate the true prevalence. Denote \(\hat{p}_{t}\) as the observed proportion who have have antibodies. We can substitute \(\hat{p}_{t}\) on the left hand side of as an estimate for \(P(T=1)\) and solve for the prevalence \(\hat{p}\). The result is equation:
\[\hat{p} = \frac{\hat{p}_{t}-(1-specificity)}{sensitivity+specificity-1}\] \[= \frac{specificity+\hat{p}_{t}-1}{sensitivity+specificity-1}\] \[= \frac{specificity-(1-\hat{p}_{t})}{sensitivity+specificity-1}\]
It is important to note that this means not every combination of sensitivity and specificity is possible for a given positive testing rate, as otherwise the estimated prevalence will be negative. Given that sensitivity and specificity are usually large (e.g.
\[sensitivity+specificity-1>0\]
In order for the prevalence estimate to be non-negative, this means that the numerator must also be non-negative, and we would expect
\[\hat{p}_{t}\geq(1-specificity) \tag{12}\]That is, the positive rates observed in a seroprevalence study, \(\hat{p}_{t}\) should be at least be large as the false positive rate of the antibody test used in that study. Indeed, if we saw fewer positive tests than the proportion of (false) positive tests expected by chance if everyone were lacking antibodies, then we would have little evidence to suggest that the prevalence is nominally different from zero. A sensitivity analysis follows for the studies in Chelsea and New York, which reported only seropositivity estimates. While the seropositive rates are not necessarily identical to the prevalence estimate, the estimated seropositivity rate was generally either close or a slight overestimate of the prevalence.
### Chelsea
In Chelsea, the original seropositivity rate was 31.5%. The updated prevalence estimates based on was 27.9%, which is about 3.6% lower than the proportion who tested positive. Using this lower prevalence yields a lower PPV or 78.6%, which would correspond to about to expecting about 49 of the positive tests to be true positives and 14 to be false positives.
### New York
In the New York serology study presented in Section 4 of the main text, there were 156 estimates of PPV, resulting from the product of 3 possible values for sensitivity, 4 potential values for specificity, and 13 potential seropositivity estimates from the two studies.
Prevalence estimates were calculated based on. Unlike in the sensitivity analysis for Chelsea, 36 scenarios resulted in negative estimated prevalence values. For these combinations, the estimated PPV would be zero, which is lower than the PPV in the paper. The false positive rate in the sensitivity analysis would be even higher in the sensitivity analysis than in the paper.
For the 120 remaining scenarios with estimated positive prevalence values, the difference between the prevalence and positivity rate was generally small and centered close to zero. Among the 120 scenarios, the differences between the two estimated proportions ranged from -6.2% to 4.7% with a median difference of -0.3% and a mean difference of 0.6%. While the distribution of differences in prevalence was approximately symmetric, the distribution of differences in PPV was strongly left-skewed. The median difference in PPV was -0.96% and mean difference was -5.44%, with a range from -41% to 1.4%. The large differences in absolute value of PPV correspond to values where the PPV in this sensitivity analysis is much lower than the PPV when using seropositivity to estimate prevalence. However, most differences were small in absolute value, meaning that most PPV estimates were similar regardless of which value was used for prevalence.
An updated plot of PPV by prevalence estimated with is shown in Figure S2. The shape is similar to in the main text, with noticeable missing segments for combinations with the lower bound of specificity and prevalence estimates outside of the range from about 5% to 20%. Small prevalence and specificity estimates likely violate Expression.
### Comparison with Other Types of Tests for SARS-Cov-2
It is important to note the difference in analysis and interpretation in this paper, compared to other tests for SARS-COV-2. Our paper showed that NPV was reasonably high and PPV was low for serology tests, with a lot of potential for harm for false positive serology tests, such as increasing risk for Covid19.
The interpretations differ for diagnostic tests. False positives for diagnostic tests would mean that an uninfected patient would be quarantined and their contacts tested. False negative diagnostic tests would mean that an infected person could be erroneously cleared, their future contacts consequently put at risk of exposure, and their past contacts less likely to be tested.
Thus, the potential harm for a false negative diagnostic test likely exceeds the potential harm for a false positive diagnostic test. Consequently, calculations and interpretations related to NPV should be emphasized for diagnostic tests to mitigate this harm.
While a rigorous analysis for other types are outside of the scope of this paper, we will provide some comments. We showed that PPV was closely related to specificity. Similarly, NPV is related closely to sensitivity. Thus, it is imperative that diagnostic tests for SARS-Cov-2 have high sensitivity. It is unclear whether this is true in practice, as there have been reports and analyses of diagnostic tests having high false negatives.
## 5 Additional Results for Tests Approved for EUA after May 2020
The tests in this section were approved after the paper was originally submitted in June 2020 and added when responding to reviewer comments in early December 2020. For completeness, graphs of PPV by prevalence are included for all of these new tests to parallel the graphs of the tests available previously.
Results are found in Figures S3 to S9.
# Figure S9.
EUA Tests: Su-Z |
127860_file02 | ## Full Model:
\[S^{\prime} = -S\left(1+\psi\right)\lambda+(1-\theta_{c})\alpha_{c}S_{c}+\alpha_{ q}S_{q}\] \[(S_{c})^{\prime} = S\frac{(1-p)}{p}\phi\lambda+\frac{(1-p)}{p}\nu_{q}\phi_{q}S_{q} \lambda-\alpha_{c}S_{c}-\nu_{c}S_{c}\lambda\] \[(S_{q})^{\prime} = \sigma S\lambda-\alpha_{q}S_{q}+\theta_{c}\alpha_{c}S_{c}-\nu_{q} \left(1+\frac{(1-p)}{p}\phi_{q}\right)S_{q}\lambda\] \[E^{\prime} = \left(1-\phi-\xi\right)S\lambda+\left(1-\phi_{c}-\xi_{c}\right) \nu_{c}S_{c}\lambda+\left(1-\phi_{q}-\xi_{q}\right)\nu_{q}S_{q}\lambda-\frac{ 1}{\tau}E \tag{1}\] \[(E_{c})^{\prime} = \phi S\lambda+\phi_{c}\nu_{c}S_{c}\lambda+\phi_{q}\nu_{q}S_{q} \lambda-\frac{1}{\tau}E_{c}\] \[(E_{q})^{\prime} = \xi S\lambda+\xi_{c}\nu_{c}S_{c}\lambda+\xi_{q}\nu_{q}S_{q} \lambda-\frac{1}{\tau}E_{q}\] \[I^{\prime} = \frac{1}{\tau}E-\frac{1}{T}I\] \[(I_{c})^{\prime} = \frac{1}{\tau}E_{c}-\frac{1}{T_{c}}I_{c}\] \[(I_{q})^{\prime} = \frac{1}{\tau}E_{q}-\frac{1}{T_{q}}I_{q}\] \[R^{\prime} = \frac{1}{T}I+\frac{1}{T_{q}}I_{q}+\frac{1}{T_{c}}I_{c}\] \[(R_{c})^{\prime} = \frac{1}{T_{c}}I_{c}-\alpha_{c}R_{c},\]
The description of all variables and parameters for the model Eq. are given in Table S1. For model fitting, we take \(\phi=\phi_{q},\phi_{c}=1,\xi=\xi_{c}=0,\xi_{q}=1-\phi_{q}\), which specifies that the proportion of non-quarantined and quarantined susceptible individuals contact-traced upon infection is uniform, while all contact-traced susceptible individuals continue to be traced and quarantined susceptibles whom are not traced remain quarantined upon infection (see in main text for the schematic diagram). For deriving final size results in next section, we specify different conditions for these parameters, which serve as approximations of the final size in the general model, along with exact formulae for important special cases which do not require some of these parameters, e.g. "perfectly shielding" quarantine.
The _time-dependent_ effective reproduction number \(\mathcal{R}_{t}\) can be defined utilizing the next-generation approach. First define the feasible region for the system Eq. as
\[\Gamma=\left\{\mathbf{x}=\left(S,S_{c},S_{q},E,E_{c},E_{q},I,I_{c},I_{q}\right) ^{T}\in\mathbb{R}_{+}^{9}\mid N:=\sum_{i=1}^{9}\mathbf{x}_{i}\leq N_{0}\right\},\]
We note that the system Eq. is quasi-positive, and thus its solutions remain non-negative when their initial values are nonnegative.
Summing the right-hand sides of Eq., we find that \(N^{\prime}(t)=0\). Thus the solutions the system Eq. remain in \(\Gamma\) when their initial values are in \(\Gamma\). Notice that any susceptible population distributed among the defined classes, \(S,S_{c},S_{q}\), \(\mathcal{E}_{0}:=(S,S_{c},S_{q},0,0,0,0,0)^{T}\) is a disease-free equilibrium of system Eq..
We define a next-generation matrix by considering the linearized system at the disease-free equilibrium, \(\mathcal{E}_{0}\). Write the linearized "infection" sub-system as \(\mathbf{y}^{\prime}=(F-V)\mathbf{y}\), where \(F\) contains entries corresponding to new infections, and \(-V\) contains all other transition terms in the Jacobian matrix evaluated at \(\mathcal{E}_{0}\). Define the current susceptibility and infection transition probabilities of the population by \(\mathcal{S}=(1-\phi-\xi)\,S+(1-\phi_{c}-\xi_{c})\,\nu_{c}S_{c}+(1-\phi_{q}-\xi_ {q})\,\nu_{s}S_{q}\), \(\mathcal{S}^{c}=\phi S+\phi_{c}\nu_{c}S_{c}+\phi_{q}\nu_{q}S_{q}\) and \(\mathcal{S}^{q}=\xi S+\xi_{c}\nu_{c}S_{c}+\xi_{q}\nu_{s}S_{q}\). Thus, we consider the following matrices:
\[F=\begin{pmatrix}0&0&0&\mathcal{S}\beta/N&\mathcal{S}\beta_{c}/N&\mathcal{S} \beta_{q}/N\\ 0&0&\mathcal{S}^{\prime}\beta/N&\mathcal{S}^{\prime}\beta_{c}/N&\mathcal{S}^{ \prime}\beta_{q}/N\\ 0&0&0&\mathcal{S}^{q}\beta/N&\mathcal{S}^{q}\beta_{c}/N&\mathcal{S}^{\prime} \beta_{q}/N\\ 0&0&0&0&0&0\\ 0&0&0&0&0&0\\ 0&0&0&0&0&0\end{pmatrix},\quad V=\begin{pmatrix}\frac{1}{\tau}&0&0&0&0&0\\ 0&\frac{1}{\tau}&0&0&0&0\\ 0&0&\frac{1}{\tau}&0&0&0\\ -\frac{1}{\tau}&0&0&1/T&0&0\\ 0&-\frac{1}{\tau}&0&0&1/T_{c}&0\\ 0&0&-\frac{1}{\tau}&0&0&1/T_{q}\end{pmatrix}.\]
The next-generation matrix describing expected number of new infections (by the different types of infectious cases) is then defined as \(FV^{-1}\). The effective reproduction number, \(\mathcal{R}_{e}\), is the spectral radius \(\varrho(FV^{-1})\):
\[\mathcal{R}_{e}=\varrho(FV^{-1})=\beta T\mathcal{S}+\beta_{c}T_{e}\mathcal{S} ^{c}+\beta_{q}T_{q}\mathcal{S}^{q} \tag{3}\]
Next we derive the following theorem about asymptotic behavior and final size of an outbreak in our model.
**Theorem 1**.: _Consider model Eq. with non-negative initial conditions satisfying \(\beta(E(t_{0})+I(t_{0}))+\beta_{q}(E_{q}(t_{0})+I_{q}(t_{0}))+\beta_{c}((E_{c}( t_{0})+I_{c}(t_{0}))>0\). Then all variables remain non-negative and \(\lim_{t\to\infty}(E(t_{0})+I(t_{0})+E_{q}(t_{0})+I_{q}(t_{0})+(E_{c}(t_{0})+I_{ c}(t_{0}))=0\). Next suppose that \(\phi=\phi_{c}=\phi_{q}\), \(\xi=\xi_{c}=\xi_{q}\), \(\alpha_{q}=0\), \((1-\theta_{e})\alpha_{c}=0\). In addition let \(\nu_{c}=\nu_{q}\), and denote \(\nu=\nu_{c}=\nu_{q}\) and \(S_{m}=S_{c}+S_{q}\). Define the final (cumulative) epidemic size \(\mathcal{C}_{\infty}\), and the final proportion of susceptible (not monitored) individuals \(U_{\infty}:=\frac{S(\infty)}{S(t_{0})}\). Then the following final size formula holds:_
\[\ln\left(U_{\infty}\right) =(1+\psi)\mathcal{R}_{e}\left(U_{\infty}-1-\frac{S_{m}(t_{0})}{S( t_{0})}\left(U_{\infty}^{\nu/(1+\psi)}+1\right)+\frac{\psi}{1+\psi-\nu}\left( \left(U_{\infty}\right)^{\nu/(1+\psi)}-U_{\infty}\right)\right)\] \[\qquad-(1+\psi)\left[\beta T(E(t_{0})+I(t_{0}))/N+\beta_{q}T_{q}( E_{q}(t_{0})+I_{q}(t_{0}))/N+\beta_{c}T_{c}(E_{c}(t_{0})+I_{c}(t_{0}))/N\right],\] \[\mathcal{C}_{\infty} =S(t_{0})\left(\frac{N}{S(t_{0})}-\frac{\psi}{1+\psi-\nu}\left( \frac{1-\nu}{\psi}U_{\infty}+U_{\infty}^{\nu/(1+\psi)}\right)\right)-S_{m}(t_{ 0})U_{\infty}^{\nu/(1+\psi)}. \tag{4}\]
Proof.: Non-negativity and boundedness of solutions has already been demonstrated. Now, inspired by final size derivation in, we write the model as follows:
\[x^{\prime} =\pi Dy\beta bx-Vx \tag{5}\] \[y^{\prime} =-Dy\beta bx+g(y)+Ay,\quad\text{where}\] \[D =\begin{pmatrix}1&0&0\\ 0&\nu_{c}&0\\ 0&0&\nu_{q}\end{pmatrix},\;b^{T}=\begin{pmatrix}0\\ 0\\ 0\\ \frac{\beta_{c}}{N\beta}\end{pmatrix},\;\pi=\begin{pmatrix}1-\phi-\xi&1-\phi_ {c}-\xi_{c}&1-\phi_{q}-\xi_{q}\\ \phi&\phi_{c}&\phi_{q}\\ \xi&\xi_{c}&\xi_{q}\\ 0&0&0\\ 0&0&0\\ 0&0&0&0\end{pmatrix},\] \[g(y) =S\begin{pmatrix}\frac{-\psi}{1-\rho}\phi\\ \frac{1-\rho}{\rho}\phi\\ \frac{1}{\rho}\phi_{q}\end{pmatrix}+\nu_{q}S_{q}\begin{pmatrix}0\\ \frac{1-\rho}{\rho}\phi_{q}\\ -\frac{T_{c}}{p}\phi_{q}\end{pmatrix},\quad A=\begin{pmatrix}0&(1-\theta_{c} )\alpha_{c}&\alpha_{q}\\ 0&-\alpha_{c}&0\\ 0&0&\alpha_{q}\end{pmatrix}.\]
Then
\[(x+\pi y)^{\prime}=-Vx+\pi g(y(t))x(t)S(t)+\pi Ay \tag{6}\] \[x(t_{0})-x(\infty)+\pi(y(t_{0})-y(\infty))=V\int\limits_{t_{0}}^ {\infty}x(t)dt+\int\limits_{t_{0}}^{\infty}\pi g(y(t))x(t)S(t)dt+\int\limits_{ t_{0}}^{\infty}\pi Ay(t)dt\] \[\Rightarrow x(t_{0})-x(\infty)+\pi(y(t_{0})-y(\infty))+\int\limits_{t_{0 }}^{\infty}\pi Ay(t)dt=V\int\limits_{t_{0}}^{\infty}x(t)dt-\int\limits_{t_{0}}^{ \infty}\pi g(y(t))x(t)S(t)dt\] \[\Rightarrow\int\limits_{t_{0}}^{\infty}x(t)dt=V^{-1}\left[\pi(y(t_ {0})-y(\infty))+x(t_{0})\right]+\int\limits_{t_{0}}^{\infty}\pi g(y(t))x(t)S(t) dt+\int\limits_{t_{0}}^{\infty}\pi Ay(t)dt.\]Note that the integrals on the right-hand side of Eq. can be bounded in norm as \(C\int\limits_{t_{0}}\left\|x(t)\right\|dt\) for an appropriate positive constant \(C\). All other terms in Eq. (including \(x(\infty)=\limsup x(t)\)) are finite in norm, in particular \(\left\|Ay(t)\right\|=0\). Therefore the integral \(C\int\limits_{t_{0}}\left\|x(t)\right\|dt\) is finite, which implies that \(\left\|x(t)\right\|\to 0\) as \(t\to\infty\). This proves the first statement.
Furthermore assuming \(\phi=\phi_{c}=\phi_{q}\), \(\xi=\xi_{c}=\xi_{q}\), \(\alpha_{q}=0\), \((1-\theta_{c})\alpha_{c}=0\), then \(\pi g(y(t))=\mathbf{0}^{T}\), and
\[S^{\prime} =-S(1+\psi)\beta bx\] \[\Rightarrow\ln\left(\frac{S(t_{0})}{S(\infty)}\right) =(1+\psi)\beta b\int\limits_{t_{0}}^{\infty}x(t)dt\] \[\Rightarrow\ln\left(\frac{S(t_{0})}{S(\infty)}\right) =(1+\psi)\beta bV^{-1}\left(\pi(y(t_{0})-y(\infty))+x(t_{0})\right)\]
Now \(y(\infty)=(S(\infty),S_{c}(\infty),S_{q}(\infty))^{T}\).
Since \(\nu=\nu_{c}=\nu_{q}\), we can derive the following relationship between \(S\) and \(S_{m}:=S_{c}+S_{q}\):
\[S^{\prime}_{c}+S^{\prime}_{q} =-\frac{(1-p)\phi}{p(1+\psi)}S^{\prime}-\frac{\sigma}{1+\psi}S^{ \prime}-S_{c}\nu_{c}\lambda(t)-S_{q}\nu_{q}\lambda(t)\] \[S^{\prime}_{m} =-c_{1}S^{\prime}+c_{2}\frac{S^{\prime}}{S}S_{m},\quad\text{where }\ c_{1}=\frac{\psi}{1+\psi},\ c_{2}=\frac{\nu}{1+\psi}\] \[\Rightarrow\left(S_{m}(t)S^{-c_{2}}(t)\right)^{\prime}=-c_{1}S^{ \prime}(t)S^{-c_{2}}(t)\] \[\Rightarrow S_{m}(\infty)S^{-c_{2}}(\infty)-S_{m}(t_{0})S^{-c_{2}}(t_{0})= \frac{c_{1}}{-c_{2}+1}\left(S^{-c_{2}+1}(t_{0})-S^{-c_{2}+1}(\infty)\right)\]
Define the _final (cumulative) epidemic size_\(\mathcal{C}_{\infty}\), and the final proportion of susceptible (not monitored) individuals \(U_{\infty}:=\frac{S(\infty)}{S(t_{0})}\). When plugging in Eq. into Eq., we derive the following relationship:
\[\ln\left(U_{\infty}\right) =(1+\psi)\mathcal{R}_{e}\left(U_{\infty}-1-\frac{S_{m}(t_{0})}{S( t_{0})}\left(U_{\infty}^{\nu/(1+\psi)}+1\right)+\frac{\psi}{1+\psi-\nu}\left((U_{\infty})^{\nu/(1+\psi)}-U_{\infty}\right)\right)\] \[\qquad-(1+\psi)\beta bV^{-1}x(t_{0})\] \[\mathcal{C}_{\infty} =N-S(\infty)-S_{m}(\infty),\] \[\mathcal{C}_{\infty} =S(t_{0})\left(\frac{N}{S(t_{0})}-\frac{\psi}{1+\psi-\nu}\left( \frac{1-\nu}{\psi}U_{\infty}+U_{\infty}^{\nu/(1+\psi)}\right)\right)-S_{m}(t_{ 0})U_{\infty}^{\nu/(1+\psi)},\]
If we start from the beginning of an outbreak, letting \(t_{0}=0\), then
\[\ln\left(U_{\infty}\right) =(1+\psi)\mathcal{R}_{0}\left(U_{\infty}-1+\frac{\psi}{1+\psi-\nu }\left(\left(U_{\infty}\right)^{\nu/(1+\psi)}-U_{\infty}\right)\right)\] \[\mathcal{C}_{\infty} =N\left(1-\frac{\psi}{1+\psi-\nu}\left(\frac{1-\nu}{\psi}U_{ \infty}+U_{\infty}^{\nu/(1+\psi)}\right)\right).\]
In the case that \(\nu=0\), the formula reduces to:
\[\ln\left(U_{\infty}\right)=\mathcal{R}_{0}\left(U_{\infty}-1\right),\quad \mathcal{C}_{\infty}=N\frac{1}{1+\psi}(1-U_{\infty}),\]
Furthermore in the above special case, along with the restriction that \(\nu=0\), a formula measuring peak infected levels can be derived along the lines of the method outlined in. For simplicity, we consider the instance of perfect quarantine (\(\beta_{q}=\beta_{c}=0\)) in model Eq.. Define \(\mathcal{Y}(t):=E(t)+I(t)\). Then it is not hard to see that \(\mathcal{Y}^{\prime}(t)=0\) when \(\mathcal{R}_{e}(t)=1\), where \(\mathcal{R}_{e}(t)=\mathcal{R}_{0}\frac{S(t)}{N}\). Let \(t_{p}\) the time of peak (non-quarantined) infected, where \(\mathcal{Y}(t_{p})=\mathcal{Y}_{peak}:=\max_{t>0}\mathcal{Y}(t)\). Then we obtain the following: If we obtain the formula if \(\mathcal{Y}=E+I\approx 0\):
\[\frac{d\mathcal{Y}}{dS} =\frac{1}{1+\psi}\left(1-\frac{1}{\mathcal{R}_{e}(t)}\right)\] \[\Rightarrow\int_{0}^{t_{p}}d(\mathcal{Y}(t)) =\int_{0}^{t_{p}}\frac{1}{1+\psi}\left(1-\frac{N}{\mathcal{R}_{0 }S(t)}\right)d(S(t))\] \[\Rightarrow\mathcal{Y}_{peak} =\frac{N}{(1+\psi)\,\mathcal{R}_{0,b}}\left(\ln\frac{1}{\mathcal{ R}_{0}}+\mathcal{R}_{0}-1\right).\]
### Data Fitting to Model
We utilize data on total reported cases and quarantined contacts in mainland China published in publicly available daily reports by NHC (National Health Commission of the People's Republic of China) []. We first fit both our full model Eq. (parameter assumptions in Sect. A and diagram in in main text) and simplest model Eq. simultaneously to (cumulatively reported case data and (daily number of) quarantined contacts utilizing a weighted least squares algorithm. We utilized a nonlinear weighted least squares algorithm, minimizing the objective function \(J(t)=R(t)+wC_{q}(t)\), where \(w=0.05\) is a chosen positive weight and the variables \(R(t)\) and \(C_{q}(t)\) represent cumulative reported cases and number of quarantined contacts, respectively. The fitting optimization algorithm is implemented in MatLab via the lsqcurvefit function, which utilizes the interior-reflective Newton method.
For the model fits presented in main text, we utilize a baseline reproduction number, \(\mathcal{R}_{0,b}=6\), fixed infectious periods and incubation periods. The fixed parameters are detailed in Table S1, and fitted parameters for simplified model ( in main text) and full model are presented in Table S1 and Table S3, respectively. Furthermore we conduct an uncertainty analysis detailed in next subsection for the simplified model fit. We note that our model initiates on January 21, 2020, when the data for reported cases begins (with the fitted initial infected \(I_{0}=778\) for the simplified model). The data for quarantined contacts begins on Jan. 26. As remarked in the main text, our model actually allows for a very similar epidemic trajectory when initiating the simulation a month earlier with one infected individual (\(I_{0}=1\)) and all other parameters the same as our fit starting from Jan. 21 (see Fig. S1).
There are possible issues with the case data as detailed by other researchers []; most notably a change in case counting procedures on Feb. 12 in Hubei province causing an abrupt decrease then sharp increase in reported cases. Although utilizing all cumulative cases reported in China was desirable for model fitting, the data discrepancies, along with potential statistical issues, motivate us to comprehensively test robustness of our results. First, because fitting of the model to cumulative incidence data leads to inconsistent assumptions on independence of errors and possible bias [], we fit the model to the actual daily incidence (inferred from cumulative case data) and to the quarantined contact data as before. Second, the outbreak was not localized to a single population during the timeframe considered, therefore we test the effects of spatial aggregation on parameter estimates. Due the case counting issues in Hubei around Feb. 12, we excluded the daily incidence numbers for this province (also when fitting incidence for all China) on Feb. 11-13 from our data fitting. We also tested smoothing the data around Feb. 12 and fitting the cumulative cases. Finally, we conducted various other explorations of different modeling assumptions including (i) investigation of susceptible self-quarantine rates dependent on mobility data or proportional to rate of reported cases (instead of force of infection), (ii) allowing more general residence time distributions for quarantine periods, and incubation and infectious periods, (iii) utilizing different baseline reproduction numbers or including unreported cases in the model. All of these additional modeling exercises are summarized below in the following subsections.
### Spatially Aggregated Daily Count (DC) Fits
For spatially aggregated we considered all of China, China less Hubei Province, and Hubei province. For all of these fits the data used were daily case totals, inferred from cumulative case totals, and nationally aggregated quarantine data. To obtain the fit for China less Hubei and Hubei in this circumstance we simultaneously fit their respective case data and the sum of their respective quarantine model compartments with initial conditions chosen where appropriate based upon initial relative reported cases and under the assumption that the probability of transmission given contact, \(p=.06\), in line with other studies []. The results of these fittings are summarized in table S5 and figure S8, along with in the main text.
### Spatially Aggregated Provincial DC Fits
To test robustness with respect to the effects of spatial aggregation on estimated parameter values, for each province we simultaneously fit model Eq. to daily case incidence and an inferred number of quarantined individuals for that province. Note that we do not include the provinces of Tibet, which had only one confirmed case, and Hong Kong, where the peak daily case total occurred well after the time frame considered. Furthermore because quarantined contact data was only available aggregated for all of China (from NHC []), we estimated the number of quarantined individuals for each province, labeled \(j=1,...:30\), as follows:
\[\begin{cases}Q_{j}=\left(\frac{C_{j}}{C}\right)Q\\ Q_{j}(t)=\left(\frac{\int_{0}^{t}e^{-s/14}C_{j}(s)ds}{\int_{0}^{t}e^{-s/14}C(s) ds}\right)Q(t),\ \ t>0,\end{cases}\]
Here the assumption is that quarantined contacts are proportional to reported case load, and as specified in our model, quarantine duration is exponentially distributed with mean \(14\ days\). Plots for these fits can be found in figures S5 and S6. Fit parameter values are presented in table S4.
By including spatial (provincial) heterogeneity, first observe that the fit parameter values of Hubei are very close to that of China aggregated. This is expected since a significant amount of total cases in China occurred in Hubei. For the remaining provinces with much smaller outbreaks, we obtain good fits that can be largely mimicked by aggregating and fitting cases to China less Hubei (see tables S4, S5). Observe that \(\sigma\) and \(\phi\) being significantly higher in these other provinces than in Hubei (or the all China fit). Indeed, comparison of the values in tables S4 and S5 suggests that segregating between China Less Hubei and Hubei alone is sufficient to capture this difference. The higher values for \(\sigma\) in China Less Hubei are likely explained by the other provinces having the advantage of responding to the outbreak in Hubei, along with their local cases, so that their lockdowns could be enacted faster (with larger magnitude relative to local force of infection). The larger values of contacttracing coverage \(\phi\) in China Less Hubei may be attributed to a smaller caseload enabling this relatively resource-intensive control strategy. Despite the heterogeneity, the conclusion that lockdowns (self-quarantine) had the overwhelming influence on the outbreak compared to contact tracing is robust, as noted in the main text and SI through sensitivity analysis on \(R_{e}\), final and peak outbreak size with respect to \(\phi\) and \(\sigma\).
### _Weekly \(\mathcal{R}_{e}\)_
In addition to computing \(\mathcal{R}_{0}\) by parameter estimation of differential equation models, we utilize an alternative purely statistical approach incorporating both the case and quarantined contact data to infer \(\mathcal{R}_{e}\) and efficacy of contact tracing developed in a prior study of the 2014-2015 Ebola outbreak []. The method, based on [], measures \(\mathcal{R}_{e}\) directly from reported case data and estimates of the serial interval (generation time) distribution. We utilize serial interval distributions from a large study of cases and their contacts in Shenzhen, China []. The serial interval for (untraced) reported cases is taken to be \(Gamma(2.29,0.36)\) resulting in mean \(6.29\ days\). The serial interval for infectious caused by contact-traced cases is taken to be \(Gamma(1.8,0.5)\) resulting in mean \(3.6\ days\). Let \(\mathcal{R}_{e}^{(j)}\) be the daily reproduction number, \(\mathcal{R}_{e,n}^{(j)}\) be the daily reproduction number if there was no contact tracing, \(U_{j}\) be the untraced reported cases on day \(j\), \(T_{j}\) be the traced reported cases on day \(j\), \(\pi_{j},\omega_{j}\) be the c.d.f. of serial interval distributions, and \(\kappa=\beta_{c}/\beta\) be the proportion of transmissions caused by traced cases (relative to untraced).
\[\mathbb{E}(\mathcal{R}_{e}^{(j)}) =\frac{1}{U_{j}+\kappa T_{j}}\sum_{n}\left(\pi_{n}U_{j+n}+\kappa \omega_{n}T_{j+n}\right)\] \[\mathbb{E}(\mathcal{R}_{e,n}^{(j)}) =\frac{1}{U_{j}+\kappa T_{j}}\sum_{n}\left(\pi_{n}U_{j+n}+\omega_{ n}T_{j+n}\right)\]
Note that \(\kappa=0\) for the simplified (perfect tracing) model. Since the amount of infected quarantined contacts is not available in the data, we utilize the predicted relative transmission and incidence of contact-traced individuals from our model fit to assess \(\mathcal{R}_{e}\) with and without contact tracing. The results (in main text) estimate the proportion of reported cases which are traced contacts and reduction of \(\mathcal{R}_{e}\) due to contact tracing.
### Uncertainty Quantification.
We used the following method to generate 95% confidence intervals for the selected quantities appearing in tables S2,S5.
1. Simultaneously fit the simplest model to daily case totals for China less Hubei Province, Hubei Province, and national quarantined data as described in the proceeding section.
2. Based on the two fit daily case total curves, and under the assumption that the reporting error is normally distributed and relative in magnitude to the reported total at each data point: \[y_{i}=g(x(t_{i}),\hat{\xi})+\epsilon_{i}\qquad\qquad\epsilon_{i}\sim n(0,y_{i} \cdot s^{2}),\] where \(g\) is the true number of daily cases and \(\hat{\xi}\) the set of true parameter values. We generated 10,000 datasets and refit the model to each of them and the original quarantine data simultaneously. For the results in tables S2,S5 a value of \(s=.5\) was used because this value causes the synthetic data-sets to cover the original data except for the outliers around February 12, when there was a change in the method of reporting cases in Hubei province (see figure S2).
3.
4. Produce scatter plots and correlation values for each of the fit parameters based on these generated data for the cumulative data fitting (see figures S3 and S4 respectively).
5. Arrange the generated values in increasing order and remove the top and bottom \(2.5\%\) in order to obtain the desired approximate 95% Confidence Intervals.
### Alternative modeling assumptions.
#### Exploration of different self-quarantine rate forms.
The models considered so far incorporate mass self-quarantine proportional to _force of infection_, e.g. \(\sigma\lambda(t)\) in Eq., as a simple proxy for reactionary lockdowns, individual behavior change, etc., occurring population-wide during the outbreak. In reality, this proportionality relationship has several limitations. In particular, there is a delay between new incidence and case reporting which may delay the action of self-quarantine with respect to force of infection. Additionally, while public health proclamations are generally reactionary, other factors may come into play. In order to test the robustness of our simplification we explore different (susceptible) self-quarantine rates here. First, if we simply take self-quarantine rate dependent on the (instantaneous) rate of change in (cumulative) reported case prevalence, \(R^{\prime}(t)/N\), then we obtain the modified factor \(\bar{\sigma}\):
\[\bar{\sigma}\frac{R^{\prime}(t)}{N}S(t)=\bar{\sigma}\left(\frac{1}{T}\right)I (t)S(t)=\sigma\lambda(t)=\sigma\frac{\beta}{N}I(t)S(t)\ \ \Rightarrow\ \ \bar{\sigma}=\sigma\mathcal{R}_{0,b}. \tag{10}\]Thus, the form of self-quarantine rate is preserved (proportional to \(I(t)S(t)\)), but the proportionality constant is modified in such a way that the factor must be \(\mathcal{R}_{0,b}\times\) larger when relative to rate of reporting to reach compared to the equivalent quarantine levels when proportional to force of infection.
Next, we consider the following delay equation with self-quarantine dependent on daily reported cases, which modifies the susceptible compartment in Eq. as
\[S^{\prime}(t)=-\,\frac{\beta}{N}\left(1+\frac{(1-p)}{p}\phi\right)I(t)S(t)- \tilde{\sigma}\frac{(R(t)-R(t-1))}{N}S(t). \tag{11}\]
Here, the factor proportional to (prevalence of) new reported cases within the past 24 hours, \(\tilde{\sigma}(R(t)-R(t-1))/N\), replaces the force of infection relationship (\(\sigma\lambda(t)\)). In Figure S9, we show simulations of the delay system plotted with the original model output (corresponding to all China daily incidence fit) for different values of \(\tilde{\sigma}\) (relative to \(\sigma\)) in Eq.. Notice that the incidence trajectory of original model fit is bounded between outbreak simulations of the delay model corresponding to \(\tilde{\sigma}=\mathcal{R}_{0,b}\sigma\) (lower bound) and \(\tilde{\sigma}=(\mathcal{R}_{0,b}/2)\sigma\). This is consistent with the predicted magnification of \(\sigma\) derived above in Eq., and possibly not exactly matching due to the fact that \((R(t)-R(t-1))>R^{\prime}(t)\) at the beginning of the outbreak.
Finally, we utilize Baidu mobility data for within-cities, namely City Movement Intensity (WCMI), as a proxy for the rate of self-quarantine in China during the timeframe. We consider the following modification to the susceptible compartment in Eq.
\[S^{\prime}(t)=-\frac{\beta}{N}\left(1+\frac{(1-p)}{p}\phi\right)I(t)S(t)- \tilde{\sigma}(t)S(t). \tag{12}\]
We consider the form
\[\tilde{\sigma}(t)=\begin{cases}\sigma_{m}&0<t\leq t_{q}\\ 0&t_{q}<t,\end{cases}\]
Utilizing this fitted self-quarantine rate \(\sigma_{m}\) in Eq., we fit the remaining model parameters to the model, this time fitting \(p\), instead of fixing \(p=.06\), with the susceptible compartment as described above. The results are consistent with our original model where \(\sigma\) is fitted proportionality constant relative to force of infection (see table S5 and figures S13-15).
### _Residence times of quarantine, exposed and infectious periods_
We considered two possible alternatives for the distribution of quarantine residence times besides the base assumption of an exponential distribution with mean time of 14 days: a gamma distribution with shape parameter \(\alpha\) and scale parameter \(\beta\) constrained by \(\beta=14\alpha^{-1}\) so that a mean residency time of 14 days was retained; and a Weibull distribution with shape parameter \(\lambda\) and scale parameter \(\kappa\) similarly constrained by \(\lambda=14\left[\Gamma(1+\kappa^{-1})\right]^{-1}\), with the unconstrained parameters being determined by nonlinear least squares fit to the data together with \(I_{0}\), \(\beta\) (and so \(\mathcal{R}_{0,b}\)), \(p\), \(\sigma\), and \(\phi\). As can be seen in figure S13 both of these resulted in distributions with similar shape, and resulted in a slight reduction in residual, with the fit Weibull distribution having the lowest residual value. These fit distributions indicate that more individuals spend close to no time in quarantine, presumably as testing results are returned, and fewer individuals spend significantly more than 14 days in quarantine as would be indicated by the baseline assumption that quarantine residency time is exponentially distributed. However the fit parameter values themselves are comparable (see table S5).
We additionally considered the possibility of the infectious and exposed residency times following an Erlang distribution via the linear chain trick using the following system of ODEs:
\[S^{\prime} =-\left(1+\psi\right)\beta SI/N,\quad E_{1}^{\prime}=\left(1- \phi\right)\beta SI/N-\frac{n_{e}}{\tau}E_{1},\] \[E_{j}^{\prime} =\frac{n_{e}}{\tau}\left(E_{j-1}-E_{j}\right)\quad 2\leq j\leq n _{e}\] \[I_{1}^{\prime} =\frac{n_{e}}{\tau}E_{n_{e}}-\frac{n_{i}}{T}I_{1},\quad I_{k}^{ \prime}=\frac{n_{i}}{T}\left(I_{k-1}-I_{k}\right)\quad\quad 2\leq k\leq n_{i}\] \[R^{\prime} =\frac{n_{i}}{T}I_{n_{i}}+\frac{n_{i}}{T_{e}}(I_{c})_{n_{i}}, \quad(S_{c})^{\prime}=\frac{(1-p)}{p}\phi\beta SI/N-\alpha_{c}S_{c}, \tag{13}\] \[(E_{c})_{1}^{\prime} =\phi\beta SI/N-\frac{n_{i}}{\tau}(E_{c})_{1},\quad(E_{c})_{j}^{ \prime}=\frac{ni}{\tau}((E_{c})_{j-1}-(E_{c})_{j})\quad 2\leq j\leq n_{e}\] \[(I_{c})_{1}^{\prime} =\frac{n_{e}}{\tau}(E_{c})_{n_{e}}-\frac{n_{i}}{T_{e}}I_{c},\quad (I_{c})_{k}^{\prime}=\frac{n_{i}}{T_{e}}((I_{c})_{k-1}-(I_{c})_{k})\quad 2 \leq k\leq n_{i}\] \[(R_{e})^{\prime} =\frac{n_{i}}{T_{e}}I_{c}-\alpha_{c}R_{c},\quad I=\sum_{s=1}^{n_{ i}}I_{s}\]In order to obtain an upper bound for the number of stages in Eq. we took the variance and standard deviation for the distributions of \(T\) and \(T_{e}\) given in (where they are assumed to be log normal), fixed the mean to be the values given in table S1, and set the variances equal, solved for \(n_{i}\) and rounded up. This process resulted in an upper bound of at most two stages.
With this in mind we considered three cases, \(n_{i}=2\) and \(n_{e}=1\), \(n_{i}=1\) and \(n_{e}=2\), and finally \(n_{i}=2\) and \(n_{e}=2\). The fit parameter values corresponding to these fittings are given in table S5, and associated fitting plots are figures S14-S16. We additionally plotted the log normal distributions given in together with exponential distributions and Erlang distributions with the same mean (figures S17,S18). In figure S19 the considered Erlang and Exponential distributions for \(\tau\) are shown. The primary difference in these distributions is that under the exponential assumption a greater proportion of individuals become rapidly infectious and have a shorter infectious period respectively. The primary effects of the Erlang assumption for infectious dwell time are to increase \(I_{0}\), as well as overall case totals, and decrease \(\sigma\), as indicated by the fit values in table S5 and the plots in figure S14. In turn an Erlang assumption for time until infectiousness lowers the fit value for \(I_{0}\) and increases \(\sigma\) and \(\phi\). Simultaneously assuming both dwell times follow an Erlang distribution results in more moderate increases in \(I_{0}\) and \(\phi\), as well as a slight decrease in \(\sigma\) (See table S5 and figures S15,S16). The assumption that infectious period (\(T\)) is exponential results in better fits than the case of Erlang distribution, whereas either distribution for time until infectiousness (\(\tau\)) provides good fits to the data.
Furthermore, we tested how varying the means for the quarantine, exposed and infectious periods affects the fitting results (see Fig. S20 for example output). For the quarantine duration, we vary the (exponential distribution) parameter from 1/20 to 1/4, with 1/14 as our baseline assumption (mean duration of 14 days). The parameter fits and results do not change significantly with the varied mean quarantine duration. For exposed (\(\tau\)) and infectious periods (\(T\) and \(T_{c}\)) under the assumption of exponential durations, we vary \(\tau\) from 2 to 4, along with varying \(T\) and \(T_{c}\) in the reported 95% confidence intervals of (4.13,5.1) and (2.08,3.31), respectively, given in. The parameter fits and results are robust to varying means \(\tau,T\) and \(T_{c}\).
### Model with unreported cases
In addition, we consider a version of the model which includes unreported cases. Let \(\rho\) be the probability a non-quarantined infected individual becomes a reported case (we assume that all contact-traced cases are reported).
The final alternative modeling assumption we consider is the possibility of time variable serial interval, as suggested by. We do so by modifying Eq. to add additional loss terms due to the lockdown (self-quarantine rate proportional to force of infection) in the Infected and Exposed compartments:
\[\begin{split} I^{\prime}&=\frac{1}{\tau}E-\frac{1} {\tau}I-\sigma\beta I^{2}/N\\ E^{\prime}&=(1-\phi)\beta SI/N-\frac{1}{\tau}E- \sigma\beta EI/N\end{split} \tag{15}\]
We assume the same (initial) infectious period value \(T=4.64\). Under this alternative assumption we fit Eq. for China less Hubei Province and Hubei Province (see figure S21). The residual for this fitting was similar to the fitting of the base simplified model. Comparing the fit parameter values to the base assumption (see table S5) this results in decreases in both \(\sigma\) and \(\phi\). It is expected with the decreasing serial interval of infected cases that less (self)-quarantine will be needed to control the disease, but simulations show that the trajectory of total (self)-quarantined is very close to the original (constant exposed and infectious period) model fit (see figure S21). Furthermore, the main result of minimal impact from contact tracing compared to self-quarantine is preserved, along with the observation that \(\sigma\) and \(\phi\) are relatively larger for China less Hubei than they are for Hubei.
### Additional model fitting tests
While the fitting procedure presented in detail in main text and here does not explicitly include unreported cases, we also checked several additional versions of the model, along with different assumptions with regard to fixing versus fitting some parameters. We tested inclusion of unreported cases (see above for model) for fitting the proportion of reported cases \(\rho\). Furthermore, we varied and fit the infectious period \(T\), incubation period \(\tau\), and transmission rate \(\beta\). In addition, we also attempted to correct for possible issues with the case data as detailed by other researchers; most notably a change in case counting procedures on Feb. 12 in Hubei province causing an abrupt increase in reported cases. We utilize this raw data for fitting, rather than separated by provinces, since a major novelty of this work is to incorporate data on the quarantined contacts which was compiled solely for the whole of China. We also tested smoothing the data around Feb. 12 and fitting the model, which resulted in slightly different parameter estimates.
Although certain parameter values changed, the qualitative results on how contact tracing and social distancing/lockdown measures affected outbreak size however were robust when utilizing raw or smoothed data, along with other versions
\begin{table}
\begin{tabular}{l c c c c c c} \hline & Parameter & 95\% CI & Point Est. & Mean & Std. Dev. & ARE \\ \hline
## China
& \(I_{0}\) & (304.06, 568.13) & 393.08 & 396.12 & 63.401 & 11.407 \\
## Less
& \(\mathcal{R}_{0,b}\) & (4.3009, 6.0) & 6.0 & 5.7742 & 0.47993 & 3.763 \\
## Hubei 1
& \(\sigma\) & (100100.0, 127610.0) & 114070.0 & 113240.0 & 7011.4 & 4.9488 \\ & \(\phi\) & (0.35645, 0.63956) & 0.58842 & 0.53327 & 0.073158 & 11.423 \\ \hline \(\sigma_{m}\) from & \(I_{0}\) & – & 457.61 & – & – & – \\ mobility & \(\mathcal{R}_{0,b}\) & – & 5.8033 & – & – & – \\ data & \(\phi\) & – & 0.59027 & – & – & – \\ \(p\) & – & 0.050985 & – & – & – \\ \(\sigma_{m}\) & – & 0.1051 & – & – & – \\ \hline time & \(I_{0}\) & – & 443 & – & – & – \\ variable & \(\mathcal{R}_{0,b}\) & – & 6.0 & – & – & – \\ serial & \(\sigma\) & – & 77068 & – & – & – \\ interval 1 & \(\phi\) & – & 0.37 & – & – & – \\ \hline \hline & \(I_{0}\) & (410.92, 648.33) & 487.2 & 516.21 & 60.431 & 10.547 \\
## Hubei\({}^{1}\)
& \(\mathcal{R}_{0,b}\) & (5.7131, 6.0) & 6.0 & 5.9804 & 0.082126 & 0.32743 \\ & \(\sigma\) & (1112.9, 1406.2) & 1260.1 & 1249.0 & 74.413 & 4.7559 \\ & \(\phi\) & (0.27846, 0.40932) & 0.32135 & 0.33809 & 0.034025 & 9.2804 \\ \hline \(\sigma_{m}\) from & \(I_{0}\) & – & 487.2 & – & – & – \\ mobility & \(\mathcal{R}_{0,b}\) & – & 6.0 & – & – & – \\ data & \(\phi\) & – & 0.32135 & – & – & – \\ & \(p\) & – &.06 & – & – & – \\ & \(\sigma_{m}\) & – & 0.1859 & – & – & – \\ \hline time & \(I_{0}\) & – & 644.44 & – & – & – \\ variable & \(\mathcal{R}_{0,b}\) & – & 6.0 & – & – & – \\ serial & \(\sigma\) & – & 699.03 & – & – & – \\ interval 1 & \(\phi\) & – & 0.21 & – & – & – \\ \hline \hline & \(I_{0}\) & (745.83, 809.05) & 787.55 & 773.52 & 17.143 & 2.2695 \\
## China\({}^{1}\)
& \(\mathcal{R}_{0,b}\) & (5.9288, 6.0) & 6.0 & 5.9955 & 0.023302 & 0.075615 \\ & \(\sigma\) & (20906.0, 25382.0) & 23495.0 & 23186.0 & 1147.4 & 3.9386 \\ & \(\phi\) & (0.32521, 0.4018) & 0.36897 & 0.3637 & 0.019656 & 4.3037 \\ \hline Gamma & \(I_{0}\) & – & 810.733 & – & – & – \\ Quarantine & \(\mathcal{R}_{0,b}\) & – & 6.0 & – & – & – \\ Assumption 1 & \(\sigma\) & – & 23463.0 & – & – & – \\ & \(\phi\) & – & 0.37296 & – & – & – \\ \hline Weibull & \(I_{0}\) & – & 812.079 & – & – & – \\ Quarantine & \(\mathcal{R}_{0,b}\) & – & 6.0 & – & – & – \\ Assumption 1 & \(\sigma\) & – & 23486.1 & – & – & – \\ & \(\phi\) & – & 0.37309 & – & – & – \\ \hline Infectious & \(I_{0}\) & – & 1259.6 & – & – & – \\ Erlang & \(\mathcal{R}_{0,b}\) & – & 6.0 & – & – & – \\ Assumption & \(\sigma\) & – & 18118.0 & – & – & – \\ only 1 & \(\phi\) & – & 0.33983 & – & – & – \\ \hline Exposed & \(I_{0}\) & – & 732.18 & – & – & – \\ Erlang & \(\mathcal{R}_{0,b}\) & – & 6.0 & – & – & – \\ Assumption & \(\sigma\) & – & 30887.0 & – & – & – \\ only 1 & \(\phi\) & – & 0.50246 & – & – & – \\ \hline Simultaneous & \(I_{0}\) & – & 1053.1 & – & – & – \\ Erlang & \(\mathcal{R}_{0,b}\) & – & 6.0 & – & – & – \\ Assumption 1 & \(\phi\) & – & 0.33983 & – & – & – \\ \hline Exposed & \(I_{0}\) & – & 732.18 & – & – & – \\ Erlang & \(\mathcal{R}_{0,b}\) & – & 6.0 & – & – & – \\ Assumption & \(\sigma\) & – & 30887.0 & – & – & – \\ only 1 & \(\phi\) & – & 0.50246 & – & – & – \\ \hline Simultaneous & \(I_{0}\) & – & 1053.1 & – & – & – \\ Erlang & \(\mathcal{R}_{0,b}\) & – & 6.0 & – & – & – \\ Assumption 1 & \(\phi\) & – & 0.32135 & – & – & – \\ \hline \hline & \(I_{0}\) & – & 0.32135 & – & – & – \\ \(\sigma\) & – & 0.06 & – & – & – \\ \(\sigma_{m}\) & – & 0.1859 & – & – & – \\ \hline time & \(I_{0}\) & – & 644.44 & – & – & – \\ variable & \(\mathcal{R}_{0,b}\) & – & 6.0 & – & – & – \\ interval 1 & \(\phi\) & – & 0.21 & – & – & – \\ \hline \hline & \(I_{0}\) & (745.83, 809.05) & 787.55 & 773.52 & 17.143 & 2.2695 \\
## China\({}^{1}\)
& \(\mathcal{R}_{0,b}\) & (5.9288, 6.0) & 6.0 & 5.9955 & 0.023302 & 0.075615 \\ & \(\sigma\) & (20906.0, 25382.0) & 23495.0 & 23186.0 & 1147.4 & 3.9386 \\ & \(\phi\) & (0.32521, 0.4018) & 0.36897 & 0.3637 & 0.01965Figure S1: Filled trajectory starting Jan. 21 (solid blue) alongside simulation with same parameters except initial infected \(I_{0}=1\) (dashed red).
Figure S4: Correlation Values for quantities of interest
Figure S5: Provincial New Daily Cases fit corresponding to values in table S4
Figure S6: Approximated Provincial Quarantine Data fit corresponding to values in table S4
Spatially segregated fits corresponding to values in table S5
Spatially segregated fits corresponding to values in table S5
Figure S11: Total self-quarantined trajectory in model fit, alongside Baidu (WCMI) mobility data, see also table S5 and Eq..
Figure S13: Fit gamma and Weibull distribution curves vs an exponential distribution, each with mean of 14 days, see also table S5
Figure S16: Model fit under the assumption that \(\tau\), \(T\), \(T_{e}\) at follow an Erlang Distribution, see also table S5
Figure S19: Distribution functions for \(\tau\), see also table S5
Figure S24: (a) The corresponding daily reported cases and total (reported and unreported) cases in model with data and inferred subset of contact-traced infected for a fit of model incorporating unreported cases. (b) Contact tracing (CT) proportion \(\phi\) versus outbreak size \(\mathcal{C}_{\infty}\) (nonlinear relationship) and reproduction number \(\mathcal{R}_{0}\) (linear relationship for 2 levels of self-quarantine (SQ) rate \(\sigma\) and 2 levels of reporting probability \(\rho\). Note the net contact tracing probability is the product \(\rho\phi\).
Figure S25: Example epidemic curve trajectories for 3 levels of CT proportion \(\phi\), corresponding to Fig.4(e)-(f) in main text, showing how contact tracing fiattens the curve. |
129668_file05 | ### Citation
Aline Rissatto Teixeira, Daniela Bicalho, Tacio de Mendonga Lima. Evidence for the validation quality of culinary skills instruments: a systematic review. PROSPERO 2019 CRD42019130836
Available from: [https://www.crd.york.ac.uk/prospero/display_record.php?ID=CRD42019130836](https://www.crd.york.ac.uk/prospero/display_record.php?ID=CRD42019130836)
### Review question
What is the scientific evidence for the quality of validated instruments for evaluating culinary skills?
### Searches
We will each the following electronic bibliographic databases: Scopus, LILACS, PubMed, Web of Science, SIBiUSP Integrated Search Portal and the grey literature (through DOAJ and Google Scholar).
In addition, the secondary references of the included articles will also be analyzed for further material.
The search strategy will include only terms relating to culinary / cooking / food skills / confidence / knowledge OR cooking abilities OR food literacy OR food agency OR food autonomy AND validation studies OR validation OR psychometrics OR scale OR instrument OR survey.
There will be no publication period restrictions.
### Studies published in English, Portuguese or Spanish will be eligible for inclusion.
Additional search strategy information can be found in the attached PDF document (link provided below).
### Types of study to be included
Inclusion:
We will include methodological studies with a psychometric approach if:
1) They present an original instrument that evaluates of culinary skills in adults (20 years of age or older and under 60, according to Brazilian Ministry of Health);
2) They present the development of such instrument based on bibliographic references combined or not with group discussions;
3) They describe the process of validation and reliability of the instrument;
4) They are published in English, Portuguese or Spanish.
### Exclusion:
Instruments tested in university students, children and adolescents or that do not present the instrument will be excluded.
## 11 NIHR | National Institute for Health Research
### 11.1 Condition or domain being studied
Culinary skills; food literacy; food agencies.
Culinary skills have been valued in public policies and national health instruments, such as the Brazilian Food Guide, and seem to be important for the individual, who must feel empowered and confident to make healthy and autonomous food choices.
Although the number of studies about this phenomenon is increasing in the last years, it is necessary to describe the evaluation of the culinary abilities in a precise way, starting from the use of validated instruments or even discussing the necessary criteria to evidence its validation.
Criteria to evaluate psychometric quality of instruments address properties such as reliability (including internal consistency), and validity (including content, construct and criteria).
### 11.2 Participants/population
Adults (20 years of age or older and under 60, according to Brazilian Ministry of Health).
Articles for the validation of instruments tested in university students, children and adolescents or that do not present the instrument will be excluded.
### 11.3 Intervention(s), exposure(s)
Validation quality of culinary skills assessment instruments.
### 11.4 Comparator(s)/control
Not applicable.
### 11.5 Main outcome(s)
A psychometric qualification of two instruments proposed will be carried out using a system of classification adapted from Terwee et al, and Hair Jr. et al.
The questions used for this classification address the following properties:
a) Reliability, including internal consistency;
\({}^{*}\) Measures of effect
Not applicable.
Additional outcome(s)
None.
\({}^{*}\) Measures of effect
Not applicable.
### 11.6 Data extraction (selection and coding)
After defining the descriptors and searching for articles in the databases, the results will be screened for relevance.
The titles and abstracts of the retrieved studies will be independently screened and selected by two authors. Studies not meeting the inclusion criteria will be eliminated from the review. For this process, a preformatted Microsoft Excel worksheet will be used. The selected articles will be grouped by database and repeated article titles eliminated. Then, a consensus will be reached by classifying the selected articles in: Yes (enter in review), No (do not enter in review) and not sure (doubtful).
## Nihr
National Institute
for Health Research
International prospective register of systematic reviews
Each measurement property will be reported by positive, (+), intermediate (?), negative (-), or no information available and the data will be organized in a preformatted Microsoft Excel worksheet, and reported in a table.
### Analysis of subgroups or subsets
Selected studies will be categorized by the country of origin, the language in which the study has been published, the number and type of participants, the type of developed instrument (i.e. scale, questionnaire), the instrument domains, and the applied methods for psychometric validation.
The analysis of the psychometric quality of the instruments will address the following properties: reliability, including internal consistency and validity, including, content, construct, and criterion validity.
### Contact details for further information
Aline Rissatto Teixeira
### Organisational affiliation of the review
Universidade de Sao Paulo
[https://www.fsp.usp.br](https://www.fsp.usp.br)
Review team members and their organisational affiliations
Ms Aline Rissatto Teixeira.
Ms Daniela Bicalho.
Mr Tacio de Mendonca Lima.
### Collaborators
Mrs Betzabeth Slater Villar.
### Type and method of review
Methodology, Systematic review
Anticipated or actual start date
01 May 2019
Anticipated completion date
21 December 2019
Funding sources/sponsors
None
## Versions
10 June 2019
PROSPERO
This information has been provided by the named contact for this review. CRD has accepted this information in good faith and registered the review in PROSPERO. The registrant confirms that the information supplied for this submission is accurate and complete. CRD bears no responsibility or liability for the content of this registration record, any associated files or external websites. |
132621_file02 | ## I.
## II.
## a.
**Figure S1: Summary of different models explaining the associations between diseases. Independent genetic associations (I) reflect the case where the number of shared genetic associations between diseases is not more than expected by chance. If the overlap is more than expected (II), it could either reflect (a) common etiology, which reflects shared causes, or (b) mediated pleiotropy, which suggests a common genetic factor influencing only one disease, which in turn increases the risk of a second disease.
* Figure S2: Participant data in UK Biobank after quality control steps. a) The number of female and male participants, b) Age distribution when participants first attended the UKBB assessment center and answered self-reported questions, c) Age at death (every 5 years are binned together) for the participants who died after attending the UKBB assessment center. The values are corrected for the number of female and male participants who passed the ages specified in the y-axis, d) Distributions of'standing height' field in the UKBB, e) Distributions of 'weight' field in the UKBB, f) Distributions of BMI field calculated using'standing height' and 'weight' fields in the UKBB (see Methods).
* Figure S3: The distribution of a) Overall health rating, b) Health satisfaction, c) Smoking status, d) Alcohol drinker status, e) Facial aging, f) Non-accidental death in close genetic family fields in the UKBB. x-axes show the number of participants, while y-axes are the answers given by the participants.
Figure S4: Distributions of a) parents’ age at death, b) age when periods started (menarche), and c) Age at menopause (last menstrual period).
* Figure S5: Self-reported health data. a) The number of self-reported medications and operations (x-axes) for the participants in the UK Biobank. The y-axis shows the number of participants on a log10 scale. b) The number of self-reported cancers (x-axis). Y-axis shows the number of participants.
* Figure S6: Pairwise correlations between traits. Each row and column shows a trait in the UKBB, and the color shows the pairwise Spearman correlation coefficients between traits. Dark red denotes a strong positive correlation, while dark blue indicates strong negative values. Traits are ordered based on the hierarchical clustering of the correlation coefficients.
* Figure S7: Disease hierarchy for the 116 diseases included in the analysis. The nodes are colored by the disease categories as indicated in the legend.
Figure S8: Sex-stratified statistics for 116 selected diseases. a) The distribution of the number of self-reported diseases (y-axis) stratified by sex (x-axis). b) The distribution of disease prevalence in males and females. The x- and y-axes show the number of cases in 1,000 males and females (on a log scale), respectively. The color of each point denotes diseases with a higher prevalence in females (rosy brown, above the dashed line) or males (state grey, below the dashed line). The linear regression line is depicted as blue. Diseases having a residual value bigger than 3 standard deviations are labeled but not excluded as they are also common in the other sex.
Figure S9: Disease co-occurrence matrix summarizing relative risk scores and correlations. Each row and column denote diseases, ordered by hierarchical clustering of risk scores. The color is defined by relative risk scores while the size is determined by \(\phi\) value, indicating the robustness of the association (see Methods). The diagonal tiles are colored by the UK Biobank's disease hierarchy to visualize if diseases from the same category cluster together. Associations for the 62 diseases that have at least one relative risk ratio higher than four (\(log_{2}RR\geq 2\)) or lower than minus four (\(log_{2}RR\leq-2\)) are plotted.
* 236 Figure S10: Age-of-onset distributions for the cardiovascular diseases. The y-axis shows how many people in 10,000 are diagnosed with that disease at a certain age (x-axis). The plots are also normalized by the number of people that are older than a given age so that it is unaffected by the distribution of ages in the UKBB (Figure S2b). We ran permutations to define confidence intervals for the disease onset rates. We thus down-sampled the UKBB population using 242 50,000 participants for 100 times and calculated the median (points, colored by the age-of-onset cluster in Figure 1) and 95% range of all points (gray error lines). A best-fit curve (calculated using loess regression between the medians and age-of-onset) is also displayed.
Figure S11: Same as Figure S10, but for endocrine / diabetes diseases.
* Figure S12: Same as Figure S10, but for gastrointestinal / abdominal diseases.
Figure S13: Same as Figure S10, but for haematology / dermatology diseases.
Figure S14: Same as Figure S10, but for immunological / systemic disorders.
Figure S15: Same as Figure S10, but for infections.
Figure S16: Same as Figure S10, but for musculoskeletal / trauma diseases.
Figure S17: Same as Figure S10, but for neurology / eye / psychiatry diseases.
Figure S18: Same as Figure S10, but for renal / urology diseases.
Figure S19: Same as Figure S10, but for respiratory / ENT diseases.
Figure S20: Distribution of median age-of-onset (y-axis) across categories (x-axis). Points show diseases, grouped by the categories (individual boxplots). Categories are ordered by the median value of the median age-of-onset.
* Figure S21: a) Number of diseases for different number of significant variants (p<=5e-8). Diseases with the highest number of associations (N>=10,000) are given as an inset table. b) Comparison of the number of significant associations (y-axis, on a log scale) across age-of-onset clusters (x-axis) (ANOVA after excluding cluster 4, p = 0.06). Since the y-axis is on a log scale, diseases with zero significant associations are not shown on the graph. c) The same as b) but for disease categories. Categories are ordered by the median number of significant SNPs.
* Figure S22: Distributions of the number of significant associations (y-axis) according to the number of diseases associated with a given SNP and the number of age-of-onset clusters (x-axis). For example, the upper left plot indicates that 50,019 polymorphisms are significantly associated with one disease in one age-of-onset cluster, while the lower right plot shows that there are 15, 1, and 3 significant SNPs associated with 9 diseases in one, two, or three age-of-onset clusters, respectively.
* Figure S23: a) The difference between genetic similarity within and across age-of-onset clusters. Y-axis shows the genetic similarity (see Methods). b) The same as a) but the y-axis is corrected for disease category and co-occurrence using a linear model. This panel is the same as and given here only for an easier comparison.
* Figure S24: Genetic similarities between cluster 1 (a, b), 2 (c, d), 3 (e, f) and other age-of-onset clusters. The y-axis shows the genetic similarity on a log2 scale as the raw values (a, c, e) or as values corrected for disease category and co-occurrence using a linear model (b, d, f) (see Methods for details).
* Figure S25: Significant genetic similarities (p\(\leq\)0.01) calculated using independent LD blocks. Diseases (n=50) with at least one significant genetic similarity are displayed. The color shows the genetic similarity score, darker red means a higher score. Annotation columns show the age-of-onset clusters and disease categories. The diseases are clustered by the hierarchical clustering of genetic similarity scores.
* Figure S27: Overlap between SNPs associated with multiple disease or disease categories in specific age-of-onset clusters (color-coded) and Townsend deprivation index or specific diet regimes. The y-axis shows the log 2 transformed Odds Ratio and the x-axis shows the p-value cutoff to consider SNPs associated with Townsend deprivation index (_i.e._, a material deprivation index incorporating unemployment, car and home ownership, and household overcrowding) or specific diet regimes. The size of the points shows the number of overlapping SNPs.
* Figure S28: Heatmap showing the enrichment of disease associated (y-axis) SNPs among eQTLs in each tissue (x-axis). Color shows the log2 odds ratio and only the significant enrichment results (as determined by Fisher's exact test, FDR corrected p-value < 0.1). a) Enrichment for only the disease-specific (private) SNPs, b) Enrichment for Multicategory SNPs (_i.e._, SNPs associated with multiple diseases spanning multiple disease categories).
* Figure S29: The distribution of the number of significant eQTL-tissue associations for s unique, multidisease, or multicategory SNPs are associated with (based on GTEx v8 data). P-values are calculated using Wilcoxon test. Dark red segments show the range between 1st and 3rd quartiles and the points show the median.
* Figure S30: Overlap between genes associated with selected few aging-related traits and genes associated with diseases in different clusters. The x-axis shows log2 enrichment score, and the y-axis shows the age-of-onset clusters. The numbers of genes in each cluster (for both multidisease and multicategory genes) are given. The size of the points shows the statistical significance (large points show marginal p-value\(\leq\)0.05, small 'x' indicates non-significant overlaps) and the color shows different aging-related GWAS Catalog traits. The colored numbers near the points show the numbers of overlapping genes.
* Figure S31: Age-related expression changes of the genes with significant eQTLs associated with unique, multidisease, or multicategory diseases in different age-of-onset clusters. In order to match age-related expression changes with the variants, tissue-specific eQTL data was used. More specifically, disease-associated SNPs were first filtered to only include those with a positive association with the gene expression (_i.e._ eQTLs associated with increased gene expression). Using GTEx expression data, mean gene expression values for each age group is calculated. Taking the difference between age groups, we calculated the expression difference at each break point (30, 40,...,70, x-axis). Differences for multiple genes for each tissue are summarized by taking the median expression difference (y-axis). Each point represents a tissue and the size indicate the number of genes averaged in that particular tissue.
* Figure S32: Age-related expression changes of the genes with significant eQTLs associated with unique, multidisease, or multicategory diseases in different age-of-onset clusters. In order to match age-related expression changes with the variants, tissue-specific eQTL data was used. More specifically, disease-associated SNPs were first filtered to only include those with a negative association with the gene expression (_i.e._ eQTLs associated with decreased gene expression). Using GTEx expression data, mean gene expression values for each age group is calculated. Taking the difference between age groups, we calculated the expression difference at each break point (30, 40,...,70, x-axis). Differences for multiple genes for each tissue are summarized by taking the median expression difference (y-axis). Each point represents a tissue and the size indicate the number of genes averaged in that particular tissue.
* Figure S33: Overlap between differentially methylated genes during ageing and genes associated with diseases in different clusters. The x-axis shows log2 enrichment score, and the y-axis shows the age-of-onset clusters. The numbers of genes in each cluster (for both multidisease and multicategory genes) are given. The size of the points shows the statistical significance (large points show marginal p-values0.05, small 'x' indicate non-significant overlaps) and the color shows different methylation datasets. The colored numbers near the points show the numbers of overlapping genes.
* Figure S34: Association between median MAF (y-axis) and the number of cases (x-axis, log10 scale) for diseases (points) in different age-of-onset clusters (shown with different colors) for a) SNPs associated with only one disease, b) SNPs associated with any number of diseases within one cluster. Linear regression lines and standard errors of the lines are shown for each age-of-onset cluster separately.
* Figure S35: The distribution of Median Risk Allele Frequencies (RAF, y-axis) for 100 randomly sampled LD blocks, for 1,000 times, using variants a) associated with one disease, b) associated with one cluster, c) with antagonistic association between cluster 1 and cluster 2.
* _ns: p>0.05, ":p<=0.05, ":p<=0.01, ":p<=0.001, ":p<=0.00001_
## Figure S36: a) Risk allele frequency distributions (y-axis) of different age-of-onset clusters (x-axis) in UK Biobank for SNPs associated with one disease. This plot is the same as Figure 394, and included here for an easier comparison. b) The same as panel a but for different 1000 Genomes super-populations (ALL: complete 1000 Genomes cohort, AFR: African, AMR: Ad Mixed American, EAS: East Asian, EUR: European, SAS: South Asian). _ns: p>0.05, *:p<0.05, *:p<=0.01, ***: p<=0.001, *
This plot is the same as Figure 4b, and included here for an easier comparison. b) The same as a) but for different 1000 Genomes super-populations (ALL: complete 1000 Genomes cohort, AFR: African, AMR: Ad Mixed American, EAS: East Asian, EUR: European, SAS: South Asian). _ns: p>0.05, ":p<=0.05, ": p<=0.01, ": p<=0.0001, ": p<=0.00001_
* Figure S38: Risk allele frequency distributions (y-axis) for the age-of-onset cluster 1 and 3 in the UKBB (x-axis) for a) SNPs that have antagonistic association with cluster 1 and 3 (excluding agonists between cluster 1 and 3). b) The same as panel a but for different 1000 Genomes super-populations (ALL: complete 1000 Genomes cohort, AFR: African, AMR: Ad Mixed American, EAS: East Asian, EUR: European, SAS: South Asian).
* Figure S39: Risk allele frequency distributions (y-axis) for the age-of-onset cluster 2 and 3 in the UKBB (x-axis) for a) SNPs that have antagonistic association with cluster 2 and 3 (excluding agonists between cluster 2 and 3). b) The same as panel a but for different 1000 Genomes super-populations (ALL: complete 1000 Genomes cohort, AFR: African, AMR: Ad Mixed American, EAS: East Asian, EUR: European, SAS: South Asian).
Figure S40: Risk allele frequencies in UK Biobank for the loci showing antagonistic associations between cluster 1 and cluster 2 filtered by different effect size cutoffs. The title of each plot shows the cutoff, where e.g. >=95 % BETA means only the SNPs with a BETA (effect size) value higher than 95% of all other antagonistic SNPs are used. >=0 % BETA means no filtering.
* Figure S41: 'Drug-target gene' interaction network for the drugs that specifically target multicategory cluster 1, cluster 2 or cluster '1 & 2' genes as determined by Fisher's exact test. Blue diamonds show the drugs with significant association or targeting only one gene in these gene groups. Diamonds without written names are only represented with the ChEMBL IDs in the datasets and did not have names. Drug labels written in bold are drugs approved for different conditions. Circles represent the genes targeted by the significant hits, colored by their age-of-onset cluster. Gray circles show the genes targeted by these drugs but are not among the gene set of interest.
* Figure S42: Distribution of a) the drugs and b) their targets approved for 13 conditions treated with the significant hits for drug repurposing. a) X-axis shows the proportion of the significant hits in the drug repurposing study approved for the treatment of the conditions listed on y-axis. b) The same as a) but showing the proportion of unique targets of the approved drugs (x-axis) for the conditions listed on the y-axis.
Figure S43: Scatter plot between logit(missingness) and PCA corrected heterozygosity measures. Each panel shows a self-declared ethnic background. Vertical red lines show the missing rate of 0.05, and horizontal grey lines show the average heterozygosity in UK Biobank.
* Figure S44: Heatmap showing the percent overlap between exclusions based on different criteria. Values show the percent of the column in the row, e.g. 19.4% of "Rec. Exclusions" are in "Hetero / missing outliers" i) "Hetero / missing outliers": '22027-0.0' (Outliers for heterozygosity or missing rate), ii) "Rec. Exclusions": field '22010-0.0' (Recommended genomic analysis exclusions), iii) "High hetero / missing": '22018-0.0', High heterozygosity rate (after correcting for ancestry) or high missing rate, iv) "Mixed Ancestry": '22018-0.0', Participant self-declared as having a mixed ancestral background, and v) "Discordant Sex": as described in the sample QC methods.
- disease co-occurrence matrix summarizing relative risk scores and correlations. Each row shows a cancer type and column shows a disease. The color is defined by relative risk scores while the size is determined by \(\phi\) value (in the same scale as Figure S9 for better comparison), indicating the robustness. Associations for the 114 diseases and 62 cancers that have at least one relative risk ratio higher than four (\(log_{2}RR\geq 2\)) or lower than minus four (\(log_{2}RR\leq-2\)) are plotted.
* Figure S46: a) Density plots showing the number of SNPs per gene, based on eQTL data (blue) and proximity (brown). b) Scatter plot between the number of SNPs per gene mapped using genomic proximity (x-axis) or eQTL data (y-axis). Each dot represents a gene and the blue line shows the linear model. Dashed red line shows one-to-one relationship. The rug-plots on the axes show the marginal distribution of genes. |
135566_file02 | ### Simulation experiment to assess potential statistical bias in post-hoc comparisons
In post-hoc analyses, we systematically explored the temporal development of rsfMRI alterations identified in T1acu \(<\) HCacu and T2acu contrasts by comparing the results between T2acu (and T3rec) and HCacu. The latter may be affected by statistical bias resulting from comparing data based on T1acu-HCacu-differences between T2acu and the same controls. To assess the effect of this potential bias, we conducted a simulation experiment. Three vectors of random normally distributed numbers (x, y, z; resembling data from T1acu, T2acu and HCacu) were generated, while accounting for the correlation between x and y. When a _t_-test comparing x to z resulted in a significant result (\(p<0.05\)), a second _t_-test comparing y to z was conducted. The process was repeated 100.000 times and the distribution of \(p\) values was plotted in figure S3. The MATLAB code to generate the \(p\) distribution is provided below.
P_all = []; rng; for i = 1:100000 xy = mvnrnd([0 0], [.9.4;.4.9], 21); z = randn; [h, p1] = ttest2(xy(:,1), z); if p1 <.05 [h, p2] = ttest2(xy(:,2), z); P_all(end+1,:) = [p1 p2];clear('p2'); end end
### Sensitivity analyses
To control for motion artifacts at the group level, we averaged frame-wise displacement (FWD) parameters to two scores representing mean translation and rotation FWD. These were included as additional covariates in group-level analyses of rsfMRI data.
We furthermore recomputed all post-hoc-comparisons that showed significant group differences by including verbal IQ as covariate (T1/T2acu vs. HCacu) to assess whether differing IQ values observed in cohort 1 influenced rsfMRI group differences; including the time between inpatient admission and T1acu as covariate (T1acu vs. T2acu) to control for the impact of delayed scanning, including BMI-standard deviation score (BMI-SDS) as covariate in all comparisons to assess the extent to which resting-state alterations in AN were mediated by starvation and excluding participants taking psychoactive medication at the time of scanning from all comparisons. For this, (repeated measures) analyses of covariances (RM-ANCOVAs) as well as paired _t_-tests were used.
Finally, we assessed all averaged resting-state measures for outliers (defined as values exceeding 2 standard deviations in relation to the group-wise mean) and recomputed corresponding significant post-hoc group comparisons using Wilcoxon or Mann-Whitney-_U_-tests.
### Additional correlation analyses
Counterintuitively, we observed a strong positive association between T1acu \(<\) HCacu network functional connectivity (FC) and self-reported eating disorder symptom severity (Eating Disorder Inventory 2 (EDI-2) total score). Precuneal Integrated Local Correlation (LC) was also positively related to EDI-2 and furthermore to the Beck Depression Inventory (BDI-2) total score. The EDI-2 is composed of 11 subscales that measure eating disorder specific (e.g. _Drive for thinness_, _Body dissatisfaction_, _Bulimia_) as well as unspecific, partly state-related characteristics (e.g. _Interpersonal distrust_, _Impulse regulation_, _Interoceptive awareness_, _Maturity fears_, _Perfectionism_, _social insecurity_). To evaluate whether specific patterns of associations between FC and the various traits and states measured by the EDI-2 emerged, we calculated Pearson correlations between T1acu \(<\) HCacu network FC and all EDI-2 subscales. Furthermore, we evaluated how the association developed over time (Pearson correlations in T2acu and T3rec groups) and whether it differed between patients with AN in different states of recovery (ANCOVA with EDI-2 total score as dependent variable; group x network FC interaction). Lastly, we explored if the EDI-2 was related to starvation severity and depressive symptoms in patients with acute AN by calculating Pearson correlations between EDI-2 total score and BMI-SDS, plasma leptin as well as BDI-2 total score.
## Supplementary Results
### Results of post-hoc group comparison simulation experiment
The above-described simulation experiment resulted in a strongly right skewed \(p\) value distribution indicating a higher probability of significant effects between y and z (resembling T2acu and HCacu) if a significant effect between x and z (resembling T1acu and HCacu) was observed (figure S3). Transferring these simulated results to our data indicating, in most cases, a normalization of rsfMRI measures at T2 (no significant T2acu \(<\) HCacu differences of clusters identified at T1), influence of statistical bias on our findings regarding rsfMRI normalization seems highly unlikely.
### Impact of potential confounders on rsfMRI results
Including possible confounding variables in group comparisons of rsfMRI results did not introduce major changes to the results. Only BMI-SDS may have a considerable impact on AN-HC-differences in acute patients.
When including FWD in Network Based Statistics (NBS) analyses (T1acu vs. HCacu), the subnetwork size increased and an additional connection between the prefrontal seed ROI and the left calorarine sulcus emerged in the post-hoc seed-to-ROI approach (table S7). When controlling for FWD in the calculation of voxel-wise rsfMRI group differences, original clusters sizes changed slightly, additional clusters of reduced LC (right temporal and orbitofrontal cortices) emerged and the T1acu \(<\) HCacu x T3rec \(>\) HCrec cluster did not remain significant (table S14).
Whilst controlling for verbal IQ in post-hoc comparisons (T1/T2acu vs. HCacu), only group differences in T1acu \(>\) HCacu network FC and bilateral sensorimotor Global Correlation (GC) lost significance (table S8). Note that verbal IQ was available for only \(N=16\) patients with acute AN. Including admission-T1-time as covariate in T1acu vs. T2acu post-hoccomparisons affected significance of GC clusters and left temporal LC (table S9). When including BMI-SDS as covariate in T1/T2acu vs. HCacu comparisons, only differences of bilateral prefrontal GC, right prefrontal LC and left parietal fractional Amplitude of Low Frequency Fluctuations (fALFF) were significant. However, T1acu vs. T2acu differences, except for sensorimotor GC, remained stable (table S10). When excluding participants taking psychoactive medication (T1acu: \(N=4\), T2acu: \(N=6\), combined: \(N=8\)), all differences remained significant with in most cases even increasing effect sizes (table S11).
Except for left temporal LC and fALFF in the T1acu vs. T2acu contrast, for all post-hoc comparisons in at least one of the included groups outlier were identified (maximum \(N=2\)). Also using non-parametric statistics, all group differences identified in the main analyses were significant (table S12).
## Exploration of rsfMRI - ED symptom severity correlations
The only significant (positive) correlations emerged between T1acu \(<\) HCacu network FC and the EDI-2 scales _Interoceptive awareness_ (\(r=0.55\), \(p=0.010\)), _Maurity fear_, _Social insecurity_ (both \(r=0.63\), \(p=0.002\)) and _Impulse regulation_ (\(r=0.45\), \(p=0.041\)), but not with eating disorder specific scales (figure S4). In T2acu and T3rec, the correlations with EDI-2 total score were not significant; T2acu: \(r=0.20\), \(p=0.440\); T3rec: \(r=-0.37\), \(p=0.098\). However, the slope of the regression function changed significantly; \(F=5.62\), \(p=0.006\). At T1, EDI-2 total score was not related to BMI-SDS (\(r=0.03\), \(p=0.884\)), nor to plasma leptin (\(r=-0.07\), \(p=0.757\)), but was strongly correlated with BDI-2 total score (\(r=0.86\), \(p<0.001\)).
# figure S3: Simulation experiment to assess potential statistical bias affecting post-hoc group comparisons
Results of a simulation (100,000 repetitions) showing the distribution of \(p\) values resulting from independent \(t\)-tests comparing two random vectors y and z (orange bars) if a \(t\)-test comparing two random vectors x and z returned a \(p\) value \(<0.05\) (blue bars). Vector lengths resembled group sizes in our study, vectors x and y were generated correlated to each other.
Figure S4: Correlations between T1acu < HCacu network FC and EDI-2 subscales Pearson correlations between T1acu < HCacu network functional connectivity (FC) and Eating Disorder Inventory 2 (EDI-2) subscales in acute Anorexia nervosa patients (T1acu). Blue scatter points represent patients with acute AN at T1. Blue lines display the fitted linear regression function, blue areas the corresponding 95% confidence interval. For descriptive purposes, HCacu subjects are shown as white squares, but do not influence the correlation calculation. r = Pearson’s \(r\). |
140186_file04 | ## ABSTRACT
& & & \\ Structured summary & 2 & Provide a structured summary including, as applicable: background; objectives; data sources; study eligibility criteria, participants, and interventions; study appraisal and synthesis methods; results; limitations; conclusions and implications of key findings; systematic review registration number. & 2 \\ \hline
## INTRODUCTION
& & \\ Rationale & 3 & Describe the rationale for the review in the context of what is already known. & 3-4 \\ \hline Objectives & 4 & Provide an explicit statement of questions being addressed with reference to participants, interventions, comparisons, outcomes, and study design (PICOS). & 4 \\ \hline
## METHODS
& & \\ Protocol and registration & 5 & Indicate if a review protocol exists, if and where it can be accessed (e.g., Web address), and, if available, provide registration information including registration number. & - \\ \hline Eligibility criteria & 6 & Specify study characteristics (e.g., PICOS, length of follow-up) and report characteristics (e.g., years considered, language, publication status) used as criteria for eligibility, giving rationale. & 5-6 \\ \hline Information sources & 7 & Describe all information sources (e.g., databases with dates of coverage, contact with study authors to identify additional studies) in the search and date last searched. & 5 \\ \hline Search & 8 & Present full electronic search strategy for at least one database, including any limits used, such that it could be repeated. & S1 Table \\ \hline Study selection & 9 & State the process for selecting studies (i.e., screening, eligibility, included in systematic review, and, if applicable, included in the meta-analysis). & 5-6 \\ \hline Data collection process & 10 & Describe method of data extraction from reports (e.g., piloted forms, independently, in duplicate) and any processes for obtaining and confirming data from investigators. & 6 \\ \hline Data items & 11 & List and define all variables for which data were sought (e.g., PICOS, funding sources) and any assumptions and simplifications made. & 6 \\ \hline Risk of bias in individual studies & 12 & Describe methods used for assessing risk of bias of individual studies (including specification of whether this was done at the study or outcome level), and how this information is to be used in any data synthesis. & 6 \\ \hline Summary measures & 13 & State the principal summary measures (e.g., risk ratio, difference in means). & 6 \\ \hline Synthesis of results & 14 & Describe the methods of handling data and combining results of studies, if done, including measures of consistency (e.g., F) for each meta-analysis. & - \\ \hline \hline \end{tabular}
PRISMA 2009 Checklist
\begin{tabular}{l|l|l|l} \hline \hline Selectotype & \(\mathcal{A}\) & Constraint Item &
\begin{tabular}{l} Reported \\ QA page \\ \end{tabular} \\ \hline Risk of bias across studies & 15 & Specify any assessment of risk of bias that may affect the cumulative evidence (e.g., publication bias, selective reporting within studies). & 6 \\ \hline Additional analyses & 16 & Describe methods of additional analyses (e.g., sensitivity or subgroup analyses, meta-regression), if done, indicating which were pre-specified. \\ \hline
## RESULTS
& & \\ \hline Study selection & 17 & Give numbers of studies screened, assessed for eligibility, and included in the review, with reasons for exclusions at each stage, ideally with a flow diagram. & \\ \hline Study characteristics & 18 & For each study, present characteristics for which data were extracted (e.g., study size, PICOS, follow-up period) and provide the citations. & Table 1 \\ \hline Risk of bias within studies & 19 & Present data on risk of bias of each study and, if available, any outcome level assessment (see item 12). & 18 \\ \hline Results of individual studies & 20 & For all outcomes considered (benefits or harms), present, for each study: (a) simple summary data for each intervention group (b) effect estimates and confidence intervals, ideally with a forest plot. & \\ \hline Synthesis of results & 21 & Present results of each meta-analysis done, including confidence intervals and measures of consistency. & - \\ \hline Risk of bias across studies & 22 & Present results of any assessment of risk of bias across studies (see item 15). & 8,18 \\ \hline Additional analysis & 23 & Give results of additional analyses, if done (e.g., sensitivity or subgroup analyses, meta-regression [see item 16]). & - \\ \hline
## DISCUSSION
& & \\ \hline Summary of evidence & 24 & Summarize the main findings including the strength of evidence for each main outcome; consider their relevance to key groups (e.g., healthcare providers, users, and policy makers). & 15 \\ \hline Limitations & 25 & Discuss limitations at study and outcome level (e.g., risk of bias), and at review-level (e.g., incomplete retrieval of identified research, reporting bias). & 19 \\ \hline Conclusions & 26 & Provide a general interpretation of the results in the context of other evidence, and implications for future research. & 20-21 \\ \hline
|
142760_file02 | ## Figure 1:** The number of genes in the Democratic Republic of the Congo
## Supplementary: Modeling impact and cost-effectiveness of gene drives for malaria elimination in the Democratic Republic of the Congo
Kasai Central
## Supplementary: Modeling impact and cost-effectiveness of gene drives for malaria elimination in the Democratic Republic of the Congo
Kinshasa
## Supplementary: Modeling impact and cost-effectiveness of gene drives for malaria elimination in the Democratic Republic of the Congo
Kwango
## Supplementary: Modeling impact and cost-effectiveness of gene drives for malaria elimination in the Democratic Republic of the Congo
Nord Ubangui
## Supplementary: Modeling impact and cost-effectiveness of gene drives for malaria elimination in the Democratic Republic of the Congo
23**Supplementary 3. Non-spatial simulation framework: ratio between current and initial numbers of adult vectors, 15-year post- single release of 300 drive mosquitoes at year 0.**
## Supplementary: Modeling impact and cost-effectiveness of gene drives for malaria elimination in the Democratic Republic of the Congo
## Supplementary: Modeling impact and cost-effectiveness of gene drives for malaria elimination in the Democratic Republic of the Congo
## Supplementary: Modeling impact and cost-effectiveness of gene drives for malaria elimination in the Democratic Republic of the Congo
## Supplementary: Modeling impact and cost-effectiveness of gene drives for malaria elimination in the Democratic Republic of the Congo
## Supplementary: Modeling impact and cost-effectiveness of gene drives for malaria elimination in the Democratic Republic of the Congo
## Supplementary: Modeling impact and cost-effectiveness of gene drives for malaria elimination in the Democratic Republic of the Congo
## Supplementary: Modeling impact and cost-effectiveness of gene drives for malaria elimination in the Democratic Republic of the Congo
## Supplementary: Modeling impact and cost-effectiveness of gene drives for malaria elimination in the Democratic Republic of the Congo
## Supplementary: Modeling impact and cost-effectiveness of gene drives for malaria elimination in the Democratic Republic of the Congo
## Supplementary: Modeling impact and cost-effectiveness of gene drives for malaria elimination in the Democratic Republic of the Congo
## Supplementary: Modeling impact and cost-effectiveness of gene drives for malaria elimination in the Democratic Republic of the Congo
## Kinshasa - scenarios without gene drives
## Supplementary: Modeling impact and cost-effectiveness of gene drives for malaria elimination in the Democratic Republic of the Congo
## Supplementary: Modeling impact and cost-effectiveness of gene drives for malaria elimination in the Democratic Republic of the Congo
## Supplementary: Modeling impact and cost-effectiveness of gene drives for malaria elimination in the Democratic Republic of the Congo
## Supplementary: Modeling impact and cost-effectiveness of gene drives for malaria elimination in the Democratic Republic of the Congo
## Supplementary: Modeling impact and cost-effectiveness of gene drives for malaria elimination in the Democratic Republic of the Congo
## Supplementary 5: Reduced migration testing
## Supplementary 6: Reduced migration testing
*
* **Table S3 Incremental cost-effectiveness ratio in year 1-5 after applying intervention(s)**Supplementary: Modeling impact and cost-effectiveness of gene drives for malaria elimination in the Democratic Republic of the Congo
* 77 **Supplementary 7: Costs of vector control approaches that involve the release of**
* A systematic scoping review.**
* 79 **Background**
* 80 **Vector control approaches that involve the release of mosquitoes to modify the vector**
* 81 **population range from** _Wolbachia_ **related technique to sterile insect production using radiation technique. For** _Wolbachia_ **related technique, the strategy proposed to infect mosquitoes**
* 83 **with** _Wolbachia_ **endosymbiotic that inhibits the viral replication and dissemination and**
* 84 **eventually completely blocks vector-borne disease transmissions. The latter strategy, sterile insect technique (SIT) exposes male mosquitoes with low radiation in the laboratory production.**
* 86 **This leads to sterilization of the male mosquitoes but maintain their copulation capacity.**
* 87 **Once released to the environment, the sterile male mosquitoes mate wild female mosquitoes**
* 88 **which would produce sterile eggs thereby eliminating the next generation progenies.**
* 89 **Producing SIT insects at a large scale requires standardized mass-rearing procedures to produce**
* 90 **good quality males that could compete with wild males to mate with females in the wild**
* 91 **environment. Later development of these strategies includes the release of genetically**
* 92 **engineered mosquitoes carrying dominant lethal allele that are capable of killing a subsequent**
* 93 **generation. The produced OX513A mosquitoes are males that once mate with wild female**
* 94 **mosquitoes will produce descendants that would not reach the adult stage due to lethal genes**
* 95 **.**
* 96 **It is necessary for the decision to adapt these strategies specifically modifying mosquito**
* 97 **vectors to be based on evidence of program effectiveness and cost-effectiveness of the**
* 98 **interventions. However, evidence on costs and cost assessments of these strategies**
* 99 **remain disparate. Data on costs could provide invaluable information for implementing vector**
* 100 **control programs as malaria and other mosquito-borne infectious diseases continue to be a**
* 101 **public health problem despite past and on-going control efforts. For**
* 102 **efforts to achieve the disease elimination goal, it is important that the most cost-effective**
* 103 **interventions are deployed. This supplementary is a systematic scoping review on costs and**
* 104 **cost analysis of vector control approaches that involve the release of mosquitoes to modify the vector population focusing relevance on mosquito-borne diseases, especially malaria.**
* 106 **Methods**
* 107 **A systematic search of literatures in English language pertaining to costs of vector**
* 108 **control methods to modify mosquito populations, published from 2010 to 2020, was performed**
* 109 **(Diagram S1). Databases include National Center for Biotechnology Information (NCBI),**
* 110 **Google Scholar, Crossref, and Scopus. Search terms include 'Culicidae' and 'genetic**
* 111 **engineering' or 'genetically modified' and 'costs' or 'cost analysis' and'malaria'.**
* 112 **3,486 records of the initial search: 761 articles in PubMed Central, 13 articles in**
* 113 **PubMed, 22 items in 13 books, 2480 articles in Google Scholar, 200 articles in Crossref, and 10**
* 114 **articles in Scopus, were screened for relevance, and those that included some forms of**
* 115 **information on costs of new vector control intended to modify mosquito populations were**
* 116 **assessed further in full texts for eligibility. 8 articles from reference lists thought to be relevant**
* 117 **based on their titles alone were included in the full-text assessment. We excluded 3,428 articles**
* 118 **that were duplicated, or full texts not provided. In full-text assessment, 66 articles were included**
* 119 **based on selection criteria suggested costs or cost analysis of vector control methods intended to**
* 120 **modify mosquito populations were described in monetary terms. 58 publications did not**
* 121 **mention costs or mentioned but did not provide estimates in terms of monetary numbers were excluded. Details of literature selection procedures are in Diagram S1.**
## 153 Discussion
During the past 10 years, only handful costing evidence of vector control approaches that involve the release of mosquitoes to modify the vector population focusing relevance on mosquito-borne diseases, especially malaria, has been made available. When costs were mentioned, the studies were often not undertaken alongside an evaluation of the clinical and epidemiological effect of the methods of interest. This systematic scoping review is an early attempt to combine evidence on costs of the approaches.
|
144212_file09 | #### Sequencing Quality Control
Small RNA was aligned using miRNAExpress and MINTmap. Total reads (after flexbar with quality control): 500,488,798. Reads per sample: 10,214,057 +/- (SD) 4,605,190. No significant difference between groups. Total miRNA: 284,749,856. miRNA hit / (hit+nohit): 56% +/- (SD) 4.4%. Total tRF (exclusive to tRNA space, see MINTmap documentation): 1,637,476. tRF (exclusive to tRNA space, see MINTmap documentation) hit / total reads: 3238 ppm +/- (SD) 1421 ppm. FastQC: All analyzed samples/bases showed exceptional quality. These metrics and FastQC results can be viewed at [https://github.com/slobentanzer/stroke-trf](https://github.com/slobentanzer/stroke-trf).
At present, no standardized method exists to directly compare absolute counts derived from two separate alignments of the same sequencing experiment, as is the case here with the miRNAExpress and MINTmap alignments; MINTmap is a much more stringent pipeline (at least for the "exclusive tRNA space" used here). Future experiments should include a spike-in procedure or a similar approach to estimate absolute transcript numbers for each smRNA species, and to enable a better comparison between those absolute values.
Large RNA: Total reads (after flexbar with quality control): 880,069,396. Reads per sample: 36,669,558 +/-(SD) 4,543,364. No significant difference between groups. Mean mapping rate 89% +/- (SD) 2%. FastQC: All analyzed samples/bases showed exceptional quality. These metrics and FastQC results can be viewed at [https://github.com/slobentanzer/stroke-trf](https://github.com/slobentanzer/stroke-trf).
#### Differential expression analysis
Differential expression was determined using the R/DESeq2 package including the log2 fold change shrinkage estimation "apegim" algorithm. Genes were considered differentially expressed at an adjusted p-value of < 0.05. The analysis was performed on the raw count tables (outliers already removed) with correction of covariates (age, batch, time2blood) in the model formula. Outliers were identified by sample clustering based on batch-corrected variance-stabilized expression, leading to exclusion of sample 4044 (stroke patient) in the small RNA sequencing experiment.
#### The count-change metric
The log-fold change metric is not ideally suited for assessing the potential impact of expression changes for individual small RNAs, because it does not reflect mean expression levels. We calculated the count-change for individual miRs and tRFs by combining base mean expression with the de-logarithmicized fold-change (from DESeq2 output).
\[CC=(BM\times 2^{LFC})-BM\]
CC: countChange, BM: baseMean, LFC: log2-fold change
#### Small RNA targeting predictions
Briefly, the database unites 10 prediction algorithms and all available experimentally validated miR:gene interactions, and unites them in a scoring system. For all analyses in this manuscript, the cutoff score for consideration of a valid miR:gene interaction was \(\geq\) 6.
Since no comprehensive tRF targeting predictions are available, we performed our own prediction based on all tRFs detected with more than 10 reads on average. We used the TargetScan 7.0 algorithm to determine putative miR-like binding of any 7-nucleotide substring ("seed") of any tRF to any human transcript 3'-UTR. Hits were scored according to conserved branch length (BL) and probability of conserved targeting (PCT) across all 23 available species and were entered into _miRNeo_ (seed-gene targeting and tRF-seed association).
#### Gene set compilation of cholinergic and associated genes
We started out with a set of 28 cholinergic genes described in, targets including ACLY, CHAT, VACnT (aka SLC18A3), the 16 nicotinic and 5 muscarinic receptor subtypes, ACHE, BCHE, PRIMA1, and CHT (aka SLC5A7). In addition, we added several groups of genes known to be associated withcholinergic functioning and of interest to our aims. These include: genes from the neurokine and neurotrophin signaling pathways; families of genes implicated in the development and differentiation of cholinergic cell types, including lim-homeobox transcription factors, bone morphogenetic protein family genes, and genes from the JAK-STAT pathway (see Data File S2)
Transcription factors were similarly associated with each transcript on the list, using the transcription factor activity derived from in circulatory immune cells.
### Permutation targeting analysis
Where appropriate, we determined permutation p-values via _miRNeo_ targeting permutation. We determined a score for the test condition (e.g. by summing the individual targeting scores of all DE miRs towards cholinergic genes) and compared it to a null distribution consisting of permutated scores resulting from random substitution of test parameters (e.g. a random selection out of all genes the same size as the cholinergic test set), the p-value being the fraction of the null distribution at least as extreme as the real score.
### Gene Ontology Analyses
We performed GO analyses on differentially expressed (DE) long RNA transcripts based on their DE p-value. GO analyses were performed using R/topGO as recommended by the authors, using the weighted method. Transcripts were ranked by p-value, and all DE transcripts (adjusted p-value < 0.05) with absolute log2 fold changes > 1.4 were tested against the background of the topmost two thousand transcripts. While GO enrichment analysis can be informative, interpretation and visualization of its results is not standardized and is often limited to presentation of top \(X\) terms by p-value. R/gsoap is an analysis tool proposed to aid in interpretation of GO enrichment results via t-SNE display of similarity of terms based on the amount of shared significant genes. GO enrichment results were processed to fulfil ssoap input criteria and visualized using R/ggplot2.
### Pathways targeted by perturbed miRs
We determined target sets of positively and negatively DE miRs (separately) via _miRNeo_ query with a threshold score of at least 6. The gene targets were ranked by the amount of miRs targeting each gene, yielding a range of 1-44 (mean 4.7 +/-SD 4.7) for positively regulated miRs, and a range of 1-155 (mean 13.5 +/-SD 15.6) for negatively regulated miRs, both resembling power law distributions. To account for possible biases in the underlying targeting dataset, targeting and scoring were then permutated for both sets with the same query and ranking, but randomized input miRs were selected from all mature miRs in the same length as the original DE set, for 10,000 times. Upon calculation of permutation p-values, we dismissed genes that were not targeted by the set of DE miRs significantly more than by the random permutation sets (p < 0.05). The larger negative-DE set in this analysis yielded a large number of highly enriched genes, such that a distinction by adjusted p-value was not possible in the top 2000 targeted genes. Thus, we repeated the analysis for negatively regulated miRs using a log2FoldChange threshold of -2, which reduced the amount of miRs to 82, and the range of miRs targeting each gene to 1-52, mean 5.8 +/-SD 6.1. This set was subjected to the same permutation approach and was used instead of the non-limited set in the p-value-based approach below.
The gene lists so derived were used in a GO analysis similar to the one described above, based on the following scorings: for positively regulated miRs, GO enrichment was based on _1)_ the significantly targeted genes (p < 0.05) as a test set, and the (non-enriched, p > 0.05) genes as background; and _2)_, to identify the most-targeted genes, the top 200 genes (sorted by amount of distinct miRs targeting each gene (also p < 0.05)) served as a test set, with all other genes (starting from 201) as the background. For negatively regulated miRs, target genes were analyzed similarly, but the non-threshold significantly targeted genes were replaced by the -2 log2FoldChange threshold set in approach _1)_. The GO terms yielded by these four analyses were visualized and clustered using the R/gsoap-approach described above.
The resulting 13 clusters were manually annotated and organized on a canvas to better understand the relationships between the targeted gene sets of positively and negatively regulated miRs (Figure S5).
Few terms fell outside the area of these manually adjoined clusters due to little similarity with the clustered terms; these were disregarded in the further analyses (but are available in Data File S6). To discern the most relevant genes and seek putative hub genes in the stroke response, the clusters identified in the gsoap visualization were imported back into the R environment. Detection of significantly enriched genes in each cluster involved hypergeometric enrichment of each gene in each cluster versus all other clusters (background) via Fisher's exact test. The resultant p-values were corrected for multiple testing using the Benjamini-Hochberg method, and genes with an adjusted p-value \(<0.05\) were considered significantly enriched in the respective cluster (Data File S6), with a range of enriched genes per cluster from 8 to 84. The final 13 clusters were ranked by the total amount of enriched genes per cluster, and cross-checked for functional implications of enriched genes in each cluster using DAVID 6.8.
### PCR quantification of inflammatory markers after LPS stimulation and Zbp1 quantification.
## LPS stimulation:
18h after LPS stimulation, cells were collected in Tri-Reagent (Sigma Aldrich, St. Louis, USA) and total RNA, including small RNAs, isolated using miRNeasy (Qiagen, Hilden, Germany). cDNA was synthesized from 100ng RNA using qScript(tm) cDNA Synthesis Kit (Quanta Biosciences, Beverly MA, USA). Expression of Cd14, Stat1, Tnfa and III10 were assessed using PerfeCTa(r) SYBR(r) Green FastMix(r) (Quanta Biosciences, Beverly MA, USA) and normalized using Peptidylprolyl isomerase A (Ppia) and 18S ribosomal RNA genes as house-keeping.
Louis, USA) and total RNA, including small RNAs, isolated using miRNeasy (Qiagen, Hilden, Germany). cDNA was synthesized from 100ng RNA using qScript(tm) cDNA Synthesis Kit (Quanta Biosciences, Beverly MA, USA), and expression of Zbp1 was assessed using PerfeCTa(r) SYBR(r) Green FastMix(r) (Quanta Biosciences, Beverly MA, USA) and normalized using Glyceraldehyde 3-phosphate dehydrogenase (Gapdh) as house-keeping.
First, we performed size selection of total RNA, to exclude molecules > 25 nt in case of human samples and > 50 nt in case of cell culture experiments with RAW 264.7 cells. 1 mg of RNA was loaded into 15% TBE-Urea-Polyacrylamide gel (Biorad, Hercules, USA) after mixing 1:1 with Gel Loading Buffer II (Thermo Fisher, Waltham, USA) and run at 200V for 40-50 minutes. When testing human CD14+ monocytes, 600 ng of RNA were loaded into the gel; in case of low total RNA concentrations (with minimum 21 ng/ml), we used the maximum accommodable volume of 20 ml. Gels were stained with SYBR Gold (Thermo Fisher, Waltham, USA) and visualized on a UV table to cut out the desired section. As size markers, miR marker and Low Range ssRNA ladder (both from New England Biolabs, Ipswitch, USA) were used. Excised gel fragments were incubated in 810ml 3M NaCl over-night at 4degC on a rotation stand. The supernatant was then transferred into a new Eppendorf and 1 volume of iso-propanol was added for 24h at -20degC. Then, RNA was precipitated.
RNA concentrations were measured using Bioanalyzer (Agilent, Santa Clara, USAu) and cDNA was prepared from 500 pg (with exception of control samples 16 and 18 yielding low concentrations after size selection - here 250pg were used) using qScript(tm) microRNA cDNA Synthesis Kit (Quanta Biosciences, Beverly MA, USA) and diluted to 200 ml total. tRFs were quantified using quantitative reverse transcription PCR (RT-qPCR) with PerfeCTa(r) SYBR(r) Green FastMix(r), Low ROX(tm) (Quanta Biosciences, Beverly MA, USA) and normalized to hsa-miR-30d-5p, hsa-miR-7d-5p, hsa-miR-06b-3p and hsa-miR-3615 (human stroke patients) or mm-miR-30d-5p, mmu-let-7d-5p for experiments with RAW 264.7 cells. In experiments with ssRNA IRF-22-WE8SPOX52 mimics, IRF-22-WE8SPOX52 levels were assessed without size-selection (measuring levels of the IRF and its parental tRNA molecule) and normalized to Snord47.
Primer sequences are listed below:
hsa/mmu-miR-30d-5p: TGTAAACATCCCCGACTGGAAG
hsa/mmu-let-7d-5p: AGAGGGTAGTAGGTTGCATAGTT
hsa-miR-106b-3p: CCGGACCTGGGGTACTTGCTGC
hsa-miR-3615: TCTCTCGCGCTCCTCGCGGTC
tRF-22-WEKSPM852: TCGATCCCCGGCATCTCACCA
tRF-22-WE8SPOX52 (and tRF-21-WE8SPOX5D): TCGATTCCCGGCCAATGCACC
tRF-18-8R6Q46D2: TCCCCGGCATCTCACCA
tRF-22-8EKSP1852: TCAATCCCCGGCACCTCCACCA
tRF-18-8R6546D2: TCCCCGGCACCTTCCACCA
tRF-18-HR0VX6D2: ATCCACCCCTGCCACCA
Snord47 (Quanta Biosciences, Beverly MA, USA):
GTGATGATTCTGCCAAATGATACAAGTGATATCACCTTTAAACCGTTCCATTTATTCTGAGG
## Figure S1 Analysis of types of DE tRFs indicates non-random cleavage of tRNA molecules.
Most DE tRFs were derived from tRNA-Ala and 3'-tRFs were the most common type in the whole DE dataset.
## Figure S2
## Cholinergic-associated small RNA empirical cumulative distribution function (ECDF) curves.
Cholinergic association was tested using _miRNeo_ targeting data of miRs and tRFs.
To assess the best-suited threshold for defining cholinergic association, ECDFs were calculated for the number of cholinergic-associated (CA) genes targeted by each unique small RNA. A) Cumulative frequency of the number of CA genes targeted by tRFs. Threshold of 80% (red line) is passed at five CA genes targeted. B) Cumulative frequency of the number of CA genes targeted by miRs. Threshold of 80% (red line) is passed at four CA genes targeted.
## Figure S3
## tRF profiles of blood compartments distinguish leukocyte subsets, excluding neutrophils, from erythrocytes and non-cellular compartments
## Figure S4****Most of top 20 stroke DE tRFs are present in immune cell compartments.
Heatmap showing the presence/absence of the 20 most highly-perturbed tRFs in defined blood compartments.
## Figure S5 (on previous page) Ontological enrichment and clustering of gene target sets of DE miRs show distinct perturbed pathways.
Gene target sets of positively and negatively perturbed miRs were subjected to gene ontology analysis separately, based on two scoring systems: "pval," based on enrichment p-value in targeting permutation, and "top200", based on the top 200 genes with highest amounts of miRs targeting each gene. Resulting GO terms were visualized using R/gsoap and clustered based on their shared genes (upper left). Circle sizes represent the number of genes in each term, their color depth denotes p-value (all p < 0.05). The single clusters were manually screened and annotated regarding their functions (right side).
## Figure S6
## Upregulated inflammatory signaling molecules and cytokines in LPS-stimulated murine RAW 264.7 cells.** A) Levels of cluster of differentiation 14 (Cd14), signal transducer and activator of transcription 1 (Stat1), tumor necrosis factor alpha (Tnfa) and interleukin 10 (ll-10) were measured with RT-qPCR using normalized expression (Ppia and 18SrRNA served as house-keeping), relative to the nonstimulated control group (line at mean normalized expression for the control group = 1), Each dot represents 2-4 technical replicates, ANOVA with Tukey post-hoc, * p < 0.05, ** p < 0.01, *
## Figure S7********RF-22-WE8SPOX52 expression in the ssRNA mimics transfection experiments.** Shown is normalized expression of fRF-22-WE8SPOX52 and parental tRNA molecule (measurement without size selection) by RT-qPCR using Snord47 as house-keeping gene. A) Experiment 1 - samples subjected to long RNA sequencing. B) Experiment 2 - samples used for RT-qPCR measurements of Zbp1 expression. Each dot represents one technical replicate in the cell culture experiment. ** p< 0.01, *
## Figure S8 LPS stimulation of human CD14+ cells yields transient nicotine-affected tRF changes
The top 6 stroke-perturbed tRFs were quantified in human CD14+ cells following LPS stimulation with and without addition of nicotine; controls were nonstimulated cells and cells with nicotine alone (for setup, see in the main manuscript). A) Cells collected 6h after LPS stimulation showed significantly elevated tRF-18-8R6546D2 under LPS + nicotine exposure alone. B) At 18h after LPS stimulation, none of thetop 6 stroke-perturbed tRFs showed significant changes, including LPS +nicotine challenged cells which showed upregulation at the 12h time point (see in the main manuscript). LPS-stimulated cells still showed the highest expression of tRFs, albeit not significant when compared to other groups. \({}^{\#}\) p! 0.05 when compared to nicotine-treated cells. Each dot represents one donor, one-way ANOVA with Tukey post-hoc; bar graphs +/- SD(lg). C) LPS-stimulation led to significantly elevated TNF\({}_{\alpha}\) levels in the supernatant of CD14+ cells (measured by ELISA). \({}^{*}\)p<0.05, \({}^{**}\)p<0.01, \({}^{***}\)p<0.001, two-way ANOVA on the influence of group and time variable on the TNF\({}_{\alpha}\) levels. F = 23.53, p!0.0001 for the main effect "group" (nonstimulated, LPS, LPS + nicotine and nicotine), F = 7.56 p = 0.0012 for the main effect "time", F p=0.02 for the interaction; with Dunnett's post-hoc performing comparisons LPS group vs. others; bar graph +/- SD.
## Figure S9 Sequence of tRF-18-HR0VX6D2 shows high similarities to two known mIRs
## Table S1
## Post-stroke DE genes are enriched in circulation- and immunity- related pathways.
Full list of GO terms used for generation of tSNE in (main manuscript).
|
151233_file02 | ### Peak Timing
In order to calculate out-of-sample predictive validity statistics on how well each model predicted the timing of peak daily deaths, we smoothed daily death data, which are highly stochastic, applied an algorithm to detect peaks in both observed data and forecasted model estimates, and calculated errors in the difference in number of days between the observed and estimated peaks.
First, observed daily death data were smoothed to provide stable time-series that could be used for local maxima detection. We used various smoothers to accomplish this task, including a LOESS smoother with a span of 0.33, run separately for each location-specific timeseries, a 7-day rolling average, and a 3-day rolling average applied tenfold to the same timeseries. We chose to present results calculated using the LOESS smoother in the main text, as it was found to be the most robust method to daily stochasticity that could introduce false peaks. Although most models produced smooth timeseries of daily deaths, some also demonstrated stochasticity, and so all forecasted daily death timeseries were also smoothed with a LOESS smoother.
Peaks in smoothed, observed daily deaths were calculated according to the following algorithm. A peak was defined as:
1. a local maximum \(p\) in the timeseries at time \(t\),
2. where no other point exists in the next 21 days (\(t\) through \(t\)+21) that exceeds the \(p\) by more than 20%,
3. \(t\) does not fall within the last seven days of the timeseries,
4.
5. and if multiple such points \(p\) exist that meet the above criteria, then the first value will be selected.
Peaks in forecasted trends were also identified with the same algorithm. For a time-series in which no peak was identified using the above algorithm, for a location which did have a peak in observed data, the global maximum value was used. This captured errors among models that failed to ever predict a peak, despite a true peak being observed. Errors for locations with a true peak in observed data, for the model runs in which the model date was at least seven days prior to the true detected peak. Errors were defined as the difference between the date of the true peak and the estimated peak from each forecasting model, in days. Summary statistics included the median absolute error in days, as a measure of accuracy, and the median error in days as a measure of bias. Errors were stratified by model, and weeks of extrapolation, which was defined as:
\[Weeks\ of\ extrapolation\ =\ floor((peak\ date-model\_release\_date)/7)\]
Summary statistics were masked for models that were not released in time to produce peak timing estimates for at least 25 total locations. Due to limited regional coverage it was not possible to stratify results by geography. This will likely become feasible as more locations pass their peak of daily mortality.
## Supplemental Figures
## Supplemental Cumulative Mortality - Median Absolute Percent Error - Month of Estimation
Median absolute percent error values were calculated across all observed errors at weekly intervals, for each model, by month of estimation, weeks of forecasting, and super regional grouping used in the Global Burden of Disease Study. Values that represent fewer than five locations are masked due to small sample size. Models were included in the global average when they included at least five locations in each region. Pooled summary statistics reflect values calculated across all errors from all models, in order to comment on aggregate trends by time or geography.
## Supplemental Cumulative Mortality - Median Percent Error - Month of Estimation
Median percent error values, a measure of bias, were calculated across all observed errors at weekly intervals, for each model, by month of estimation, weeks of forecasting, and super regional grouping used in the Global Burden of Disease Study. Values that represent fewer than five locations are masked due to small sample size. Models were included in the global average when they included at least five locations in each region. Pooled summary statistics reflect values calculated across all errors from all models, in order to comment on aggregate trends by time or geography.
## Supplemental Weekly Mortality - Median Absolute Percent Error - Month of Estimation
Median absolute percent error values were calculated for weekly mortality rates across all observed errors at weekly intervals, for each model, by month of estimation, weeks of forecasting, and super regional grouping used in the Global Burden of Disease Study. Values that represent fewer than 5 locations are masked due to small sample size. Models were included in the global average when they included at least five locations in each region. Pooled summary statistics reflect values calculated across all errors from all models, in order to comment on aggregate trends by time or geography.
## Supplemental Cumulative Mortality - Median Absolute Error - Month of Estimation
Median absolute error values were calculated for cumulative mortality rates across all observed errors at weekly intervals, for each model, by month of estimation, weeks of forecasting, and super regional grouping used in the Global Burden of Disease Study. Values that represent fewer than 5 locations are masked due to small sample size. Models were included in the global average when they included at least five locations in each region. Pooled summary statistics reflect values calculated across all errors from all models, in order to comment on aggregate trends by time or geography.
## Supplemental Accuracy and Bias in Peak Timing by Month of Estimation
Median error in days are shown by model, weeks of forecasting, and estimation month. Models that are not available for at least 40 peak timing predictions are not shown. Errors only reflect models released at least seven days before the observed peak in daily mortality. One week of forecasting refers to errors occurring from seven to 13 days in advance of the observed peak, while two weeks refers to those occurring from 14 to 20 days prior, and so on, up to six weeks, which refers to 42-48 days prior.
## Supplemental Smoothing Method - Example for nine Countries
Daily deaths are shown for nine locations, as well as three methods used to smooth them prior to peak date calculation. Calculated peaks from each method are shown with dashed vertical lines. Smoothing method is shown by color. |
153114_file02 | ## Figure S3. Sequence features of immune receptors in the plasma B-cell repertoire across cohorts.****(A)** Scatter plot shows log\({}_{10}\) relative abundance of clonal lineages constructed from the plasma B-cell and bulk repertoire data from all time points and replicates in each patient (colors). To avoid primer-specific amplification biases, the relative abundance is estimated as the total read count of a clonal lineage relative to the total reads in the data associated with a specific primer amplification. Lineages with only bulk reads or only plasma reads are displayed as having log\({}_{10}\) relative abundance = 1e-8. Pearson correlations (r) between abundances of lineages which were present in both the bulk and the plasma B-cell repertoires and the corresponding p-values are indicated in the legend for each patient. **(B-D)** Similar statistics are shown as in (A,C,D), but for progenitors of clonal lineages with minimum size of three, in which at least one BCR is found in the plasma B-cell repertoire data; statistics of these lineages are reported in Tables S1, S2. Smaller read counts in the plasma B-cell data compared to the bulk do not allow for comparative analysis of receptor statistics across cohorts. **(D-F)
Similar statistics are shown as in Fig. S2 (A-C), but for unique receptors harvested from the plasma B-cell repertoires. Statistics of these receptors in each individual is described in Table S2. Smaller read counts in the plasma B-cell data compared to the bulk don't allow for comparative analysis of receptor statistics across cohorts. Colors are consistent across panels.
Full lines show distributions averaged over individuals in each cohort, and shadings indicate regions containing one standard deviation of variation among individuals within a cohort. **(B)** The scatterplot shows log \(P_{\text{post}}\) obtained by evaluating 500,000 generated sequences using the inferred selection (SONIA) models (Sethna et al., 2020) trained on the healthy cohort (x-axis) and 30 SONIA models trained on independent samples of the GRP dataset (Briney et al., 2019) down-sampled to the size of the healthy cohort in this study (7,161 receptors) (y-axis). The scatterplots show all unique pairwise comparisons between SONIA models trained on independent subsets with each cohort for **(C)** GRP (30 models), and COVID-19 patients with **(D)** mild (two models), **(E)** moderate (13 models), and **(F)** sever (three models) symptoms (Methods). The Pearson correlation between for pairwise model comparisons are shown in each panel.
## Figure S5. ELISA binding assays for IgG and IgM repertoires against SARS-CoV-2 and SARS-CoV.
Plasma binding levels (measured by OD\({}_{450}\) in ELISA) against RBD, NTD, and S2 subdomain of SARS-CoV-2 and against RBD and NTD epitopes of SARS-CoV are shown. As seen in binding assays, many individuals developed a cross-reactive response to SARS-CoV-2 and SARS-CoV. Some individuals showed no increase in IgG binding to SARS-CoV-2 RBD due to already high levels at sampling time or natural variation. For the expansion analysis, we analyzed only individuals whose IgG repertoires showed an increase in binding to SARS-CoV-2 (RBD): 2, 3, 4, 5, 6, 7, 9, 10, 11, 13, and 14.
Figure S6. **Expansion supplement.** BCR repertoires are highly under-sampled, and relatively few BCR lineages appear in multiple time points and replicates. **(A)** Fraction of lineages present in only one time point before (blue) and after (red) filtering out small lineages (i.e., those with less than three unique sequences per time point) are shown. **(B)** Fraction of lineages present in only one replicate before (blue) and after (red) filtering out small lineages (i.e., those with less than three unique sequences per time point) are shown. **(C)** The log-ratio of abundance of receptors for all clonal lineages present in two replicates are shown. Each panel shows the test result for a given patient, as indicated in the label. The count density indicates the number of lineages at each point. Lineages that show a significant expansion over time are indicated in red.
**(D)**\(\log_{10}\) p-values of the expansion test versus \(\log_{10}\) fold change (or odds ratio) for replicate data are shown. Color indicates density of points, and p-values of zero are displayed at the minimum nonzero value. See Methods for normalization, data processing, and hypothesis test. **(E)** Empirical cumulative density functions (CDF) of expansion data from multiple time points (red) and replicate data (blue) show that many more tests in expansion data result in low p-values compared to replicate data. **(F)** Ratio of empirical cumulative density functions (CDF) indicates that at a significance threshold of \(10^{-300}\) there are roughly 12.3 times more positives than false positives. **(G)**\(\log_{10}\) p-values of the expansion test versus \(\log_{10}\) fold change (or odds ratio) for data corresponding to is shown. Color indicates density of points, and p-values of zero are displayed at the minimum nonzero value. See Methods for normalization, data processing, and hypothesis test. **(H)** Fraction of lineages expanded for different individuals is shown. HCDR3 length distributions of expanded and non-expanded lineages, **(I)** with each lineage having equal weight, and **(J)** with each lineage weighted by the number of unique sequences per time point (excluding singletons) are shown.
## Figure S7. Sharing of BCRs among healthy individuals.****(A)** The density plot shows the distribution of \(\log_{10}P_{\rm post}\) for progenitors of clonal lineages shared in a given number of healthy individuals, indicated on the horizontal axis; histogram bin size is 0.5. The clonal lineages are constructed from the bulk data (Tables S1). The counts in each bin are scaled such that the maximum is equal to one for each column. The numbers above each column indicate the total number of sequences in the respective column. Sharing of rare lineages with \(\log_{10}P_{\rm post}\) below the dashed line is statistically significant (see Methods). **(B)** Similar statistics as in **(A)** are shown but for healthy individuals in the Great Repertoire Project (Briney et al., 2019). Sharing of rare lineages with \(\log_{10}P_{\rm post}\) below the black dashed line is statistically significant (see Methods). For comparison, the dashed line in **(A)** is shown as a red dashed line in **(B)
## Figure S8. Sequence features of heavy and light chain receptors in sorted single cells and monoclonal antibodies.** The bar graphs show the relative counts for **(A)** the \(\kappa-\)chain IGKV-gene usage and **(B)** the \(\lambda-\)chain IGLV-gene usage for the verified mAbs reactive to RBD (pink) and NTD (green) epitopes of SARS-CoV-2 (Table S7) and the light chain receptors obtained from the RBD- (yellow) and NTD- (blue) sorted single cell data (Methods). Distributions of the lengths of **(C)** of HCDR (heavy chain), **(D)** KCDR3 (\(\kappa-\)chain), and **(E)** LCDR3 (\(\lambda-\)chain ) amino acid sequences are shown. **(F)** IGHJ-gene usage, **(G)** IGKJ-gene usage, and **(H)** IGLJ-gene usage of the sorted single cells is shown in relative counts in bar graphs. Colors are consistent between panels and the number of samples used to evaluate the statistics in each panel is indicated in the legend. **(I-L)** Circos plots show matches between the light chain CDR3 sequences of progenitors in the sorted single cell dataset (black) and light chain CDR3 sequences in the verified mAbs (colors) for RBD-reactive **(I)** IG\({}_{\kappa}\), and **(J)** IG\({}_{\lambda}\) sequences, and for NTD-reactive **(K)** IG\({}_{\kappa}\), and **(L)
IG\({}_{\lambda}\) sequences. Different colors indicate different studies from which mAbs were pooled. The reference to each study, the total number of mAbs in the study, and the number of mAbs with matching light chain CDR3 to the single cell data are reported in each panel.
TableS1.xlsx
## Table S3. Statistics of IgG BCR repertoire sequence data from individuals in the Great Repertoire Project.
Because of the massive amount of data provided by the Great Repertoire Project (Briney et al., 2019), only the first three biological replicates were used for each individual to be comparable to the data sampled in this study. Detailed statistics of the processed data for productive BCRs are shown for the number of unique sequences pooled from all replicates for each individual. For each individual, the number of lineages with more than two and ten unique sequences are shown in separate columns. Read statistics for unproductive receptors pooled from all individuals and replicates are shown separately.
## Table S4.xlsx Table S4. Statistics of plasma B-cell repertoire sequence data from COVID-19 patients.
The information about individuals in each cohort is shown. Detailed statistics of the processed data for productive BCRs are shown for read abundance, number of singletons, and number of unique sequences for all replicates and sampled time points in each individual. For each individual, the amounts of lineages with more than two and ten unique sequences across all time points are shown in separate columns which are split further by whether the lineages also contained bulk reads.
## Table S5.xlsx Table S5. Rare expanding BCRs shared among individuals.
The list of 38 rare progenitors of clonal lineages (i.e., with \(P_{\text{post}}\) below the dashed line in Fig. 6) that exhibit lineage expansion in at least one individual is shown. These receptors are indicated by green diamonds in The presence of these lineages in the plasma B-cell repertoire is indicated in the last column (orange triangles in Fig. 6). The 38 rare expanding lineage progenitors shown here are shared among four to 12 COVID-19 patients.
TableS7.xlsx **Table S7. Verified antibodies detected in BCR repertoires of COVID-19 patients.** HCDR3 and IGHV-gene of verified monoclonal antibodies responsive to SARS-CoV-2 (RBD, NTD, and S1) or SARS-CoV-1 epitopes, whose HCDR3 sequences match with a receptor (with up to Hamming distance of one amino acid) in the bulk+plasma B-cell repertoires of patients in this study are shown. Each row indicates a monoclonal antibody family, whose members have similar HCDR3, up to one amino acid difference. Mutations in the repertoire-matched receptors with respect to the original HCDR3 are in red. Single amino acid mutation differences in HCDR3s of monoclonal antibody families are shown in cyan. Patient ID for each repertoire-matched receptor is indicated in the last column. The complete list of verified antibodies is given in Table S8.
TableS8.xlsx **Table S8. Complete list of verified monoclonal antibodies.** |
154294_file02 | ### Model
Our model (equations 1-4) links two subpopulations (groups 1 and 2) by means of an interaction matrix in which \(\delta\) (\(0<\delta<1\)) specifies the degree of within-group mixing in a subpopulation of proportion \(p\) with the smaller total number of total contacts (equal to \(p_{C_{1}}\), where \(c_{1}\) is the contact rate of that group). Thus, all contacts are within the respective groups (i.e. mixing is fully assortative) when \(\delta=1\), and between-group mixing is maximised at \(\delta=0\). Random mixing occurs when \(\delta=p_{C_{1}}/(p_{C_{1}}+(1-p_{C_{2}}))\).
\[\dot{z_{i}}=\lambda_{i}(1-z_{j})-\gamma_{i}z_{i} \tag{1}\]
\[\dot{y_{i}}=\lambda_{i}(1-z_{j})-\sigma y_{i} \tag{2}\]
\[\lambda_{1}=\beta_{1}c_{1}[\delta y_{1}+(1-\delta y_{2})] \tag{3}\]
\[\lambda_{2}=\beta_{2}c_{2}[(1-\delta y_{C_{1}})y_{1}+(1-\frac{(1-\delta)p_{C_ {1}}}{(1-p_{C_{2}})}y_{2}] \tag{4}\]
The proportion infected (and infectious) is termed \(y\) and \(z\) (infected plus recovered) is the proportion already exposed; \(\lambda_{1}\) and \(\lambda_{2}\) are the per capita rates of infection of group 1 (of proportion \(p\)) and group 2 (of proportion \(1-p\)) and is determined by the product of the intrinsic transmission rate \(\beta_{i}\) and contact rate \(c_{i}\) of each group (with \(i=1,2\)) in addition to the distribution of the contacts between the different groups. We define the basic reproduction number (\(R_{0}\)) for each group as the fundamental transmission potential of the virus within a homogenous population consisting of members of that group; hence \(R_{0_{i}}=\beta_{i}c_{i}\sigma_{i}\) where \(\sigma_{i}\) is the group-specific recovery rate and \(\gamma_{i}\) is the group-specific rate of loss of immunity (with \(i=1,2\)).
If a fraction \(p\) of the population is resistant to infection (\(R_{0_{i}}=0\)), the 'herd' immunity threshold (HIT) is given as \(z^{*}=(1-p)(1-\frac{1}{R_{0}}[1/(1-\frac{(1-\delta)x_{1}p}{c_{21-\eta}})])\), for all values of \(\gamma\).
The model was solved numerically in R.
### Deriving incidence of deaths
Our overall approach rests on the assumption that only a fraction of the population is at risk of death. This proportion is itself only a fraction of the risk groups already well described in the literature, including the elderly and those carrying critical comorbidities (e.g. asthma). Cumulative death counts (\(\Lambda\)) are obtained by considering that mortality occurs with frequency \(\eta\) (i.e. a small group of proportion \(\eta\) exists in the population, whom will experience death upon infection), effectively defining the infection fatality ratio (IFR) as \(\eta\). We consider the delay between the time of infection and of death (\(\psi\)) as a combination of incubation period and time to death after onset of symptoms.
If \(\beta_{1}c_{1}=\beta_{2}c_{2}\), then:
\[\Lambda_{t}=\eta\,N\,z_{r-\psi}\]
We calibrate this model to cumulative reported SARS-CoV-2 associated deaths from the United Kingdom (UK) starting on 05/03/2020 (first death) and ending 15 days later (19/03/2020) to avoid potential effects of local control strategies implemented (for dates of interventions, see). In **Figure 1** we present a summary of model output after being fit to the number of deaths in the UK while setting key parameters to restricted priors well within reported ranges (**Table 1**). The model was able to approximate cumulative death counts (**Figure 1A**) for a wide range of possible IFRs.
Fitting summary for R0=2.5 and various possible IFRs. (A) Data points (black diamonds) and mean model output after fitting (full points) for cumulative mortality. Coloured areas are the model 95% CI. (B) Mean model output after fitting (full points) for the proportion of susceptibles. Model posteriors for (C) time (day) of introduction, (D) herd-immunity on 19/03/2020, (E) R0, (F) doubling time and (G) infectious period. Boxplot hinges present the 25th and 75th percentiles. MCMC ran for 1 million steps. Results presented are the posteriors (model output) using 1000 samples after a burnout of 50%.
As the prior for the IFR is reduced from mean 0.66% to 0.01%, fitting death counts adjusts the introduction date further back to late January, more than a month before the first reported death (**Figures 1D**). As a consequence, accumulated herd-immunity by 19/03/2020 presents an inverse relationship with the assumed IFR prior (**Figures 1C**), with the possibility of thousands of infections having occurred undetected, even before the first death is reported. Generally, the model respected the priors (**Table 1**) but also adjusted parameters (e.g. **Figure 1G**) required to replicate the necessary doubling times (**Figure 1F**). The latter were estimated to be the same across all considered IFRs (e.g. at 2.07 days, 95% Cl 1.78-2.40 for IFR=0.2%), well within a range obtained in a sensitivity analysis (**Extra Figure 1**).
A higher \(R_{0}\) (=4) leads to a commensurate increase in the level of herd immunity, but has a minimal effect on the date of introduction; while a longer infection period is required to fit the mortality data but this is still within reported ranges (**Extra Figure 2**). Including an exposed (but not yet infectious) class resulted in a longer doubling time with \(R_{0}=2.5\) (**Extra Figure 3**) but accords well with \(R_{0}=\)4 provided infectious periods are lower (**Extra Figure 4**).
Finally we considered the effects of an external contribution to the risk of infection growing exponentially with a doubling time of 5 days from the (estimated) time of first introduction until the date of lockdown (similar to, see Methods) to reflect influx of infected individuals into the UK. This had the general effect of delaying our estimates of the date of first introduction by \(\sim\)7 days (on average) (**Extra Figure 5**). Across such alternative exercises, model output still demonstrated the inverse relationship between the IFR and the proportion currently immune, with the possibility of accumulation of significant levels of herd immunity depending on the IFR considered.
An observation rate (\(\theta\), ratio between confirmed cases and total infections) is not explicitly modelled, but can be defined as \(\theta=IFR/CFR=(D/I)/(D/C)=C/I\); where D is the number of deaths, I the infections, C the confirmed infections (cases) and CFR the case fatality ratio. From the model's assumed IFR and four CFR independent estimations, we obtained possible distributions for \(\theta\) (with introduction of the virus is done as a single event (number of individuals 1/N) at estimated time of introduction T\({}_{\text{J}}\)).
With the true IFR in the UK being unknown, the IFR-dependent scenarios presented (**Figure 1**) remain theoretical projections of both the epidemic duration and accumulation of herd-immunity up to 19/03/2020. We thus looked at contextualizing such projections in light of four previous estimates of the case fatality ratio (CRF) in other epidemiological contexts (see **Methods**). From the relationship \(\theta=IFR/CFR\) we obtain the observation rate \(\theta\) for each of our modelled scenarios using the respective IFR prior and each of the literature CFRs - effectively considering that any of the reported CFRs could apply to the UK epidemic (**Figure 2**). The CFR considered were: 2.6% (95% Cl 0.89-6.7) for the Diamond Princess cruise ship (**Figure 2A**), 3.67% (95% Cl 3.56-3.80) for China (**Figure 2B**), 1.2% (95% Cl 0.3-2.7) for China (**Figure 2C**), and 1.4% (95% Cl 0.9-2.1) for Wuhan (China) (**Figure 2D**). Although there were significant differences when considering each of the four CRFs (**Figures 2ABCD**), there was a positive relationship between the IFR and the observation rate. The three smallest IFRs modelled (\(IFR\textlessdot=0.04\%\)) were found to be compatible with the reported CRFs when the observation rate \(\theta\) was generally close to, or lower than 5% (i.e. 1 or less in 20 infections being confirmed / reported). The \(IFR\textgreaterdot 0.66\%\) is similar to the one recently estimated by Verity and colleagues for China (0.66%, 95% Cl 0.39-1.33). This IFR has been the basis of model projections informing the UK government (see for details). In our model (without control) it resulted in mean herd-immunity of 7.05% by 19/03/2020, estimated introduction on 07/02/2020, and was compatible with the CFR of the same study for an observation rate of 18.6%.
The UK exercises presented in for \(R_{0}=2.5\) and Extra for \(R_{0}=4\) were repeated for Italy. This resulted in very similar conclusions (**Extra Figures 6-7**), albeit with higher population-level immunity for Italy at 15 days post first reported death.
Overall, these results underscore the dependence of the inferred epidemic curve on the real IFR, showing that accumulation of significant population-level immunity is possible, depending on the currently unknown IFR and observation rate. They also demonstrate how informative the proportion of the population already exposed to SARS-CoV-2 is to determining the IFR.
Model observation rates for R0=2.5 and various possible IFRs. Four CFR estimations from the literature (**panels A-D**, see main text for references) are used to derive model observation rates for each modelled IFR (color legend). Horizontal dotted line marks the 10% observation rate, and dashed line marks the 5% observation rate. Observation rate is the ratio of reported cases and total infections. See Methods for details. Boxplot hinges present the 25th and 75th percentiles. MCMC ran for 1 million steps. Results presented are the posteriors (model output) using 1000 samples after a burnout of 50%.
**- SIR model, UK, single introduction, \(R_{0}=4\). Figure legend the same as main text.**
We implemented SEIR by introducing an extra variable \(e\) to represent the exposed class and the following parameters:
\begin{tabular}{|c|c|c|} \hline incubation period (days) & \(1/\gamma\) & Gaussian distribution & 41,45,46 \\ & & 1/G1(M=1/5,SD=0.05) & \\ time (days) between symptom & \(\psi\) & Gaussian distribution & 45 \\ onset and death & & G1(M=12,SD=1.5) & \\ \hline \end{tabular}
**equation 1a:**\(de/dt=\beta y\) (\(1-z\)) - \(\gamma e\)
**equation 2a:**\(dy/dt=\gamma e-\sigma y\)
**equation 3a:**\(dz/dt=\beta y\) (\(1-z\))
**equation 4a:**\(\Lambda_{s}=\eta\,N\,z_{\tau\cdot\psi}\)
**equation 5a:**\(R_{0}=\beta(\sigma+\gamma)\)SEIR model, UK, single introduction, \(R_{0}=4\). Figure legend the same as main text.
## Extra - SIR model, UK, with influx of infected, \(R_{0}=4\).
Figure legend the same as main text.
We model an external contribution to the force of infection growing at an exponentially rate (with a doubling time of 5 days) starting at estimated time of introduction \(\mathsf{T}_{i}\) (similar to); stopping on 24/03/2020 for the UK and 11/03/2020 for IT (according to lockdown dates). This external forcing was modelled by changing the term \(\beta i\left(1-z\right)\) in **equations 1, 2** (SIR model) or **equations 1a, 3a** (SEIR model) to \(\beta(i+m)\left(1-z\right)\), with \(m=e^{n_{i}}/N\). Model variables are summarized in Table 1, except:
\begin{tabular}{|c|c|c|} \hline introduction external forcing & \(\tau\) & 0.1386 & 38 \\ growth rate & & & \\ \hline \end{tabular}
SIR model, IT, single introduction, \(R_{0}=2.5\). Figure legend the same as main text.
|
154302_file08 | \begin{table}
\begin{tabular}{l c c c c c c} \hline & & & & & & Endpoint of death \\ \hline & Full population & With the end-point event & Without the end-point event & Crude analysis & Multivariable analysis (df=20) \\ & (N=7,345) & (N=994) & (N=6,351) & & & & \\ \hline & N (\%) & N (\%) & N (\%) & HR (SE) / p-value & HR (SE) / p-value & \begin{tabular}{} \end{tabular} \\ & N (\%) & N (\%) & N (\%) & HR (SE) / p-value & HR (SE) / p-value &
\begin{tabular}{} \end{tabular} \\ \hline Age & & & & & 1.06 \\ _18 to 50 years_ & 2709 (36.9\%) & 42 (4.23\%) & 2667 (42.0\%) & Ref. & Ref. & Ref. & \\ _51 to 70 years_ & 2530 (34.4\%) & 240 (24.1\%) & 2290 (36.1\%) & 5.31 (0.17) /\textless{}0.001* & 2.82 (0.20) /\textless{}0.001 & & \\ _71 to 80 years_ & 942 (12.8\%) & 273 (27.5\%) & 669 (10.5\%) & 14.86 (0.17) /\textless{}0.001* & 7.53 (0.20) /\textless{}0.001 & & \\ _More than 80 years_ & 1164 (15.8\%) & 439 (44.2\%) & 725 (11.4\%) & 16.99 (0.16) /\textless{}0.001* & 11.35 (0.19) /\textless{}0.001 & & \\ Sex & & & & & & 1.06 \\ _Women_ & 3619 (49.3\%) & 359 (36.1\%) & 3260 (51.3\%) & Ref. & Ref. & \\ _Men_ & 3726 (50.7\%) & 635 (63.9\%) & 3091 (48.7\%) & 1.68 (0.07) /\textless{}0.001* & 1.32 (0.08) /\textless{}0.001 & & \\ Obesity * & & & & & & 1.06 \\ _Yes_ & 975 (13.3\%) & 216 (21.7\%) & 759 (12.0\%) & 1.51 (0.08) /\textless{}0.001* & 1.23 (0.09) /\textless{}0.021 & & \\ _No_ & 6370 (86.7\%) & 778 (78.3\%) & 5592 (88.0\%) & Ref. & Ref. & Ref. & \\ Smoking \({}^{\beta}\) & & & & & & 1.03 \\ _Yes_ & 623 (8.48\%) & 149 (15.0\%) & 474 (7.46\%) & 1.51 (0.09) /\textless{}0.001* & 0.93 (0.10) /\textless{}0.452 & & \\ _No_ & 6722 (91.5\%) & 845 (85.0\%) & 5877 (92.5\%) & Ref. & Ref. & \\ Number of medical conditions \({}^{\gamma}\) & & & & & & 1.12 \\ \(0\) & 4750 (64.7\%) & 319 (32.1\%) & 4431 (69.8\%) & Ref. & Ref. & \\ \(1\) & 534 (7.27\%) & 63 (6.34\%) & 471 (7.42\%) & 2.29 (0.14) /\textless{}0.001* & 1.78 (0.16) /\textless{}0.001 & & \\ _2 or more_ & 2061 (28.1\%) & 612 (61.6\%) & 1449 (22.8\%) & 4.71 (0.07) /\textless{}0.001* & 3.49 (0.09) /\textless{}0.001 & & \\ \hline \end{tabular}
\end{table}
Table 1: Associations of baseline clinical characteristics with the endpoint of death in the cohort of patients who had been admitted to the hospital for Covid-19 (N=7,345).
\begin{tabular}{l c c c c c} \multicolumn{6}{l}{Clinical severity of Covid-19} \\ at admission \({}^{\ast}\) & & & & & \\ _Yes_ & 1564 (21.3\%) & 421 (42.4\%) & 1143 (18.0\%) & 1.81 (0.08) / \textless{}0.001\({}^{\ast}\) & 1.69 (0.09) / \textless{}0.001 \\ _No_ & 1858 (25.3\%) & 265 (26.7\%) & 1593 (25.1\%) & Ref. & Ref. \\ _Missing_ & 3923 (53.4\%) & 308 (31.0\%) & 3615 (56.9\%) & 0.59 (0.08) / \textless{}0.001\({}^{\ast}\) & 1.66 (0.11) / \textless{}0.001 \\ Biological severity of Covid-19 at admission \({}^{\ast}\) & & & & & \\ _Yes_ & 2439 (33.2\%) & 592 (59.6\%) & 1847 (29.1\%) & 1.94 (0.08) / \textless{}0.001\({}^{\ast}\) & 1.51 (0.09) / \textless{}0.001 \\ _No_ & 1861 (25.3\%) & 257 (25.9\%) & 1604 (25.3\%) & Ref. & Ref. \\ _Missing_ & 3045 (41.5\%) & 145 (14.6\%) & 2900 (45.7\%) & 0.39 (0.1) / \textless{}0.001\({}^{\ast}\) & 0.75 (0.12) / 0.022 \\ \end{tabular}
\({}^{\ast}\) Defined as having a body-mass index higher than 30 kg/m\({}^{2}\)or an International Statistical Classification of Diseases and Related Health Problems (ICD-10) diagnosis code for obesity (E66.0, E66.1, E66.2, E66.8, E66.9).
\({}^{\ast}\)Smoking status was self-reported.
\({}^{\ast}\) Assessed using ICD-10 diagnosis codes for diabetes mellitus (E11), diseases of the circulatory system (I00-I99), diseases of the respiratory system (I00-I99), neoplasms (C00-D49), diseases of the blood and blood-forming organs and certain disorders involving the immune mechanism (D5-D8), delirium (F05, R41) and dementia (G30, G31, F01-F03).
\({}^{\ast}\) Any medication prescribed as part of a clinical trial or according to compassionate use (e.g., hydroxychloroquine, azithromycin, remdesivir, toticizumab, sarilumab or dexamethasone).
\({}^{\ast}\) Assessed using ICD-10 diagnosis codes for anxiety, dissociative, stress-related, somatoform and other nonpsychotic mental disorders (F40-F48) and insomnia (G47).
\({}^{\ast}\) Included lithium or antiepileptic medications with mood stabilizing properties.
\({}^{\ast}\) Defined as having at least one of the following criteria: respiratory rate \(>\) 24 breaths/min or \(<\) 12 breaths/min, resting peripheral capillary oxygen saturation in ambient air \(<\) 90%, temperature \(>\) 40\({}^{\circ}\)C, or systolic blood pressure \(<\) 100 mm Hg.
\({}^{\ast}\) Defined as having at least one of the following criteria: high neutrophil-to-lymphocyte ratio, low _lymphocyte_-to-_C-reactive protein_ (both variables were dichotomized at the median of the values observed in the full sample), and plasma _lactate_ levels _higher than 2 mmo/L_.
\({}^{\ast}\) p-value is significant (p\textless{}0.05).
Abbreviations: HR, hazard ratio; SE, standard error; GVIF, generalized variance inflation factor. |
154708_file02 | ## Inclusion
* Minimum age of 18 years and maximum of 50 years old.
* Cocaine use for at least 1 year, with current average use of at least 3 times a week, with periods of continuous abstinence of less than one month during the last year.
* Reading level of at least 6th grade of primary school.
* Ability to give valid informed consent.
* Right-handed (to avoid laterality bias).
* Body mass index \(\leqq 30\).
## Exclusion
* First-degree personal or family history of any clinically defined neurological disorder.
* Any electronic or metal implants or device (i.e., aneurysm clips, shunts, stimulators, cochlear implants, or electrodes, etc.).
* Splinters of metal or metal projectiles to the head or body.
* Current use of any investigational drug or of any medicine with anti- or pro-convulsive action such as tricyclic antidepressants or neuroleptics, unless prescribed for craving symptoms.
* History of schizophrenia, bipolar disorder, mania, or hypomania.
* History of any heart condition currently under medical care (i.e., myocardial infarction, angina pectoris, congestive heart failure, etc.)
* Women with reproductive potential not using an acceptable form of contraception, as well as pregnant or lactating women.
* Any history of seizures.
* Current dependence (by DSM-5 criteria) on substances other than cocaine and / or nicotine (cocaine use disorder).
* Claustrophobia.
* History of HIV infection or HIV antibody test positive (due to potential neuroinfection).
## Elimination
* Expressed desire to stop participating.
* Those who for any reason stopped attending rTMS sessions, for 2 or more days for those in the acute phase, or 2 weeks for those in the maintenance phase.
* Those who presented abnormal radiological findings warranting clinical attention outside the study to ensure the health of the participant.
* The appearance of psychotic symptoms related to addictive disorder.
* Presence of adverse effects related to the application of rTMS such as seizures and abnormal elevation of mood.
## rTMS = repeated transcranial magnetic stimulation.
## Table S2.
Standard treatments received by each participant during rTMS therapy.
## Table S2.
Standard treatments received by each participant during rTMS therapy.
### Study attrition
Of the 54 recruited patients, 30 were randomly allocated to active treatment and 24 to sham rTMS (Figure S1). Five patients assigned to active rTMS and four assigned to sham discontinued the study, leaving 25 patients in the Active group and 20 in the Sham group who completed the acute phase. Following the double-blind phase, 14 patients in the Sham group opted for compassionate use and received 2 weeks of acute phase rTMS therapy. In the maintenance phase: 1) 20 patients (15 initially allocated to Active and 5 to Sham) finished 3 months of twice-weekly rTMS sessions (T2); 2) 15 patients (initially 10 Active and 5 Sham) finished 6 months of rTMS sessions (T3); and 3) 7 patients (initially 3 Active and 4 Sham) finished 12 months of twice-weekly rTMS sessions (T4). None of the patients who discontinued the study at any point reported adverse effects from rTMS as their reason. Due to substantial attrition at T1 (2 weeks), when the study was at ~30% completion we changed the maintenance phase to last 3 months instead of 12 months for new participants after approval by the ethics committee. Data collected up to the 6-months visit were analyzed due to the small sample size at 12 months (n = 7).
## Figure S1.
CONSORT flow diagram.
## CONSORT 2010 Flow Diagram
## Figure S1.
CONSORT flow diagram.
### Study timeline
Patients were phone screened by RAL and AD (Figure S1). At Visit 1, screened patients arrived for a clinical screening interview by RAL and AD to confirm they met criteria. At Visit 2, enrolled patients underwent a full clinical assessment (Time 0 or T0). Initial MRI scanning occurred at Visit 3 (Baseline or MRI-T0). The clinical interview preceded MRI acquisition and always occurred within 3 days. Following MRI acquisition, we initiated the double-blind rTMS/sham _acute phase_ (see below). Patients underwent regularly scheduled sessions (Active or Sham rTMS) for 10 days over 2 weeks. At the conclusion of 2 weeks (Visit 4; T1), they underwent clinical assessment and repeated MRI scanning, marking the end of the acute phase and the start of the open-label _maintenance phase_. The blind (active vs. sham) was decoded for each participant at the end of their acute phase. Patients assigned to Active rTMS entered the maintenance phase directly after T1. Patients assigned to Sham rTMS were given the choice to leave the study or continue with active open-label rTMS for compassionate use. Patients assigned to the Sham group who agreed to continue, received 2-weeks (10 days) acute treatment before continuing to the maintenance phase. The maintenance phase was initially designed to include 2 weekly rTMS sessions and clinical assessments and MRI scans at 3 months, 6 months and 12 months. However, the maintenance phase was subsequently changed to 3 months for new enrollments (see study attrition).
### Clinical Assessments details
The following instruments were used in the overall clinical trial:
1. **MINI-PLUS**: Is a structured diagnostic interview, of short duration in which the main psychiatric disorders of Axis I of DSM-V and ICD-10 are explored for detection and / or diagnostic orientation, it is divided into modules, identified by letters, each corresponding to a diagnostic category. At the beginning of each module (except in the psychotic disorders module), the interview has one or more "filter" questions corresponding to the main diagnostic criteria for the disorder. At the end of each module, one or more diagnostic boxes are presented that allow the interviewer to indicate whether or not the diagnostic criteria for the disorder were met. This instrument will be used for the initial evaluation of the patient and verification of the inclusion and exclusion criteria.
2. **SCID-II**: Evaluate personality disorders in a categorical way according to DSM-IV criteria. Each of the criteria is valued from the following score: 1: absent, 2: Present or true, itconsists of 119 questions with a dichotomous answer that reduces the test administration time, The test was applied only in the baseline measurement (T0), since it is a constant clinical feature.
3. **SCL90 R**: The SCL-90-R is a self-applied symptom questionnaire consisting of 90 items. Each item is answered on a 5-point Likert-type scale, from "0" (absence of the symptom) to "4" (total presence of the same). By correcting the test we obtain 9 symptomatic scales and 3 indexes of psychological distress. The symptomatic scales are as follows: Somatization, Obsession-compulsion, Interpersonal sensitivity, Depression, Anxiety, Hostility, Phobic anxiety, Paranoid ideation and Psychoticism. The discomfort indices are: a) the global severity index (GSI), b) the positive symptomatic discomfort index (PSDI) and c) the total of positive symptoms (PST). The test was applied in each clinical measurement (T0 to T4) to assess changes in symptoms in each phase.
4. **Addiction Severity Index (ASI)**: The ASI is a semi-structured interview designed to address seven potential problem areas in substance-abusing patients: medical status, employment and support, drug use, alcohol use, legal status, family/social status, and psychiatric status. In 1 hour, a skilled interviewer can gather information on recent (past 30 days) and lifetime problems in all of the problem areas. The ASI provides an overview of problems related to substance, rather than focusing on any single area. The test was applied in each clinical measurement (T0 to T4) to assess changes in symptoms in each phase.
5. **BIS11**: The 11th version of the Barratt Impulsivity Scale is one of the most widely used instruments for assessing impulsivity. Its application is self-administered and it consists of 30 questions, grouped into three subscales: Cognitive impulsivity, Motor impulsiveness, Unplanned impulsiveness. Each of the questions has 4 possible answers (rarely or never, occasionally, often and always or almost always. The total score is the sum of all the items and the total of the subscales are the sum of the items corresponding to each of them.
6. **Hamilton Depression Rating Scale (HDRS)**: The Hamilton Rating Scale for Depression was used to provide a measure of the severity of depression. The version we used is the one of 17 items, recommended by the United States National Institute of Mental Health. Its content focuses on the basic aspects and behavior of depression, with vegetative, cognitive and anxiety symptoms having the greatest weight in the total calculation of the scale. The cutoff points to define severity are: no depression; mild depression; moderate depression; and severe depression (\(\geq\)24). This scale was applied in the basal measurement (T0) and all subsequent measurements. The test was applied in each clinical measurement (T0 to T4) to assess changes in symptoms in each phase.
7. **Hamilton Anxiety Rating Scale (HARS)**: This scale assesses the severity of anxiety globally and is useful for monitoring response to treatment. It is made up of 14 items, with 13 references to anxious signs and symptoms and the last one that evaluates the patient's behavior during the interview. The interviewer scores from 0 to 4 points each item, assessing both its intensity and frequency. The total score is the sum of those of each of the articles. The range is from 0 to 56 points. The optimal HAM-A score ranges were: no/minimal anxiety \(\leq\) 7; mild anxiety = 8-14; moderate = 15-23; severe \(\geq\) 24. The test was applied in each clinical measurement (T0 to T4) to assess changes in symptoms in each phase.
8. **Pittsburgh Sleep Quality Index (PSQI)**: This instrument has been created to measure the quality of sleep in patients with psychiatric disorders. It is made up of 24 items, although only 19 are taken into account for its correction. In addition, it is divided into 7 dimensions: Subjective sleep quality, Sleep latency. Duration of sleep, Usual sleep efficiency, Sleep disturbances, Use of medication, Daytime dysfunction. It is answered with a Likert-type scale that goes from 0 to 4. For its correction, a sleep profile is obtained in each of the dimensions ranging from 0 to 3 and a total score that can range from 0 to 21. The test was applied in each clinical measurement (T0 to T4) to assess changes in symptoms in each phase.
9. **Treatment-As-Usual follow-up**: Consists of a record of the treatment that each subject had indicated at the beginning of the study, which was prescribed by the treating physician in the addiction clinic of the National Institute of Psychiatry, according to the protocols that they normally follow. The record indicated whether the subject received psychotherapy and/or pharmacological treatment, together with the type of psychotherapy and the name of the drug received, as well as changes to these treatments in each of the following measurements. This record was made in a format created for the present study which was applied both in the baseline assessment and in each of the subsequent assessments.
10. **Timeline Followback Method Assessment modified (mTLFB)**: This is a record of the pattern of cocaine/crack use of each subject, made on a calendar-based format, where the consumption of the last two years up to the present was evaluated, indicating the number of days of use per month and the amount in grams consumed each full month (30 days). This format was applied in the baseline measurement (T0) where previous consumption was recorded and in each subsequent measurement to assess the longitudinal pattern of substance use every month before and during the trial [].
11. **Cocaine Craving Questionnaire (CCQ)**: This instrument evaluates the intensity of cocaine craving. The version used in this study has a format that evaluates craving at the present time, and a format that evaluates the general state of craving during the last week. Each form consists of 45 items, each item is made up of a 7-point Likert scale in which the subject must indicate their degree of agreement or disagreement, with some items scored inversely. For its interpretation, the total of the items is added. The test was applied at each clinical measurement (T0 to T4) to assess changes in craving in each phase [].
12. **Cocaine Craving visual analogue scale (VAS)**: This is an instrument for the subjective evaluation of the subject's craving at the present moment. The visual scale consists of a continuous 100 mm line, in which the left endpoint refers to "no craving" and the right endpoint "the most intense craving" and the subject must mark with a cross the intensity of their craving at that moment between one of the two extremes. This scale was applied in each clinical measurement (T0 to T4) to assess changes in craving in each phase [].
13. **Alcohol breath test**: An alcohol monitoring test was performed to identify the possible presence of substances in the subject before performing the MRI study. This was done in the initial evaluation (T0) and in each subsequent measurement (T1 to T4), with a breath alcohol analyzer, Lifeloc model FC10 (Wheat Ridge, CO, USA), which has a detection accuracy of \(\pm\).005 BAC.
14. **Urine drug test**: Performed to identify the possible presence of substances of abuse in subjects prior to performing the MRI study. This test was performed with a Kabla (Monterrey, NL, Mexico) reagent strip device, model Instant view-Drug screen, using the lateral flow chromatographic immunoassay technique. The substances detected and their cut-off points are as follows: Amphetamines (1000 ng/mL), Benzodiazepines (300 ng/mL), Cocaine (300 ng/mL), Methamphetamine (1000 ng/mL), Morphine/Opiates (2000 ng/mL), Marijuana/Hashish (50 ng/mL). This test was applied in the baseline measurement and each of the subsequent ones. Results in Tables S6 & S7.
15. **Reincidence/Relapse follow-up**: A record of the cocaine abuse patterns of patients was carried out, to identify if they presented reincidence or relapses. This was applied in each of the subsequent measurements (T1 to T4). "Reincidence" was defined as the presence of at least one episode of consumption but without returning to previous consumption, and "relapse" was defined when consumption returned to the previous pattern.
16. **WHODAS**: Instrument that assesses the psychological and social functioning of people affected by a mental disorder. It provides information on four areas: Personal Care, Occupation, Family/Housing and Social Functioning. The clinician scores to what extent there is a degree of deterioration in the interviewed person through a visual analog scale, which goes from 0 (absence of deterioration) to 5 (great deterioration). It is a descriptive scale that provides a total score and scores in each of the 4 dimensions. There are no cut points; the higher the score, the greater the disability. It was obtained in the baseline evaluation (T0) and in each of the subsequent ones (T1 to T4).
17. **Edinburgh Handedness**: The Edinburgh Manual Laterality Inventory aims to assess manual dominance. This instrument evaluates the degree to which the subject uses the left or right hand for 4 predetermined actions and provides a numerical result, which is used to form three categories: predominant use of the left hand, similar use of both hands, and predominant use of the right hand. This instrument was applied in the baseline assessment (T0) only.
## Clinical outcome measures
Primary Outcome Measures:
1. Change in Cocaine Craving (CCQ) [ Time Frame: Baseline, 2 weeks, 3 months ]: Measured using a craving questionnaire for cocaine validated in Mexican population (Cocaine Craving Questionnaire or CCQ).
2. Change in Cocaine Craving (VAS) [ Time Frame: Baseline, 2 weeks, 3 months ]: Measured using a 100 mm visual analog scale (VAS).
3. Change in Cocaine Urine Test [ Time Frame: Baseline, 2 weeks, 3 months ]: Frequency of cocaine use measured using reagent strips from Instant View drug screening (> 300 ng/mL). Results are Positive or Negative.
Secondary outcome measures:
1. Changes in Psychopathological Symptoms [ Time Frame: Baseline, 2 weeks, 3 months ]: Measured by the 90 Symptoms Questionnaire (SCL-90).
2. Changes in Depression [ Time Frame: Baseline, 2 weeks, 3 months ]: Measured by Hamilton Depression Rating Scale (HDRS) (21 items).
3. Changes in Anxiety [ Time Frame: Baseline, 2 weeks, 3 months ]: Measured by Hamilton Anxiety Rating Scale (HARS).
Changes in Drug Consumption and Related Problems [ Time Frame: Baseline, 2 weeks, 3 months ]: Measured by the Addiction Severity Index (ASI-lite).
5. Changes in Sleep Quality: PSQI [ Time Frame: Baseline, 2 weeks, 3 months ]: Measured by the Pittsburgh Sleep Quality Index (PSQI).
6. Changes in Impulsivity [ Time Frame: Baseline, 2 weeks, 3 months ]: Measured by the Barratt Impulsivity Scale-11 (BIS-11).
7. Lapse rate [ Time Frame: Baseline, 2 weeks, 3 months ]: Lapse is defined as at least one consumption event not in the same pattern as the baseline consumption. The report of self-consumption of cocaine and urine drug tests, with special attention to the presence of traces of cocaine.
8. Relapse rate [ Time Frame: Baseline, 2 weeks, 3 months ]: Relapse is defined as consumption events in the same pattern as the baseline consumption. The report of self-consumption of cocaine and urine drug tests, with special attention to the presence of traces of cocaine.
* Tertiary outcome measure:
1.
### Clinical statistical analysis
All baseline tables were constructed using R toolbox moonBook ([https://github.com/cardiomoon/moonBook](https://github.com/cardiomoon/moonBook)), which performs Shapiro-Wilks test for normality, then provides a statistical test for 2 independent groups as follows: 1) continuous normal = unpaired t-test, 2) continuous not normal = Wilcoxon test, 3) nominal = chi-square or Fisher's test, with 2-tailed alpha 0.05. Longitudinal tables were also constructed with moonBook, however statistical tests were independent of the toolbox. Group and time interaction of primary and secondary outcome continuous variables in the acute phase were analyzed with a 2 x 2 Mixed Model in R and RStudio (lme4), with craving (CCQ-Now and VAS) or impulsivity as dependent variables, age and sex as covariates (fixed effects) and patients as a random effect. For the mixed models we calculated effect sizes using Cohen's d and the EMAtools package, with correction for samples smaller than 50 subjects. Urine tests for cocaine (nominal) were analyzed using the Cochran-Mantel-Haenszel test and classifying individual trajectories into four patterns: 1) Maintained negative results, 2) maintained positive results, 3) changedfrom negative to positive, and 4) changed from positive to negative. We expected the Active group would have the highest percentages of the first and fourth patterns. Finally, correlation was followed by a multiple regression analysis using all demographic measures, years of cocaine use, craving (CCQ-Now and VAS) and impulsivity, with the delta correlation (functional connectivity) being the dependent variable. We used a stepwise regression with both forward and backward selection for searching the minimum Akaike Information Criterion (AIC) which provides a means for model selection, providing the loss of information for each model tested after removing the multicollinearity.
For the open maintenance phase, we pooled subjects from both groups regardless of initial assignment (Sham and Active). Primary and secondary outcome measures were analyzed with a Mixed Model using the _lme4_ package and age and sex as covariates, with unequal sample sizes between time points, and the _multcomp_ package for post hoc contrasts. Urine test for cocaine (nominal) was analyzed using Cochran's Q test, so it could only be computed for the 15 subjects with complete urine tests up to 6 months. All longitudinal tests were corrected for multiple comparisons when a similar test was repeated, using false discovery rate (FDR) at q < 0.05, with the number of tests grouped into either primary n = 2 or secondary outcomes n = 4. For _post hoc_ contrasts in mixed models we used the Tukey correction. For the mTLFB we used the Friedman test on the sample that completed 6 months (n = 15), and _post hoc_ contrasts using the Wilcox test corrected with FDR for the variables _frequency of use per month_ and _grams per month_. Effect size was calculated with Kendall's W.
### Transcranial magnetic stimulation
We performed a double-blind randomized controlled trial (RCT) with parallel groups (Sham/Real) with a final allocation ratio of 1:1.25 for 2 weeks of acute treatment named the _acute phase_, following with an open-label trial at timepoints 3, 6 and up to 12 months of chronic treatment maintenance, named the _maintenance phase_. The allocation was 1:1, however it would have been simple for TMS technicians to guess the group allocation for the last patients as they knew the final sample size and group membership of previous patients. Therefore, we decided to include a bigger sample for the randomization to avoid guessing of the group. For the acute phase, we used a MagPro R30+Option magnetic stimulator and an eight-shaped B65-A/P coil (Magventure, Denmark), and for the maintenance phase, we used a MagPro R30 stimulator and an eight-shaped MCF-B70 (Magventure, Denmark). The reason for using 2 different TMS models was practical, to be able to stimulate more patients. However, there are no differencesin the induced field between models, only the cooling system and the sham possibility from the MagPro R30+Option. Also, the eight-shaped coil B65-A/P coil is angled while the eight-shaped MCF-B70 is flat. We used a 5-Hz excitatory frequency as it is standard in our clinical setting due to the low presence of secondary effects and similar clinical improvement to 10-Hz in major depression, Alzheimer's disease, among others []. Safety outcomes are reported in Table S3. The motor threshold was determined in each patient as described by Rossini et al. [], localizing M1 from vertex 5 cm along and 2 cm anteriorly the interaural line. The coil was placed at 45\({}^{\circ}\) with respect to the interhemispheric fissure (anterior-medial induced current) and single pulses were applied separated by 5 seconds. The intensity that caused at least 5 responses of the abductor _pollicis brevis_ (APB) muscle from 10 pulses was considered the MT []. MT was determined before the first session and on the 6th day of treatment. For the maintenance phase, MT was determined in each session (once per week). We localized left DLPFC using the 5 cm method in the first 16 participants and the Beam F3 method (Beam, Borckardt, Reeves, & George, 2009) in the rest of the subjects to optimize DLPFC localization (only n = 11 were available at the time for this analysis). Sham electrodes were placed to simulate muscle contraction in the Sham group. The acute phase comprised 10 weekdays of 5,000 pulses per day (two sessions of 50 trains at 5 Hz, 50 pulses/train, 10 s inter-train interval and 15 min inter-session interval). The maintenance phase comprised 3 and 6 months of 5,000 pulses per day, 2 sessions per week. The motor threshold was maintained at 100% in all patients. Because a Brain Navigator was not available, we used a vitamin E capsule fiducial during MRI acquisition to identify the actual stimulation target where rTMS was delivered in n = 27. EMS oversaw all rTMS sessions and determined the capsule's location before the first MRI session using either the 5.5 cm anatomic criterion or the Beam F3 method (Table S4 & Fig. S2). We changed to the superior Beam F3 method after the first 16 participants to improve IDLPFC localization []. EMS marked IDLPFC on the scalp with a marker, then maintained the capsule's position using removable tape and a swimmer's cap. Subsequently, EMS checked the capsule location before scanning. That same marked location on the scalp based on the coordinates at which the fucidal (capsule) was placed was used for rTMS sessions.
## Table S3.
Safety outcomes for the acute phase.
\begin{tabular}{l c c} & SHAM & ACTIVE & p \\ & (N=240) & (N=300) \\ Headache & & 0.026 \\ -0 & 216 (97.7\%) & 244 (90.7\%) \\ -1 & 1 ( 0.5\%) & 5 ( 1.9\%) \\ -2 & 0 ( 0.0\%) & 10 ( 3.7\%) \\ -3 & 3 ( 1.4\%) & 7 ( 2.6\%) \\ -4 & 1 ( 0.5\%) & 2 ( 0.7\%) \\ -5 & 0 ( 0.0\%) & 1 ( 0.4\%) \\ Neck pain & & 0.058 \\ -0 & 188 (85.1\%) & 242 (90.0\%) \\ -1 & 1 ( 0.5\%) & 5 ( 1.9\%) \\ -2 & 18 ( 8.1\%) & 17 ( 6.3\%) \\ -3 & 11 ( 5.0\%) & 4 ( 1.5\%) \\ -4 & 3 ( 1.4\%) & 1 ( 0.4\%) \\ -5 & 0 (0.0\%) & 0 (0.0\%) \\ Scalp pain & & 0.17 \\ -0 & 219 (99.1\%) & 261 (97.0\%) \\ -1 & 2 ( 0.9\%) & 2 ( 0.7\%) \\ -2 & 0 ( 0.0\%) & 5 ( 1.9\%) \\ -3 & 0 ( 0.0\%) & 1 ( 0.4\%) \\ -4 & 0 (0.0\%) & 0 (0.0\%) \\ -5 & 0 (0.0\%) & 0 (0.0\%) \\ \end{tabular}
Cognitive decline 0.567
-0 221 (100.0%) 267 (99.3%)
-1 0 (0.0%) 0 (0.0%)
-2 0 ( 0.0%) 2 ( 0.7%)
-3 0 (0.0%) 0 (0.0%)
-4 0 (0.0%) 0 (0.0%)
-5 0 (0.0%) 0 (0.0%)
Concentration decline 0.346
-0 221 (100.0%) 265 (98.5%)
-1 0 ( 0.0%) 1 ( 0.4%)
-2 0 ( 0.0%) 1 ( 0.4%)
-3 0 ( 0.0%) 2 ( 0.7%)
-4 0 (0.0%) 0 (0.0%)
-5 0 (0.0%) 0 (0.0%)
Hearing decline 0.479
-0 221 (100.0%) 266 (98.9%)
-1 0 ( 0.0%) 1 ( 0.4%)
-2 0 ( 0.0%) 1 ( 0.4%)
-3 0 (0.0%) 0 (0.0%)
-4 0 ( 0.0%) 1 ( 0.4%)
-5 0 (0.0%) 0 (0.0%)
Irritation 0.053
-0 218 (98.6%) 259 (96.3%)
-1 0 ( 0.0%) 7 ( 2.6%)
## Table S4.
Type of IDLPFC localization per patient.
### Fiducial to standard space
First, we registered the location of the stimulation region on the scalp, by manually locating the coordinates of the fiducial in the participants' space using fslview. To avoid any distortion in the algorithm, we co-registered a different high-definition structural image to the space of the fiducial image and made a deskulled version of it; this was done with ANTs. Using both the full-head and brain co-registered images, with MATLAB 2019a we located the point most proximal to the cortex in the projection with a 90\({}^{\circ}\) angle to the tangent of the head surface in a coronal slice. A single point-seed mask with these cortex coordinates was created for each participant and registered to the standard MNI152 template with ANTs. Finally, we registered the coordinates of all of these normalized stimulation locations with their coordinates in the standard MNI space and with this information calculated the average central stimulation region in the brain cortex.
### TMS regions of interest
The IDLPFC ROIs were specified as per. Briefly, cones with 12 mm radius were centered at each individual stimulation coordinate in MNI (Figure 2, main manuscript). The cones were built with decreasing intensity from the center to the periphery and were based on an approximation of the electric field induced by a standard figure-eight coil. A gray matter mask was used to mask the cones and each cone was normalized to an average value of 1. Normative connectivity was determined using this cone as a weighted mask and n = 1000 subjects from the Human Connectome Project.
### Magnetic resonance imaging
Neuroimaging data were acquired using a Philips Ingenia 3T scanner (Philips, USA) with a 32-channel Philips head coil. For each MRI session we acquired the following sequences in order: 1) Resting state functional magnetic resonance imaging (rsfMRI), gradient echo planar imaging, TR/TE = 2000/30 ms, FOV = 240 mm, Matrix = 70 x 70, ReconMatrix = 80, slice thickness = 3.33 mm, FA = 75 degrees, voxel = 3 x 3 x 3.33 mm, axial, slices = 37, direction = AP, 2) Structural T1w 3D FFE Sagittal, TR/TE = 7/3.5 ms, FA = 8 degrees, FOV = 240 mm, matrix = 240 x 240, voxel = 1 x 1 x 1 mm, gap = 0. To correct for field inhomogeneities we acquired a rsfMRI sequence with 5 volumes in the opposite phase-encoding direction (PA). We also acquired a high angular diffusion-weighted imaging (HARDI) sequence not reported here.
### MRI preprocessing
Image processing was performed with FMRIPREP version 1.5.5 [1, 2, RRID:SCR_016216], a Nipype [3, 4, RRID:SCR_002502] based tool. Each T1w (T1-weighted) volume was corrected for INU (intensity non-uniformity) using N4BiasFieldCorrection v2.1.0 and skull-stripped using antsBrainExtraction.sh v2.1.0 (using the OASIS template). Spatial normalization to the ICBM 152 Nonlinear Asymmetrical template version 2009c [7, RRID:SCR_008796] was performed through nonlinear registration with the antsRegistration tool of ANTs v2.1.0 [8, RRID:SCR_004757], using brain-extracted versions of both T1w volume and template. Brain tissue segmentation of cerebrospinal fluid (CSF), white-matter (WM) and gray-matter (GM) was performed on the brain-extracted T1w using fast (FSL v5.0.9, RRID:SCR_002823).
Functional data was slice-time corrected using 3dTshift from AFNI v16.2.07 [11, RRID:SCR_005927] and motion corrected using mcflirt (FSL v5.0.9). Distortion correction was performed using an implementation of the TOPUP technique using 3dQwarp (AFNI v16.2.07). This was followed by co-registration to the corresponding T1w using boundary-based registration with six degrees of freedom, using flirt (FSL). Motion correcting transformations, field distortion correcting warp, BOLD-to-T1w transformation and T1w-to-template (MNI) warp were concatenated and applied in a single step using antsApplyTransforms (ANTs v2.1.0) using Lanczos interpolation.
Physiological noise regressors were extracted applying CompCor. Principal components were estimated for the two CompCor variants: temporal (tCompCor) and anatomical (aCompCor). A mask to exclude signals with cortical origin was obtained by eroding the brain mask, ensuring it only contained subcortical structures. Six tCompCor components were then calculated including only the top 5% variable voxels within that subcortical mask. For aCompCor, six components were calculated within the intersection of the subcortical mask and the union of CSF and WM masks calculated in T1w space, after their projection to the native space of each functional run. Framewise displacement was calculated for each functional run using the implementation of Nipype. Many internal operations of FMRIPREP use Nilearn [22, RRID:SCR_001362], principally within the BOLD-processing workflow. For more details of the pipeline see _[https://fmriprep.readthedocs.io/en/stable/workflows.html_](https://fmriprep.readthedocs.io/en/stable/workflows.html_).
Post-processing was done using XCP Engine, which is a free and open-source software package with a modular design that incorporates the functions of several neuroimaging analysistools. It has an optimized confound regression procedure to reduce the influence of subject motion. The code for the whole pipeline is freely and publicly available in the repo ([https://github.com/PennBBL/xcpEngine](https://github.com/PennBBL/xcpEngine)). The output data from FMRIPREP (i.e. both the minimally preprocessed images and the functional nuisance regressors matrices) were fed into XCP and preprocessed following the regression strategy of 36 parameters and scrubbing, which included: i) correction for distortions induced by inhomogeneities in the magnetic field, ii) removal of the 4 initial volumes, iii) realignment of all volumes to a selected reference volume, iv) demeaning and removal of linear and quadratic trends, v) co-registration of functional data to the high-resolution structural image, vi) removal of nine confounding signals (six motion parameters; global, white matter and cerebrospinal fluid) as well as their derivatives, quadratic terms, and squares of derivatives, vii) motion scrubbing, as in, the removal of every volume that surpassed the motion threshold of 0.5 mm of framewise displacement, as well as both contiguous volumes; and, viii) temporal filtering with a first-order Butterworth filter using a bandpass between 0.01 and 0.08 Hz.
### Functional connectivity analysis
Because we were interested in the effects of rTMS on IDLPFC-vmPFC FC, we first determined the regions of interest (ROIs) of the IDLPFC circuit by obtaining its normative FC using the methods described in Weigand et al.. Briefly, we obtained the MNI coordinates for each subject's stimulated region using its individual fiducial location (n = 27) (Figure 2, main manuscript). We then calculated the average MNI coordinates of IDLPFC stimulation (x = -31,y = 46, z = 36) which was fed to an in-house pipeline by members of the M. D. Fox laboratory to obtain the normative IDLPFC FC map. The pipeline creates a "cone" shaped mask that emulates the induced electric field's decreasing intensity from center to periphery on the cortex when using the standard figure-eight coil. From that weighted mask, correlation maps were calculated in Human Connectome Project fMRI data (n = 1000). The final normative IDLPFC FC map was then clustered using FSL with a Pearson's correlation threshold of r = +- 0.2 and a minimum cluster size of 10 voxels. The cluster corresponding to vmPFC (Figure S3) was used to determine its connectivity with the stimulated IDPFC and potential changes in response to rTMS. Other clusters found included bilateral DLPFC, frontal pole, posterior cingulate cortex (PCC), precuneus, anterior cingulate cortex (ACC), bilateral insula, left striatum, bilateral hippocampus, middle temporal gyrus, supramarginal gyrus and bilateral cerebellum, which were used for exploratory analyses (Table S5).
To calculate IDLPFC FC in each subject and session, we used the average IDLPFC cone mask in FSL on the individual 4D residual volumes, which has yielded similar results to using individualized masks. Because our primary interest was IDLPFC - vmPFC FC, the _acute phase_ was analyzed with a 2 x 2 Mixed Model (group by session interaction) using FSL randomise at alpha 0.05 with TFCE correction, with the vmPFC cluster as our ROI. Afterwards, we explored the remaining cluster ROIs with the same model. Depending on the results of the clinical and MRI analyses, we correlated the significant FC clusters with significant clinical variables using their delta scores (T1-T0) and Pearson's correlation at alpha 0.05. The maintenance phase was analyzed using the mean FC from the resulting cluster or clusters in the acute phase analysis using a Mixed Model in R (lme4) to account for different sample sizes up to 6 months. Post-hoc, we calculated the individual FC maps of the significant vmPFC cluster (as seed) from the acute phase analysis, and performed a whole-brain 2 x 2 mixed model analysis (group by session) of the acute phase and the maintenance phase.
\begin{table}
\begin{tabular}{l l c c c c} Hemisphere & Brain region & **Voxels Peak r-value** & **Peak MNI coordinates** \\ & & & & \(x\) & \(y\) & \(z\) \\
## Positive
& & & & & \\ Left & Dorsolateral prefrontal cortex & 3179 & 0.913 & -30 & 44 & 38 \\ Left & Anterior cingulate cortex & 3170 & 0.465 & -4 & 18 & 36 \\ Left & Anterior insula & 1317 & 0.442 & -34 & 14 & 8 \\ Left & Supramarginal gyrus & 1036 & 0.369 & -62 & -38 & 34 \\ Left & Superior frontal gyrus & 457 & 0.395 & -16 & 6 & 70 \\ Left & Cerebellum VI & 169 & 0.275 & -34 & -50 & -32 \\ Left & Middle frontal gyrus & 67 & 0.286 & -26 & 44 & -12 \\ Left & Precuneus & 32 & 0.217 & -10 & -74 & 42 \\ Left & Cerebellum VIIb & 20 & 0.215 & -40 & -42 & -48 \\ Left & Putamen & 17 & 0.216 & -20 & 14 & -2 \\ Right & Dorsolateral prefrontal cortex & 1858 & 0.547 & 32 & 48 & 32 \\ Right & Midcingulate cortex & 1202 & 0.353 & 12 & -32 & 42 \\ Right & Anterior insula & 1105 & 0.394 & 36 & 16 & 8 \\ Right & Supramarginal gyrus & 805 & 0.352 & 62 & -34 & 36 \\ Right & Cerebellum VI & 194 & 0.279 & 36 & -48 & -32 \\ Right & Cerebellum VIIIa & 80 & 0.235 & 38 & -44 & -52 \\
## Negative
& & & & & & \\ Left & Superior lateral occipital cortex/Angular gyrus & 378 & -0.238 & -50 & -66 & 30 \\ Left & Anterior middle temporal gyrus & 235 & -0.245 & -60 & -8 & -14 \\ Left & Hippocampus & 36 & -0.227 & -24 & -16 & -18 \\ Right & Ventromedial prefrontal cortex & 925 & -0.307 & 2 & 52 & -12 \\ Right & Posterior cingulate cortex/Precuneous & 902 & -0.273 & 2 & -56 & 26 \\ Right & Anterior middle temporal gyrus & 322 & -0.264 & 62 & -4 & -20 \\ Right & Superior lateral occipital cortex/Angular gyrus & 300 & -0.254 & 52 & -60 & 32 \\ \end{tabular}
\end{table}
Table S4: Normative Left DLPFC average stimulation cone seed map.
## Figure S3.
## Supplementary Results
## Table S6.
Urine test results of the acute phase.
\begin{tabular}{l c c c c} & **T0** & & & **T1** \\ & **SHAM** & **ACTIVE** & p-value & **SHAM** & **ACTIVE** & p-value \\ & (N=20) & (N=24) & (N=20) & (N=24) \\ Cocaine & & & 0.89 & & 1 \\ - positive & 7 (35.0\%) & 10 (41.7\%) & 9 (45.0\%) & 10 (41.7\%) \\ - negative & 13 (65.0\%) & 14 (58.3\%) & 11 (55.0\%) & 14 (58.3\%) \\ Amphetamines & & & & \\ - positive & 0 ( 0.0\%) & 0 ( 0.0\%) & 0 ( 0.0\%) & 0 ( 0.0\%) \\ & & & & 24 \\ - negative & 20 (100.0\%) & 22 (100.0\%) & 19 (100.0\%) & (100.0\%) \\ Benzodiazepines & & & 0.75 & 1 \\ - positive & 2 (10.0\%) & 4 (18.2\%) & 3 (15.8\%) & 3 (12.5\%) \\ - negative & 18 (90.0\%) & 18 (81.8\%) & 16 (84.2\%) & 21 (87.5\%) \\ Methamphetamines & & & & \\ - positive & 0 ( 0.0\%) & 0 ( 0.0\%) & 0 ( 0.0\%) & 0 ( 0.0\%) \\ & & & & 24 \\ - negative & 20 (100.0\%) & 22 (100.0\%) & 19 (100.0\%) & (100.0\%) \\ Opioids & & & & \\ - positive & 0 ( 0.0\%) & 0 ( 0.0\%) & 0 ( 0.0\%) & 0 ( 0.0\%) \\ & & & & 24 \\ - negative & 20 (100.0\%) & 22 (100.0\%) & 19 (100.0\%) & (100.0\%) \\ Cannabis & & & 1 & 0.79 \\ & & & & \\ - positive & 5 (25.0\%) & 5 (20.8\%) & 4 (20.0\%) & 3 (12.5\%) \\ \end{tabular}
## Table S7.
Urine test results of the maintenance phase.
## BASELINE** **2W** **3M** **6M
(N=41) (N=37) (N=19) (N=14)
Cocaine
- positive 17 (41.5%) 16 (43.2%) 6 (31.6%) 4 (28.6%)
- negative 24 (58.5%) 21 (56.8%) 13 (68.4%) 10 (71.4%)
Amphetamines
- positive 0 ( 0.0%) 0 ( 0.0%) 0 ( 0.0%) 1 ( 7.1%)
- negative 41 (100.0%) 37 (100.0%) 19 (100.0%) 13 (92.9%)
Benzodiazepipes
- positive 7 (17.1%) 4 (10.8%) 5 (26.3%) 3 (21.4%)
- negative 34 (82.9%) 33 (89.2%) 14 (73.7%) 11 (78.6%)
Methamphetanines
- positive 0 ( 0.0%) 0 ( 0.0%) 0 ( 0.0%) 1 ( 7.1%)
- negative 41 (100.0%) 37 (100.0%) 19 (100.0%) 13 (92.9%)
Opioids
- positive 0 ( 0.0%) 0 ( 0.0%) 0 ( 0.0%) 0 ( 0%)
- negative 41 (100.0%) 37 (100.0%) 19 (100.0%) 14 (100.0%)*
## Table S9. Cocaine urine tests in the maintenance phase.
## Table S10.
Maintenance phase multiple comparisons with Tukey correction.
Contrast Estimate Std.
CCQ-Now
2W - BASELINE -23.24 6.94 -3.35 0.00
3M - BASELINE -35.48 8.77 -4.05 0.00
6M - BASELINE -28.92 9.81 -2.95 0.02
3M - 2W -12.24 8.85 -1.38 0.50
6M - 2W -5.68 9.88 -0.57 0.94
6M - 3M 6.56 10.65 0.62 0.93
VAS
2W - BASELINE -2.01 0.48 -4.20 0.00
3M - BASELINE -2.96 0.60 -4.91 0.00
6M - BASELINE -0.92 0.67 -1.36 0.52
3M - 2W -0.95 0.61 -1.56 0.40
6M - 2W 1.09 0.68 1.61 0.37
6M - 3M 2.04 0.74 2.78 0.03
Impulsivity
2W - BASELINE -9.51 2.68 -3.55 0.00
3M - BASELINE -13.40 3.40 -3.94 0.006M - BASELINE -8.45 3.80 -2.22 0.11
3M - 2W -3.89 3.42 -1.14 0.66
6M - 2W 1.07 3.82 0.28 0.99
6M - 3M 4.95 4.11 1.21 0.62
Anxiety
2W - BASELINE -6.12 1.82 -3.36 0.00
3M - BASELINE -6.01 2.30 -2.61 0.04
6M - BASELINE -3.06 2.57 -1.19 0.63
3M - 2W 0.11 2.32 0.05 1.00
6M - 2W 3.06 2.59 1.18 0.63
6M - 3M 2.95 2.80 1.05 0.71
Depression
2W - BASELINE -5.42 1.44 -3.75 0.00
3M - BASELINE -5.64 1.80 -3.14 0.01
6M - BASELINE -5.02 2.01 -2.50 0.06
3M - 2W -0.22 1.83 -0.12 1.00
6M - 2W 0.40 2.03 0.20 1.00
6M - 3M 0.62 2.22 0.28 0.99*
## Figure S4.
WHODAS and SCL90-R measures in the acute phase.
## Table S11.
Other clinical measures in the acute phase.
## Figure S5.
WHODAS and SCL90-R measures in the maintenance phase.
## Table S12.
Other clinical measures in the maintenance phase.
MONTH-1 MONTH-2 15 15 13.5 0.136 0.408 ns MONTH-1 MONTH-3 15 15 9 0.787 0.932 ns MONTH-1 MONTH-4 15 15 6 0.855 0.932 ns MONTH-1 MONTH-5 15 15 19.5 0.888 0.932 ns MONTH-1 MONTH-6 15 15 15.5 0.866 0.932 ns MONTH-2 MONTH-3 15 15 2 0.789 0.932 ns MONTH-2 MONTH-4 15 15 2 0.789 0.932 ns MONTH-2 MONTH-5 15 15 8.5 0.752 0.932 ns MONTH-2 MONTH-6 15 15 9 0.833 0.932 ns MONTH-3 MONTH-4 15 15 1.5 1 1 1 ns MONTH-3 MONTH-5 15 15 9 0.786 0.932 ns MONTH-3 MONTH-6 15 15 4 0.85 0.932 ns MONTH-4 MONTH-5 15 15 12.5 0.75 0.932 ns MONTH-4 MONTH-6 15 15 4 0.855 0.932 ns MONTH-5 15 15 12.5 0.75 0.932 ns MONTH-4 MONTH-6 15 15 4 0.855 0.932 ns MONTH-5 15 15 12.5 0.75 0.932 ns MONTH-4 MONTH-6 15 15 4 0.855 0.932 ns MONTH-5 15 15 8 0.673 0.932 ns
### Extended study limitations
Study limitations include substantial dropout, which is common in the treatment of SUDs. A 12-month treatment study found an overall dropout rate of 31%, varying between 15 and 56% across subgroups []; the same group found 30% dropout in CUD psychological treatment in another study []. A 69% dropout rate for a 4-week treatment has also been reported in CUD []. Reasons suggested for dropout included age, education, SUD severity, comorbidities, family problems and work incompatibility []. Attrition in our study was: 1) 17% at 2 weeks; 2) 63% at 3 months; and 3) 72% at 6 months. The most common reasons were "poor adherence to treatment" followed by "incompatibility due to work." Overall, rTMS as an add-on treatment did not improve adherence beyond standard treatment. CUD patients' motivation to start and adhere to treatment may differ between subjects and timepoints. For example, initial motivation may be to please one's family. However, the urge to consume cocaine often eventually overcomes this initial motivation even in the face of improvement. Motivation to remain in treatment should be measured in future studies to improve dropout rates. Moreover, all our CUD patients had to follow standard treatment, consisting of group psychotherapy, individual psychotherapy and pharmacotherapy. Several of our patients received pharmacotherapy concurrently with starting rMTS treatment but we did not find any effects of pharmacotherapiesbetween active and sham groups. Our double-blind acute phase arm was limited to 2 weeks for ethical reasons, so as not to extend placebo treatment more than necessary for a vulnerable population. Nevertheless, that time window seemed sufficient to detect positive clinical effects. Although 5-Hz of excitatory rTMS was enough to produce significant effects in craving VAS and impulsivity, a stronger effect may be obtainable with 10-20 Hz, as 5-Hz is in the low-range of excitatory frequencies. The lack of neuronavigation is a limitation. However, most outpatient clinics use the 5.5 cm method or the Beam F3 system due to the high cost of neuronavigation. To account for the lack of neuronavigation, we used fucidals in 27 patients to allow for some individual cortical localization in the analysis. Finally, we measured common subjective variables such as craving and impulsivity, and future studies may benefit from using more objective measures such as cue-reactivity. The overall goal of our study was to assess rTMS as an add-on therapy to the standard combination of CUD treatment as this is what clinicians will encounter in their daily work. Despite these limitations, we were able to find a positive add-on effect of rTMS in the first 2 weeks.
|
154955_file02 | Appendix: Operational details for government-managed quarantine in New Zealand
### Managed isolation and quarantine (MIQ) facilities in New Zealand
The following is a summary of MIQ operational details extracted from MIQ (2020a) and current in December 2020.
All arrivals to New Zealand undergo initial screening at the border and, where required, undergo a health screen including a COVID-19 symptom check and temperature assessment. All arrivals are then transferred to a MIQ facility, except for those in urgent need of hospital-level medical care who are transferred directly to hospital. Transportation of arrivals (via bus, minivan or aircraft) from the port of arrival to a MIQ facility, or transfers between MIQ facilities, must comply with the following:
* All passengers (and drivers/crew) must wear a medical face mask during transportation, and until reaching their room in the MIQ facility.
* 2 metre physical distancing should be maintained on entering/exiting the vehicle and inside the vehicle if possible.
* Basic hand hygiene should be performed on entering/exiting the vehicle and immediately after handling luggage.
* When rest stops are required, these must be located away from major traffic routes. Staff must supervise rest stop areas to prevent entry by members of the public and to ensure 2 metre physical distancing is maintained. After use, rest-stop areas must be cleaned using hospital-grade detergent/disinfectant before being re-opened to the public.
* A domestic flight transporting new arrivals to a MIQ facility must not have other passengers on board. Air crew must wear face masks and gloves. The aircraft must be cleaned after use.
At time of writing, New Zealand has 32 MIQ facilities, located on its North Island in Auckland, Hamilton, Rotorua and Wellington, and on its South Island in Christchurch (MIQ, 2020b). Facilities are either lower-risk managed isolation facilities (for arrivals who are asymptomatic, have not tested positive for COVID-19, and are not a close contact of confirmed or probable COVID-19 cases) or higher-risk quarantine facilities (for confirmed or probable COVID-19 cases and their close contacts) or dual-use facilities, which have a designated and clearly delineated quarantine zone.
A close contact is defined as any person who is exposed to (within 2 metres for at least 15 minutes) or a household member of a confirmed or probable case during the case's infectious period, without appropriate personal protective equipment (PPE) (Ministry of Health, 2020). Facilities are located within hotels and satisfy the following criteria:
* Appropriate security and entry/exit points.
* Suitable room and bathroom facilities.
* Adequate provision of food and drink delivered to rooms.
* Safe laundry protocols.
* Ability to ensure people's wellbeing through the provision of online access and services.
Within 48 hours of arrival in a MIQ facility, arrivals undergo a health and wellbeing screen by a registered nurse, including COVID-19 symptom check and temperature assessment. All arrivals receive a welcome pack that includes information on COVID-19 and their stay in MIQ. Arrivals should isolate in their rooms as much as possible. They should perform regular hand hygiene and in shared spaces (e.g. reception areas, hallways) must maintain 2-metre physical distancing and wear a medical face mask. During their stay, arrivals can isolate within 'bubbles' (groups of people who are isolating together, e.g. family groups or other groups travelling together) in a single room or across two rooms in close proximity. People can interact with others in their bubble without use of face masks or physical distancing. If anyone within a bubble tests positive for COVID-19, all other members are considered close contacts and are moved to quarantine.
Routine testing of all arrivals (except infants aged under 6 months who are asymptomatic and are not a close contact of a confirmed or probable case) is conducted on around day 3 and day 12 of their stay in the MIQ facility. Additionally, all arrivals undergo daily health and wellbeing checks (in-person or via phone) by registered nurses or delegated health staff. Symptomatic COVID-19 cases undergo checks at least twice-daily. Anyone developing symptoms consistent with COVID-19 is immediately isolated to their room along with other members of their bubble, and tested as soon as possible. Similarly, close contacts of confirmed or probable cases are immediately isolated to their room. While awaiting test results and subject to approval, they are still offered opportunities for outdoor exercise and/or smoking under supervision to ensure PPE and 2-metre physical distancing is maintained. Anyone who receives a positive test is transferred to a quarantine facility or quarantine zone of a dual-use MIQ facility, along with their close contacts.
Arrivals have access to outdoor exercise at least once per day and access to outdoor smoking areas, under supervision by MIQ facility staff. Face masks must be worn (except when smoking), hand hygiene performed and at least 2-metre physical distancing must be maintained between all people at all times, except those who are isolating within the same bubble. Additional indoor exercise areas (including gym facilities, pools, saunas and spas) are not to be used.
Within all MIQ facilities, all surfaces and common areas (including lifts, hallways, stairwells, lobby and reception areas, and other areas) are regularly cleaned using hospital-grade detergents/disinfectant. Each facility implements a plan to ensure guests and staff can move around the facility while minimising or eliminating the potential risk of transmission to others in the facility. All facilities also have an infection prevention control training program in place to provide education to all staff, including comprehensive information and guidance on keeping themselves and their families safe.
For those who have completed their 14 days in managed isolation (or in quarantine and who have not tested positive), a medical examination and negative test result on day 12 is required for approval to exit the facility; all members of their bubble must also satisfy these criteria. Quarantined close contacts of a confirmed or probable case must re-start their 14 days of quarantine (beginning from the day after their last contact with the case while that case was deemed infectious) and a negative test on day 12 and medical examination is required to exit quarantine. For those in quarantine who have tested positive for COVID-19, no further testing is needed; instead, they must have spent at least 14 days total in a managed facility, have spent at least 10 days in a quarantine facility since testing positive or since symptom onset, have been free of symptoms for 72 hours, and receive approval from a qualified health practitioner. |
155218_file02 | ## ISARIC Clinical Characterisation Group
Abdukahil, Sheryl Ann; Abdulkadir, Nurul Najimee; Abe, Ryuzo; Abel, Laurent; Absil, Lara; Acharya, Subhash; Acker, Andrew; Adachi, Shingo; Adam, Elisabeth; Adriao, Diana; Ageel, Saleh Al; Ein, Quratul; Ainscough, Kate; Ait Hssain, Ali; Ait Tamlihat, Younes; Akimoto, Takako; Akmal, Ernita; Al Qasim, Eman; Al-dabbous, Tala; Al-Fares, Abdulrahman; Alalqam, Razi; Alam, Tanvir; Alegre, Cynthia; Alessi, Marta; Alex, Beatrice; Alexandre, Kevin; Alfoudri, Huda; Ali Shah, Naseem; Alidjnotu, Kazali Enagnon; Aliudin, Jeffrey; Allavena, Clotilde; Allou, Nathalie; Altaf, Aneela; Alves, Joao; Alves, Joao Melo; Alves, Rita; Amaral, Maria; Amira, Nur; Ammerlaan, Heidi; Ampaw, Phoebe; Andini, Roberto; Andrejak, Claire; Angheben, Andrea; Angoulvant, Francois; Ansart, Severine; Anthonidass, Sivanesen; Antonelli, Massimo; Antunes de Brito, Carlos Alexandre; Apriyana, Ardiyan; Arabi, Yaseen; Aragao, Irene; Arali, Rajeshwari; Arancibia, Francisco; Arcadipane, Antonio; Archambault, Patrick; Arenz, Lukas; Arie Zainul, Fatoni; Arlet, Jean-Benoit; Arnold-Day, Christel; Aroca, Ana; Arora, Lovkesh; Arora, Rakesh; Artaud-Macari, Elise; Aryal, Diptesh; Asaki, Motohiro; Asensio, Angel; Ashley, Elizabeth; Ashraf, Muhammad; Asie, Jean Baptiste; Asyraf, Amirul; Atique, Anika; Attanyake, AM Udara Lakshan; Auchabie, Johann; Aumaitre, Hugues; Auvet, Adrien; Azemar, Laurene; Azoulay, Cecile; Bach, Benjamin; Bachelet, Delphine; Badr, Claudine; Baillie, J. Kenneth; Bak, Erica; Bakakos, Agamemmon; Bakar, Nazreen Abu; Bal, Andriy; Balakrishnan, Mohanaprasanth; Banheiro, Bruno; Bani-Sadr, Firouze; Barbalho, Renata; Barclay, Wendy S.; Barnett, Saef Umar; Barnikel, Michaela; Barrasa, Helena; Barrelet, Audrey; Barrigoto, Cleide; Bartoli, Marie; Bartone, Cheryl; Baruch, Joaquin; Basmaci, Romain; Basri, Muhammad Fadhili Hassin; Bastos, Diego; Battaglini, Denise; Bauer, Jules; Bautista, Diego; Bazan Dow, Denisse; Beane, Abigail; Bedossa, Alexandra; Bee, Ker Hong; Behilill, Sylvie; Beishuizen, Albertus; Beljantsev, Aleksandr; Bellemare, David; Beltrame, Anna; Beluze, Marine; Benech, Nicolas; Benjamin, Lionel Eric; Benkerrou, Dehba; Bennett, Suzanne; Bento, Luis; Berdal, Jan-Erik; Bergeaud, Delphine; Bernal Salvador, Gabriela; Bernal Sobrino, Jose Luis; Bertolino, Lorenzo; Bessis, Simon; Betz, Adam; Bevilcaqua, Sybille; Bezulier, Karine; Bhatt, Amar; Bhavsar, Krishna; Bianchi, Isabella; Bianco, Claudia; Bidin, Farah Nadiah; Bikram Singh, Moirangthem; Bin Humaid, Felwa; Bin Kamarudin, Mohd Nazlin; Bissuel, Francois; Biston, Patrick; Bitker, Laurent; Blanco-Schweizer, Pablo; Blier, Catherine; Bloos, Frank; Blot, Mathieu; Blumberg, Lucille; Boccia, Filomena; Bodemes, Laetitia; Bogaarts, Alice; Bogaert, Debby; Boivin, Anne-Helene; Bolze, Pierre-Adrien; Bompart, Francois; Booth, Gareth; Borges, Diogo; Borie, Raphael; Bosse, Hans Martin; Botelho-Nevers, Elisabeth; Bouadma, Lila; Bouchaud, Olivier; Bouchez, Sabelline; Bouhmani, Dounia; Bouhour, Damien; Bouiller, Kevin; Bouillet, Laurence; Bouisse, Camille; Boureau, Anne-Sophie; Bouscambert, Maude; Bousquet, Aurore; Bouziotis, Jason; Boxma, Bianca; Boyer-Besseyre, Marielle; Boylan, Maria; Bozza, Fernando; Brack, Matthew; Braconnier, Axelle; Braga, Cynthia; Brandenburger, Timo; Bras Monteiro, Filipa; Brazzi, Luca; Breen, Dorothy; Breen, Patrick; Brickell, Kathy; Broadley, Tessa; Browne, Alex; Brozzi, Nicolas; Buchtele, Nina; Buesaquillo, Christian; Bugaeva, Polina; Buisson, Marielle; Burhan, Erlina; Burrell, Aidan; Bustos, Ingrid G.; Butnaru, Denis; Cabie, Andre; Cabral, Susana; Caceres, Eder; Cadoz, Cyril; Callahan, Mia; Calligy, Kate; Calvache, Jose Andres; Camoes, Joao; Campana, Valentine; Campbell, Paul; Canepa, Cecilia; Cantero, Mireia; Caraux-Paz, Pauline; Carcel, Sheila; Cardellino, Chiara; Cardoso, Filipa; Cardoso, Filipa; Cardoso, Nelson; Cardoso, Sofia; Carelli, Simone; Carlier, Nicolas; Carmoi, Thierry; Carney, Gayle; Carpenter, Chloe; Carret, Marie-Christine; Carrier, Francois Martin; Carson, Gail; Casanova, Maire-Laure; Cascao, Mariana; Casimiro, Jose; Cassandra, Bailey; Castaneda, Silvia; Castanheira, Nidyanara;Castro-Alexandre, Guylaine; Castrillon, Henry; Castro, Ivo; Catarino, Ana; Catherine, Francois-Xavier; Cavalin, Roberta; Cavalli, Giulio Giovanni; Cavayas, Alexandros; Ceccato, Adrian; Cervantes-Gonzalez, Minerva; Chair, Anissa; Chakveatze, Catherine; Chan, Adrienne; Chand, Meera; Chantalat Auger, Christelle; Chaplain, Jean-Marc; Chas, Julie; Chaudary, Mobin; Chavez Ihiguez, Jonathan Samuel; Chen, Anjellica; Chen, Yih-Sharng; Cheng, Matthew Pellan; Cheret, Antoine; Chiarabini, Thibault; Chica, Julian; Chidambaram, Suresh Kumar; Chirouze, Catherine; Chiumello, Davide; Cho, Hwa Jin; Cho, Sung Min; Cholley, Bernard; Chopin, Marie-Charlotte; Chow, Ting Soo; Chow, Yock Ping; Chua, Hiu Jian; Chua, Jonathan; Cidade, Jose Pedro; Cisneros Herreros, Jose Miguel; Citarella, Barbara Wanjiru; Ciullo, Anna; Clarke, Jennifer; Clohisey, Sara; Coca, Necsoi; Codan, Cassidy; Cody, Caitriona; Coelho, Alexandra; Colin, Gwenhael; Collins, Michael; Colombo, Sebastiano Maria; Combs, Pamela; Connor, Marie; Conrad, Anne; Contreras, Sofia; Conway, Elaine; Cooke, Graham S.; Copland, Mary; Cordel, Hugues; Corley, Amanda; Cormican, Sarah; Cornelis, Sabine; Cornet, Alexander Daniel; Corpuz, Arianne Joy; Cortegiani, Andrea; Corvaisier, Gregory; Couffignal, Camille; Couffin-Cadiergues, Sandrine; Courtois, Roxane; Cousse, Stephanie; Crepy D'Orleans, Charles; Croonen, Sabine; Crowl, Gloria; Crump, Jonathan; Cruz, Claudina; Cruz Bermudez, Juan Luis; Cruz Rojo, Jaime; Csete, Marc; Cucino, Alberto; Cullen, Caroline; Cummings, Matthew; Curley, Gerard; Curlier, Elodie; Custodio, Paula; D'Amico, Federico; D'Aragon, Frederick; D'Ortenzio, Eric; da Silva Filipe, Ana; Da Silveira, Charlene; Dbaliz, Al-Awwab; Dalton, Heidi; Daneman, Nick; Daniel, Corinne; Dankwa, Emmanuelle; Dantas, Jorge; Dantas, Vicente; de Boer, Mark; de Mendoza, Diego; De Montmollin, Etienne; de Oliveira Franca, Rafael Freitas; de Pinho Oliveira, Ana Isabel; De Rosa, Rosanna; de Silva, Thushan; De vries, Peter; Deacon, Jillian; Dean, David; Debard, Alexa; Debray, Marie-Pierre; DeCastro, Nathalie; Dechert, William; Deconninck, Lauren; Decours, Romain; Defous, Eve; Delacroix, Isabelle; Delaneuve, Eric; Delavigne, Karen; Delfos, Nathalie M.; Deligiannis, Ionna; Dell'Amore, Andrea; Delmas, Christelle; Delobel, Pierre; Demonchy, Elisa; Denis, Emmanuelle; Deplanque, Dominique; Depuydt, Pieter; Desai, Mehul; Descamps, Diane; Desvallee, Mathilde; Dewayanti, Santi; Diallo, Alpha; Diamantis, Sylvain; Dias, Andre; Diaz, Juan Jose; Diaz, Priscila; Diaz, Rodrigo; Didier, Kevin; Diehl, Jean-Luc; Dieperink, Wim; Dimet, Jerome; Dinot, Vincent; Diop, Fara; Diouf, Alphonsine; Dishon, Yael; Djossou, Felix; Docherty, Annemarie B.; Dondorp, Arjen M; Dong, Andy; Donnelly, Christl A.; Donnelly, Maria; Donohue, Chloe; Dorival, Celine; Doshi, Yash; Doshi, Yash; Douglas, James Joshua; Douma, Renee; Dournon, Nathalie; Downer, Triona; Downing, Mark; Drake, Tom; Driscoll, Aoife; Dryden, Murray; Duarte Fonseca, Claudio; Dubee, Vincent; Dubos, Francois; Ducancelle, Alexandre; Duculan, Toni; Dudman, Susanne; Dunand, Paul; Dunning, Jake; Duplaix, Mathilde; Durante Mangoni, Emanuele; Durham III, Lucian; Dussol, Bertrand; Duthoit, Juliette; Duval, Xavier; Dyrhol-Risse, Anne Margarita; Fan, Sim Choon; Echeverria-Villalobos, Marco; Egan, Siobhan; Eira, Carla; El Sanharawi, Mohammed; Elapavaluru, Subbarao; Elharrar, Brigitte; Ellerbroek, jacobien; Ellis, Rachael; Eloy, Philippine; Elshazly, Tarek; Enderle, Isabelle; Eng, Chan Chee; Engelmann, Ilka; Enouf, Vincent; Epaulard, Olivier; Escher, Martina; Esperatti, Mariano; Esperou, Helene; Esposito-Farese, Marina; Estevao, Joao; Etienne, Manuel; Etalhaoui, Nadia; Everding, Anna Greti; Evers, Mirjam; Fabre, Isabelle; Fabre, Marc; Faheem, Anna; Fahy, Arabella; Fairfield, Cameron J.; Faria, Pedro; Farooq, Ahmed; Farshait, Nataly; Fateena, Hanan; Faure, Karine; Favory, Raphael; Fayed, Mohamed; Feely, Niamh; Fernandes, Jorge; Fernandes, Marilia; Fernandes, Susana; Ferrand, Francois-Xavier; Ferrand Devouge, Eglantine; Ferrao, Joana; Ferraz, Mario; Ferreira, Benigno; Ferrer-Roca, Ricard; Ferriere, Nicolas; Ficko, Celine; Figueiredo-Mello, Claudia; Fiorda, Juan; Flament, Thomas; Flateau, Clara; Fletcher, Tom;Florio, Letizia Lucia; Flynn, Brigid; Foley, Claire; Fomin, Victor; Fonseca, Tatiana; Fontela, Patricia; Forsyth, Simon; Foster, Denise; Foti, Giuseppe; Fourn, Erwan; Fowler, Robert A.; Fraher, Dr Marianne; Franch-Llasat, Diego; Fraser, Christophe; Fraser, John F.; Freire, Marcela Vieira; Freitas Ribeiro, Ana; Friedrich, Caren; Fritz, Ricardo; Fry, Stephanie; Fuentes, Nora; Fukuda, Masahiro; Gaborieau, Valerie; Gaci, Rostane; Gagliardi, Massimo; Gagnard, Jean-Charles; Gagne, Nathalie; Gagneux-Brunon, Amandine; Galao, Sergio; Gail Skeie, Linda; Gallagher, Phil; Gallego Curto, Elena; Gamble, Carrol; Gani, Yasmin; Garan, Arthur; Garcia, Rebekha; Garcia Barrio, Noelia; Garcia-Gallo, Esteban; Garimella, Navva; Garot, Denis; Garrait, Valerie; Gault, Nathalie; Gavin, Aisling; Gavrilov, Anatoliy; Gaymard, Alexandre; Gebauer, Johanes; Geraud, Eva; Gerbaud Morlaes, Louis; Germano, Nuno; Ghosn, Jade; Giani, Marco; Giaquinto, Carlo; Gibson, Jess; Gigante, Tristan; Gilg, Morgane; Giordano, Guillermo; Girvan, Michelle; Gissot, Valerie; Giwangkancana, Gezy; Glikman, Daniel; Glybochko, Petr; G Small, Eric; Goco, Geraldine; Goehringer, Francois; Goepel, Siri; Goffard, Jean-Christophe; Goh, Jin Yi; Golob, Jonathan; Gomes, Rui; Gomez-Junyent, Joan; Gominet, Marie; Gonzalez Gonzalez, Alicia; Gorenne, Isabelle; Goubert, Laure; Goujard, Cecile; Goulenok, Tiphaine; Grable, Margarite; Graf, Jeronimo; Grandin, Edward Wilson; Granier, Pascal; Grasselli, Giacomo; Grazioli, Lorenzo; Green, Christopher A.; Greenhalf, William; Greffe, Segolene; Grieco, Domenico Luca; Griffee, Matthew; Griffiths, Fiona; Grigoras, Ioana; Groenendijk, Albert; Grosse Lordemann, Anja; Gruner, Heidi; Gu, Yusing; Guarracino, Fabio; Guedj, Jeremie; Guego, Martin; Guellec, Dewi; Guerguerian, Anne-Marie; Guerreiro, Daniela; Guery, Romain; Guillaumot, Anne; Guilleminault, Laurent; Guimard, Thomas; Haalboom, Marieke; Haber, Daniel; Hachemi, Ali; Hadri, Nadir; Haidash, Olena; Hakak, Sheeba; Hall, Adam; Hall, Matthew; Halpin, Sophie; Hamer, Ansley; Hamidfar, Rebecca; Hammond, Terese; Han, Lim Yuen; Haniffa, Rashan; Hao, Kok Wei; Hardwick, Hayley; Harley, Kristen; Harrison, Ewen M.; Harrison, Janet; Harrison, Samuel Bernard Ekow; Hayat, Muhammad; Hays, Leanne; Heerman, Jan; Heggelund, Lars; Hendry, Ross; Hennessy, Martina; Henriquez, Aquiles; Hentzien, Maxime; Herekar, Fivzia; Hernandez-Montfort, Jaime; Herr, Daniel; Hershey, Andrew; Hesstvedt, Liv; Hidaya, Astarini; Higgins, Dawn; Higgins, Eibhilin; Hing, Nickolas; Hinton, Samuel; Hipolito-Reis, Ana; Hiraiwa, Hiroaki; Hirkani, Haider; Hitoto, Hikombo; Ho, Antonia Ying Wai; Ho, Yi Bin; Hoctin, Alexandre; Hoffmann, Isabelle; Hoh, Wei Han; Hoiting, Oscar; Holt, Rebecca; Holter, Jan Cato; Horby, Peter; Horcajada, Juan Pablo; Hoshino, Koji; Hoshino, Kota; Houas, Ikram; Hough, Catherine L.; Hsu, Jimmy Ming-Yang; Hulot, Jean-Sebastien; Ijaz, Samreen; Illes, Hajnal-Gabriela; Imbert, Patrick; Inacio, Hugo; Infante Dominguez, Carmen; Ing, Yun Si; Iosifidis, Elias; Ippolito, Mariachiara; Irvine, Lacey; Isgett, Sarah; Ishani, Palliya Guruge Pramodya Ishani; Isidoro, Tiago; Ismail, Nadih; Isnard, Margaux; tai, Junji; Ivulich, Daniel; Jaafar, Danielle; Jaafoura, Salma; Jabot, Julien; Jackson, Clare; Jacquet, Pierre; Jamieson, Nina; Jassat, Waasila; Jaud-Fischer, Coline; Jaureguberry, Stephane; Javidfar, Jeffrey; Jawad, Israh; Jayakumar, Devachandran; Jego, Florence; Jelani, Anilawati Mat; Jenum, Synne; Jimbo-Sotomayor, Ruth; Joe, Ong Yiaw; Jorge Garcia, Ruth N.; Joseph, Cedric; Joseph, Mark; Joshi, Swosti; Jourdain, Merce; Jouvet, Philippe; jung, Anna; Jung, Hanna; Juzar, Dafsah; Kaff, Ouifiya; Kaguelidou, Florentia; Kaisbain, Neervisha; Kaleesvran, Thavamany; Kali, Sabina; Kalomori, Smaragdi; Kamal, Saima; Kamaluddin, Muhammad Aisar Ayadi; Kamaruddin, Zul Amali Che; Kamarudin, Nadiah; Kambiya, Paul; Kandamy, Darshana Hewa; Kandel, Chris; Kang, Kong Yeow; Kant, Ravi; Kanyawati, Dyah; Karpayah, Pratap; Karsies, Todd; Kartsonaki, Christiana; Kasugai, Daisuke; Kataria, Anant; Katz, Kevin; Kaur Johal, Simreen; Kawasaki, Tatsuya; Kay, Christy; Keating, Sean; Kedia, Pulak; Kelly, Andrea; Kelly, Sadie; Kennedy, Lisa; Kennedy, Ryan; Kennon, Kalynn; Kerroumi, Younes; Kestelyn, Evelyne; Khalid,Imrana; Khalid, Osama; Khalil, Antoine; Khan, Coralie; Khan, Irfan; Khanal, Sushil; kherajani, Krish; Kho, Michelle E; Khoo, Denisa; Khoo, Ryan; Khoo, Saye; Khoso, Nasir; Kiat, Khor How; Kida, Yuri; Kiiza, Peter; Kildal, Anders Benjamin; Kim, Jae Burm; Kimmoun, Antoine; Kindgen-Milles, Detlef; Kitamura, Nobuya; Klenerman, Paul; Kloumann Bekken, Gry; Knight, Stephen; Kobbe, Robin; Kodippily, Chamira; Kohns Vasconcelos, Malte; Koirala, Sabin; Komatsu, Mamoru; Korten, Volkan; Kosgei, Caroline; Kpangon, Arsene; Krawczyk, Karolina; Krishnan, Vinothini; Kruglova, Oksana; Kumar, Ashok; Kumar, Deepali; Kumar, Ganesh; Kumar, Mukesh; Kumar Tirupakuzhi Vijayaraghavan, Bharath; Kumar Vecham, Pavan; Kurtzman, Ethan; Kusumastuti, Neurinda Permata; Kutsogiannis, Demetrios; Kutsyna, Galyna; Kyriakoulis, Konstantinos; L'Her, Erwan; Lachatre, Marie; Lacoste, Marie; Laffey, John G; Lagrange, Marie; Laine, Fabrice; Liarez, Olivier; Lalueza Blanco, Antonio; Lambert, Marc; Lamontagne, Francois; Langelot-Richard, Marie; Langlois, Vincent; Lantang, Eka Yudha; Lanza, Marina; Laouenan, Cedric; Laribi, Samira; Lariviere, Delphine; Lasry, Stephane; Lath, Sakshi; Launay, Odile; Laureillard, Didier; Lavie-Badie, Yoan; Law, Andrew; Lawrence, Cassie; Le, Minh; Le Bihan, Clement; Le Bris, Cyril; Le Falher, Georges; Le Fevre, Lucie; Le Hingrat, Quentin; Le Marechal, Marion; Le Mestre, Soizic; Le Moal, Gwenael; Le Moing, Vincent; Le Nagard, Herve; Le Turnier, Paul; Leal, Ema; Leal Santos, Marta; Lee, Biing Horng; Lee, Heng Gee; Lee, James; Lee, Su Hwan; Lee, Todd C.; Lee, Yi Lin; Leeming, Gary; Lefebvre, Benedicte; Lefebvre, Laurent; Lefevre, Benjamin; LeGac, Sylvie; Lelievre, Jean-Daniel; Lellouche, Francois; Lemaignen, Adrien; Lemee, Veronique; Lemeur, Anthony; Lemmink, Gretchen; Lene, Ha Sha; Leon, Rafael; Leone, Marc; Leone, Michela; Lepiller, Quentin; Lescure, Francois-Xavier; Lesens, Olivier; Lesouhaitier, Mathieu; Levy, Bruno; Levy, Yves; Levy-Marchal, Claire; Lewandowska, Katarzyna; Li Bassi, Gianluigi; Liang, Janet; Liaquat, Ali; Liegeon, Geoffrey; Lim, Kah Chuan; Lim, Wei Shen; Lima, Chantre; Lina, Bruno; Lina, Lim; Lind, Andreas; Lingas, Guillaume; Link, Linda; Lion-Daolio, Sylvie; Lissauer, Samantha; Liu, Keibun; Livrozet, Marine; Loforte, Antonio; Lolong, Navy; Loon, Leong Chee; Lopes, Diogo; Lopez-Colon, Dalia; Loubet, Paul; Loufti, Bouchra; Louis, Guillaume; Lourenco, Silvia; Lovelace-Macon, Lara; Low, Lee Lee; Loy, Jia Shyi; Lucet, Jean Christophe; Lumbreras Bermejo, Carlos; Luna, Carlos M.; Lungu, Olguta; Luong, Liem; LUQUE, NESTOR; Luton, Dominique; Lwin, Nilar; Lyons, Ruth; Maasikas, Olavi; Mabiala, Oryane; MacDonald, Samual; MacDonald, Sarah; Machado, Moise; Macheda, Gabriel; Macias Sanchez, Juan; Madhok, Jai; Madiha, Hashmi; Maestro de la Calle, Guillermo; Mahieu, Rafael; Mahy, Sophie; Maia, Ana Raquel; Maier, Lars Siegfrid; Maillet, Mylene; Maitre, Thomas; Malertheiner, Maximilian; Malik, Nadia; Maltez, Fernando; Malvy, Denis; Manda, Victoria; Mandei, Jose M.; Mandelbrot, Laurent; Mankikian, Julie; Manning, Edmund; Manuel, Aldric; Maria Sant'Ana Malaque, Ceila; Marino, Daniel; Marino, Flavio; Mariz, Caroline de Araujo; Markowicz, Samuel; Maroun Eid, Charbel; Marques, Ana; Marquis, Catherine; Marsh, Brian; Marshall, John; Martelli, Celina Turchi; Martin, Dori-Ann; Martin, Emily; Martin-Blondel, Guillaume; Martin-Loeches, Ignacio; Martin-Quiros, Alejandro; Martinelli, Alessandra; Martinot, Martin; Martins, Ana; Martins, Joao; Martins, Nuno; Martins Rego, Caroline; Martucci, Gennaro; Martynenko, Olga; Marwali, Eva Miranda; Marzukie, Marsilla; Masa Jimenez, Juan Fernando; Maslove, David; Mason, Phillip; Mason, Sabina; Mat Nor, Basri; Matan, Moshe; Mathieu, Daniel; Mattei, Mathieu; Matulevics, Romans; Maulin, Laurence; May, Jennifer; Maynar, Javier; Mazzoni, Thierry; Mc Evoy, Natalie; McArthur, Colin; McCarthy, Aine; McCarthy, Anne; McCloskey, Colin; McConnochie, Rachael; McDermott, Sherry; McDonald, Sarah; McElwee, Samuel; McGeer, Allison; McGuinness, Niki; McKay, Chris; McKeown, Johnny; McLean, Kenneth A.; McNicholas, Bairbre; Meaney, Edel; Mear-Passard, Cecile; Mechlin, Maggie; Meher, Maqsood; Mehkri, Omar; Mele, Ferruccio; Melo, Luis;Memon, Kashif; Mendes, Joao Joao; Menkiti, Ogechukwu; Menon, Kusum; Mentre, France; Mentzer, Alexander J.; Mercier, Emmanuelle; Mercier, Noemie; Merckx, Antoine; Mergeay-Fabre, Mayka; Mergler, Blake; Merson, Laura; Mesquita, Antonio; Meybeck, Agnes; Meyer, Dan; Meynert, Alison M.; Meysonnier, Vanina; Meziane, Amina; Mezidi, Mehdi; Michelagnoli, Giuliano; Michelanglei, Celine; Michelet, Isabelle; Mihelis, Efstathiia; Mihnovits, Vladislav; Miranda-Maldonado, Hugo; Misman, Nor Arishah; Mohamed, Nik Nur Eliza; Mohamed, Tahira Jamal; Moin, Asma; Molina, David; Molinos, Elena; Mone, Mary; Monteiro, Agostinho; Montes, Claudia; Montrucchio, Giorgia; Moore, Sarah; Moore, Shona C.; Morales Cely, Lina; Moro, Lucia; Morocho, Diego; Morton, Ben; Motherway, Catherine; Motos, Ana; Mouquet, Hugo; Mouton Perrot, Clara; Moyet, Julien; Mudara, Caroline; Muh, Ng Yong; Muhamad, Dzawani; Mullaert, Jimmy; Muller, Fredrik; Muller, Karl Erik; Munblit, Daniel; Muneeb, Syed; Murris, Marlene; Murthy, Srinivas; Muyandy, Gugapriyaa; Myrodia, Dimitra Melia; Nagpal, Dave; Nagrebetsky, Alex; Narasimhan, Mangala; Nasim Khan, Rashid; Neant, Nadege; Neb, Holger; Nekliudov, Nikita A; Neto, Raul; Neumann, Emily; Neves, Bernardo; Ng, Pauline Yeung; Ng, Wing Yiu; Nghi, Anthony; Nguyen, Duc; Ni Cholieain, Orna; Nichol, Alistair; Nonas, Stephanie; Noordin, Nurul Amani Mohd; Noret, Marion; Norharizam, Nurul Faten Izzati; Norman, Lisa; Notari, Alessandra; Noursadeghi, Mahdad; Nowicka, Karolina; Nowinski, Adam; Nseir, Saad; Nunez, Jose I; Nurnaningsih, Nurnaningsih; Nyamankolly, Elsa; O'Donnell, Max; O'Hearn, Katie; O'Neil, Conar; Occhipinti, Giovanna; Ogston, Tawnya; Ogura, Takayuki; Oh, Tak-Hyuk; Ohshimo, Shinichiro; Oinam, Budhacharan Singh; Oliveira, Joao; Oliveira, Larissa; Olliaro, Piero L.; Ong, David S.Y.; Ong, Jee Yan; Oosthuyzen, Wilna; Opavsky, Anne; Openshaw, Peter; Orakzai, Saijad; Orozco-Chamorro, Claudia Milena; Oraquera, Andres; Ortoleva, Janel; Osatnik, Javier; Othman, Siti Zubaidah; Ouamara, Nadia; Quissa, Rachida; Owayang, Clark; Oziol, Eric; Pabasara, H M Upulee; Pagadoy, Maider; Pages, Justine; Palacios, Amanda; Palacios, Mario; Palmarini, Massimo; Panarello, Giovanna; Panda, Prasan Kumar; Paneru, Hem; Pang, Lai Hui; Panigada, Mauro; Pansu, Nathalie; Papadopoulos, Aurelie; Parke, Rachael; Parker, Melissa; Parra, Briseida; Parrini, Vieri; Pasha, Taha; Pasquier, Jeremie; Pastene, Bruno; Patauner, Fabian; Patel, Drasthi; Patel, Junaid; Pathmanathan, Mohan Dass; Patrao, Luis; Patricio, Patricia; Patrier, Juliette; Patterson, Lisa; Pattnaik, Rajyabardhan; Paul, Christelle; Paul, Mical; Paulos, Jorge; Paxton, William A.; Payen, Jean-Francois; Peariasamy, Kalaiarasu; Pearse, India; Pedrera Jimenez, Miguel; Peek, Giles; Peelman, Florent; Peiffer-Smadja, Nathan; Peigne, Vincent; Pejkovska, Mare; Pelosi, Paolo; Peltan, Ithan D.; Pereira, Rui; Perez, Daniel; Periel, Luis; Perpoint, Thomas; Pesenti, Antonio; Pestre, Vincent; Petrousova, Lenka; Petrov-Sanchez, Ventzislava; Pettersen, Frank Olav; Peytavin, Gilles; Pharand, Scott; Pignerelli, Michael; Picard, Walter; Picone, Olivier; Piero, Maria de; Pierobon, Carola; Pimentel, Carlos; Pinto, Raquel; Pirathayini, Vicknesha; Pironneau, Isabelle; Pirth, Lionel; Pius, Riinu; Piva, Simone; Plantier, Laurent; Plotkin, Daniel; Png, Hon Shen; Poissy, Julien; Pokerebux, Ryadh; Pokorska-Spiewak, Maria; Poli, Sergio; Pollakis, Georgios; Ponscarme, Diane; Popielska, Jolanta; Post, Andra-Maris; Postma, Douwe F.; Povoa, Pedro; Povoa, Diana; Powis, Jeff; Prapa, Sofia; Preau, Sebastien; Prebensen, Christian; Preiser, Jean-Charles; Prinssen, Anton; Pritchard, Mark; Priyadarshani, Gamage Dona Dilanthi; Proenca, Lucia; Prompak, N; Puechal, Oriane; Pujo Semedi, Bambang; Pulicken, Mathew; Purcell, Gregory; Quesada, Luisa; Quinones-Cardona, Vilmaris; Quiros Gonzalez, Victor; Quist-Paulsen, Else; Quraishi, Mohammed; Rabaud, Christian; Rafael, Aldo; Rafiq, Marie; Ragazzo, Gabrielle; Rahman, Ahmad Kashfi Haji Ab; Rahman, Rozanah Abd; Rahutullah, Arsalan; Rainieri, Fernando; Rajahram, Giri Shan; Ralib, Azrina; Ramakrishnan, Nagarajan; Ramanathan, Kollengode; Ramli, Ahmad Afiq; Rammaert, Blandine; Ramos, Grazielle Viana;Rana, Asim; Rapp, Christophe; Rashan, Aasiyah; Rashan, Thalha; Rasmin, Menaldi; Ratsep, Indrek; Rau, Cornelius; Ravi, Tharmini; Raza, Ali; Real, Andre; Rebaudet, Stanislas; Redl, Sarah; Reeve, Brenda; Rehan, Ali; Rehman, Attaur; Reid, Liadain; Reikvam, Dag Henrik; Reis, Renato; Rello, Jordi; Remppis, Jonathan; Remy, Martine; Ren, Hongru; Renk, Hanna; Resende, Liliana; Resseguier, Anne-Sophie; Revest, Matthieu; Rewa, Oleksa; Reyes, Luis F.; Reyes, Tiago; Ribeiro, Maria Ines; Richardson, David; Richardson, Denise; Richier, Laurent; Ridzuan, Siti Nurul Atikah Ahmad; Riera, Jordi; Rios, Ana Lucia; Rishu, Asgar; Rispal, Patrick; Risso, Karine; Rivera Nuñez, Maria Angelica; Rizer, Nicholas; Robb, Doug; Robba, Chiara; Roberto, Andre; Robertson, David L.; Robineau, Olivier; Roche-Campo, Ferran; Rodari, Paola; Rodeia, Simao; Rodriguez Abreu, Julia; Roger, Claire; Roger, Pierre-Marie; Roilides, Emmanuel; Rojek, Amanda; Romaru, Juliette; Roncon-Albuquerque Jr, Roberto; Roriz, Melanie; Rosa-Calatrava, Manuel; Rose, Michael; Rosenberger, Dorothea; Roslan, Nurul Hidayah Mohammad; Rossanese, Andrea; Rossetti, Matteo; Rossignol, Benedicte; Rossignol, Patrick; Rossler, Bernhard; Rousset, Stella; Roy, Carine; Roze, Benoit; Rusmawatiningtyas, Desy; Russell, Clark D.; Ryckaert, Steffi; Rygh Holten, Aleksander; Saba, Isabela; Sadaf, Sairah; Sadat, Musharaf; Sahraei, Valla; Saint-Gilles, Maximilien; Sakiyalak, Pranya; Salahuddin, Nawal; Salazar, Leonardo; Sales, Gabriele; Sallaberry, Stephane; Salmon Gandonniere, Charlotte; Salvador, Helene; Sanchez, Angel; Sanchez, Olivier; Sanchez Choez, Xavier; Sancho-Shimizu, Vanessa; Sandhu, Gyan; Sandrine, Pierre-Francois; Sandulescu, Oana; Santos, Marlene; Sarfo-Mensah, Shirley; Sarmiento, Iam Claire E.; Sarton, Benjamine; Satya, Ankana; Satyapriya, Sree; satyawati, Rumaishah; Savvidou, Parthena; Saw, Yen Tsen; Scarsbrook, Joshua; Schaffer, Justin; Schermer, Tjard; Scherpereel, Arnaud; Schneider, Marion; Schroll, Stephan; Schwameis, Michael; Scott, Janet T.; Scott-Brown, James; Sedillot, Nicholas; Seitz, Tamara; Selvanayagam, Jaganathan; Selvarajoo, Mageswari; Semaille, Caroline; Semple, Malcolm G.; Semple, Malcolm G.; Senian, Rasidah Bt; Senneville, Eric; Sepulveda, Claudia; Sequeira, Filipa; Sequeira, Tania; Serpa Neto, Ary; Serrano Balazote, Pablo; Shadowitz, Ellen; Shahidan, Syamin Asyraf; Shamsah, Mohammad; Sharma, Pratima; Shaw, Catherine A.; Shaw, Victoria; Sheharyar, Ashraf; Shetty, Rohan; Shi, Haixia; Shiban, Nisreen; Shiekh, Mohiuddin; Shiga, Takuya; Shime, Nobuaki; Shimizu, Hiroaki; Shimizu, Keiki; Shimizu, Naoki; Shrapnel, Sally; Shuker, Tristan; Shum, Hoi Ping; Si Mohammed, Nassima; Siang, Ng Yong; Sibiude, Jeanne; Siddiqui, Atif; Sigrid, Louise; Sillaots, Piret; Silva, Catarina; Silva, Maria Joao; Silva, Rogerio; Sim Lim Heng, Benedict; Sin, Wai Ching; Sitompul, Pompini Agustina; Sivam, Karisha; Skogen, Vegard; Smith, Sue; Smood, Benjamin; Smyth, Michelle; Snacken, Morgane; So, Dominic; Soh, Tze Vee; Solis, Monserrat; Solomon, Joshua; Solomon, Tom; Somers, Emily; Sommet, Agnes; Song, Myung Jin; Song, Rima; Song, Tae; Sonntagbauer, Michael; Soom, Azlan Mat; Sotto, Alberto; Soum, Edouard; Sousa, Ana Chora; Sousa, Marta; Sousa Uva, Maria; Souza-Dantas, Vicente; Sperry, Alexandra; Sri Darshana, B. P. Sanka Ruwan; Sriskandan, Shiranee; Stabler, Sarah; Staudinger, Thomas; Stecher, Stepanie-Susanne; Steinsvik, Trude; Stienstra, Ymkje; Stiksrud, Birgitte; Streinu-Cercel, Adrian; Streinu-Cercel, Anca; Strudwick, Samantha; Stuart, Ami; Stuart, David; Suen, Gabriel; Suen, Jacky Y.; Sultana, Asfia; Summers, Charlotte; Suppiah, Deepashankari; Surovcova, Magdalena; Svistunov, Andrey A; Syahrin, Sarah; Syrigos, Konstantinos; Sztajnbok, Jaques; Szuldrzynski, Konstanty; Tabrizi, Shirin; Taccone, Fabio S.; Tagherset, Lysa; Taib, Shahdattul Mawarni; Talarek, Ewa; Taleb, Sara; Talsma, Jelmer; Tampublolon, Maria Lawrensa; Tan, Kim Keat; Tan, Le Van; Tan, Yan Chyi; Tanaka, Clarice; Tanaka, Hiroyuki; Tanaka, Taku; Taniguchi, Hayato; Tanveer, Hussain; Tardivon, Coralie; Tattevin, Pierre; Taufik, M Azhari; Tedder, Richard S.; Tee, Tze Yuan; Teixeira, Joao; Tejada, Sofia; Tellier, Marie-Capucine; Teoh, Sze Kye; Teotonio, Vanessa; Teoule, Francois; Terpstra,Pleun; Terrier, Olivier; Terzi, Nicolas; Tessier-Grenier, Hubert; Thabit, Alif Adlan Mohd; Tham, Zhang Duan; Thangavelu, Suvintheran; Thibault, Vincent; Thiberville, Simon-Djamel; Thill, Benoit; Thirumanickam, Jananee; Tho, Leong Chin; Thompson, Shaun; Thomson, David; Thomson, Emma C.; Thurai, Surain Raaj Thanga; Thuy, Duong Bich; Thwaites, Ryan S.; Tieroshyn, Vadim; Timashev, Peter S; Timsit, Jean-Francois; Tissot, Noemie; Toh, Jordan Zhien Yang; Toki, Maria; Tolppa, Timo; Tonby, Kristian; Tonnii, Sia Loong; Torres, Antoni; Torres, Margarida; Torres Santos-Olmo, Rosario Maria; Torres-Zevallos, Hernando; Trapani, Tony; Treoux, Theo; Trieu, Huynh Trung; Tromeur, Cecile; Trontzas, Ioannis; Troost, Jonathan; Trouillon, Tiffany; Truong, Jeanne; Tual, Christelle; Tubiana, Sarah; Tuite, Helen; Turmel, Jean-Marie; Turtle, Lance C.W.; Tveita, Anders; Twardowski, Pawel; Uchiyama, Makoto; Udayanga, PG Ishara; Udy, Andrew; Ullrich, Roman; Uribe, Alberto; Usman, Asad; Val-Flores, Luis; Valle, Ana Luiza; Valran, Amelie; Van De Velde, Stijn; van den Berge, Marcel; Van der Feltz, Machteld; Van Der Vekens, Nicky; Van der Voort, Peter; Van Der Werf, Sylvie; van Dyk, Marlice; van Gulik, Laura; Van Hattem, Jarne; van Lelyveld, Steven; van Netten, Carolien; van Twillert, G; Vanel, Noemie; Vanoverschede, Henk; Vasudayan, Shoban Raj; Vauchy, Charline; Veeran, Shaminee; Veislinger, Aurelie; Ventura, Sara; Verbon, Annelies; Vidal, Jose Ernesto; Vieira, Cesar; Villanueva, Joy Ann; Villar, Judit; Villeneuve, Pierre-Marc; Villodlo, Andrea; Vinh Chau, Nguyen Van; Vishwanathan, Gayatri; Visseaux, Benoit; Visser, Hannah; Vitiello, Chiara; Vuorinen, Aapeli; Vuotto, Fanny; Wahab, Suhaila Abdul; Wahid, Nadirah Abdul; Wan Muhd Shukeri, Wan Fadzina; Wang, Chih-Hsien; Wei, Jia; Weil, Katharina; Wen, Tan Pei; Wesselius, Sanne; West, T. Eoin; Wham, Murray; Whelan, Bryan; White, Nicole; Wicky, Paul Henri; Wiedemann, Aurelie; Wijaya, Surya Oto; Wille, Keith; Willems, Suzette; Williams, Virginie; Wils, Evert-Jan; Wong, Calvin; Wong, Teck Fung; Wong, Xin Ci; Wong, Yew Sing; Xian, Gan Ee; Xian, Lim Saio; Xuan, Kuan Pei; Xynogalas, Ioannis; Yacoub, Sophie; Yakop, Siti Rohani Binti Mohd; Yamazaki, Masaki; Yazdanpanah, Yazdan; Yelnik, Cecile; Yeoh, Chian Hui; Yerkovich, Stephanie; Yokoyama, Toshiki; Yonis, Hodane; Yuliarto, Saptadi; Zaaqoq, Akram; Zabbe, Marion; Zacharowski, Kai; Zahid, Masliza; Zahran, Maram; Zaidan, Nor Zaila Bint; Zambon, Maria; Zambrano, Miguel; Zanella, Alberto; Zawadka, Konrad; Zaynah, Nurul; Zayyad, Hiba; Zoufaly, Alexander; Zucman, David. |
155473_file02 | ## S2 Table. Demographics Questionnaire in the Baseline Survey.
\begin{tabular}{l|l|l} \hline \multicolumn{2}{l}{Section Title, Question No.} & \multicolumn{1}{c}{Question} \\ \hline Demographics & & \\ & 1 & Age \\ & 2 & Sex \\ & 3 & Hispanic or Spanish Origin \\ & 4 & Race or Ethnicity \\ & 5 & Education \\ & 6 & Annual Income \\ \end{tabular}
## S3 Table. Questions in the Follow-Up Surveys.
\begin{tabular}{l|l|l} \hline \multicolumn{2}{l}{Section Title, Question No.} & \multicolumn{1}{c}{Question} \\ \hline Hospital Readmission & & \\ & & Have you been hospitalized within the last 4 weeks/3 months/6 \\ & & months? (Do not include Emergency Room visits where you were not \\ & 1 & admitted to the hospital.) \\ \hline \end{tabular}
When was the first day of your first hospitalization?
3 What is the name of the hospital where you were first hospitalized How many times were you hospitalized in the last 4 weeks/3
4 months/6 months?
5 How many nights were you in the hospital?
ER
Have you visited the emergency room within the last 4 weeks/3 months/6 months (whether or not you were admitted to the
1 hospital)?
2 When was the first visit to the emergency room?
3 What is the name of the emergency room you first visited?
How many visits to any emergency did you have in the last 4 weeks/3
4 months/6 months?
Device
On a scale of 1-5, with 1 being not at all helpful and 5 being extremely helpful did you find the Fitbit?
What did you like and/or dislike about the Fitbit? Follow up: how easy
2 was incorporating the Fitbit into your daily life?
3 Did the Fitbit help you adhere to your care plan? Why or why not?
On a scale of 1-5, with 1 being not at all helpful and 5 being extremely helpful did you find the scale?
What did you like and/or dislike about the scale? Follow up: how easy
5 was incorporating the scale into your daily life?
6 Did the scale help you adhere to your care plan? Why or why not?
On a scale of 1-5, with 1 being not at all helpful and 5 being extremely helpful did you find the pill bottle cap?
What did you like and/or dislike about the pill bottle cap? Follow up: how easy
how easy was incorporating the pill bottle cap into your daily life?
Did the pill bottle cap help you adhere to your care plan? Why or why not?
9 not?
Extra Question Upon
Completion
Are you willing to allow our study team to continue to access data
1 from your monitoring devices?
S4 Table: Questionnaires Scores at Baseline and Follow-Up.
Questionnaire
Baseline (_n_)
Median Score (IQR)
Follow-up (n)
Median Score (IQR)
Self-Care of Heart Failure Index
Maintenance
13
70.0 (52.6-75.0)
14
76.7 (70.0-93.3)
Management
12
62.5 (45.0-75.0)
8
62.5 (47.5-72.5)
Confidence
13
72.3 (58.4-91.8)
14
58.4 (44.5-66.7)
Seattle Angina Questionnaire
12
56.4 (51.1-69.2)
6
62.8 (55.3-79.3)
Kansas City Cardiomyopathy
Questionnaire
13
45.7 (39.3-60.7)
14
67.9 (47.1-85.7)
PROMIS Global Health
Physical
12
41.1 (34.9-49.3)
14
39.8 (37.4-42.3)S5 Table. Ratings of the Study Devices.
Question \(n\) & Median Score (IQR)
On a scale of 1-5, with 1 being not at all helpful and 5 being extremely helpful, how helpful did you find the Fitbit?
On a scale of 1-5, with 1 being not at all helpful and 5 being extremely helpful, how helpful did you find the scale?
On a scale of 1-5, with 1 being not at all helpful and 5 being extremely helpful, how helpful did you find the pill bottle cap?
S6 Table. Usage of the Study Devices at 30, 90, and 180 Days After Discharge.
S7 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S8 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S9 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S10 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S11 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S12 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S13 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S14 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S15 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S16 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S17 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S18 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S19 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S12 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S13 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S14 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S15 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S16 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S17 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S18 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S19 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S10 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S11 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S12 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S13 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S14 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S15 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S16 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S17 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S18 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S19 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S10 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S11 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S12 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S13 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S14 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S15 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S16 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S17 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S18 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S19 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S10 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S11 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S12 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S13 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S14 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S15 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S16 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S17 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S18 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S19 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S14 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S19 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S12 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S13 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S14 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S15 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S16 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S17 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S18 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S19 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S14 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S15 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S16 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S17 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S18 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S19 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S19 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S19 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S19 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S19 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S19 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S19 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S19 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S19 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S19 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S19 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S19 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S19 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S19 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S19 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S19 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S19 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S19 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S19 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S19 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S19 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S19 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S19 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
S19 Table. Questionnaires Scores at Baseline and 30-Day Follow-Up.
\begin{tabular}{}
## S1 Fig. Average Changes in Patient-Reported Outcomes 30 Days After Discharge.
For non-PROMIS questionnaires, a positive change indicates improvement in health status. A positive change also signifies improvement in health status for the following PROMIS questionnaires: Global Physical Health, Global Mental Health, and Physical Function. Conversely, a negative change is indicative of improvement in health status for the following PROMIS questionnaires: Fatigue, Anxiety, Depression, Sleep Disturbance, and Social Isolation.
**S8 Table. Questionnaires Scores at Baseline, 90-Day Follow-Up, and 180-Day Follow-Up.** |
160028_file02 | ## 1 COVID-19 epidemiological model
### Model description
We introduced a compartmentalized epidemiological model that we named SEIRSD as it is based on the core elements found in the already known SEIRS models with four population classes: susceptible (S), exposed (E), infected (I), and recovered (R), to which we added a class counting the deceases (D). This model allows recovered cases to become susceptible after some finite time (duration of immune memory) that we denote as \(\tau\).
Our model incorporates several infected compartments to account for different known stages of the COVID-19 infection: asymptomatic (\(I_{A}\)), with mild symptoms (\(I_{M}\)), with severe symptoms that need hospitalization (\(I_{S}\)), with critical symptoms that require necessary access to an Intense Care Unit (ICU, \(I_{C}\)). Within each of the infected compartments, a fraction of the population \(f_{XY}\) worsens and consequently proceeds to the following infection level, while its reciprocal fraction \(1-f_{XY}\) recovers.
The transition between critical cases (\(I_{C}\)) and deaths depends strongly on ICU bed availability. To describe this, we calculate the number of ICUs that are occupied by critical cases as \(g(I_{C};ICU)=min(I_{C},ICU)\). All this means COVID-19's main departure from the SEIR archetype (aside from the existence of a contagious asymptomatic stage) is that there are two mortality rates. We discuss the parameters of the model in the next section (see also Table S1). We did not considered ICUs in the test bed to simplify because each country has a different number of ICUs, and because for realistic values of ICUs, \(<10\) per \(10^{5}\) inhabitants, they quickly become irrelevant during an active epidemic as the total number of infected population greatly surpasses that number.
\[\frac{\mathrm{d}S}{\mathrm{d}t}=-\frac{\beta}{N}S\sum_{i}I_{i}+ \frac{R}{\tau} \tag{1}\] \[\frac{\mathrm{d}E}{\mathrm{d}t}=\frac{\beta}{N}S\sum_{i}I_{i}- \frac{E}{\tau_{E}}\] \[\frac{\mathrm{d}I_{A}}{\mathrm{d}t}=\frac{E}{\tau_{E}}-\frac{I_{A }}{\tau_{A}}\] \[\frac{\mathrm{d}I_{M}}{\mathrm{d}t}=\frac{I_{A}}{\tau_{A}}-f_{MS} \frac{I_{M}}{\tau_{M}}-(1-f_{MS})\frac{I_{M}}{\tau_{MR}}\] \[\frac{\mathrm{d}I_{S}}{\mathrm{d}t}=f_{MS}\frac{I_{M}}{\tau_{M}}-f _{SC}\frac{I_{S}}{\tau_{S}}-(1-f_{SC})\frac{I_{S}}{\tau_{SR}}\] \[\frac{\mathrm{d}I_{C}}{\mathrm{d}t}=f_{SC}\frac{I_{S}}{\tau_{S}}- (1-f_{CD})\frac{g(I_{C};ICU)}{\tau_{CR}}-f_{CD}\frac{g(I_{C};ICU)}{\tau_{CD}^{ ICU}}-\frac{I_{C}-g(I_{C},ICUs)}{\tau_{CD}}\] \[\frac{\mathrm{d}R}{\mathrm{d}t}=(1-f_{MS})\frac{I_{M}}{\tau_{MR}} +(1-f_{SC})\frac{I_{S}}{\tau_{SR}}+(1-f_{CD})\frac{g(I_{C};ICU)}{\tau_{CR}}- \frac{R}{\tau}\] \[\frac{\mathrm{d}D}{\mathrm{d}t}=f_{CD}\frac{g(I_{C};ICU)}{\tau_{ CD}^{ICU}}+\frac{I_{C}-g(I_{C},ICUs)}{\tau_{CD}} \tag{8}\]
### Model parametrization
Model parameters necessarily came from very recent bibliography by scientific standards, often drawing from _preprint_ repositories and otherwise grey literature. However paper methodologies do seem sound and the sources are reliable. When possible, we drew information from meta studies rather than particular institutions or individual papers, e.g.,.
## There exist two mortality rates.
One of the key elements in most up-to-date models was the conditional mortality rate of patients that get critical symptoms, which depends on whether there are available beds in ICUs. When intensive care is required to keep someone alive, as in 6% of COVID-19 cases (this percentage will change with age distribution and hospital admission across populations), death will occur soon unless the patient in question can be provided with it. Thus, the mortality of COVID-19 will amount to roughly the same number of patients that reach a critical state if ICUs are swamped. If instead, there are ICU beds available, most casualties will be from patients that cannot defeat the disease even when mechanical ventilation, oxygen, dialysis, antibiotics, and other resources are an option. This mortality is far from 100%, and more than half the patients that enter the ICU with COVID-19 leave it recovered.
## Mortality in the ICUs.
Different values ranging from 8 to 50% have been reported ever since the pandemic started. Part of this variability could be linked to age distribution and hospital admission in the population considered. Some studies, like those done by the UK's Intensive Care National Audit Research Center, received a lot of attention and reported very high mortalities above 5 in every 10 patients. However, these and other studies suffered (to their credit often self-reportedly) of a statistical fallacy: the average time it takes COVID-19 patients to die in the ICU is lower than the time it takes them to recover to the point of not needing intensive care. So studies that follow a population for a fixed number of days rather than to the ultimate outcomes will overestimate mortality. Since we were using New York City (NYC) data, we prioritized information coming from similarly urban, western areas. With this in mind, we settled for \(f_{CD}=0.30\) as a reasonable mortality rate (tests with values up to 0.40 did not considerably affect our results).
## ICU occupancy times.
Different papers have listed different measures of centrality for the time that takes a critical COVID-19 patient to leave the ICU, \(\tau_{CD}^{ICU}\), ranging from 4 to 12 days, and for the time it takes them to be discharged should they recover, \(\tau_{CR}\), from 6 to 21 days. Here, as in the case of mortality, a plethora of reasons may be responsible for variability, with some of them being biases and artifacts. Some others may stem from genuine population differences owing to physiological, ethological, or political factors. There certainly seemed to be differences due to region of study, with Chinese, Italian, and otherwise western studies apparently forming three separate clusters. However, occupancy for deceased patients was usually lower than occupancy for recovered ones across studies. Taking all this into account, we settled for \(\tau_{CD}^{ICU}=7\) and \(\tau_{CR}=14\) days as reasonable estimates. With these, as with all other parameters, getting an actual reliable functional population average estimate may be impracticable. However, when choosing a value, we do so considering as much evidence as possible, the origin of our data series, and the sensibility of the model to noise in these parameters within arguably accurate ranges. By reasonable, we mean our selection is consistent with data, and they do not significantly favor nor compromise the accuracy of predictions or the estimation of immunity when compared to other values.
## Additional parameters.
The variability within reported ranges in additional parameters (namely, those about the timeline of disease progression and the times to transition from one variable to the next) was less relevant to the model's predictivity than that in ICU-related parameters. Medians and averages for the total time from contagion to the onset of symptoms change from 5 to 7 days, depending on the study, with the majority of the distribution being included between 2 and 14 days. The time from contagion to infectivity, or latency time \(\tau_{E}\), is given as 2 or 3 days in the literature. We thus used 2 days for and 4 days for the time \(\tau_{A}\) that it then takes to show symptoms (\(\tau_{E}+\tau_{A}=6\)). Chinese/WHO estimations for the remaining progression times and fractions such as the times \(\tau_{MR}\) that it takes for mild cases to recover, the time \(\tau_{MS}\) that it takes them to report tothe hospital and/or progress to a severe state or the fraction of total cases that are mild have remained relevant in the face of western epidemics.
### Equivalence with a \(\mathsf{SEIRS}\) model
To test the equivalence between our model and a minimal -\(\mathsf{SEIRS}\) model, we computed a set of "equivalent parameters" that would result in equal epidemic exponential growth rates \(\mu\). Starting from our COVID-19 model-specific parameters \(\vec{\theta}_{\text{COV-19}}=(\vec{\tau},\vec{f})\), we obtain \(\mu\) and the population distribution when \(E_{0}=1\) as a solution to the linearization of the ODE system.
\[\frac{\text{d}E}{\text{d}t} =\beta I-\gamma E \tag{9}\] \[\frac{\text{d}I}{\text{d}t} =\gamma E-\sigma I\] \[\frac{\text{d}R}{\text{d}t} =\sigma I. \tag{11}\]
to find the equivalent set of \(\mathsf{SEIRS}\) parameters \(\vec{\theta}_{\text{SEIRS}}=(\gamma,\sigma)\):
\[\gamma=\beta I_{0}/E_{0}-\mu,\text{ and }\sigma=\beta-\mu(1+E_{0}/I_{0}), \tag{12}\]
For example, the results are, in the case where the infection rates \(\beta_{\text{COV-19}}=\beta_{\text{SEIRS}}=1\), the total populations \(N_{\text{COV-19}}=N_{SEIRS}=10^{6}\), the immune memories \(\tau_{\text{COV-19}}=\tau_{\text{SEIRS}}=10^{10}\) and without ICU beds:
\[\lambda=0.479\;\;,\;\;I_{0}=0.979\;\;,\;\;\gamma=0.5\;\;\text{and}\;\;\sigma=0.032. \tag{13}\]We used numerical calculations because the analytical computation of \(\mu\) becomes intricate for complex models. Figure S1 displays the matching dynamics of a SEIRS and our COVID-19 model that yield the exact same initial epidemic dynamics. Observe that although the starting of the epidemic is equivalent, the dynamics at the end of the exponential regime are notably different for the infected and recovered classes.
### Computing \(R_{e}(t)\) with Next Generation Matrices
To obtain the characteristic reproductive numbers for our compartmentalized model, we computed the corresponding next generation matrices following. The transmission and transition matrices, \(T\) and \(\Sigma\), respectively, reads as:
\[T(t)=\frac{S(t)\beta(t)}{N}\begin{bmatrix}0&1&1&1&1\\ 0&0&0&0&0\\ 0&0&0&0&0\\ 0&0&0&0&0\\ 0&0&0&0&0\end{bmatrix}\text{ and }\Sigma=\begin{bmatrix}\frac{-1}{\tau_{E}}&0&0&0&0 \\ \frac{1}{\tau_{E}}&\frac{-1}{\tau_{A}}&0&0&0\\ 0&\frac{1}{\tau_{A}}&\frac{f_{MS}-1}{\tau_{MR}}-\frac{f_{MS}}{\tau_{M}}&0&0\\ 0&0&\frac{1}{\tau_{M}}&\frac{f_{SC}-1}{\tau_{SR}}-\frac{f_{SC}}{\tau_{S}}&0\\ 0&0&0&\frac{f_{SC}}{\tau_{S}}&\frac{-1}{\tau_{CD}}\end{bmatrix} \tag{14}\]
The time-dependent number of secondary infections \(R_{e}(t)\) is computed as the largest eigenvalue of the large-domain NGM matrix \(K_{L}(t)=T(t)\Sigma^{-1}\). Analytically:
\[R_{e}(t)=\frac{S(t)\beta(t)}{N}\left(\tau_{A}+\frac{\tau_{M}\tau_{MR}}{C_{1}}+ \frac{f_{MS}\tau_{MR}\tau_{S}\tau_{SR}}{C_{1}C_{2}}+\frac{f_{MS}f_{SC}\tau_{CD} ^{ICU}\tau_{CR}\tau_{MR}\tau_{SR}}{C_{1}C_{2}C_{3}}\right) \tag{15}\]
Observe that in the early dynamics, when \(S(t)/N\sim 1\) then \(R_{e}(t)\) is independent of \(\tau\). However, in the later dynamics the effect of \(\tau\) is reflected on the behaviour of \(S(t)\). Therefore, the immune memory \(\tau\) has no impact whatsoever in the linear regime of the ODE system, i.e., the initial dynamics of the epidemic.
### Parameter sensitivity of \(R_{e}(t)\)
We analyzed the sensitivity of \(R_{0}\) to every other model parameter with its analytical solution computed before (and the parameters as in Table S1). In Fig.S5 we show the local derivative of \(R_{0}\) around different values of \(\beta\). We find that \(R_{0}\) depends strongly on \(\beta\) in all situations. Surprisingly we also find that the fraction of mild cases that become severe, \(f_{MS}\), can be as relevant as \(\beta\) in reducing the number of secondary infections of a single individual. These results endorse the two main intervention measures most commonly found across regions: i) social distancing reduces the contact and infection rates, and consequently \(\beta\), and ii) expanding hospital resources reduces conceivably \(f_{MS}\), the fraction of mild cases that worsen.
## 2 Introduction to Ensemble Adjustment Kalman Filter algorithms.
### Motivation
Ensemble adjustment Kalman filter (EAKF) methods are a suite of well-known algorithms for data assimilation, first designed for linear models but also helpful for non-linear ones. Despite the many books and online resources, the use (and perhaps misuse) of technical jargon obscures its understanding at first. Our goal here is to present a brief introduction to the uninitiated. See, for instance, for more details and technical references.
### Bayes' theorem in data assimilation
The fundamental component of these methods is the "assimilation" of available data with the model prediction.
\[P(B|A)=\frac{P(A|B)P(B)}{P(A)}, \tag{16}\]
In our context, the posterior probability of a new observation B given a series of previous observations \(A\), i.e., \(P(B|A)\), is proportional to the product of the prior distribution \(P(A|B)\), and the likelihood, or marginal probability, of observation B \(P(B)\). Here \(P(A)\) is considered to be a normalization constant so that the total probability is equal to 1.
After a new data point is assimilated and we have computed the posterior probability, we can then consider it our initial state to assimilate the next data point, e.g., C,
\[P(C|A,B)=\frac{P(A,B|C)P(C)}{P(A,B)}. \tag{17}\]
We can then apply this iteratively to advance in space and/or time and improve our subsequent predictions. To ease the implementation of this approach, we may consider all probability distributions to be normal. In this way, if the prior and the likelihood are normal, the posterior is also normal and its mean and variance can be easily computed as is explained later.
### Algorithm components and definitions
These algorithms have the following minimal ingredients:
* State vectors \(\vec{x}(t)\). They describe the system state at a specific time and they are comprised of the state variables and the free parameters, which in these algorithms are necessarily time-dependent.
* The model \(\mathcal{M}\). The model allows to obtain the system state in the next time point: \(\vec{x}(t)=\mathcal{M}\vec{x}(t-1)\).
* An observable operator \(\mathcal{H}\). It turns a model state vector into an observable value: \(\vec{y}(t)=\mathcal{H}\vec{x}(t)\). This is because in some cases an observable is not directly a state variable, but rather a function of the state vector.
* Experimental measurements of the observable and their corresponding error: \(\mu_{\omega}(t)\) and \(\sigma_{\omega}(t)\).
* An initial guess for all variables and parameters. During the algorithm initialization, the j-eth variable of the i-eth ensemble member \(\vec{x}_{i,j}(t=0)\) is drawn from a random, normal distribution centered around the initial guesses. Although state vectors tend to converge across time, a reasonable initial guess improves the overall performance of the algorithms. Moreover, small variances in the initial distribution are likely to keep the protocol in its linear regime.
### Main algorithm
Once these ingredients are clear, and assuming that we have an observation every \(\Delta t=1\) time units, the algorithm goes as follows:
1. Initialization. Create an ensemble \(\epsilon\) of S members. Each member is a state vector with its values drawn from random normal distributions: \(\epsilon=\{\vec{x}_{i}(t=0)\}_{i=1,\ldots,S}\).
1. Integrate model. Integrate every ensemble member to obtain the prior ensemble state at the time of next data point \(\tilde{\epsilon}=\{\vec{\tilde{x}}_{i}(t=0)\}_{i=1,...,S}\).
2. Obtain the prior distribution of your observable. From every ensemble member, obtain your sample of prior observations \(\tilde{y}_{i}\) with \(i=1,...,S\). From the sample, compute its mean and variance \(\mu_{\tilde{y}}\) and \(\sigma_{\tilde{y}}\).
3. Compute posterior distribution of observations. Following Bayes' rule, compute \(\mu_{y}\) and \(\sigma_{y}\). See sections 2.5 and 2.6 for univariate and multivariate computation of the posterior.
4. Update the ensemble members. Compute the updated ensemble \(\epsilon\) by shifting \(\tilde{\epsilon}\) according to the posterior distribution of observations. See sections 2.5 and 2.6 for univariate and multivariate update rules.
5. For the assimilation of the next data point, start from pt.1 and consider \(\epsilon\) as your initial condition.
### Single observations
The case with a single vector of observations, and its errors, is the simplest and most geometrically accessible.
\[\sigma_{y}^{2}(t)=\frac{\sigma_{\tilde{y}}^{2}\sigma_{\omega}^{2}}{\sigma_{ \tilde{y}}^{2}+\sigma_{\omega}^{2}} \tag{18}\]
\[\mu_{y}=\frac{\sigma_{y}^{2}}{\sigma_{\tilde{y}}^{2}}\mu_{\tilde{y}}+\frac{ \sigma_{y}^{2}}{\sigma_{\omega}^{2}}\mu_{\omega} \tag{19}\]
The update formula for the j-eth observed variables in the i-eth ensemble member,
\[\vec{x}_{i,j}(t)=(\tilde{x}_{i}(t-1)-\mu_{\tilde{y}})\sqrt{\frac{\sigma_{y}^{ 2}}{\sigma_{\tilde{y}}^{2}}}+\mu_{y}, \tag{20}\]
And the update formula for the j-eth unobserved variable in the i-eth ensemble member is:
\[x_{i,j}(t)=\tilde{x}_{i,j}(t)+p_{1}(y-\tilde{y}), \tag{21}\]
### Multiple observations
When using multiple observations in a time point, we need to use multivariate normal distributions. The product \(\mathcal{N}_{3}(\vec{\mu}_{3},\Sigma_{3})\), of two probability density functions \(\mathcal{N}_{1}(\vec{\mu}_{1},\Sigma_{1})\) and \(\mathcal{N}_{2}(\vec{\mu}_{2},\Sigma_{2})\) can be computed from its individual parameters:
\[\Sigma_{3}=\Sigma_{1}s^{-1}\Sigma_{2} \tag{22}\]
\[\vec{\mu}_{3}=\Sigma_{2}s^{-1}\vec{\mu}_{1}+\Sigma_{1}s^{-1}\vec{\mu}_{2} \tag{23}\]
The update formula for the j-eth observed variable in the i-eth ensemble member is:
\[x_{i,j}=(y_{i,j}-\mu_{\tilde{y}_{j}})V_{1}D_{1}^{-1}D_{2}V_{2}^{-1}+\mu_{y_{j}}, \tag{24}\]where \(V_{x}\) and \(D_{x}\) are the diagonalization matrices of \(\Sigma_{x}\) such that \(\Sigma_{x}V_{x}=V_{x}D_{x}\).
An the formula for the j-eth unobserved variable in the i-eth ensemble member is:
\[x_{i,j}(t)=\tilde{x}_{i,j}(t)+\sum_{k=1}^{N}p_{k}(y_{k}-\tilde{y}_{k}), \tag{25}\]
### Single rank correlations
Perhaps, the linear least squares fit becomes a poor fitting method, apparent when there is a non-linear relationship between the prior parameter distribution and the prior observable distribution. We can then improve its performance with non-linear fits, but this would imply prior knowledge of the shape of this relationship. When this is not available, and the relationship is monotonic, we can resort to rank correlations. Briefly, we transform the j-eth state variable prior distribution \(\tilde{x}_{i,j}(t)\), and the prior and posterior observations \(\tilde{y}_{i}(t)\) and \(y_{i}(t)\), respectively, into their corresponding ranks \(\tilde{r}_{i,j}^{x}(t)\) and \(\tilde{r}_{i}^{y}(t)\). We perform the update in generalized continuous ranks, and then revert them into variable values. Here is an example code in matlab:
% Step 1. Compute ranks of a prior state variable and prior observable. rx = tiedrank(State_prior); ry = tiedrank(Obs_prior);
% Step 2. Compute generalized rank of the posterior observations ry_ = interp1(Obs_prior, ry, Obs_post,'linear','extrap');
% Step 3. Compute observation rank increments Dry = (ry_-ry);
% Step 4. Compute the regression between rank statistics fr = fit(rx,ry,'poly1');
% Step 5. Compute posterior state generalized rank rx_ = rx + fr.p1.*Dry;
% Step 6.
It is common to find that the bare algorithm itself tends to reduce the ensemble variance, and although this is desirable to some extent, when the ensemble members are almost identical to each other it may cause model divergence, which leads to assimilation problems. The most relevant to us was that since the prior distribution becomes extremely narrow compared to observational variance,i.e. \(\sigma_{\omega}^{2}\ll\sigma_{\tilde{y}}^{2}\), then equations 18 and 19 yield a posterior distribution essentially equal to the prior, in other words, observations are ignored.
\[x_{i,j}\leftarrow\sqrt{\lambda}(x_{i,j}-\langle x_{j}\rangle_{i})+\langle x_{j }\rangle_{i}, \tag{26}\]where \(\langle x_{j}\rangle_{i}=\sum_{i=1}^{S}x_{i,j}/S\) is the mean value of the j-eth variable across all ensemble members. Typical values for inflation are \(\lambda=1.02,1.05\) or even 1.10.
There is also the possibility of adding a time-dependent inflation that, for example depends on the distance between your likelihood and prior distributions.
# Figure S5. Parameter sensitivity of \(R_{0}\).
We computed the numerical value of the local partial derivative of \(R_{0}\) with respect to every other model parameter. We find that \(R_{0}\) strongly depends, in all cases, on \(\beta\). However it also depends strongly on \(f_{MS}\), the fraction of mild cases that worsen, which supports the importance of prevention, early detection of symptoms and palliative care measures. |
160317_file02 | ## Figure S4.
Age distribution of COVID-19 symptomatic cases, asymptomatic subjects as well as their close contacts. (A) Age and sex distribution of COVID-19 symptomatic cases. (B) Age distributions of travel related COVID-19 cases and locally acquired COVID-19 cases. (C) Age distributions of sporadic cases, index cases and successively transmitted cases in clusters. (D) Age distribution by clinical severity. (E) Age distribution of contacts. (F) Age distributions of COVID-19 cases by type of exposure.
Characteristics of clusters of COVID-19
Cluster size was defined as the total number of _COVID-19 symptomatic cases_ and
We characterized 123 clusters with clear evidence of human-to-human transmission, which includes 499 of the COVID-19 cases presented in Tab. S2. Cluster size distribution was bimodal, with most clusters were between 2 and 4 cases (94/123, corresponding to 76.4%). The largest cluster included 20 cases. The median cluster size was 3 (Tab. S2).
### Incubation period
We estimated the time from infection to symptom onset (i.e., the incubation period) based on information about the likely exposure of confirmed COVID-19 cases. Only cluster cases with confirmed human-to-human transmission and no travel history to Wuhan/Hubei were included for estimation. The rationale for this choice is that in multiple circumstances entire clusters took part in the same trip to/from Wuhan, thus preventing the unambiguous identification of the source of infection and transmission chain. Therefore, to provide more robust estimates and avoid multiplicity of biases, we have filtered those clusters. The exposure information was provided in the form of a time interval bounded by the dates of the first and last possible exposure. If the exposure start date of the case was missing or before that of the first infector, it was replaced by the exposure start date of the first infector. For the rest cases without dates of first exposure (17 individuals), they were imputed by the random numbers generated from a gamma distribution that best fitted the data of time intervals between the first and last exposure. As a sensitivity analysis, first exposure date of 7 individuals was imputed using the date when their infector came back to Hunan from Wuhan. Another sensitivity analysis was performed by excluding these 17 cases. We estimated the distribution of interval-censored exposure data by using maximum likelihood and compared three distributions (Weibull, gamma, and lognormal). The goodness of fit was assessed using Akaike information criterion (AIC). Results are presented in Tab. S3.
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
## Distribution** & **Parameters** & **Mean** & **Quantiles (0.025-0.975, days)** & **AIC** \\ & **[mean (SD)]** & **(days)** & **0.975, days)** & **782.6
\\ \hline
## Gamma
& shape = 2.08(0.21), rate = 0.33 (0.04) & 6.3 & 0.8 – 17.7 & 782.6 \\
## Weibull
& shape = 1.58 (0.09), scale=7.11(0.33) & 6.4 & 0.7 – 16.6 & 775.5 \\
## Lognormal
& meanlog = 1.57(0.06), sdlog = 0.82(0.04) & 6.7 & 1.0 – 23.9 & 839.7 \\
## Sensitivity analysisa
& & & & \\
## Gamma
& shape = 2.05(0.22), rate = 0.33 (0.04) & 6.2 & 0.7 – 17.4 & 751.3 \\
## Weibull
& shape = 1.57 (0.09), scale=6.95(0.33) & 6.3 & 0.6 – 16.3 & 744.4 \\
## lognormal
& meanlog = 1.55(0.06), sdlog = 0.83(0.04) & 6.6 & 0.9 – 23.6 & 806.7 \\
## Sensitivity analysisb
& & & & \\
## Gamma
& shape = 2.05 (0.22), rate = 0.33 (0.04) & 6.1 & 0.7 – 17.1 & 733.6 \\
## Weibull
& shape = 1.57 (0.09), scale=6.85(0.33) & 6.2 & 0.6 – 16.1 & 726.8 \\
## lognormal
& meanlog = 1.53(0.06), sdlog = 0.83(0.05) & 6.4 & 0.9 – 23.3 & 788.4 \\ \hline \hline \end{tabular}
* Sensitivity analysis performed based on 258 cases including 7 individuals for which the first exposure date was imputed using the date when their infector came back to Hunan from Wuhan.
* Sensitivity analysis performed based on 251 cases (i.e., excluding 17 individuals without first exposure date).
\end{table}
Table S3: Estimates of the incubation period based on the analysis of 114 clusters and 268 cases.
### Serial interval
We analyzed clusters of COVID-19 cases with known epidemiological links and no travel history to Wuhan/Hubei to estimate the interval between onset of symptoms in primary (index) cases and the onset of symptoms in secondary cases generated by these primary cases (i.e., the serial intervals). For cases with several possible infectors, a time interval bounded by the symptom-onset dates of the first and last possible infectors was provided as the symptom onset interval of primary cases. Using dates of symptom onsets for consecutive generations of cases within clusters, we fitted a gamma distribution with a shift parameter allowing negative serial intervals of interval-censored data by maximum likelihood to estimate the distribution of serial interval. The epidemic was further divided into two time periods (January 5 to January 23, and January 24 to April 2) by using the date of symptom onset relative to the date of level 1 emergency response activation in Hunan province (January 24). The overall and phased-in estimation of serial intervals are presented in main text and Tab. S4. Only the transmission pairs with a unanimously identified infector were used in this analysis.
### Infectiousness profile over time
Following the approach similar to He, et al, and accounting for the correction proposed byAshcroft, et al, the infectiousness profile (i.e., transmission probability from primary cases to a secondary case) was inferred using the serial intervals from confirmed transmission pairs combined with the incubation period distribution fitted in our analysis. Assuming that the infectiousness profile \(\beta_{c}(t_{I}-t_{SI})\) follows a gamma distribution with a time shift c to allow for start of infectiousness (\(t_{t}\)) c days prior to the date of symptom onset (_ts1_). The serial intervals distribution _f(tS2- tS1_) would be the convolution between the infectiousness profile and incubation period distribution g(_ts2- t1_), where _ts2_ is the date when secondary case shows symptoms. The parameter vector \(\theta\), which includes shape and scale of the gamma distribution and the time shift c, were estimated using maximum likelihood based on the convolution of serial interval and incubation period.
\[L(t_{S1u},t_{S1l},t_{S2}|\theta)=\int_{t_{S1l},}^{t_{S1u}}\int_{-\infty}^{t_{S 2}}\beta_{c}(t_{I}-t_{S1})g(t_{S2}-t_{I})d_{t_{I}}d_{t_{S1}}\]
The results of the estimation are presented in the main text.
#### Generation time
Generation time - that is the time interval between infection of the primary case (_t11_) and infection of the secondary cases (_t12_) generated by such primary case - was inferred using the data of incubation period combined with infectiousness profile estimated in our analysis. We considered that infected cases would show symptoms at certain time (_ts_) before or after onset of infectiousness. Assuming that the distribution of generation time follows a gamma distribution \(\varphi(t_{I2}\)- t1_), the observed distribution of incubation period \(g(t_{S}\)- t1_) can be inferred as the convolution between the infectiousness profile \(\beta_{c}(t_{I2}\)- tS) and the generation time distribution.
\[L(t_{E1},t_{E2},t_{S}|\alpha,\beta)=\int_{t_{E1}}^{t_{E2}}\int_{t_{I1}}^{+\infty }\varphi(t_{I2}-t_{I1})\beta_{c}(t_{I2}-\ t_{S})d_{t_{S}}d_{t_{I1}}\]
Shape parameter (\(\alpha\)) and rate parameter (\(\beta\)) of the gamma distribution of generation time were estimated using maximum likelihood method. The generation time was estimated to be 5.7 days (median: 5.5 days, interquartile range: 4.5, 6.7 days) based on a gamma distribution (shape=10.56, rate=1.85).
Other key time-to-event intervals
Other key time-to-event distributions were estimated by using maximum likelihood. In particular, we estimated: i) the time from symptom onset to the date of collection of the first sample for PCR testing and ii) the time from symptom onset to laboratory confirmation. Three distributions (Weibull, gamma, and lognormal) with shift parameters allowing negative intervals were fitted and compared. The goodness of fit was assessed using AIC.
As described above, the infectiousness profile peaked before the day of symptom onset. This may be driven by the control measures like isolation of infectors. We estimated the distribution of interval from symptom onset to the sampling date of first PCR and to laboratory confirmation to evaluate the timing of identification, isolation, and diagnosis of infectious individuals. Results are presented in the main text and Tab. S5 (where only the best fitting distribution is shown).
_Table S5. Estimates of other key time-to-event intervals_From the analysis of contact tracing records, we identified 8 clusters with evidence of asymptomatic transmission as shown in Fig. S5.
## Figure. S5.
Transmission chain in all the clusters showing evidence of asymptomatic SARS-CoV-2 transmission. Square symbols indicate symptomatic cases and circular symbols indicate asymptomatic subjects. Age, sex and generation in a cluster are shown for each SARS-CoV-2 infected individual (left panels), with information on date of diagnosis to the first RT-PCR positive for asymptomatic subjects. Timeline of events (right panels).
Total and mean number of infections by age of infector and of infectee
From 254 certain transmission pairs, we estimate the total (Fig. S6A) and mean (Fig. S6B) number of infections by age. These matrices are descriptive and do not account for confounding factors other than age. Therefore, they cannot be used to estimate susceptibility and infectivity by age group. For example, the lower mean number of infections generated by children (0-14 years old) with respect to adults is the joint effect of several factors. According to our regression analysis, one of these factors is the generation of infection. Infected individuals in generation one have much higher odds of transmitting the infection, probably due to the case isolation and quarantine of close contacts that increase with the generation. Coupled with the low proportion of children in the first generation as compared to adults (we remind that the schools were closed during the entire study period and close community management policies were in place), this may have contributed to lower number of infections generated by children. The summary tables by age and generation are reported in Tab. S6 and Tab. S7.
## Figure S6. Number of infections by age of infector and of infectee. Each cell in the matrices refers to the total number of infections (A) and the mean number of infections (B) caused by an infector of a given age.
## Table S6. Summary of contact tracing data by age of infectors and generation of transmission.
### Descriptive univariate analysis
To describe the correlations between the single factors and the probability of successful/unsuccessful transmission, we performed a univariate generalized linear model analysis. The results are presented in Tab. S8. It is important to note that this analysis does not account for the confounding effect of multiple factors and thus does not provide reliable estimates for the inference of the effect of the covariates and their statistical significance. For this reason, in the following section, we performed a multivariate analysis.
patters._
Quantifying the impact of potential drivers on the susceptibility and infectivity of We analyzed the odds ratio of SARS-CoV-2 transmission given the characteristics of the infectors and their contacts. To consider the clustering effect of an infector and a cluster, mixed effect logit models (i.e., generalized linear mixed-effect model, GLMM, for binary data with the logit link) were used to explore potential drivers of the susceptibility and infectivity of SARS-CoV-2 virus. The specifications of the GLMM models are defined as follows:
\[g(u_{i})=\alpha+\beta_{1}Age\_infector_{i}+\beta_{2}Age\_contact_{i}+\beta_{3} Contact\_type_{i}\]
\[\hskip 14.226378pt+\beta_{4}Generation\_infector_{i}+\beta_{5}Exposure\_level_{i}+ \beta_{6}Gender\_infector_{i}\]
\[\hskip 14.226378pt+\beta_{7}Gender\_contact_{i}+\beta_{8}Case\_type_{i}+\beta_{9} Observation\_period_{i}+u_{0}\]
\[\hskip 14.226378pt+u_{1}\]
Where:
* g is a logit link function;
* \(\alpha\) is the intersect
* \(Age\_infector_{i}\) is the fixed effects of the age group of the infector in the successful or unsuccessful transmission event \(i\);
* \(Age\_contact_{i}\) is the age group of the contact (potential infectee) in the successful/unsuccessful transmission event \(i\);
* \(Contact\_type_{i}\) is the type of contact occurred in the successful/unsuccessful transmission event \(i\);
* \(Generation\_infector_{i}\) is the generation of the successful/unsuccessful transmission event \(i\);
* \(Exposure\_level_{i}\) is the number of close contacts of the infector involved in the successful/unsuccessful transmission event \(i\);* _Gender_infector\({}_{i}\)_ is the gender of the infector in the successful/unsuccessful transmission event \(i\);
* _Gender_contact\({}_{i}\)_ is the gender of contact in the successful/unsuccessful transmission event \(i\);
* _Case_type\({}_{i}\)_ discriminates whether the infector involved in the successful/unsuccessful transmission event \(i\) is symptomatic or asymptomatic;
* _Observation_period\({}_{i}\)_ indicates the observation period for an infector/contact involved in the successful/unsuccessful transmission event \(i\);
* \({}_{0}\) and \({}_{1}\) are random effects attributed to an infector and a cluster, respectively. \({}_{i}=E[Y|(u_{0},u_{1})]\) is the mean of the response variable \(Y_{i}\) of a given value of the random effects.
The results of the multivariate analysis based on GLMM are presented in Table S9. The results for fixed effects, including 3 age groups for infector's and infectee's age, are presented in the Table S10 and Figure S8. To evaluate the disaggregated effects of age, we also used transformed (log) continuous age variables (i.e., age of infectors and contacts) (Tab. S11). The goodness-of-fit evaluation was based on the estimates provided in the Table S12. Model diagnostic measures and residuals plots (Fig. S7) were evaluated by DHARMa residual diagnostics for hierarchical models.
To further explore how the probability of SARS-COV-2 infections changes with a change in each covariate, the average marginal effects of age of infector and contacts, type of contact between infector and contact were estimated across all contacts, holding the effect of other covariate constant (Fig. S9).
\begin{tabular}{l c c c c} Step 2-3 & 3.01 & 1.74 & 1.06 & 1.03 \\ Step 2-4 & 2.94 & 1.71 & 1.01 & 1.00 \\ Step 2-5 & 2.94 & 1.71 & 1.01 & 1.00 \\ Step 2-6b & 2.85 & 1.69 & 1.08 & 1.04 \\ Step 2-7 & 2.78 & 1.67 & 0.97 & 0.98 \\ Step 2-8 & 2.78 & 1.67 & 0.97 & 0.98 \\ Step 2-9 & 2.94 & 1.71 & 1.01 & 1.00 \\ Step 2-6b & 2.85 & 1.69 & 1.08 & 1.04 \\ Step 2-7 & 2.78 & 1.67 & 0.97 & 0.98 \\ Step 2-9 & 2.78 & 1.67 & 0.97 & 0.98 \\ Step 2-10 & 2.94 & 1.71_Table S10. Stepwise regression analysis of factors associated with the probability of acquiring SARS-CoV-2 infections in generalized linear mixed models with categorized age of infections and contacts._
\begin{table}
\begin{tabular}{l c c c c c c c c c c c c c c} \hline \hline Characteristic & No of & \multicolumn{3}{c}{Sap 2-1} & \multicolumn{3}{c}{Sap 2-2} & \multicolumn{3}{c}{Sap 2-3} & \multicolumn{3}{c}{Sap 2-4} & \multicolumn{3}{c}{Sap 2-5} & \multicolumn{3}{c}{Sap 2-6a } & \multicolumn{3}{c}{Sap 2-7} \\ \cline{3-14} & const & OR (95/SC) & P-value OR (BP5/SC) & P-value OR (BP5/SC) & P-value OR (BP5/SC) & P-value OR (BP5/SC) & P-value OR (BP5/SC) & P-value OR (BP5/SC) & P-value OR (BP5/SC) & P-value \\ \hline Intercept & - & 0 & 0.01 & -0.001 & 0.01 & 0.19 & 0.001 & 0.02 & 0.20 & 0.22 & 0.21 & 0.02 & 0.02 & 0.02 & 0.02 & 0.003 & 0.02 & 0.21 & 0.002 \\ \hline Age of detection & & & & & & & & & & & & & & & & \\ Log-transformed age & 8,159 & 1.92 (0.98, 3.72) & 0.054 & 1.63 (0.87, 3.01) & 0.128 & 1.61 (0.90, 2.90) & 0.108 & 1.62 (0.91, 2.89) & 0.103 & 1.62 (0.91, 2.90) & 0.104 & 1.57 (0.87, 2.81) & 0.134 & 1.56 (0.88, 2.77) & 0.130 \\ Age of sources & & & & & & & & & & & & & & \\ Log-transformed age & 8,159 & 1.28 (1.04, 1.59) & 0.019 & 1.26 (1.01, 1.50) & 0.028 & 1.26 (1.02, 1.55) & 0.029 & 1.26 (1.02, 1.55) & 0.028 & 1.26 (1.02, 1.55) & 0.028 & 1.26 (1.02, 1.55) & 0.028 & 1.26 (1.02, 1.55) & 0.028 \\ \hline Type of content & & & & & & & & & & & & & & & \\ Household contacts & 1,021 & Reference & - & Reference & - & Reference & - & Reference & - & Reference & - & Reference & - & Reference & - \\ \hline \hline \end{tabular}
\end{table}
Table 31: Stepwise regression analysis of factors associated with the probability of acquiring SARS-CoV-2 infections in generalized linear mixed models with log-transformed age of infectors and contacts.
\begin{table}
\begin{tabular}{l c c c c c c} \hline \hline \multicolumn{1}{c}{Model} & AIC (\(\Delta\)AIC) & BIC & loglikelihood & deviance & \(\chi^{2}\) & P-valuea \\ \hline Step 1-1 & 1577.5 & 1647.6 & -778.8 & 1557.5 & - & - \\ Step 1-2 & 1541.9(35.6) & 1640.0 & -756.9 & 1513.9 & 43.612 & \textless{}0.001 & \\ Step 1-3 & 1539.5 (2.4) & 1644.6 & -754.7 & 1509.5 & 4.433 & 0.035 & \\ Step 1-4 & 1538.0 (1.5) & 1650.1 & -753.0 & 1506.0 & 3.456 & 0.063 & \\ Step 1-5b & 1540.0 (-2.0) & 1659.1 & -753.0 & 1506.0 & 0.014 & 0.907 & \\ Step 1-6 & 1541.4 (-1.4) & 1667.6 & -752.7 & 1505.4 & 0.553 & 0.457 & \\ Step 1-7 & 1542.2 (-0.8) & 1682.4 & -751.1 & 1502.2 & 3.187 & 0.203 & \\ Step 2-1 & 1579.1 & 1635.2 & -781.6 & 1563.1 & - & - \\ Step 2-2 & 1541.9 (37.2) & 1626.0 & -759.0 & 1517.9 & 45.188 & \textless{}0.001 & \\ Step 2-3 & 1539.9 (2.0) & 1631.0 & -757.0 & 1513.9 & 4.024 & 0.045 & \\ Step 2-4 & 1538.4 (1.5) & 1636.5 & -755.2 & 1510.4 & 3.529 & 0.060 & \\ Step 2-5c & 1540.4 (-2.0) & 1645.5 & -755.2 & 1510.4 & 0.001 & 0.974 & \\ Step 2-6 & 1542.0 (-1.6) & 1654.1 & -755.0 & 1510.0 & 0.410 & 0.522 & \\ Step 2-7 & 1543.0 (-1.0) & 1669.2 & -753.5 & 1507.0 & 2.932 & 0.231 & \\ \hline \hline \end{tabular}
\end{table}
Table S12: Assessing the fit of generalized linear mixed model with categorized age of infectors and contacts.
## Figure S7. DHARMa residual diagnostics for GLMM models. A: DHARMa residual diagnostics for model 1. B: DHARMa residual diagnostics for model 2.
## Figure S8.
Potential drivers of COVID-19 transmissions in Hunan Province, China. (A) The relative susceptibility of contacts who were younger than 15 years of age and of those who were older than 65 years of age (the reference group [red lines] was contacts who were 15-64 years of age); (B) The relative risk of SARS-CoV-2 infections among contacts with different type of exposures to an infector (the reference group [red lines] was contacts who were exposed to an infector in households); (C) The relative risk of SARS-CoV-2 infections among contacts with exposures to infectors with different generations of SARS-CoV-2 transmission (the reference group [red lines] was contacts who were exposed to an index case-patients); (D) The probability of SARS-CoV-2 infections at a given age of contacts in a specific setting.
## Figure S9.
The marginal effects of various covariates in GLMM model. The smoothed lines and shared areas represent the point estimates and 95% confidence interval for the probability of SARS-CoV-2 infections, respectively.
\begin{table}
\begin{tabular}{l c c c c c} \hline \hline \multirow{2}{*}{Characteristics} & \multirow{2}{*}{No.
## Parametric coefficients
& & & & & \\ \hline Intercept & - & 0.25 (0.12, 0.51) & \textless{}0.001 & 0.23 (0.11, 0.47) & \textless{}0.001 \\ Age of infectors & & & & & \\
0-14 y & 193 & 0.33 (0.06, 1.66) & 0.177 & - & - \\
15-64 y & 6,833 & Reference & - & - & - \\
65+ y & 1,133 & 0.60 (0.29, 1.23) & 0.166 & - & - \\ Age of contacts & & & & & \\
0-14 y & 936 & 0.62 (0.38, 1.01) & 0.055 & - & - \\
15-64 y & 6,411 & Reference & - & - & - \\
65+ y & 812 & 1.54 (0.99, 2.39) & 0.055 & - & - \\ Type of contact & & & & & \\ Household contacts & 1,021 & Reference & - & Reference & - \\ Relative contacts & 3,084 & 0.14 (0.09, 0.21) & \textless{}0.001 & 0.14 (0.09, 0.21) & \textless{}0.001 \\ Social contacts & 2,227 & 0.09 (0.05, 0.15) & \textless{}0.001 & 0.08 (0.05, 0.14) & \textless{}0.001 \\ Other contacts & 1,827 & 0.10 (0.06, 0.17) & \textless{}0.001 & 0.10 (0.06, 0.17) & \textless{}0.001 \\ Generation of SARS-CoV-2 transmission & & & & & \\ G1 & 2,121 & Reference & - & Reference & - \\ G2 & 2,987 & 0.27 (0.15, 0.48) & \textless{}0.001 & 0.27 (0.15, 0.48) & \textless{}0.001 \\ G3-4 & 965 & 0.17 (0.08, 0.38) & \textless{}0.001 & 0.18 (0.08, 0.40) & \textless{}0.001 \\ Multiple exposureb & 598 & 0.26 (0.10, 0.70) & 0.007 & 0.28 (0.10, 0.75) & 0.011 \\ Unknown & 1,488 & 0.07 (0.03, 0.18) & \textless{}0.001 & 0.08 (0.03, 0.20) & \textless{}0.001 \\ \hline Gender of infectors & & & & & \\ Female & 4,067 & Reference & - & Reference & - \\ Male & 4,092 & 1.62 (1.02, 2.57) & 0.041 & 1.65 (1.04, 2.62) & 0.035 \\ Gender of contacts & & & & & \\ Female & 4,017 & Reference & - & Reference & - \\ \hline \hline \end{tabular}
\end{table}
Table 3: Stepwise regression analysis of factors associated with the probability of acquiring SARS-CoV-2 infections in generalized additive mixed models with splines for age of infectors and contacts, as well as number of contacts.
## Figure S10
GAMM-predicted non-linear 3-knot splines for age of infector, age of contacts, and the number of contacts. A. model 4-1; B to D. model 4-2. The shaded area delimits the 95% confidence intervals of the spline functions._
References
1. National Health Commission of the People's Republic of China. Diagnosis and treatment guideline on pneumonia infection with 2019 novel coronavirus (6th trial edn). 2020.
2. He X, Lau EHY, Wu P, et al. Temporal dynamics in viral shedding and transmissibility of COVID-19. _Nat Med_ 2020; **26**: 672-5.
3. Ashcroft P, Huisman JS, Lehtinen S, et al. COVID-19 infectivity pro1e correction. _ArXiv e-prints_ 2020.
4. Florian Hartig. DHARMa: Residual Diagnostics for Hierarchical (Multi-Level / Mixed) Regression Models. 2016. |
165092_file02 | ###### Abstract
Figure S1 **[Models' extraction flow. Scheme of the models' exploration and evaluation process. We use a fivefold CV with two hundred iterations of random hyperparameters (HP) selection process for each of the features groups. We then select the top-scored HP for each feature's group and Train a new model based on the train set and measure the auROC using the validation set. Out of the models validated, we chose the models that comply with objectives of minimal features and high performance. The reported results are of the held-out test set.**
## Figure S2 | Stratified populations according to HbA1c% - models comparison.****A)
Although the five-blood-tests model achieves more accurate scores than the anthropometric model in both populations, the anthropometry model's results approach the five blood tests model in the normoglycemic group. Both models outperform the FINDRISC and GDRS models.
## B) Comparison of model's APS within the HbA1c% stratified groups.** Left Y-axis indicates the APS of the models' in the prediabetics group, the right Y-axis indicates APS in the normoglycemic group, we see again that the order of model's predictability remains Five blood tests; Anthropometry; FINDRISC and lastly the GDRS model. **C)** A summary table for the various models AuROC, Average-Precision and deciles risk fold scores for the HbA1c% stratified subpopulations. **D)** A feature importance comparison of the Anthropometric model within the HBbA1c% stratified groups. showing a stronger impact of WHR and BMI in the normoglycemic group and a stronger negative impact of the bias - indicating the higher prevalence in the pre-diabetic group. **E)
A feature importance comparison of the five-blood-tests model within the HBbA1c% stratified groups. showing a stronger negative impact of HDL cholesterol in the normoglycemic group and a stronger negative impact of the bias - indicating the lower prevalence in the normoglycemic group.
Comparing the five blood tests model's features importance, the features importance values do not vary much. The main differences are the stronger negative impact of HDL cholesterol on the prediction results and the trivial bias term, which indicates the lower prevalence in the normoglycemic group (Figure S2 E).
Exploring the full features' space using gradient boosted decision trees.
To select features for our simple models, we analysed the features' importance of features that we sought of having some relation to T2D. We analyse what is the power of a predictive model with a vast amount of information, to compare it to our minimal features models.
We started by sorting out a list of 279 covariates from the first visit to the UKB assessment centre to be used as our preliminary features. On top of these features, we used the UKB single-nucleotide polymorphisms (SNPs) genotyping data and their calculated PRS.
We inspected the impact of various features' groups, using the lightGBM gradient decision trees model using SHAP (See methods). We aggregated the features into thirteen seperate groups: age and sex; genetics; early life factors; sociodemographics; mental health; blood pressure and heart rate; family and ethnicity; medication; diet; lifestyle and physical activity; physical health; anthropometry; blood tests. All of these groups included age and sex.
We also tested the impact of HbA1c% with sge and dex; genetics without age and Sex (Table S1). The top five predictive GBDT models, according to their auROC, APS, and decile folds, in descending order are: the "All features" model with auROC 0.9 (0.88-0.92 95%CI), APS of 0.28 (0.22-0.35 95% CI) and a deciles' OR of x65; The "full-blood-tests" model with auROC 0.89 (0.86-0.9), APS 0.25 (0.2-0.31), and deciles' OR x62; The "five blood tests" model with auROC 0.87(0.85-0.89), APS 0.21 (0.17-0.27) and deciles' OR of x59; the HbA1c% based model with auROC 0.81 (0.78-0.84), APS 0.18 (0.13-0.23) and deciles' OR of x32; and the anthropometry model with auROC 0.76 (0.73-0.79), APS 0.07 (0.06-0.1) and deciles' OR x30 (Table 1S).
To explore the heritability impact on the predictability of the models, we used two main features groups. One is a broad sense heritability based on SNPs and PRSs, and the other one is heritability which includes family and ethnicity. Adding the SNPs and PRSs data to the age and sex group, elevated the APS and auROC from 0.03 (0.02-0.04), 0.58 (0.54-0.62) to 0.04 (0.03-0.05) and 0.61 (0.57-0.65) respectively.
Adding this DNA array data to all other features together did not provide a considerable contribution to prediction. Using the family and ethnicity features with age and sex provides an APS of 0.04 (0.03-0.05),auROC of 0.63(0.58-0.67), and deciles' OR of x5.4 (Table S1), considerably lower than other features' groups such as the anthropometry group with auROC 0.76(0.73-0.79) and deciles' OR of x30 and from the lifestyle and physical activity group, scoring auROC of 0.69 (0.65-0.72) and deciles' OR of x16.
Another interesting result is a lifestyle and physical activity model, which includes ninety-eight features related to: physical activity; addictions; alcohol, smoking and cannabis use; electronic device use; employment; sexual factors; sleeping; social support and sun exposure. This model achieves an auROC of 0.69 (0.65-0.72) and deciles' OR of x16, and it provides better prediction scores than the diet features' group. This model includes thirty-two diet features from the UKB touchscreen questionnaire on the reported frequency of type and intake of a range of common food and drink items. The diet based model achieved auROC of 0.64 (0.6-0.67) and deciles' OR of x6 (Table S1).
We then examined the additive contribution of each predictive group to the total predictive power of the "all features" model (Figure S4-A).
\begin{table}
\begin{tabular}{l c c c} \hline & **Label** & **APS** & **AUROC** & **Deciles fold** \\ \hline \hline
## All
& 0.28 (0.22–0.35) & 0.90 (0.88-0.92) & 65.48 \\
## Blood Tests
& 0.25 (0.20–0.31) & 0.89 (0.86–0.90) & 62.18 \\
## Five blood tests
& 0.21 (0.17-0.27) & 0.87 (0.85-0.89) & 59.30 \\
## HbA1c\%
& 0.18 (0.13–0.23) & 0.81 (0.78-0.84) & 31.60 \\
## Anthropometry
& 0.07 (0.06–0.10) & 0.76 (0.73-0.79) & 29.84 \\
## Physical health
& 0.05 (0.04–0.07) & 0.69 (0.65-0.73) & 15.44 (5.-29) \\
## Lifestyle and physical activity
& 0.05 (0.04-0.07) & 0.69 (0.65-0.72) & 16.40 (6.-29) \\
## Diet
& 0.04 (0.03–0.05) & 0.64 (0.60-0.67) & 6.03 (2.-17) \\
## Medication
& 0.04 (0.03-0.05) & 0.63 (0.59-0.67) & 5.60 (2.-14) \\
## Family and Ethnicity
& 0.04 (0.03-0.05) & 0.63 (0.58-0.67) & 5.35 (2.-14) \\
## BP and HR
& 0.04 (0.03-0.05) & 0.62 (0.58-0.66) & 8.54 (3.-20) \\
## Mental health
& 0.04 (0.03-0.05) & 0.62 (0.57-0.66) & 6.12 (2.-17) \\
## Socio demographics
& 0.04 (0.03-0.05) & 0.61 (0.57-0.65) & 5.19 (2.-15) \\
## Genetics Age and Sex
& 0.04 (0.03–0.05) & 0.61 (0.57-0.65) & 5.31(2.-13) \\
## Early Life Factors
& 0.03 (0.02-0.04) & 0.58 (0.54-0.62) & 2.57 (1.1-5.9) \\
## Age and Sex
& 0.03 (0.02-0.04) & 0.58 (0.54-0.62) & 2.16 (0.9-4.4) \\
## Only genetics
& 0.03 (0.02-0.04) & 0.56 (0.52-0.60) & 2.50 (1.1-5.5) \\ \hline \end{tabular}
\end{table}
Table S1:Predicting using features domain groups, Results table of GBDT models for various features domains. The logistic regression models provided better results than the GBDT models for the blood tests and anthropometrics based models.
We conclude that using the five-blood-test model substantially increase the prediction results when compared to a model based only on HbA1c% with age, and sex.
The auROC, APS and deciles' OR increases from 0.81(0.78-0.84), 0.18(0.13-0.23) and x32 to 0.87(0.85-0.89), 0.21(0.17-0.27) and x59 respectively.
When we use the full blood tests model, the performance slightly increases to auROC, APS, and deciles' OR of 0.89(0.86-0.9), 0.25(0.2-0.31), and x62 respectively. We did not identify any major increase in results adding any other specific group to this list, suggesting that most of the predictive power of our models are captured by the blood test features or has collinearity with it. Using all features together provided an increase of performance to auROC, APS, and the deciles' OR of 0.9(0.88-0.92), 0.28(0.22-0.35), and x65 respectively (Figure S4 A-B).
To get some insights for the features that drive the T2D prediction, we built an additional model using all features excluding the HbA1c% and non-fasting glucose, as these features are highly predictive and might screen out other clinically interesting covariates. The auROC, APS, and the deciles' prevalence OR results that we achieved using this model are 0.13 (0.1-0.16), 0.84 (0.82-0.86), and x49, respectively.
To gain understanding into the features that contribute the most to the GBDT model predictions, we used the SHAP package feature importance framework. SHAP uses Shapley values, which are essentially the average marginal contribution of a feature over all possible combinations (see methods).
The top ten important features include Gamma-glutamyl-transferase (GGT) (1st in the list), and Alanine-aminotransferase (ALT) (9th in the list), positively related to T2D onset prediction; high levels of these enzymes usually signal for liver damage, which might occur from fatty liver. Increased values of waist circumference (2nd), body mass index (BMI) (3rd), and weight (10th) are all in the ten leading predictors for T2D in this model. Sex hormone-binding globulin (SHBG) (4th), which is a protein produced by the liver and transports sex hormones blood, is also related to a decreased probability of developing T2D in our model. This result aligns with research showing that raised SHBG levels reduce the risk of T2D. High levels of triglycerides (5th), which is long known to precede T2D, also drive the prediction of developing T2D in this model. High levels of HDL (8th) cholesterol reduce the probability of developing T2D in this model, which aligns with the literature findings regarding correlations; although, a genetic mendelian randomization study found it as correlated but non-causal for T2D
Having no vascular or heart problems diagnosed reduces the probability of developing T2D. According to the National Health Interview Survey (NHIS) published in 1989, 14% of the diabetic population at the ages 45-64, also reported having ischemic heart disease, and both conditions are known to be related to the metabolic syndrome. The time between visits, i.e., time from taking the features measurements to time of prediction is also in the top ten list, which implies that the cumulative probability of developing T2D increases over time.
Two features that are absent from this list are age and sex. While SHBG might confound sex - age seems to be irrelevant once we provide a model with the blood test results as features, and probably reflect a T2D "biological age" of the participant(Figure S4-C)
## Figure S4 \(|\) Summary of Incremental feature's model: A. Comparison table of APS, auROC, and deciles' OR metrics for GBDT models, where each model is embedding the preceding model's features plus additional features domain. The largest increase in prediction is upon adding the HbA1C% feature, which is also a biomarker of T2D diagnosis. Adding the DNA sequencing data did not contribute much to the prediction power of the model. B. Deciles-prevalence-fold-ratio (DFPR) graph. The five blood tests model considerably outperforms the HbA1C% model. C. Shapley values feature's importance of the "All features without HbA1c% nor glucose" GBDT model. Removal of the HbA1c% and non-fasting glucose enables other major contributors to T2D prediction to be seen having an impact on T2D prediction.
|
166215_file02 | ## Supplementary Figure S2. Supervised beego maintains hemostasis capacity. a-d.** Coagulation tests. Clotting dynamics was measured at five time points (wFD1, wFD4, wFD7, wFD14 and rFD7). The tests include activated partial thromboplastin time (APTT, male=2, female=3), prothrombin time (PT, male=2, female=3), internal normalized ratio (INR, male=2, female=3), thrombin time (TT, male=2, female=3). **e-g.** Plasma levels of hemostatic biomarkers. The levels of critical proteins in hemostasis were measured at five time points as indicated. The tests include Antithrombin III (AT III, male=2, female=3); fibrinogen (FIB, male=2, female=3); Ca2+ in plasma, male=3, female=4). Data are means +- SEM. *P < 0.05; **P < 0.01; *
< 0.001. *significant compared to the wFD1 (7:00 am) right before fasting starts.
## Supplementary Figure S3. Supervised beego improves cardiovascular physiology. a-d.** Violin plots of vascular health measured with mobil-O-Graph PWA and analyzed by repeat measurement analysis and multiple comparison. Measurements include peripheral resistance (male=3, female=3), reflection coefficient (male=3, female=3), augumentation index(Ala, male=3, female=3), pulse wave velocity (PWV, male=3, female=3). **e-g.
Violin plots of cardiac health measured with mobil-O-Graph PWA. Measurements include stroke volume (male=3, female=3), cardiac output (male=3, female=3) and cardiac index (male=3, female=3). Data are means \(\pm\) SEM. *_P_ < 0.05; **_P_ < 0.01; ***_P_ < 0.001. *significant compared to the wFD1 (7:00 am) right before fasting starts.
## Supplementary Figure S4. Supervised beego reduces platelet counts but retains platelet function.****a.** Platelet (PLT) count in PLT normal (male=3, female=3) or low groups (female=1). **b-d.** Platelet hematocrit (PCT, male=3, female=3), Mean platelet volume (MPV, male=3, female=3), Platelet distribution width (PDW, male=3, female=3). **e.** Platelet aggregation test. The platelet aggregation after stimulation was tested at the days as indicated. male=3, female=4). **f.** ELISA measurement of P-selectin level in plasma, male=3, female=4). **g-j.** Flow cytometric measurement of platelet biology at the time points indicated. Total reactive oxygen species (ROS) levels in platelets (male=3, female=4); \(\Delta\)**U**m depolarization of mitochondria (JC-1, male=3, female=4); Percentage of Annexin V positive platelets (male=3, female=4). **j.
ELISA measurement of Thrombopoietin (TPO) level in plasma, male=3, female=4). Data are means \(\pm\) SEM. *_P_ < 0.05; ***_P_ < 0.01; ***_P_ < 0.001. *significant compared to the wFD (7:00 am) right before fasting starts.
### Refeeding Protocol
Following the water-only fasting, subjects refeed for a period of time lasting no less of half of the fasting length. We specified a specific diet and eating protocol for each of 7 refeeding days. Note that ingredient availability and typical kitchen implements are quite homogenous for most Chinese households, and counselors worked with the participants to customize serving sizes.
-Refeeding day 1 and 2:
Morning, midday, and evening: prepare a rice soup cooked with a small amount of millet by boiling the rice thoroughly with water. Only the liquid soup should be consumed (i.e., do not eat rice grains, consume no more than half a bowl of this soup at a given feeding session, but feel free to consume this soup as many as 6 or 7 times on day 1 and day 2. If it is inconvenient for you at workplace or office, you may use baby rice noodles instead. The baby rice noodles should be with millet original flavor for zero stage baby use. Don't eat too much, and do it step by step.
-Refeeding day3:
You may take vegetable soup (except spinach). For preparation the soup, wash and chop the vegetables, add water and boil; do not add oil, salt or any other seasoning. Take less veg and more soup, about half a bowl each. You may also buy baby rice noodles and eat them between meals. The baby rice noodles should be with millet original flavor for zero stage baby use. Don't eat too much, and do it step by step.
-Refeeding day 4:
You may have gruel in the morning and noodles with fresh tender vegetable leaves in the noon and evening. Make sure to boil them thoroughly. A small amount of oil and salt, but not other seasonings, may be added to the noodle. Must be tiny oil and salt, and noodles must be cooked soft. Never eat too much.
-Refeeding day 5:
For breakfast, you may have gruel or boiled noodles, with small amount of oil and salt ; you may eat boiled eggs, but only eat egg yolk. For noon meal, you may eat a small amount of rice, and rice should be soft, and eat fried green vegetables with less oil and salt. it is best to drink gruel in the evening. On the fifth day of reacting, you may add an appropriate amount of fruits, such as pears, watermelons and other fruits with more water. Don't eat too much.
-Refeeding day 6:
For breakfast, you may eat rice porridge or noodles, and boiled eggs, but only eat egg yolk. For noon and evening meal, you may eat rice (should be well done cooked) and fried green vegetables and fried tofu with less oil and salt. It is necessary to control the amount of food you take, chew food thoroughly and swallow slowly when eating. Do not drink tea and alcohol in the refeeding period.
-Refeeding day 7:
You may eat almost normally, but do not eat fried, spicy and meat food, step by step, so that your intestines and stomach can gradually return to normal function.
## Supplementary Table S1
\begin{tabular}{c c c c c c c c c c} \hline & & & & & Mean [SEM] & & & & Adjusted \(P\)-value vs wFD1 \\ \hline Index & Gender & wFD1 & wFD4 & wFD7 & rFD7 & wFD4 & wFD7 & rFD7 \\ \hline TG (mmol/L) & & & & & & & & & \\ \multicolumn{1}{c}{Normal} & & & & & & & & & \\ & & M, n=6 & 1.172[0.164] & 1.538[0.169] & 1.417[0.151] & 1.333[0.070] & & & & \\ & & F, n=16 & 0.959[0.074] & 1.458[0.116] & 1.352[0.122] & 1.133[0.070] & & & & \\ & & High & & & & & & & \\ & & M, n=4 & 2.788[0.535] & 2.003[0.150] & 1.713[0.142] & 1.280[0.245] & & & & \\ & & F, n=3 & 2.027[0.230] & 1.323[0.139] & 1.283[0.089] & 1.363[0.055] & & & & \\ \hline TC (mmol/L) & & & & & & & & & \\ & & M, n=5 & 4.408[0.243] & 5.454[0.364] & 6.046[0.528] & 4.266[0.126] & & & & \\ & & F, n=12 & 4.201[0.117] & 5.062[0.165] & 5.608[0.217] & 3.918[0.151] & & & & \\ & & High & & & & & & & \\ & & M, n=5 & 6.476[0.332] & 7.658[0.289] & 8.580[0.528] & 6.222[0.588] & & & & \\ & & F, n=7 & 5.697[0.131] & 7.210[0.313] & 7.647[0.261] & 5.197[0.195] & & & & \\ \hline LDL-C (mmol/L) & & & & & & & & & \\ & & Normal & & & & & & & \\ & & M, n=5 & 2.752[0.147] & 3.650[0.316] & 4.510[0.470] & 2.690[0.169] & & & & \\ & & F, n=13 & 2.322[0.141] & 3.002[0.175] & 3.766[0.221] & 2.325[0.195] & & & & \\ & & High & & & & & & & \\ & & M, n=5 & 4.244[0.367] & 5.718[0.270] & 6.946[0.525] & 4.728[0.558] & & & & \\ & & F, n=6 & 3.750[0.087] & 5.025[0.345] & 5.700[0.290] & 3.465[0.182] & & & & \\ \hline HDL-C (mmol/L) & & & & & & & & & \\ & & Normal & & & & & & & \\ & & M, n=7 & 1.183[0.063] & 1.143[0.067] & 0.931[0.057] & 0.994[0.077] & & & & \\ & & F, n=10 & 1.278[0.050] & 1.387[0.056] & 1.240[0.045] & 1.083[0.055] & & & & \\ & & Low & & & & & & & \\ & & M, n=4 & 0.938[0.033] & 0.973[0.048] & 0.793[0.067] & 0.838[0.060] & & & & \\ & & F, n=1 & 1.010[0.000] & 1.550[0.000] & 1.450[0.000] & 1.030[0.000] & & & & \\ \hline \end{tabular}
\begin{tabular}{c c c c c c c c} \hline \hline APTT (second) & & & & & & & \\ & M, n=11 & 31.555[0.644] & 30.700[1.090] & 29.027[0.806] & 30.382[1.036] & & \\ & F, n=17 & 30.400[0.719] & 29.129[0.757] & 28.124[0.770] & 29.182[0.751] & \(P\)=0.529 & \(P\)=0.282 & \(P\)=0.529 \\ \hline PT (second) & & & & & & \\ & M, n=11 & 10.500[0.148] & 10.670[0.159] & 11.327[0.175] & 10.691[0.212] & \(P\)=0.841 & \(P\)=0.015 & \(P\)=0.841 \\ & F, n=17 & 10.319[0.147] & 10.876[0.176] & 11.253[0.160] & 10.312[0.126] & \(P\)=0.0525 & P\({}_{}\)=0.0001 & \(P\)=1.0000 \\ \hline INR (ratio value) & & & & & & \\ & M, n=11 & 0.905[0.013] & 0.922[0.013] & 0.977[0.015] & 0.923[0.018] & \(P\)=0.787 & \(P\)=0.012 & \(P\)=0.787 \\ & F, n=17 & 0.889[0.013] & 0.938[0.015] & 0.970[0.014] & 0.889[0.011] & \(P\)=0.0495 & P\({}_{}\)=0.0001 & \(P\)=1.0000 \\ \hline TT (second) & & & & & & & \\ & M, n=11 & 18.300[0.350] & 17.660[0.246] & 17.918[0.233] & 18.382[0.308] & & \\ & F, n=17 & 17.963[0.168] & 17.676[0.098] & 18.065[0.107] & 18.324[0.243] & & \\ \hline AT III (\%) & & & & & & \\ & M, n=11 & 97.982[2.319] & 99.900[1.615] & 97.527[1.493] & 100.891[0.906] & & \\ & F, n=17 & 103.375[2.000] & 97.965[1.551] & 94.835[0.780] & 96.953[1.137] & \(P\)=0.0260 & P\({}_{}\)=0.0001 & \(P\)=0.0105 \\ \hline FIB (g/L) & & & & & & & \\ & M, n=11 & 2.505[0.265] & 3.114[0.275] & 2.895[0.158] & 2.454[0.128] & \(P\)=0.3960 & \(P\)=0.6405 & \(P\)=0.9960 \\ & F, n=17 & 2.458[0.099] & 2.968[0.143] & 2.645[0.121] & 2.252[0.104] & \(P\)=0.03 & \(P\)=0.55 & \(P\)=0.55 \\ \hline Ca\({}^{2+}\) (mmol/L) & & & & & & & \\ & M, n=11 & 2.364[0.028] & 2.429[0.025] & 2.446[0.021] & 2.337[0.042] & \(P\)=0.450 & \(P\)=0.435 & \(P\)=0.870 \\ & F, n=20 & 2.320[0.019] & 2.360[0.021] & 2.384[0.026] & 2.341[0.035] & & \\ \hline Peripheral resistance (s\({}^{*}\)mmHg/mL) & & & & & & & \\ & M, n=10 & 1.323[0.059] & 1.248[0.032] & 1.241[0.038] & 1.241[0.070] & & \\ & F, n=18 & 1.219[0.051] & 1.237[0.038] & 1.310[0.026] & 1.099[0.060] & \(P\)=1.0000 & \(P\)=0.8445 & \(P\)=0.8445 \\ \hline Reflection coefficient (\%) & & & & & & & \\ & M, n=10 & 66.200[2.043] & 65.400[1.240] & 61.200[2.313] & 56.444[1.582] & \(P\)=0.980 & \(P\)=0.2265 & \(P\)=0.0060 \\ & F, n=18 & 63.333[1.499] & 63.500[1.781] & 60.833[2.054] & 61.294[2.480] & & \\ \hline Alx (\%) & & & & & & \\ & M, n=10 & 21.300[3.134] & 25.400[2.247] & 25.400[1.996] & 11.889[3.545] & \(P\)=0.588 & \(P\)=0.588 & \(P\)=0.180 \\ & F, n=18 & 21.222[2.285] & 29.667[2.623] & 31.667[2.752] & 17.059[2.833] & \(P\)=0.099 & \(P\)=0.051 & \(P\)=0.550 \\ \hline PWV (m/s) & & & & & & & \\ & M, n=10 & 6.320[0.318] & 6.310[0.360] & 6.070[0.361] & 6.244[0.364] & & \\ \hline \hline \end{tabular}
\begin{tabular}{c c c c c c c c} \multicolumn{2}{c}{Low} & & & & & & & \\ & F, n=5 & 61.111[11.205] & 122.444[29.375] & 109.333[27.872] & 92.222[25.196] & & & \\ \hline PCT (\%) & & M, n=11 & 0.146[0.009] & 0.103[0.007] & 0.122[0.014] & 0.090[0.010] & \(P\)=0.0255 & \(P\)=0.2610 & \(P\)=0.0060 \\ & F, n=20 & 0.135[0.012] & 0.128[0.010] & 0.116[0.009] & 0.093[0.008] & \(P\)=0.9250 & \(P\)=0.6195 & \(P\)=0.0360 \\ \hline MPV (IL) & & & & & & & \\ & M, n=11 & 9.355[0.142] & 9.782[0.165] & 9.455[0.122] & 9.745[0.167] & & & \\ & F, n=20 & 9.560[0.192] & 9.750[0.151] & 9.600[0.167] & 10.026[0.211] & \(P\)=0.997 & \(P\)=0.997 & \(P\)=0.540 \\ \hline PDW (\%) & & & & & & & \\ & M, n=11 & 45.955[1.017] & 50.891[1.529] & 49.809[1.753] & 52.236[1.030] & \(P\)=0.0585 & \(P\)=0.1320 & \(P\)=0.0210 \\ & F, n=20 & 45.770[1.669] & 48.325[1.074] & 50.735[1.221] & 51.337[1.505] & \(P\)=0.419 & \(P\)=0.051 & \(P\)=0.051 \\ \hline Aggregation (\%) & & & & & & & \\ & M, n=11 & 70.600[4.966] & 64.444[6.594] & 81.800[5.825] & 67.143[7.732] & & & \\ & F, n=20 & 74.200[9.332] & 75.533[5.012] & 87.722[2.843] & 70.154[5.938] & & & \\ \hline P-selectin (ng/mL) & & & & & & & \\ & M, n=11 & 12.341[0.634] & 10.454[0.678] & 9.199[0.558] & 9.185[0.538] & \(P\)=0.084 & \(P\)=0.003 & \(P\)=0.003 \\ & F, n=19 & 11.359[0.418] & 10.699[0.458] & 9.749[0.430] & 9.574[0.479] & \(P\)=0.5950 & \(P\)=0.0525 & \(P\)=0.0510 \\ \hline ROS (MFI) & & & & & & & \\ & M, n=5 & 18.290[1.466] & 12.236[0.952] & 10.034[1.311] & 8.518[0.668] & \(P\)=0.0070 & \(P\)=0.0015 & \(P\)<0.0001 \\ & F, n=5 & 17.092[0.658] & 14.894[0.962] & 7.378[1.087] & 8.684[0.327] & \(P\)=0.175 & \(P\)<0.0001 & \(P\)<0.0001 \\ \hline JC-1 (\%) & & & & & & & \\ & M, n=5 & 57.097[1.911] & 17.996[3.308] & 21.794[3.116] & 28.378[5.076] & \(P\)<0.0001 & \(P\)<0.0001 & \(P\)=0.001 \\ & F, n=5 & 57.148[2.009] & 41.102[10.411] & 44.160[14.892] & 33.844[4.403] & & & \\ \hline Annexin V (\%) & & & & & & & \\ & M, n=5 & 6.886[3.372] & 3.280[0.089] & 2.822[1.179] & 0.960[0.670] & & & \\ & F, n=5 & 1.286[0.260] & 3.118[1.232] & 3.896[2.226] & 0.720[0.163] & & & \\ \hline TPO (pg/mL) & & & & & & & & \\ & M, n=11 & 94.155[5.821] & 97.658[3.387] & 101.340[5.207] & 95.152[3.613] & & & \\ & F, n=20 & 92.113[3.408] & 94.344[3.470] & 98.447[3.501] & 98.765[3.479] & & & \\ \end{tabular}
## Supplementary Table S2
|
171132_file02 | ### Data source
## 1.1 Epidemiological SARS-CoV-2 data
We collected data on 1,178 confirmed SARS-CoV-2 infections in Hunan Province, China, from January 16 to April 2, 2020, following a protocol for field epidemiological investigation developed by the National Health Commission of the People's Republic of China to identify potential COVID-19 cases. Primary and secondary SARS-CoV-2 infections were identified through: (i) active screening of incoming passengers into Hunan province and high-risk populations in the community who had a history of travel to Wuhan City/Hubei Province, capturing travel-associated symptomatic and asymptomatic infections; (ii) passive surveillance in hospitals and outpatient clinics, involving testing of individuals whose symptoms were compatible with COVID-19, capturing symptomatic cases; (iii) contact tracing of all confirmed infections identified by the above screening, followed by systematic monitoring of close contacts of these confirmed infections, capturing symptomatic and asymptomatic infections. All SARS-CoV-2 positive individuals in this database received positive laboratory confirmation of SARS-CoV-2 infection by RT-PCR test. Before February 7, 2020, contacts were tested if they developed symptoms during the quarantine period. After February 7, specimens were collected at least once from each contact during quarantine, regardless of symptoms. In total, 794 of the 1178 (67.8%) confirmed SARS-CoV-2 infections were diagnosed before February 7. Of the 794 infections detected before February 7th, only 3% were asymptomatic. After February 7th, the asymptomatic proportion among confirmed SARS-CoV-2 infections increased to 35.5%. A detailed flowchart of case ascertainment process is shown in Fig. S1.
The information collected for each case includes age, sex, prefecture (of case being reported), clinical severity (asymptomatic, mild, moderate, severe, or critical, see Table S1 for definition), potential exposures (travel history to Wuhan or contact with confirmed SARS-CoV-2 infection), time windows of potential exposures, date of the start of isolation/pre-symptomatic quarantine, date of symptom onset (list of symptoms below), date of healthcare consultation, date of hospital admission and ICU admission (if applicable), and date of laboratory-confirmation. The list of symptoms observed and documented among all patients includes: _fever (57.7%), dry cough (36.4%), fatigue (23.9%), sputum (19.6%), headache (10.3%), muscle ache (8.6%), sore throat (7.8%), chills (7.6%), chest tightness (5.4%), diarrhea (5.2%), shortness of breath (5%), runny nose (4.2%), stuffy nose (4.2%), vomiting (2.2%), joint pain (2.0 %), nausea (1.9%), breathing difficulty (1.4%), chest pain (1.3%), abdominal pain (0.5%), conjunctival hyperemia (0.3%)._ "Loss of taste/smell" was not included as a separate symptom as it was not known to be a symptom specific to COVID-19 at the time. However, if loss of taste/small had been reported by a patient it would have been included in the "other symptoms" category and used to estimate onset date along with other symptoms. All epidemiological information and testing data were collected by the Hunan CDC staff or by trained local CDC personnel and entered into a systematic database.
For each SARS-CoV-2 positive individual in the database, information was compiled on the start/end date of exposure, along with the dates of symptom onset (for symptomatic individuals) and laboratory confirmation. Biologically, the time of infection should occur before the onset of symptom or a positive RT-PCR test. Thus, we update the patient's end date of putative exposures in the database as the earliest of the reported exposure end date, date of symptom onset, or date of laboratory confirmation. If the start date of exposure is later than the date of symptom onset or positive RT-PCR test, it likely reflects recall error and we update the exposure start date as missing (1.9% of the records).
### Contact tracing database
We collected data on 15,648 individuals in close contact with the 1,178 confirmed SARS-CoV-2 infections identified in Hunan Province based on the national protocol, representing 19,227 unique exposure events. Information included age, and sex of the contacts, type of contacts (household, extended family, social, community, and healthcare, see Table S2 for definition), as well as the start and end dates of contact exposure. If the contact was confirmed with SARS-CoV-2 by RT-PCR, a unique identifier mapping the individual to the SARS-CoV-2 patient database was provided.
Any individual reporting encounters as described in Table S2 and occurring within \(<\)1m of a SARS-CoV-2 infected individual (irrespective of displaying symptoms) was considered a close contact, at risk of SARS-CoV-2 infection. All records were extracted from the electronic database managed by Hunan Provincial Center for Disease Control and Prevention. All individual records were anonymized and de-identified before analysis.
### Definition of a SARS-CoV-2 cluster
Based on the contact tracing database, we define a SARS-CoV-2 cluster as a group of two or more confirmed SARS-CoV-2 cases or asymptomatic infections with an epidemiological link, i.e. occurring through the same contact type (e.g. home, work, community, healthcare, or other) and for which a direct contact between successive cases can be established within two weeks of symptom onset of the most recent case (alternatively, the date of RT-PCR test for asymptomatic infections). In total, there are 210 clusters recorded in the database, for a total of 831 SARS-COV-2 infections.
While clusters of cases are grouped together based on shared exposures, a subset of cases report additional exposures outside the cluster as possible causes of infection as well. As a result, there can be more than one primary case within each cluster. In addition, for cases that only report exposures within the cluster, a unique infector cannot always be identified, given simultaneous SARS-CoV-2 exposures within the same cluster.
A sporadic case is defined as a laboratory-confirmed SARS-CoV-2 individual who does not belong to any of the reported clusters (i.e. a singleton who has no epidemiological link to other infections identified). In total, there are 347 sporadic cases recorded in the database.
Since the source and direction of transmission within a cluster cannot always be defined based on epidemiological grounds alone, we next turn to a modeling approach to probabilistically reconstruct infector-infectee transmission chains and further evaluate predictors of transmission.
## 2 Reconstruction of SARS-CoV-2 transmission chains
Reconstruction of transmission chains based on contact tracing data have been done with prior emerging outbreaks. In this section, we describe our sampling algorithm to stochastically reconstruct the transmission chains, which is customized to the unique contact tracing data of SARS-CoV-2 outbreaks in Hunan collected by the Hunan CDC and accounting for uncertainties in multiple plausible transmission routes compatible with the observation.
### Sampling algorithm
For each cluster and each patient \(i\) in the cluster, the time of infection \(t_{i}^{inf}\) is stochastically sampled by randomly drawing from the incubation period distribution and subtracting this value from the reported time of symptom onset, i.e. \(t_{i}^{inf}\) = \(t_{i}^{sym}\) \(-\)\(\tau_{i}^{incu}\), where \(t_{i}^{incu}\) is the sampled incubationperiod and \(t_{i}^{\rm sym}\) the date of symptom onset. The incubation period follows a Weibull distribution:
\[g_{incu}(\tau)=\frac{k}{\lambda}\Big{(}\frac{\tau}{\lambda}\Big{)}^{k-1}\ exp \left(-\Big{(}\frac{\tau}{\lambda}\Big{)}^{k}\right)\]
The median incubation period is taken to be 5.56 days with IQR (3.14, 8.81) days.
The sampled time of infection \(t_{i}^{inf}\) must satisfy the following constrains:
* \(t_{i}^{\rm inf}\) must fall within the start and end dates of the exposures identified by epidemiological investigation.
* For any infector-infectee pair, the time of infection of the infector \(t_{infector}^{inf}\) must be earlier than the time of infection of the infectee \(t_{infectee}^{inf}\), i.e. \(t_{infector}^{inf}<t_{infectee}^{inf}\).
A SARS-CoV-2 infected individual may have multiple exposures (either through contacts with multiple SARS-CoV-2 infected individuals, or travel history to Wuhan in addition to contact with a SARS-CoV-2 individual). For an individual \(i\) who has multiple sources of exposure with a cluster, all other cases in contact with \(i\) are potential sources of infection, except for those whom \(i\) has infected. If the sampled infection time of infectee \(i\), \(t_{i}^{inf}\), satisfies the constraints of multiple exposures, we randomly choose one as the source of infection. If \(t_{i}^{inf}\) satisfies the constrains of none of the plausible exposures, we resample \(t_{i}^{inf}\) until individual \(i\) has one and only one valid source of infection. For individuals with missing onset dates (including all asymptomatic individuals), we set the time of infection as missing. The source of infection is then randomly chosen from all plausible exposures identified from epidemiological investigation.
We stochastically reconstruct 100 realizations of transmission chains to account for uncertainties in both the timing and source of exposures. 375 of the 831 (45%) SARS-CoV-2 infections do not have unique epidemiological link and their transmission routes may vary from one realization to another. In addition, only 35 of the 831 (4.2%) have missing onset dates.
We remove all singletons from the reconstruction of transmission chains, since they are not epidemiologically linked to other cases, but we consider these singletons when we analyze the distribution of secondary cases and when we represent the transmission network in
## 2.2 Distribution of the number of secondary infections among transmission chains
Next, we calculate the number of secondary infections for each of the 1,178 SARS-CoV-2 individuals based on the 100 reconstructed transmission chains among 831 cluster cases, and the 347 singletons. The distribution of secondary infections is shown in We fit a negative binomial distribution to these data using package "pystan" version v2.19.1.1 with uniform prior. We estimated mean \(\mu=0.40\), 95% CI 0.35 to 0.46 and dispersion parameter \(k=0.30\), 95%CI 0.23 to 0.39. In addition, we fit the geometric and Poisson distributions to the data. The negative binomial distribution best describes the data based on Akaike information criterion.
## 3.
## 3.1 Generation interval and serial interval distribution
The generation interval is defined as the time interval between the dates of infections in the infector and the infectee. We calculate the generation intervals of all the infector-infectee pairs based on 100 realizations of the reconstructed transmission chains. The cumulative distribution of the generation interval is shown in Fig. S7A, C. The observed serial interval is defined as the time interval between dates of symptom onsets in the infector and the infectee. We calculate the serial interval of all the infector-infectee pairs based on 100 realizations of the reconstructed transmission chains with known dates of symptom onset. To further reduce potential recall bias on the timing of symptom onset/exposure, we down-sample the outlier incubation period pairs. To do this in a statistically sound manner, we rely on the independence of the incubation periods of the infector and the infectee, and down-sample infector-infectee pairs whose joint likelihood of the observed incubation period pair is very low. Specifically, we first estimate the joint empirical distribution of the incubation periods of both the infector and infectee using the gaussian kernel density estimate in the package "scipy" version v1.5.0 function "scipy.stats.gaussian_kde". The joint likelihood of observing the incubation periods of a given infector-infectee pair based on the kernel density estimate is denoted as \(p_{kde}(\tau_{i}^{incu},\tau_{j}^{incu})\). The joint likelihood of the incubation period of the same infector-infectee pairs based on two independent draws from the Weibull distribution \(g_{incu}(\tau)=\frac{k}{\lambda}\left(\frac{\tau}{\lambda}\right)^{k-1}exp \left(-\left(\frac{\tau}{\lambda}\right)^{k}\right)\) with shape parameter \(k=1.58\) and scale parameter \(\lambda=7.11\) (Section 2.1) is denoted as \(p_{E}(\tau_{i}^{incu},\tau_{j}^{incu})\). If \(p_{kde}\big{(}\tau_{i}^{incu},\tau_{j}^{incu}\big{)}>p_{E}\big{(}\tau_{i}^{ incu},\tau_{j}^{incu}\big{)}\), it suggests the observed incubation periods are over-represented relative to expectations, and vice versa. We introduce a down-sampling weight in accordance with the incubation period distribution as \(w_{incu}=p_{E}\big{(}\tau_{i}^{incu},\tau_{j}^{incu}\big{)}/p_{kde}\big{(}\tau _{i}^{incu},\tau_{j}^{incu}\big{)}\). The distribution of the serial interval is shown in Fig. S7B, D.
### Gauging the impact of case isolation on the distribution of the serial and generation intervals
We select all infector-infectee pairs for which the infector has been isolated during the course of his/her infection, date of symptom onset is available, and times of infection have been estimated (range from 348 to 372 pairs across 100 sampled transmission chains). We stratify the data by the infector's time interval between onset and isolation, \(\tau_{iso}\), with \(\tau_{iso}\in\{(-\infty,2),[2,4),[4,6),[6,+\infty)\ days\}\), and assess how the generation interval and serial interval distributions change with the timeliness of case isolation (and Fig. 3B). We use Mann-Whitney U test to compare the statistical significance in the differences of serial/generation interval distribution across different strata.
### Speed of case isolation and relative contribution of pre-symptomatic transmission
As cases are isolated earlier in the course of infection, we expect that the contribution of pre-symptomatic transmission will increase. This is because symptomatic transmission occurs after pre-symptomatic transmission and transmission will be blocked after effective isolation. In other words, isolated individuals remain infectious, but they can only effectively transmit before isolation, which is predominantly in their symptomatic phase. To validate the hypothesis that the contribution of pre-symptomatic transmission is affected by interventions, we first estimate the overall contribution of pre-symptomatic transmission among all reconstructed transmission chains. Let \(tr_{i,j}^{k}\) represent each transmission event from an infector to infectee \(i\), in realization \(j\) of the 100 sampled transmission chains; \(k=0\) indicates that infection in an infectee occurred before the time of symptom onset of his/her infector, denoting pre-symptomatic transmission, while \(k=1\) indicates that the time of infection occurred after the infector's symptom onset (i.e. post symptomatic transmission). Thus, the overall fraction of pre-symptomatic transmission in realization \(j\) can be calculated using the following formula:
\[P_{j}^{pre}=\frac{\sum_{i}tr_{i,j}^{k=0}}{\sum_{i}\sum_{k}tr_{i,j}^{k}}\]
Mean and 95% CI of \(P^{pre}\) can be estimated over the 100 realizations of the reconstructed transmission chains.
### Relative infectiousness profiles over time adjusted for case isolation.
In Hunan province, all COVID-19 cases regardless of clinical severity were managed under medical isolation in appointed hospitals; while contacts of SARS-CoV-2 infections were quarantined in designated medical observation centers. In Section 4, we estimate that the risk of transmission through healthcare contacts is the lowest among all contact types, thus case isolation and contact quarantine are highly effective to block onward transmission after isolation/quarantine. As a result, the observed serial/generation intervals are shorter than they would be in the absence of case isolation and contact quarantine. The censoring effects are clearly demonstrated in and Fig. 3B, where we observe that the median generation time drops from 7.1 days for \(\tau_{iso}>6\) (\(days\)) after symptom onset, to 4.0 days for \(\tau_{iso}<2\) (\(days\)).
Moreover, the timeliness of case isolation is not static over time. Fig. S8 shows the distribution of time from symptom onset to isolation in three different phases of epidemic control (_Phase I, II, and III_) defined by two major changes in COVID-19 case definition issued by National Health Commission on Jan. 27 and Feb. 4. The median time from symptom onset to isolation decreases from 5.4 days in _Phase I_ to -0.1 days in _Phase III_, due to the expansion of "suspected" case definition and strengthening of contact tracing effort (Fig. S8).
#### 3.4.1 Generation interval adjusted for case isolation.
Estimating the generation interval distribution in the absence of interventions is important to understand the kinetics of SARS-CoV-2 transmission, as the shape of the generation interval distribution represents the population-average infectiousness profile since the time of infection. To minimize the potential error of flipping the directionality of infector-infectee relationship during contact tracing, we further limit our analysis to the infector-infectee pairs where the primary case had a travel history to Wuhan (and no other SARS-CoV-2 contact), while the secondary case did not have a travel history to Wuhan but was epidemiological linked to the primary case. To further reduce potential recall bias on the timing of symptom onset/exposure, we down-sample the outlier incubation period pairs. To do this in a statistically sound manner, we rely on the independence of the incubation periods of the infector and the infectee, and down-sample infector-infectee pairs whose joint likelihood of the observed incubation period pair is very low. Specifically, we first estimate the joint empirical distribution of the incubation periods of both the infector and infectee using the gaussian kernel density estimate in the package "scipy" version v1.5.0 function "scipy.stats.gaussian_kde". The joint likelihood of observing the incubation periods of a given infector-infectee pair based on the kernel density estimate is denoted as \(p_{kde}(\tau_{i}^{incu},\tau_{j}^{incu})\). The joint likelihood of the incubation period of the same infector-infectee pairsbased on two independent draws from the Weibull distribution \(g_{incu}(\tau)=\frac{k}{\lambda}\left(\frac{\tau}{\lambda}\right)^{k-1}exp\left(- \left(\frac{\tau}{\lambda}\right)^{k}\right)\) with shape parameter \(k=1.58\) and scale parameter \(\lambda=7.11\) (Section 2.1) is denoted as \(p_{E}(\tau_{i}^{incu},\tau_{j}^{incu})\). If \(p_{kde}\left(\tau_{i}^{incu},\tau_{j}^{incu}\right)>p_{E}\left(\tau_{i}^{incu},\tau_{j}^{incu}\right)\), it suggests the observed incubation periods are over-represented relative to expectations, and vice versa. We introduce a resampling weight in accordance with the incubation period distribution as \(w_{incu}=p_{E}\left(\tau_{i}^{incu},\tau_{j}^{incu}\right)/p_{kde}\left(\tau_{ i}^{incu},\tau_{j}^{incu}\right)\). The resampling weights as a function of the incubation periods among the infector and infectee are visualized in Fig. S11.
To account for the "censoring" of generation interval distribution due to quarantine/case isolation, we first exclude generation intervals where transmission occurred after isolation of the infector (only 4.3% of the reconstructed transmission events, attesting to the effectiveness of isolation). We then divide the generation intervals into three groups based whether the date of symptom onset of the infectors fall within a given phase of epidemic control in Hunan. In Group 1 the illness onset of the infectors occurred before Jan. 27th (_Phase I_); in Group 2 the illness onset of the infector occurred between Jan. 27th and Feb. 4th (_Phase II_); in Group 3, the illness onset of the infector occurred after Feb. 4th (_Phase III_). For a given generation interval \(\tau_{GI}\) of an infector-infectee pair in each group, we denote:
* The time of symptom onset of the infector as \(t_{onset}\).
* The time of case isolation/quarantine of the infector as \(t_{iso}\).
* The time of transmission from the infector to the infectee as \(t_{inf}\).
* The time interval between onset of the infector and transmission to the infectee \(\tau_{oi}=t_{onset}-t_{inf}\).
* The time interval between infection times in the infector and infectee, i.e. the generation interval \(\tau_{li}\)
* The probability distribution from symptom onset to isolation as \(P_{l}(\tau_{iso})\), where \(i\in\{I,II,III\}\) denotes the different phases of epidemic control, determined by symptom onset in the infector \(t_{onset}\). The functional form of \(P_{l}(\tau_{iso})\) is shown in Fig. S8. The corresponding cumulative probability distribution is denoted as \(C_{OI}^{i}(\tau_{iso})\).
The probability of this infection-infectee pair escaping the "censoring" due to quarantine and case isolation is \(p_{i}^{esc.}=1-C_{OI}^{i}(\tau_{oi})\). For every n observations of the generation interval \(\tau_{li}\) under intervention \(p_{i}(\tau_{iso})\) given \(\tau_{oi}\), there should be \(m=\frac{n}{p_{i}^{esc.}}\) observations of \(\tau_{GI}\) given \(\tau_{oi}\) without intervention \(p_{i}(\tau_{iso})\). Thus, we denote the sampling weight adjusted for case isolation as \(w_{iso}=\frac{1}{p_{i}^{esc.}}\). The overall resampling weight of generation interval \(\tau_{li}\) between infector \(i\) and infectee \(j\) considering both incubation period distribution and censoring due to case isolation is given by \(w_{sample}(i,j)=w_{incu}\times w_{iso}=\frac{p_{E}\left(\tau_{i}^{incu},\tau_{ j}^{incu}\right)}{p_{i}^{esc.}\times p_{kde}\left(\tau_{i}^{incu},\tau_{j}^{incu}\right)}\). We resample from \(\{\tau_{li}(i,j)\}\) with sampling weights \(w_{sample}(i,j)\) until we reach a sample size of \(n=100\) to obtain the distribution of generation time \(\{\tau_{li}^{adj.}\}\) adjusted for censoring. The distribution of \(\tau_{li}^{adj.}\) reflects the generation interval that would have been observed in the absence of quarantine and case isolation/quarantine. We fit Weibull, gamma, and lognormal function to \(\{\tau_{li}^{adj.}\}\). The distribution of \(\tau_{li}^{adj.}\) is best described by the Weibull distribution:
\[g_{GI}^{adj.}(\tau)=\frac{k}{\lambda}\left(\frac{\tau}{\lambda}\right)^{k-1} exp\left(-\left(\frac{\tau}{\lambda}\right)^{k}\right)\]with \(k~{}=~{}1.60\) and \(\lambda=~{}6.84\) (Fig. S10).
4.2 Distribution of time interval between symptom onset and transmission, adjusted for case isolation
In contrast to the generation interval distribution, which characterizes the relative infectiousness of a SARS-CoV-2 infection over time with respect to the time of infection, we now focus on the interval between symptom onset and transmission. This shifts the reference point of the infectiousness profile from the time of infection to the time of symptom onset. Namely the distribution of symptom onset to transmission adjusted for case isolation \(\{\tau_{OT}^{adj.}\}\) represents the population-average relative infectiousness profile over time since the onset of symptom. Of note, since we observe substantial pre-symptomatic transmission for SARS-CoV-2, negative values of \(\tau_{OT}^{adj.}\) are allowed.
Similarly to the previous section, we resample from \(\{\tau_{OT}(i,j)\}\) with sampling weights \(w_{sample}(i,j)\) until a sample of size \(n=100\) is reached to obtain the distribution of symptom onset to transmission \(\{\tau_{OT}^{adj.}\}\). The resampled distribution represents the infector's relative infectiousness (population average) with respect to the infector's symptom onset (Fig. S6B). The best-fit distribution is a normal distribution:
\[f_{OT}^{adj.}\big{(}\tau_{OT}^{adj.}\big{)}=\frac{1}{\sigma\sqrt{2\pi}}e^{- \frac{1}{2}\left(\frac{\tau_{OT}^{adj.}-\mu}{\sigma}\right)^{2}}\]
After adjusting for case isolation, the fraction of transmission occurring during the pre-symptomatic phase of SARS-CoV-2 infection is 54%, (95%CI 38%, 0.70%).
### Estimating the basic reproduction number in Wuhan before lockdown
A recent study estimated the initial growth rate of the epidemic in Wuhan at 0.15 day-1 95% CI (95% CI, 0.14 to 0.17) ahead of the lockdown. The estimate is based on the daily rise in reported cases by onset date; adjustment for increased reporting due to a broadening case definition places the growth rate at 0.08 day-1. The Euler-Lotka equation describes the relationship between the basic reproduction number \(R_{0}\), the epidemic growth rate \(\tau\), and the generation interval distribution \(g(\tau)\):
\[R_{0}=\frac{1}{\int exp(-r*\tau)\times g(\tau)d\tau}\]
We assume that no effective intervention had been implemented in Wuhan by the time of the lockdown (Jan. 23). Using the generation time distribution adjusted for "censoring" due to quarantine and case isolation \(g_{GI}^{adj.}(\tau)\) described in the previous section, we estimate the basic reproduction number in Wuhan during the exponential growth phase at \(R_{0}^{Wuhan}=2.17\), (95% CI, 2.08 to 2.36), based on the conservatively higher estimate of growth rate in this city (0.15 day-1 95% CI (95% CI, 0.14 to 0.17). If we rescale the adjusted generation time distribution \(g_{GI}^{adj.}(\tau)\) by a factor of \(R_{0}^{Wuhan}\), the function
\[r_{GI}(\tau)=g_{GI}^{adj.}(\tau)\times R_{0}^{Wuhan}\]
The red line in visualizes the functional form of \(r_{GI}(\tau)\).
Similarly, if we rescale the adjusted distribution of symptom onset to transmission \(f_{OT}^{adj.}(\tau)\) with \(R_{0}^{Wuhan}\), the function
\[r_{OT}(\tau)=f_{OT}^{adj.}(\tau)\times R_{0}^{Wuhan}\]
The red line in visualizes the functional form of \(r_{OT}(\tau)\).
## 3.6 Evaluating the impact of case isolation and quarantine on SARS-CoV-2 transmission.
To evaluate the impact of quarantine and case isolation on the reduction of SARS-CoV-2 transmission at different phases of epidemic control, we denote the time intervals between a patient's time of infection to his/her time of isolation as \(\tau_{inf}^{iso}\). The corresponding probability distribution is \(p_{ii}^{j}(\tau)\), where \(j\in\{I,II,III\}\) denotes the phase of epidemic control. We denote the distribution of the incubation period \(\tau_{incu}\) as \(p_{incu}(\tau)\) and the distribution of symptom onset to isolation \(\tau_{onset}^{iso}\) as \(p_{oi}^{j}(\tau)\), for each phase \(j\) of epidemic control. We sample \(\tau_{inf}^{iso}=\tau_{incu}+\tau_{onset}^{iso}\) numerically through independently sampling of \(\tau_{incu}\) and \(\tau_{onset}^{iso}\) and add them together. Fig. S9 shows the distribution of 100 numerical sampling of \(\tau_{inf}^{iso}\) at different phases of epidemic control. We fit the sampled distribution of \(\tau_{inf}^{iso}\) to various probability distributions including normal, lognormal, gamma, Cauchy, logistic, and hyperbolic secant distribution. The top three fits are show in Fig. S9 and the best fit is selected based on the Akaike information criterion during each of the three phases of epidemic control.
\[C_{ii}^{j}(\tau)=\int_{-\infty}^{\tau}P_{ii}^{j}(\tau^{\prime})d\tau^{\prime}\]
The shaded areas in Fig. S9 visualize the probabilities \(C_{ii}^{j}(\tau)\) for the best-fit distribution.
Assuming that all SARS-CoV-2 patients are subject to case isolation and quarantine efforts carried out in Hunan province, we can estimate the average risk of transmission \(r_{GI}^{control(j)}(\tau)\) of an infected individual at time \(\tau\) since his/her infection, during phase \(j\in\{I,\ II,\ III\}\) of epidemic control as:
\[r_{GI}^{control(j)}(\tau)=r(\tau)\times\left(1-C_{li}^{j}(\tau)\right)=g_{GI}^ {adj.}(\tau)\times R_{0}^{Wuhan}\times\left(1-C_{li}^{j}(\tau)\right)\]
The corresponding basic reproduction number assuming 100% SARS-CoV-2 infection detection rate is given by:
\[R_{0}^{j}=\int_{0}^{\infty}r_{GI}^{control(j)}(\tau)\ d\tau\,,j\in\{I,II,III\}\]
In Fig. 3D, we visualize the transmission profile with respect to infection time \(r_{GI}^{control(j)}\) for all three phases of epidemic control (dashed lines) and shows the estimated values of the corresponding basic reproduction number \(R_{0}^{j}\).
Similarly, following Section 3.4.1, \(C_{oi}^{j}(\tau)\) gives the probability that transmission is blocked after time \(\tau\) since symptom onset in the infector, for the 3 phases of epidemic control \(j\in\{I,II,III\}\). We can estimate the average risk of transmission \(r_{OT}^{control(j)}(\tau)\) of an infected individual at time \(\tau\) since his/her onset of symptom, during phase \(j\in\{l,\ l,\ l,\ lill\}\) of epidemic control as:
\[r_{0T}^{control(J)}(\tau)=r(\tau)\times\left(1-C_{oi}^{J}(\tau)\right)=f_{0T}^{ adj\cdot}(\tau)\times R_{0}^{Wuhan}\times\left(1-C_{oi}^{J}(\tau)\right)\]
In Fig. 3E, we visualize the transmission profile with respect to symptom onset time \(r_{0T}^{control(J)}\) for all three phases of epidemic control (dashed lines).
## 3.7 Evaluating synergistic effects of individual-level and population-level interventions on SARS-CoV-2 transmission.
We start by characterizing the controllability of SARS-CoV-2 (measured as \(R_{0}\) under control measures) as a function of infection isolation rate and the speed of case isolation/pre-symptomatic quarantine. In Fig. 3F, we plot the phase diagram of \(R_{0}\) as a function of infection detection proportion (fraction of all SARS-CoV-2 infections detected) and the mean time from symptom onset to isolation/quarantine \(\tau_{iso}\). Contour lines indicates reductions in R0 from baseline non-intervention conditions. It is worth noting that we do not know the precise prevalence of truly asymptomatic infections as well as their role in transmission. Here we assume that asymptomatic cases have a similar shape of infectiousness profile over the course of infection as symptomatic cases, and a peak of infectiousness corresponding to the time of symptom onset in symptomatic cases, as shown in Fig. S10. The corresponding \(\tau_{iso}\) for asymptomatic cases is measured as time from peak infectiousness to isolation. Here we assume that the distribution of symptom onset/peak infectiousness to isolation follows a normal distribution with mean \(\tau_{iso}\) and standard deviation of 2 days.
We further consider the synergic effects of layering individual-based intervention (case isolation, contact tracing, and quarantine) with population-based interventions (i.e., via physical distancing, measured as a reduction in effective contact rates). In Fig. 3G, we plot the phase diagram of \(R_{0}^{E}\) as a function of the proportion of population-level contact reduction and infection isolation rate, with the average speed of isolation 0 days after symptom onset/peak infectiousness and standard deviation of 2 days. The base \(R_{0}\)_is_ 2.19, which is compatible with a growth rate of 0.15 observed in Wuhan without the adjustment for change in reporting (Section 3.5). The blue area indicates the region below the epidemic threshold, where control is achieved, and the red area indicates the region above the epidemic threshold. The phase diagram shows the effect of ramping up population-based interventions (i.e. increasing percent reduction in the effective contact rate) and strengthening individual-based interventions (i.e. increasing fraction of active infections identified and isolated). Both types of interventions act synergistically to reduce the effective reproduction number and consequently slow down the transmission. The dashed line in indicates the minimum level of individual and population-based interventions required to stop transmission (i.e. bring \(R_{0}^{E}=1\)), separating the regime of controlled and uncontrolled epidemics. It also demonstrates the trade-off between individual and population-based interventions: expanding efforts in case detection and isolation will reduce the amount of population-level interventions required to maintain control of the epidemic and vice versa.
Last, we consider a sensitivity analysis of lower baseline transmission scenario with base \(R_{0}=1.57\), using a growth rate of \(r=0.08\), as observed in Wuhan data after adjustment for changes in reporting (Section 3.5). In Fig. 3H, we plot the phase diagram of \(R_{0}\) as a function of proportion of population-level contact reduction (i.e. through physical distancing) and isolation rate, assuming that SARS-CoV-2 infections are isolated 2 days after symptom onset/peak infectiousness on average with a standard deviation of 2 days. Overall, the phase diagram bears similar interpretations as which represents the scenario where \(R_{0}=2.19\) and infections are isolated immediately upon symptom onset or at peak infectiousness. With a lower base reproduction number of 1.57, the requirements for both individual and population-based interventions to achieve control are lower. For instance, with a "relaxed" timeliness of isolation 2 days after symptom onset on average, control can be achieved by detection and isolation of 40% of all infections, associated with a reduction of 25% of effective contacts through population-level interventions. In contrast, in the high baseline transmission scenario, a 25% reduction in effective contacts needs to be coupled with an 80% infection detection and isolation, promptly upon symptom presentation, to achieve control. This is a much higher bar when compared to the low baseline transmission scenario.
## 4 Evaluating individual-level transmission heterogeneity of SARS-CoV-2
Regression analysis to evaluate the "per-exposure" risk of SARS-CoV-2 transmission as a function of demographical, epidemiological, clinical, and behavioral predictors.
In this section, we use a mixed effects multiple logistic regression model to evaluate the risk of SARS-CoV-2 transmission for each exposure reported in the contact tracing database. we analyze the infection risk among a subset of 14,622 individuals who were close contacts of 870 SARS-CoV-2 patients. This dataset excludes primary cases whose infected contacts report a travel history to Wuhan, to avoid confounding in the source of infection. The dataset represents 74% of all SARS-CoV-2 cases recorded in the Hunan patient database. Each entry in the database represents a contact exposure between a SARS-CoV-2 infected individual and his/her contact. For individuals who were in contact with SARS-CoV-2 infected individual, the contact individual's age, sex, type of contact, the start/end dates of exposure, as well as the infection status (whether the exposed individuals was eventually infected with SARS-CoV-2) are carefully documented (Section 1.2). All SARS-CoV-2 infected individual (both primary cases and secondary infections via contact exposures) have unique identifiers that can be mapped to the SARS-CoV-2 patient line-list database, where additional information about the course of infection is also available (see Section 1.1 for detailed information). An individual in the contact tracing database can be exposed to multiple SARS-CoV-2 cases; further, an individual in the contact tracing database can be exposed to the same SARS-CoV-2 case through multiple independent exposures. All exposures are recorded independently.
For each exposure in the contact-tracing database, the regression outcome is coded as 1 if the contact eventually becomes infected and 0 if not infected. For each exposure, a list of independent variables, their definitions, and corresponding values are shown in Table S3 (fixed effects in the mixed model).
We also introduce random effects for each SARS-CoV-2 case, representing the individual-level infectiousness heterogeneity that is not explained by the independent variables representing fixed effects. These random effects also take into account the lack of independence of our observations.
A contact could report more than one SARS-CoV-2 exposure. If the contact eventually becomes infected, however, only one of the many exposures will be the actual source of infection. In this case, if we denote the number of exposures as \(n^{expo}\), for each of the contact's \(n^{expo}\) exposure entries in the database with two different outcomes, either the contact became infected (1 as regression outcome) with regression weight \(1/n^{expo}\) or the contact avoided infection from the same exposure (0 as regression outcome) with regression weight \((n^{expo}-1)/n^{expo}\). We exclude primary cases whose infected contacts report a travel history to Wuhan, as the infection could possibility originate from exposures in Wuhan in addition to exposure to local cases in Hunan.
A fraction of the regression variables has missing values in the contact-tracing database (see Table S3, column 3). We adopted the state-of-the-art "Multivariate Imputation by Chained Equations" algorithm (implemented in R package "MICE" version 3.9.1 [https://cran.r-project.org/web/packages/mice/index.html](https://cran.r-project.org/web/packages/mice/index.html)) to impute missing values in the database. All independent variables in Table S3 are used as predictors for data imputation. The number of multiple imputations is set as 10 with each imputation running 10 realizations. For each of the 5 realizations of imputed contact-tracing databases, we independently perform mixed effects multiple logistic regression of the risk of SARS-CoV-2 transmission with all exposures and variables described in Table S3 as covariates. The regression is performed using R package "lme4" (_60_) version v1.1-23 function "glmer" ([https://cran.r-project.org/web/packages/lme4/index.html](https://cran.r-project.org/web/packages/lme4/index.html)). The final odds-ratio estimates are pooled from the 5 independent regressions on 5 imputed databases using "MICE" package's "pool" function, based on Rubin's rule. The point (maximum likelihood) estimates of the odds ratios of independent variables, their 95%CIs, and the baseline odds (intercept) are reported in Fig. S3A.
To examine the model's fit to the data, we explore (i) how well the model reproduces the age profiles of infector-infectee pairs and (ii) whether the model captures the amount of transmission that occurs through different contact types (household, family, transportation, etc). We first randomly choose one of the five imputed contact-tracing databases. For each exposure entry in the imputed contact-tracing database, we calculate the model predicted risk of infection based on all fixed variables in the regression. We simulate the infection status of the contact according to the predicted risk by drawing from a binomial distribution. We repeat the process for all contacts, and further simulate 100 realizations of projected infection databases to gauge variability. Fig. S3C shows the observed age distribution of the infector-infectee pairs in the original data, and Fig. S3B visualizes the projected age distribution based on the regression model, averaged over 100 realizations. Violin plots in Fig. S3D show the relative fraction (with projection uncertainties) of transmission that is explained by each type of contacts, based on the model, while the dots in Fig. S3D represents the empirical observations. We find that the model accurately captures the strong assertiveness of transmission in the 30-50 years age group, and the off diagonals that represent transmission between different generations. Further, the model reproduces the relative contribution of different types of contacts seen in the empirical data (Fig. S3D).
### 4.2 Sensitivity analyses
#### 4.2.1 On contact type categories
We use sensitivity analyses to answer two questions related to the role of contacts (i) Are the 5 categories of contacts, as defined in the main analysis and broken down by timing of exposure, the most parsimonious way to explain transmission risk? This is especially important as there is overlap in the 95% CIs of the odds ratios associated with each type of contact. We can test this by collapsing some of the contact categories, and/or collapsing contacts of the same type over timing of exposure and assessing model fit. (ii) Does contact duration have similar effect on different types of contacts? In the reference model, we used duration as an independent variable that modulates the baseline risk of each contact type. But what if duration has a differential effect on each contact type? To address this question, we can incorporate the additional interaction between contact type and duration to the regression and assess model fit.
To test hypothesis (i), we fit the data to 5 other candidate regression models M1, M2, M3, M4, and M5, collapsing contact categories and time. We compare models M1-M5 to the reference model (M0) of the main analysis, while keeping other predictors of the regression unchanged. We find that M0 has the lowest AIC scores of all candidate models, indicating that distinguishing the timing of exposure as well as contact type best explains the data (Table S4).
Another sensitivity analysis (M6) was performed to examine whether including the interaction term between contact types and duration of contacts improves model fit. Our baseline model (M0) still best explains the data based on Akaike information criterion (Table S4).
#### 4.2.2 On missing data and change in testing protocols
As a sensitivity analysis for missing data imputation (especially addressing the issue of imputing "onset within exposure" for SARS-CoV-2 infected individuals that are asymptomatic), we perform a GLMM-logit regression with entries of missing data removed. To explore transmissibility from younger and older children, we further break-up the age bracket of predictor "Age (case)" (Table S3) into _0-12 years_, _12-25 years_, _26-64 years_, and _65+ years_. We remove the predictor of "onset within exposure", however, for predictor "clinical severity (case)", we break down the category "mild & moderate", and "severe & critical" based on whether the onset of the primary case occurred within the exposure time window. "(-)" indicate symptom onset outside the exposure time window, while "(+)" indicate symptom onset within the exposure time window. There was a change in the testing protocol for close contacts during the outbreak: prior to February 7, only contacts displaying symptoms were tested, while after February 7 all contacts were tested regardless of symptoms (Section 1.1). To evaluate the impact of the change in testing protocol before and after February 7 on age-dependent susceptibility, we further stratify the age groups of the contacts by the date of diagnostic of the corresponding primary (before/after February): 4 age groups (_0-12_, _12-25_, _26-64_, _65+ years_) whose primary cases were diagnosed prior to February 7 and four additional age groups (_0-12_, _12-25_, _26-64_, _65+ years_) whose primary cases were diagnosed after February 07, resulting a total of 8 age groups for the contacts. The results of the regression are shown in Fig. S4. Compared, to the main analysis in Fig S3, we see that the gradient in susceptibility is preserved in both time periods. Further, we find odds ratio (OR) for susceptibility among children under 12 years (relative to 26-64 years) in the data after February 7th is comparable with the main analysis (OR=0.3 with 95% CI 0.11 to 0.86 v.s. OR=0.41 with 95% CI 0.26 to 0.63 in the main analysis).
Regression analysis evaluating predictors of individual contact patterns among SARS-CoV-2 cases and the impact of interventions
While Section 4.1 addresses predictors of "per-contact" transmission risk heterogeneity, in this section we aim to characterize variation in individual contact patterns of SARS-CoV-2 cases by type of contact. We are particularly interested in the impact of both individual-based and population-based intervention on contact rates. Intuitively, the overall transmission rate of an infectious individual can be interpreted as the sum of contact rates across contact categories weighted by the "per-contact" transmission risk. Thus, conditioning on all other predictors, higher contact rates would translate to higher transmission rates.
We use regression analysis to model the individual contact patterns of each symptomatic SARS-CoV-2 case, whose contacts are traced and documented in the contact-tracing database. We focus on symptomatic cases (the majority of our data) because we are particularly interested in contactsnear the time of symptom onset, since we have previously shown that transmission risk is highest near symptom onset. We first define a time window \(\tau_{symp.}\)of peak infectiousness as \(\pm 5\) days before and after each case's symptom onset \(t_{symp.}\). This time window accounts for a majority (87%) of the total infection risk of a typical symptomatic SARS-CoV-2 infection (Fig. S10B, D). In addition, we consider the 4 main contact types separately: community, social, family, and household contacts. For each symptomatic SARS-CoV-2 case and contact type \(s\), we denote the number of contacts on day \(i\) as \(k_{i}^{s}\). Here each contact in \(k_{i}^{s}\) is weighted by the regression odds ratios of GLMM-logit, excluding effects from duration of exposure and if onset is within exposure time window. The cumulative daily contact rate \(CCR_{\tau_{symp.}}^{s}\) within the time window \(\tau_{symp.}\) for a given case is given by:
\[CCR_{\tau_{symp.}}^{s}=\sum_{i=t_{symp.}-5}^{t_{symp.}+5}k_{i}^{s}\times w(t_{ symp.}-i)\]
Here \(w(\tau)\) is the infectiousness profile with respect to symptom onset (Fig. S10B, D). Clearly, case isolation will impact an infected individual's contact rate, irrespective of whether the case is symptomatic. However here we restrict our analysis to symptomatic cases as the speed of case isolation and pre-symptomatic quarantine can be quantitatively measured as the time from isolation/pre-symptomatic quarantine to symptom onset.
To quantify the impact of socio-demographic factors and interventions on \(CCR_{\tau_{symp.}}^{s}\), we consider a negative binomial regression with \(CCR_{\tau_{symp.}}^{s}\) as the dependent variable and proxies of interventions intensities as independent variables in the regression. Specifically, we use a within-city mobility index as a proxy for the intensity of population-level social distancing, while we use time between isolation and symptom onset to measure the intensity of individual-level interventions (here, case isolation). We also include demographic and clinical predictors as independent variables to adjust for age and sex differences, as well as other changes in contact patterns. A full description of all regression variables is shown in Table S5.
The regression is performed using the R package "MASS" version 7.3-51.6 function "glm.nb" ([https://cran.r-project.org/web/packages/MASS/index.html](https://cran.r-project.org/web/packages/MASS/index.html)). The point (maximum likelihood) estimates rate ratios along with their 95% CIs for each of the variables are presented in the bottom panels of We identify an effect of interventions on contact rates, along with clinical factors; these effects tend to be most intense for social and community contacts.
## Fig. S1.
Flowchart of SARS-CoV-2 cases/asymptomatic infection ascertainment process.
## Fig. S2. The topological uncertainties of transmission chains reconstruction and spatial variation of contact patterns.
Left: The network of the aggregation of 100 sampled transmission chains. Each node in the network represents a patient infected with SARS-CoV-2 and each link represents an infector-infectee relationship. The weights (visualized as widths) of the links are proportional to the probability of occurrence among 100 samples. Colors of the node denote the reporting preference of infected individuals. Right: The variation of contact patterns of the top 5 prefectures in Hunan with most SARS-CoV-2 infections, based on the contact tracing database. Bar plots are the age distribution of close contacts of SARS-CoV-2 infected individuals, across 4 age groups (\(<\)13 years, 13-25 years, 26-64 years, and \(>\)65 years), and stratified by contact types, based on the contact tracing database. Legends also reported the average number of close contacts of a SARS-CoV-2 infection in each of the 4 contact types.
# Independent variable** & **Definition
\\ \hline Age (categorical) & Age category of the SARS-CoV-2 case. We consider three age categories: _0-18 years_, _19-64 years_, _65 years and older_, _19-64 years_ is the reference category. \\ \hline Sex (Male/Female) & Sex of the contact (_male/female_). _Female_ is the reference category. \\ \hline Symptom fever (Y/N) & Whether the SARS-CoV-2 case had _"fever"_. Cases without _"fever"_ are the reference class. \\ \hline Symptom dry cough & Whether the SARS-CoV-2 case had _"dry cough"_. Cases without symptom _"dry cough"_, i.e. Dry Cough (N), is the reference class. \\ \hline Travel history to Wuhan & If the SARS-CoV-2 case reported a _travel history to Wuhan_: cases without _travel history to Wuhan_ are the reference category. \\ \hline Physical distancing & Based on the within-city mobility index (Fig. S3A, insert) provided by Baidu Qianxi __, we grouped the individual patients into categories depending on whether the patients symptom onsets occurred before and after January 25, 2020, corresponding to weak/strong physical distancing. Onsets occurred _before Jan. 25_ (weak physical distancing) is the reference class. \\ \hline Isolation to onset (days) & Time from case isolation to symptom onset. This is used as a proxy for individual-level intervention intensity. The larger the value, the earlier the case is being isolated. Positive values indicate isolation before symptom onset, negative values indicate isolation after symptom onset. \\ \hline \end{tabular} |
171363_file11 | ### Determination of PS3 and BS3
These attributes were annotated using manual literature screening to check for variants for which in vivo and in vitro functional studies have been performed. If in the studies, a variant was reported to be responsible for affecting the protein function, it was marked as PS3. In case, the functional studies reported a benign effect then they were marked as BS3.
### Determination of PS4
We manually screened literature containing case-control studies to determine the Odds Ratio. If the OR was found to be greater than 5 and the Confidence interval (CI) was more than 1, then the variant was regarded as PS4.
### Determination of PP1 and BS4
We manually performed literature searches to analyze if the variants co-segregate with the family members. If the variant was present in all affected individuals in a family, then it is marked as PP1. If the variant was not present in any of the members of a family or present in an unaffected member of the family, then due to lack of segregation it was marked as BS4.
### Determination of PP2 and BP1
We calculated the total number of pathogenic missense and stop gain variants for each gene using Clinvar. if the percentage of missense variant was >80% and stop-gain variant was <20% then for the nonsynonymous variant was marked as PP2. Otherwise, if the stop-gain variant was more than 80% and the nonsynonymous variant was < 20%, then the nonsynonymous variant was marked as BP1.
### Determination of PP3 and BP4
The variants were annotated using the jjb26_all database of the ANNOVAR annotation tool to determine the PP3 and BP4 parameters. The variants were scored using the SIFT and PolyPhen2, two of the popularly used in-silico callers to score the variants for their predicted pathogenicity. While SIFT cut-offs classify the variants as deleterious or tolerated, PolyPhen2 predictions classify them into 3 categories as probably damaging, Possibly Damaging or Benign. We also considered CADD scores which contain PHRED scaled score, if the score is 10 predicts, the 10% most deleterious variants, similarly a score of 20 predicts 1% the most deleterious variant. However, we rationally considered the CADD scores above 15 to be interpreted as deleterious in our analysis. The variants classified as deleterious/damaging by at least two of the three in-silico callers were marked as PP3 (pathogenic). Similarly, variants were marked as BP4 if the majority of the in-silico tools predicted them to be benign/tolerated.
### Determination of PP4
We used the OMIM database which is a comprehensive database of human genes and genetic phenotype whose main focus on the relationship of phenotype and genotype in Mendelian disorder and 15,000 genes. It is used to determine whether the disease was associated with just a single gene etiology. The variant was consistent means inherited in the family. The total number of benign should be less than 50% in a gene. All the variants fulfilling these criteria were marked as PP4.
### Determination of PP5 and BP6
Variants were marked as PP5 and BP6 using publicly available database Clinvar. Those variants which had non-conflicting pathogenic/likely pathogenic calls from reputable laboratories were marked as PP5. Similarly, variants having non-conflicting benign/likely benign calls were marked as BP6.
### Determination of PM1
We took the protein domains and their corresponding coordinates from the PFAM in UCSC gene track present in the UCSC browser and intersected the variant coordinates upon them. If the mutation hotspot was within these domains, then the variant was marked as PM1.
### Determination of PM2, BA1, BS1, and BS2
Population datasets like 1000 Genome Project (ALL.sites.2015_08), Exome Sequencing Project (esp6500siv2_all), Exome Aggregation Consortium (exac03) and gnomAD derived from ANNOVAR tool databases were used to annotate the variants as BA1, BS1, and PM2. All those variants which had MAF more than 5% in any of the four population datasets were marked as BA1 whilst variants having MAF between 1 and 5% were considered as strong evidence to be benign for Mendelian disorder were marked as BS1. In case the variant is absent from all of the control population datasets or is at extremely low frequency in autosomal recessive i.e. < 0.01%, it was classified as moderate evidence to be pathogenic (PM2). All variants that occurred in genes at greater than 1% frequency in Qatar population dataset, regardless of population allele frequency, were marked as BS2.
### Determination of PM3 and BP2
We first determined the mode of inheritance using OMIM. Using literature screening, we checked whether there were two heterozygous variants and the disorder was autosomal recessive. If both the mutations were found to be in trans they were marked as PM3. Similarly, if these were in cis they were considered to be BP2.
### Determination of PM4 and BP3
For annotating in-frame insertions or deletions by overlapping them with the repeated region in the human genome using repeat masker. If the in-frame insertions or deletions fall in the repeated they were marked as BP3, otherwise, they were marked as PM4
### Determination of BP7
Synonymous variant not in splice site was marked as BP7. |
171447_file02 | ## Table S4. Rasagiline cohort characteristics.
Shown are the mean, standard deviation (in parentheses), and the first, second (median), and third quartile (in brackets).
\begin{tabular}{l c c} \hline & **MarketScan** & **Explorys** \\ \hline
## Patient count
& 3,094 & 1,988 \\ \hline
## Patient timeline [years]
& & \\
## Total
& 4.1 (1.0) [3.0; 4.6; 5.0] & 11.2 (5.1) [7.0; 10.6; 14.8] \\
## Before index date
& 2.5 (1.0) [1.6; 2.4; 3.2] & 7.3 (4.8) [3.3; 6.3; 10.6] \\
## After index date
& 1.6 (1.0) [0.8; 1.5; 2.4] & 3.9 (2.5) [2.0; 3.5; 5.4] \\ \hline
## No.
& 15.6 (9.3) [9.0; 14.0; 21.0] & 20.7 (18.2) [7.0; 15.0; 29.0] \\ \hline
## Insurance
& & \\
## Medicare, Medicaid, other public
& 60\% & 80\% \\
## Commercial, private only
& 40\% & 18\% \\
## Other or unknown
& 0\% & 2\% \\ \hline
## Baseline characteristics (during \(\leq\)1 year index date)
& & \\
## Age at index date
& 68.5 (8.5) [61.8; 66.2; 74.7] & 70.7 (7.7) [64.8; 70.4; 76.4] \\
## Women
& 38\% & 37\% \\
## Charlson's Comorbidity Index
& 1.1 (1.5) [0.0; 0.0; 2.0] & 0.6 (1.2) [0.0; 0.0; 1.0] \\
## PD related diagnoses
& & \\
## Falls
& 3\% & 4\% \\
## Psychosis
& 1\% & 1\% \\ \hline
## Follow-up characteristics (during \(\leq\)2 years following index date)
& & \\
## PD Progression
& & \\
## Dementia
& 15\%\({}^{\dagger}\) (11\%) & 12\%\({}^{\dagger}\) (11\%) \\
## Charlson's Comorbidity Index
& 1.4 (1.9) [0.0; 1.0; 2.0] & 1.1 (1.8) [0.0; 0.0; 2.0] \\ \hline \end{tabular}
* 15% and 12% are Kaplan-Mayer estimators in MarketScan and Explorys resp., which adjust for censoring.
## Table S5. Zolpidem cohort characteristics.
Shown are the mean, standard deviation (in parentheses), and the first, second (median), and third quartile (in brackets).
\begin{tabular}{l c c} \hline & **MarketScan** & **Explorys** \\ \hline
## Patient count
& 847 & 1,828 \\ \hline
## Patient timeline [years]
& & \\
## Total
& 4.0 (1.1) [3.0; 4.1; 5.0] & 11.4 (5.1) [7.2; 11.1; 15.2] \\
## Before index date
& 2.2 (1.0) [1.4; 2.0; 2.8] & 7.5 (4.7) [3.6; 6.7; 10.7] \\
## After index date
& 1.8 (1.1) [0.9; 1.6; 2.6] & 3.9 (2.6) [1.8; 3.4; 5.4] \\ \hline
## No.
& 25.1 (12.7) [16.0; 23.0; 32.0] & 40.3 (25.8) [20.0; 35.0; 55.0] \\ \hline
## Insurance
& & \\
## Medicare, Medicaid, other public
& 77\% & 83\% \\
## Commercial, private only
& 23\% & 9\% \\
## Other or unknown
& 0\% & 8\% \\ \hline
## Baseline characteristics (during \(\leq\)1 year before index date)
& & \\
## Age at index date
& 71.4 (10.1) [62.6; 70.0; 79.5] & 73.9 (7.8) [67.8; 74.8; 80.2] \\
## Women
& 43\% & 45\% \\
## Charlson's Comorbidity Index
& 2.1 (2.3) [0.0; 1.0; 3.0] & 1.7 (2.1) [0.0; 1.0; 3.0] \\
## PD related diagnoses
& & \\
## Falls
& 8\% & 11\% \\
## Psychosis
& 5\% & 4\% \\ \hline
## Follow-up characteristics (during \(\leq\)2 years following index date)
& & \\
## PD Progression
& & \\
## Dementia
& 26\%\({}^{\dagger}\) (20\%) & 23\%\({}^{\dagger}\) (21\%) \\
## Charlson's Comorbidity Index
& 2.8 (2.9) [0.0; 2.0; 4.0] & 3.0 (3.0) [1.0; 2.0; 5.0] \\ \hline \end{tabular}
\(\dagger\) 26% and 23% are Kaplan-Mayer estimators in MarketScan and Explorys resp., which adjust for censoring.
## Table S6. N04 cohort characteristics.
Shown are the mean, standard deviation (in parentheses), and the first, second (median), and third quartile (in brackets).
\begin{tabular}{l c c} \hline & **MarketScan** & **Exploys** \\ \hline
## Patient count
& 10,289 & 12,408 \\ \hline
## Patient timeline [years]
& & \\
## Total
& 4.1 (1.0) [3.1; 4.8; 5.0] & 10.9 (5.1) [6.8; 10.5; 14.6] \\
## Before index date
& 2.5 (1.1) [1.6; 2.3; 3.3] & 7.5 (4.7) [3.6; 6.5; 10.6] \\
## After index date
& 1.6 (1.0) [0.8; 1.4; 2.4] & 3.5 (2.6) [1.5; 2.8; 4.8] \\ \hline
## No.
& 17.4 (10.4) [10.0; 16.0; 23.0] & 18.3 (17.8) [5.0; 13.0; 25.0] \\ \hline
## Insurance
& & \\
## Medicare, Medicaid, other public
& 79\% & 82\% \\
## Commercial, private only
& 21\% & 12\% \\
## Other or unknown
& 0\% & 6\% \\ \hline
## Baseline characteristics (during \(\leq\)1 year before index date)
& & \\
## Age at first diagnosis
& 73.3 (9.8) [64.6; 73.6; 81.1] & 73.7 (7.9) [67.9; 74.5; 79.9] \\
## Women
& 42\% & 44\% \\
## Charlson's Comorbidity Index
& 1.7 (2.0) [0.0; 1.0; 3.0] & 0.8 (1.3) [0.0; 0.0; 1.0] \\
## PD related diagnoses
& & \\
## Falls
& 5\% & 4\% \\
## Psychosis
& 3\% & 1\% \\ \hline
## Follow-up characteristics (during \(\leq\)2 years following index date)
& & \\
## PD progression
& & \\
## Dementia
& 28\%\({}^{\dagger}\) (21\%) & 19\%\({}^{\dagger}\) (17\%) \\
## Charlson's Comorbidity Index
& 2.2 (2.5) [0.0; 1.0; 3.0] & 1.6 (2.1) [0.0; 1.0; 2.0] \\ \hline \end{tabular}
\(\dagger\) 28% and 19% are Kaplan-Mayer estimators in MarketScan and Explorys resp., which adjust for censoring.
## Table S7. N05 cohort characteristics.
Shown are the mean, standard deviation (in parentheses), and the first, second (median), and third quartile (in brackets).
\begin{tabular}{l c c} \hline & **MarketScan** & **Exploys** \\ \hline
## Patient count
& 3,116 & 9,067 \\ \hline
## Patient timeline [years]
& & \\
## Total
& 4.0 (1.1) [3.0; 4.2; 5.0] & 10.4 (5.0) [6.5; 9.6; 14.1] \\
## Before index date
& 2.3 (1.0) [1.5; 2.1; 3.0] & 7.1 (4.6) [3.4; 6.1; 10.1] \\
## After index date
& 1.7 (1.1) [0.8; 1.5; 2.6] & 3.3 (2.4) [1.5; 2.8; 4.5] \\ \hline
## No.
& 19.4 (10.0) [12.0; 18.0; 25.0] & 24.4 (17.8) [11.0; 20.0; 33.0] \\ \hline
## Insurance
& & \\
## Medicare, Medicaid, other public
& 83\% & 84\% \\
## Commercial, private only
& 17\% & 9\% \\
## Other or unknown
& 0\% & 7\% \\ \hline
## Baseline characteristics (during \(\leq\)1 year before index date)
& & \\
## Age at first diagnosis
& 74.0 (9.9) [65.1; 74.4; 82.1] & (7.9) [68.9; 75.4; 80.8] \\
## Women
& 48\% & 45\% \\
## Charlson's Comorbidity Index
& 1.8 (2.1) [0.0; 1.0; 3.0] & 1.1 (1.7) [0.0; 0.0; 2.0] \\
## PD related diagnoses
& & \\
## Falls
& 6\% & 10\% \\
## Psychosis
& 7\% & 4\% \\ \hline
## Follow-up characteristics (during \(\leq\)2 years following index date)
& & \\
## PD progression
& & \\
## Dementia
& 38\%\({}^{\dagger}\) (30\%) & 29\%\({}^{\dagger}\) (27\%) \\
## Charlson's Comorbidity Index
& 2.4 (2.7) [0.0; 2.0; 4.0] & 2.3 (2.6) [0.0; 2.0; 4.0] \\ \hline \end{tabular}
\(\dagger\) 38% and 29% are Kaplan-Mayer estimators in MarketScan and Explorys resp., which adjust for censoring.
## Table S8. Estimated effects on dementia onset for emulated RCTs involving rasagiline and its encompassing ATC classes.
For composition of treatment and control cohorts, see Table S10. Beneficial effect is highlighted in green and non-beneficial effect is highlighted in red.
## Table S9. Estimated effects on dementia onset for emulated RCTs involving zolpidem and its encompassing ATC classes.
For composition of treatment and control cohorts, see Table S10. Beneficial effect is highlighted in green and non-beneficial effect is highlighted in red. |
171454_file02 | ### Accounting for population immunity: modification to theory for \(R_{e}>R_{e}^{*}\)
Infections decline when \(R_{e}<1\). \(R_{e}(t)=R_{0}\times S(t)/N\) is in general time-dependent, composed of two factors, \(R_{0}=\beta/\gamma\), which for simplicity we assume is time-independent and \(S(t)/N\), which will tend to decrease in time as more susceptibles become infected, so the rate of decline \(\rho_{e}=\gamma(1-Re)\) is in general time-dependent and increasing over time, as shown in Fig.2a, where the initial decline of infections is non-exponential. When \(R_{e}\ll 1\), reductions in transmissions due to NPIs dominates the decrease in infections, compared to the fractional change in the susceptible pool and so \(R_{e}\approx R_{0}S_{0}/N\) is constant to a good approximation. However, when \(R_{e}<1\) but close to \(1\), this is no longer true, and the assumption that the number of susceptibles is roughly constant \(S(t)\approx S_{0}\) with respect to changes in \(I(t)\) and \(R_{e}(t)\) is a poor one.
It is within this context that we would like to calculate the extinction time distribution. Although, an exact solution is not easily obtainable, we can make a semi-heuristic approximation that works very well. Initially \(R_{e}\) is time-dependent since the changing susceptible pool has significant affect on the decline in infections. However, once infections become sufficiently small the change in the susceptible pool, per unit time, once again becomes relatively small compared to its current value and \(S(t)\to S^{\infty}\) attains its asymptotic value \(S^{\infty}\), at which point the constant \(R_{e}\) assumption becomes accurate again and infections decline at a constant rate (Fig.2a). The asymptotic value \(S^{\infty}\) cannot be calculated via standard fixed point analysis of the SIR differential equations, since the only condition for a fixed point is that \(I=0\), and this can happen for any value of \(S\); the final asymptotic values depend on the initial conditions.
\[\frac{\mathrm{d}S}{\mathrm{d}R}=-\frac{\beta S}{\gamma N}=\frac{R_{0}}{N}S.\] (S15)
Integrating this equation, starting from an initial condition \(S=S_{0}\) and \(R\) to their final asymptotic values \(S^{\infty}\) and \(R^{\infty}=N-I^{\infty}-S^{\infty}=N-S^{\infty}\), then we arrive at the following transcendental equation for \(S^{\infty}\):
\[S^{\infty}=S_{0}e^{R_{0}(1-S^{\infty}/N-R/N)}.\] (S16)
The solution can however, be expressed using the Lambert \(W\) function:
\[S^{\infty}=-\frac{N}{R_{0}}W\left(-\frac{R_{0}S_{0}}{N}e^{-R_{0}(1-R/N)} \right),\] (S17)
We are interested in finding the asymptotic effective reproductive number \(R_{e}^{\infty}=R_{0}S^{\infty}/N\) in terms of the initial effective reproductive number \(R_{e}=R_{0}S_{0}/N\), for which the above expression can be rearranged to give
\[R_{e}^{\infty}=-W\left(-R_{e}e^{-R_{0}(1-R/N)}\right).\] (S18)
We can replace \(R_{e}\to R_{e}^{\infty}\) in Eqn.3 of the main text to calculate the distribution of extinction times to give a good approximation of the extinction times when \(R_{e}\approx 1\) and where the abovecondition for constant \(R_{e}\) is not met. However, this gives a systematic underestimate of the time to extinction, since it effectively ignores the time it takes to attain these asymptotic values, which takes of order \(1/\rho_{e}^{\infty}\) days, where \(\rho_{e}^{\infty}=\gamma(1-R_{e}^{\infty})\). So finally an accurate and robust approximation to the extinction time distribution is obtained by the replacement \(R_{e}\to R_{e}^{\infty}\) and \(\tau^{\dagger}\rightarrow\tau^{\dagger}+1/\rho_{e}^{\infty}\), as we can see in Fig.2b for simulations of \(R_{e}=0.99\) and \(1/\gamma=7\) days. Note that for sufficiently small \(R_{e}\) the correction to \(\tau\) is not needed, as \(R_{e}^{\infty}\approx R_{e}\) and the assumption of constant \(R_{e}\) is very accurate. We approximate this threshold value of \(R_{e}\) as the value of \(R_{e}^{\infty}(R_{e}\to 1)\):
\[R_{e}^{*}=R_{e}^{\infty}(R_{e}=1)=-W(-e^{-R_{0}(1-R/N)}).\] (S19)
We can then also stitch together \(\tau^{\dagger}\) for \(R_{e}<R_{e}^{*}\) and \(\tau+1/\rho^{\infty}\) for \(R_{e}>R^{*}\) using a standard \(\tanh\) switching function centred on \(R_{e}^{*}\) and with width \(0.05\), which is used in Fig.3 and Fig.4 in the main text to provide the extinction time predictions across the whole range of \(0<R_{e}<1\).
### Invariance of extinction time distribution to population sub-division
If we imagine a single population to be divided into \(n\) equally sized sub-populations, each with a reproductive number \(R_{e}\) and zero-migration between, then the extinction time distribution of \(t_{k}\) in the \(k^{th}\) sub-population will be given by Eqn.7 in the main text, but with \(I_{0}\to I_{0}/n\). Now we want to calculate the extinction time distribution of the whole population. Extinction will occur when all sub-populations have zero infected individuals. We can record the extinction times in each sub-population: \(t_{1},t_{2},...,t_{k},...,t_{n}\) and the extinction time of the whole population will be the maximum of this set: \(\tilde{t}=\max\{t_{1},t_{2},...,t_{k},...,t_{n}\}\). The cumulative distribution function of the maximum time \(\tilde{t}\) will be the probability of the joint event that each sub-population \(k\) has an extinction time less than \(\tilde{t}\):
\[P_{n}(\tilde{t}) =P(t_{1}<\tilde{t},t_{2}<\tilde{t},...,t_{k}<\tilde{t},...,t_{n}< \tilde{t})\] \[=P(t_{1}<\tilde{t})P(t_{2}<\tilde{t})...P(t_{k}<\tilde{t})...P(t_ {n}<\tilde{t})\] (S20) \[=(P(\tilde{t}))^{n}\]
Given the form of this equation, these calculations can be performed exactly, whereas using extreme value theory it usually required that the tails of the distribution asymptotically obey some exponential form, which allows approximate calculation. Doing these calculations we find \((P(\tilde{t}))^{n}=(\exp(-e^{-\rho_{e}(\tilde{t}-\tau_{n}^{\dagger})}))^{n}\), where \(\tau_{n}^{\dagger}=\frac{1}{\rho_{e}}\ln(I_{0}/nI^{\dagger})\).
\[P_{n}(\tilde{t})=P(\tilde{t})=\exp(-e^{-\rho_{e}(\tilde{t}-\tau^{\dagger})}).\] (S21)
In other words, population sub-division into equal sized isolated populations does not affect the extinction time distribution of the whole global population. In fact, it is simple to extend these arguments to any population sub-division, where \(I_{0}=\sum_{k=1}^{n}I_{k}\), where \(I_{k}\) is the initial infected population in each, as long as the fraction of susceptible and \(R_{e}\) is the same in each sub-population. This is not surprising, as it is just a restatement of the mean-field/well-mixed approximation that infected individuals and sub-populations all experience the same probability of encountering a susceptible individual \(S_{0}/N\) which is set by the global number of susceptible individuals \(S_{0}\).
|
171876_file02 | ## A: electrophysiological signal input
The EEG cohort described above is the input of the signal processing algorithm presented as the first step of the process.
## B: Wavelet Packet Analysis
For a given cohort of EEG recordings, a family of _wavelet packet trees_ is created. For the mathematical description, we follow the notation and construction provided in chapters 5, 6 and 7 of Wickerhauser's book.
To demonstrate the process; let \(g\) and \(h\) be a set of _biorthogonal quadrature filters_ created from the filters \(G\) and \(H\) respectively. Each of these is a convolution-decimation operator, where in the case of the simple _Haar_ wavelet, \(g\) is a set of averages and \(h\) is a set of differences.
The construction of the full wavelet packet tree is by successive application of these functions (Figure A2), so that at every level, a new full orthogonal decomposition of the original signal \(x\) is created. In the classical wavelet decomposition by Daubechies, only the marked parts are used and the signal is decomposed into _Gx, GHx etc.,_ but the full construction of the tree continues recursively, on _Gx, GHx_ and so forth, to create a full binary tree. Coifman and Wickerhauser observed that a large number of orthogonal decompositions can be constructed from the full tree by mixing between the different levels and different blocks of the tree, following a simple rule. The recursive construction of the full tree is described next.
Let \(\psi_{1}\) be the _mother wavelet_ associated to the filters \(s\in H\), an \(d\in G\). Then, the collection of _wavelet packets_\(\psi_{n}\), is given by:
\[\psi_{2n}=H\psi_{n}; \psi_{2n}(t)=\sqrt{2}\sum_{j\in\mathbb{Z}} s(j)\psi_{n}(2t-j),\] \[\psi_{2n+1}=G\psi_{n}; \psi_{2n+1}(t)=\sqrt{2}\sum_{j\in\mathbb{Z}} d(j)\psi_{n}(2t-j).\]
The recursive form provides a natural arrangement in the form of a binary tree (Figure A2).
The functions \(\psi_{n}\) have a fixed scale. A library of wavelet packets of any scale \(s\), frequency \(f\), and position \(p\) is given by:\[\psi_{sfp}(t)=2^{-s/2}\psi_{f}(2^{-s}t-p).\]
The wavelet packets \(\{\psi_{sfp}\colon p\in Z\}\) are an orthonormal basis for every \(f\) (under orthogonality condition of the filters \(H\) and \(G\)) and are called
## orthonormal wavelet packets
Using this construction, Coifman and Wickerhauser applied the _best basis_ algorithm to search for an orthonormal base that satisfies a specific optimality condition. The optimality condition that was chosen is Shannon's entropy of the coefficients of each component (or wavelet packet atom). It is a measure that prefers coefficients with a distribution that is far from uniform, in the sense that it prefers a distribution with a small number of high value coefficients and a long tale, namely, a large number with low value coefficients. The full details of the best basis search are described in chapter 7 of Wickerhaser's book.
The process of creating a best basis from the wavelet packet tree can be further iterated by an optimization on the mother wavelet using a gradient descent in wavelet space as is described in Neretti and Intrator.
## C: Pruning the optimal representation
The outcome of the best basis algorithm is an orthogonal decomposition that is adapted to the stochastic properties of the collection of EEG signals. However, there is a risk that the decomposition is "overfitting" namely it is too adapted to the EEG signals from which it was created. To avoid this phenomenon, we first have to get rid of "small" coefficients. This can be done by the denoising technique of Coifman and Donoho. The next step is introducing a validation set, which is another collection of EEG-recordings that was not used in the creation of the best basis. Using this set, we can determine which atoms maintain a high energy (some large coefficients) when decomposing the new signals. These atomswill remain in the representation. At the end of this part, the resulting set of decomposing signal contains only a part of the full orthonormal basis that was found. We then reorder the basis components not based on the binary tree that created them, but based on the correlation between the different components In this way, we created a brain activity representation in which components that are more correlated to each other, are also geographically close to each other within the representation. This is done for the purpose of improved visualization.
## D: brain activity representation output
The result of the signal processing module is the brain activity representation. Specifically, it is a collection of 121 energy components, emanating from the wavelet packets as well as standard frequency bands which are updated each second. The representation (D) shows a color heatmap of each of the 121 X time matrix, so that the x axis represents time and the y axis represents the different components.
## Creation of Novel features based on the BAFs
The signal components, which we termed BAFs, were constructed from single EEG channel recordings in an unsupervised manner, namely, there were no labels attached to the recordings for the purpose of creating the decomposition. To create biomarkers based on the BAFs, task labels are used, indicating the nature of cognitive, emotional, or resting challenge the subject is exposed to during the recording.
Given labels from a collection of subjects, and the corresponding high-dimensional BAF data, a collection of models attempting to differentiate between the labels based on the BAF activity can be used. In the linear case, these models are of the form:\[V_{k}(w,x)=\Psi\left(\sum_{i}\quad w_{i}x_{i}\right),\]
For each predictor, which we term biomarker, a standard machine learning procedure is applied as follows:
1. Choose a labeled data set with at least two different tasks (e.g. cognitive, emotional, or resting challenge). The data set may include the same challenge but for a non-homogenous group.
2. Separate the data into three sets: training, validation, and test.
3. Choose a model to train on from a family of models that includes linear regression, linear regression with binary constrains (zero and one values for the weights), linear regression with only positive values, logistic regression, discriminant analysis and principal components analysis. In the non-linear models, use neural networks, support vector machine and the like.
4. Train each model on several sets of train/test and validation to best estimate internal model such as the variance constraints, on the ridge regression, the kernel size and number of kernels in a support vector machine, or the weight constraints in a neural network model.
5. From the above models, obtain predictors to be tested on other data with potentially other cognitive, emotional and rest challenges.
6. The last step in the process includes testing the biomarkers using a test data labeled set that was not used in the creation of these features. This allows removal of features that were overfitting to the training data, namely, they do not produce high significant difference on the validation data. This is still part of the model creation and not part of the model testing that is done on new data and is described in step 3.
All above steps are described in the scheme on Figure A3.
#### Examination of the features on previously unseen data
Following the creation of BAFs and the creation of features as described above, the features relevance can be tested on various cognitive or emotional challenge. The testing scheme is described in Figure A4. Specifically, data is collected with the sensor system and sent to the cloud for creation of a BAF representation using the previously determined wavelet packet atoms. The BAF representation is provided to previously determined ML models, which convert the BAF activity into features. Statistical tests are then applied to determine the quality of the predictions and the correlation of the features to the cognitive and emotional challenges that the participants undergo. This may include single subject analysis as well as group analysis.
In the process of testing the features on new data, we may want to get an _upper bound_ to the performance of the feature, by seeking an _overfitting biomarker_ on the currently tested data. This is only done to get an idea of the potential upper bound on prediction abilities from the existing data, and indirectly can tell us more about the optimality of the actual features that were constructed from a different data set and are assumed to be more general in this sense.
|
171876_file03 | ## A: electrophysiological signal input
The EEG cohort described above is the input of the signal processing algorithm presented as the first step of the process.
## B: Wavelet Packet Analysis
For a given cohort of EEG recordings, a family of _wavelet packet trees_ is created. For the mathematical description, we follow the notation and construction provided in chapters 5, 6 and 7 of Wickerhauser's book.
To demonstrate the process; let \(g\) and \(h\) be a set of _biorthogonal quadrature filters_ created from the filters \(G\) and \(H\) respectively. Each of these is a convolution-decimation operator, where in the case of the simple _Haar_ wavelet, \(g\) is a set of averages and \(h\) is a set of differences.
The construction of the full wavelet packet tree is by successive application of these functions (Figure A2), so that at every level, a new full orthogonal decomposition of the original signal \(x\) is created. In the classical wavelet decomposition by Daubechies, only the marked parts are used and the signal is decomposed into _Gx, GHx etc.,_ but the full construction of the tree continues recursively, on _Gx, GHx_ and so forth, to create a full binary tree. Coifman and Wickerhauser observed that a large number of orthogonal decompositions can be constructed from the full tree by mixing between the different levels and different blocks of the tree, following a simple rule. The recursive construction of the full tree is described next.
Let \(\psi_{1}\) be the _mother wavelet_ associated to the filters \(s\in H\), an \(d\in G\). Then, the collection of _wavelet packets_\(\psi_{n}\), is given by:
\[\psi_{2n}=H\psi_{n}; \psi_{2n}(t)=\sqrt{2}\sum_{j\in\mathbb{Z}} s(j)\psi_{n}(2t-j),\] \[\psi_{2n+1}=G\psi_{n}; \psi_{2n+1}(t)=\sqrt{2}\sum_{j\in\mathbb{Z}} d(j)\psi_{n}(2t-j).\]
The recursive form provides a natural arrangement in the form of a binary tree (Figure A2).
The functions \(\psi_{n}\) have a fixed scale. A library of wavelet packets of any scale \(s\), frequency \(f\), and position \(p\) is given by:\[\psi_{sfp}(t)=2^{-s/2}\psi_{f}(2^{-s}t-p).\]
The wavelet packets \(\{\psi_{sfp}\colon p\in Z\}\) are an orthonormal basis for every \(f\) (under orthogonality condition of the filters \(H\) and \(G\)) and are called
## orthonormal wavelet packets
Using this construction, Coifman and Wickerhauser applied the _best basis_ algorithm to search for an orthonormal base that satisfies a specific optimality condition. The optimality condition that was chosen is Shannon's entropy of the coefficients of each component (or wavelet packet atom). It is a measure that prefers coefficients with a distribution that is far from uniform, in the sense that it prefers a distribution with a small number of high value coefficients and a long tale, namely, a large number with low value coefficients. The full details of the best basis search are described in chapter 7 of Wickerhaser's book.
The process of creating a best basis from the wavelet packet tree can be further iterated by an optimization on the mother wavelet using a gradient descent in wavelet space as is described in Neretti and Intrator.
## C: Pruning the optimal representation
The outcome of the best basis algorithm is an orthogonal decomposition that is adapted to the stochastic properties of the collection of EEG signals. However, there is a risk that the decomposition is "overfitting" namely it is too adapted to the EEG signals from which it was created. To avoid this phenomenon, we first have to get rid of "small" coefficients. This can be done by the denoising technique of Coifman and Donoho. The next step is introducing a validation set, which is another collection of EEG-recordings that was not used in the creation of the best basis. Using this set, we can determine which atoms maintain a high energy (some large coefficients) when decomposing the new signals. These atomswill remain in the representation. At the end of this part, the resulting set of decomposing signal contains only a part of the full orthonormal basis that was found. We then reorder the basis components not based on the binary tree that created them, but based on the correlation between the different components In this way, we created a brain activity representation in which components that are more correlated to each other, are also geographically close to each other within the representation. This is done for the purpose of improved visualization.
## D: brain activity representation output
The result of the signal processing module is the brain activity representation. Specifically, it is a collection of 121 energy components, emanating from the wavelet packets as well as standard frequency bands which are updated each second. The representation (D) shows a color heatmap of each of the 121 X time matrix, so that the x axis represents time and the y axis represents the different components.
## Creation of Novel features based on the BAFs
The signal components, which we termed BAFs, were constructed from single EEG channel recordings in an unsupervised manner, namely, there were no labels attached to the recordings for the purpose of creating the decomposition. To create biomarkers based on the BAFs, task labels are used, indicating the nature of cognitive, emotional, or resting challenge the subject is exposed to during the recording.
Given labels from a collection of subjects, and the corresponding high-dimensional BAF data, a collection of models attempting to differentiate between the labels based on the BAF activity can be used. In the linear case, these models are of the form:\[V_{k}(w,x)=\Psi\left(\sum_{i}\quad w_{i}x_{i}\right),\]
For each predictor, which we term biomarker, a standard machine learning procedure is applied as follows:
1. Choose a labeled data set with at least two different tasks (e.g. cognitive, emotional, or resting challenge). The data set may include the same challenge but for a non-homogenous group.
2. Separate the data into three sets: training, validation, and test.
3. Choose a model to train on from a family of models that includes linear regression, linear regression with binary constrains (zero and one values for the weights), linear regression with only positive values, logistic regression, discriminant analysis and principal components analysis. In the non-linear models, use neural networks, support vector machine and the like.
4. Train each model on several sets of train/test and validation to best estimate internal model such as the variance constraints, on the ridge regression, the kernel size and number of kernels in a support vector machine, or the weight constraints in a neural network model.
5. From the above models, obtain predictors to be tested on other data with potentially other cognitive, emotional and rest challenges.
6. The last step in the process includes testing the biomarkers using a test data labeled set that was not used in the creation of these features. This allows removal of features that were overfitting to the training data, namely, they do not produce high significant difference on the validation data. This is still part of the model creation and not part of the model testing that is done on new data and is described in step 3.
All above steps are described in the scheme on Figure A3.
#### Examination of the features on previously unseen data
Following the creation of BAFs and the creation of features as described above, the features relevance can be tested on various cognitive or emotional challenge. The testing scheme is described in Figure A4. Specifically, data is collected with the sensor system and sent to the cloud for creation of a BAF representation using the previously determined wavelet packet atoms. The BAF representation is provided to previously determined ML models, which convert the BAF activity into features. Statistical tests are then applied to determine the quality of the predictions and the correlation of the features to the cognitive and emotional challenges that the participants undergo. This may include single subject analysis as well as group analysis.
In the process of testing the features on new data, we may want to get an _upper bound_ to the performance of the feature, by seeking an _overfitting biomarker_ on the currently tested data. This is only done to get an idea of the potential upper bound on prediction abilities from the existing data, and indirectly can tell us more about the optimality of the actual features that were constructed from a different data set and are assumed to be more general in this sense.
|
177162_file03 | ## Ecuador
\begin{tabular}{|l|l|l|l|l|l|l|} \hline
## Inflammatory** & **eosinophilic** & **mixed** & **neutrophilic** & **paucigranulocytic** & **Asthmatics without** & **Controls
(with sputum result) \\
## phenotype** & & **granulocytic** & & & **sputum result** & **gutum results)** \\ \hline & **35** & **5** & **8** & **77** & **51** & **41
\\ \hline Female (\%) & 10 (29\%) & 2 (40\%) & 3 (38\%) & 44 (57\%) & 17 (33\%) & 11 (27\%) \\ \hline Age at questionnaire, years: mean (range) & 12.4 (10.5 – 16.2) & 13.8 (11.7 – 16.8) & 12.3 (10.3 – 14.6) & 11.9 (10.3 – 16.9) & 11.8 (10.3 – 14.3) & 11.7 (11.0 – 12.1) \\ \hline Asthma diagnosis confirmed by doctor & 29 (83\%) & 5 (100\%) & 5 (63\%) & 40 (52\%) & 29 (57\%) & - \\ \hline Age at asthma diagnosis, years: median (range) & 4 (0.08 – 9) & 4 (0.7 – 13) & 1.3 (0.3 – 6) & 2 (0 – 14) & 2 (0 – 10) & - \\ \hline
## Asthma severity in past 12 months*
& & & & & & - \\ \hline mild or moderate & 20 (57\%) & 3 (60\%) & 4 (50\%) & 45 (59\%) & 24 (47\%) & \\ \hline severe & 15 (43\%) & 2 (40\%) & 4 (50\%) & 31 (41\%) & 27 (53\%) & \\ \hline missing & & & & 1 & & \\ \hline
## Severe asthma
(\textgreater{}12 & 0 & 0 & 0 & 0 & 0 & \\ attacks in past 12 months) & & & & & & \\ \hline
## Asthma medication in past 12 months** & & & & & & - \\ \hline none & **13 (37\%)** & **1 (20\%)** & **5 (63\%)** & **52 (68\%)** & **28 (55\%)** & \\ \hline ICS (preventer inhaler) & 0 & 0 & 0 & 6 (8\%) & 0 & \\ \hline Bronchodilator (reliever inhaler) & **7 (20\%)** & **1 (20\%)** & **0** & **10 (13\%)** & **9 (18\%)
& \\ \hline
## ACQ score (past week)
& & & & & & \\ \hline Median (IQR, range) & 0 (0 – 0, 0 – 2.67) & 0 (0 – 0, 0 – 2) & 0 (0 – 0, 0 – 0) & 0 (0 – 0, 0 – 1.5) & 0 (0 – 0, 0 – 2.67) & - \\ \hline \end{tabular}
\begin{tabular}{|l|l|l|l|l|l|l|} \hline Well controlled & 32 (91\%) & 4 (80\%) & 8 (100\%) & 76 (99\%) & 48 (94\%) & \\ (score\(<\)1.5) & & & & & & \\ \hline Not well controlled & 3 (9\%) & 1 (20\%) & 0 & 1 (1\%) & 3 (6\%) & \\ (score \(\geq\)1.5) & & & & & & \\ \hline \multicolumn{5}{|l|}{**Lung function** absolute values (L) \& & & & & \\ GLI-2012 z-scores & n=34 & n=5 & n=8 & n=77 & n=48 & n=41 & \\ \hline - FEV1, mean (SD) & 2.11 (0.56) & 2.36 (0.52) & 2.03 (0.49) & 2.15 (0.43) & 2.00 (0.39) & 2.05 (0.35) \\ range & 1.16 - 3.75 & 1.62 - 3.00 & 1.58 - 2.86 & 1.37 - 3.79 & 1.31 - 2.88 & 1.35 - 3.19 \\ \hline - FEV1,2-score, mean & -0.48 (0.96) & -0.63 (1.07) & -0.50 (0.80) & -0.07 (0.92) & -0.49 (1.01) & -0.002 (0.93) \\ (SD) range & -3.03 - 1.26 & -2.11 - 0.70 & -1.37 - 0.97 & -2.31 - 2.07 & -2.46 - 2.17 & -1.99 - 2.80 \\ - FVC, mean (SD) & 2.39 (0.65) & 2.58 (0.52) & 2.25 (0.61) & 2.36 (0.46) & 2.25 (0.48) & 2.25 (0.38) \\ range & 1.28 - 4.21 & 1.76 - 3.07 & 1.69 - 3.38 & 1.49 - 4.23 & 1.34 - 3.29 & 1.57 - 3.46 \\ \hline - FVC z-score, mean & -0.56 (0.95) & -0.86 (1.29) & -0.69 (1.10) & -0.33 (0.94) & -0.62 (1.11) & -0.34 (0.94) \\ (SD) range & -3.21 - 1.45 & -2.25 - 0.45 & -1.78 - 1.01 & -2.75 - 1.53 & -3.30 - 2.71 & -2.25 - 2.07 \\ \hline - FEV1/FVC, mean (SD) range & 0.89 (0.06) & 0.91 (0.06) & 0.91 (0.03) & 0.91 (0.05) & 0.89 (0.06) & 0.91 (0.05) \\ (SD) range & 0.75 - 1.00 & 0.85 - 1.00 & 0.85 - 0.93 & 0.74 - 1.00 & 0.77 - 0.99 & 0.81 - 0.99 \\ \hline - FEV1/FVC z-score, mean (SD) range & 0.16 (1.07) & 0.38 (1.22) & 0.35 (0.68) & 0.54 (1.01) & 0.26 (1.11) & 0.67 (0.96) \\ - mean (SD) range & -1.91 - 2.29 & -0.87 - 2.29 & -0.99 - 1.19 & -2.34 - 2.61 & -1.76 - 2.47 & -1.20 - 2.46 \\ \hline \multicolumn{5}{|l|}{**FeNO level**} & & & & & \\ \hline normal & 12 & 3 & 8 & 60 & 29 & 32 \\ elevated & 23 (66\%) & 2 (40\%) & 0 (0\%) & 17 (22\%) & 21 (42\%) & 9 (22\%) \\ \hline not measured & & & & & 1 & \\ \hline \multicolumn{5}{|l|}{**Skin pick test positive**} & & & & & \\ \hline \multicolumn{5}{|l|}{**Blood eosinophils**} & n=35 & n=5 & n=8 & n=77 & n=51 & n=41 \\ absolute values & 0.65 & 0.70 & 0.40 & 0.48 & 0.50 & 0.49 \\ (10\({}^{9}\)/L) median & (0.002 - 2.74) & (0.19 - 1.18) & (0.11 - 1.68) & (0.07 - 3.40) & (0.04 - 1.85) & (0 - 1.88) \\ \hline \end{tabular}
## New Zealand
\begin{tabular}{|l|l|l|l|l|l|l|} \hline
## Inflammatory** & **eosinophilic** & **mixed** & **neutrophilic** & **paucigranulocytic** & **Asthmatics without** & **Controls
(with sputum results) \\
## phenotype** & & **granulocytic** & & & **sputum result** & **sputum results)** \\ \hline & **99** & **5** & **14** & **89** & **28** & **104
\\ \hline Female (\%) & 45 (45\%) & 2 (40\%) & 10 (71\%) & 46 (52\%) & 10 (36\%) & 62 (60\%) \\ \hline Age at questionnaire, years: mean (range) & 14.0 (9.1 - 20.0) & 11.8 (8.6 - 16.0) & 11.8 (8.8 - 15.7) & 15.1 (9.3 - 20.3) & 12.6 (9.0 - 17.9) & 14.9 (9.0 - 18.8) \\ \hline Asthma diagnosis confirmed by doctor & 94 (95\%) & 5 (100\%) & 13 (93\%) & 77 (87\%) & 25 (89\%) & - \\ \hline Age at asthma diagnosis, years: median (range) & 3 (0 - 13) & 2 (1 - 4) & 4 (1 - 8) & 5 (1 - 16) & 3 (1 - 11) & - \\ \hline missing & 20 & 0 & 2 & 19 & 4 & \\ \hline
## Asthma severity in past 12 months*
& & & & & & \\ \hline mild or moderate & 45 & 1 & 7 & 56 & 14 & \\ \hline severe & 54 (55\%) & 4 (80\%) & 7 (50\%) & 33 (37\%) & 14 (50\%) & \\ \hline missing & & & & & & \\ \hline
## Severe asthma
(\textgreater{}12 & 18 (18\%) & 1 (20\%) & 2 (14\%) & 8 (9\%) & 7 (25\%) & \\ attacks in past 12 months & & & & & & \\ \hline
## Asthma medication in past 12 months** & & & & & & \\ \hline none & 2 (2\%) & 0 & 0 & **11 (12\%)** & 1 (4\%) & \\ \hline ICS (preventer inhaler) & **72 (73\%)** & 5 (100\%) & 9 (64\%) & 56 (63\%) & **20 (71\%)** & \\ \hline Bronchodilator (reliever inhaler) & **91 (92\%)** & 5 (100\%) & 14 (100\%) & 74 (83\%) & **26 (93\%)
& \\ \hline
## ACQ score (past week)
& & & & & & \\ \hline Median (IQR, range) & & & & & \\ \hline \end{tabular}
\begin{tabular}{|l|l|l|l|l|l|l|} \hline Well controlled & 67 (76\%) & 2 (40\%) & 14 (100\%) & 66 (84\%) & 21 (88\%) & \\ (score\(<\)1.5) & & & & & & \\ \hline Not well controlled & 21 (24\%) & 3 (60\%) & 0 & 13 (16\%) & 3 (12\%) & \\ (score \(\geq\)1.5) & & & & & & \\ \hline missing & 11 & 0 & 0 & 10 & 4 & \\ \hline
## Lung function** & & & & & & \\ absolute values (L) \& & & & & & \\ GLI-2012 z-scores & n=99 & n=5 & n=14 & n=89 & n=27 & n=104 \\ \hline - FEV\({}_{1}\), mean (SD) & 2.65 (0.88) & 1.78 (0.44) & 2.14 (0.61) & 3.18 (0.94) & 2.29 (0.75) & 3.12 (0.97) \\ range & 1.13 - 4.84 & 1.20 - 2.11 & 1.46 - 3.34 & 1.36 - 5.37 & 1.41 - 4.27 & 1.31 - 5.42 \\ \hline - FEV\({}_{1}\) z-score, mean & -0.72 (0.98) & -0.87 (1.77) & -0.28 (1.07) & -0.21 (0.97) & -0.58 (1.37) & -0.12 (0.99) \\ (SD) range & -2.95 - 1.61 & -3.52 - 0.89 & -1.94 - 1.51 & -2.24 - 2.36 & -3.08 - 2.13 & -2.41 - 2.60 \\ \hline - FVC, mean (SD) & 3.30 (1.10) & 2.45 (0.81) & 2.56 (0.69) & 3.81 (1.09) & 2.94 (1.09) & 3.63 (1.14) \\ range & 1.62 - 6.05 & 1.36 - 3.62 & 1.80 - 3.64 & 1.81 - 6.05 & 1.79 - 5.78 & 1.44 - 6.31 \\ \hline - FVC z-score, mean & -0.07 (0.95) & 0.35 (1.17) & 0.23 (1.35) & 0.19 (0.86) & 0.19 (1.21) & -0.01 (0.89) \\ (SD) range & -2.15 - 2.15 & -1.42 - 1.24 & -2.07 - 2.58 & -2.56 - 2.57 & -1.62 - 2.97 & -2.16 - 2.28 \\ \hline - FEV\({}_{1}\)/FVC, mean (SD) range & 0.82 (0.07) & 0.76 (0.13) & 0.83 (0.05) & 0.84 (0.07) & 0.79 (0.07) & 0.87 (0.06) \\ (SD) range & 0.59 - 0.99 & 0.60 - 0.88 & 0.77 - 0.92 & 0.68 - 0.99 & 0.62 - 0.90 & 0.67 - 0.99 \\ \hline - FEV\({}_{1}\)/FVC z-score, & -0.94 (0.99) & -1.81 (1.49) & -0.87 (0.75) & -0.49 (1.07) & -1.25 (0.97) & -0.11 (0.89) \\ mean (SD) range & -3.62 - 2.29 & -3.59 - 0.51 & -1.50 - 0.51 & -2.70 - 2.28 & -3.00 - 0.69 & -2.68 - 2.14 \\ \hline \multicolumn{8}{l|}{**FeNO level
\\ \hline normal & 31 & 2 & 8 & 69 & 13 & 88 \\ \hline elevated & 68 (69\%) & 3 (60\%) & 6 (43\%) & 19 (22\%) & 15 (54\%) & 15 (15\%) \\ \hline not measured & 0 & 0 & 0 & 1 & 0 & 1 \\ \hline
## Skin prick test
& 83 (85\%) & 4 (80\%) & 11 (79\%) & 67 (75\%) & 22 (79\%) & 40 (39\%) \\
## positive
& & & & & & \\ \hline Not done & 1 & 0 & 0 & 0 & 0 & 1 \\ \hline
## Blood eosinophils
& n=73 & n=4 & n=9 & n=77 & n=20 & n=88 \\ absolute values & 0.60 (0 − 1.90) & 0.60 (0.10 – & 0.50 (0.10 – & 0.30 (0 – 1.90) & 0.45 (0.10 – 1.10) & 0.20 (0.10 – \\ (10\({}^{9}\)/L) median (range) & & 1.00) & 0.70) & & & 2.20) \\ \hline \end{tabular}
## Uganda
\begin{tabular}{|p{56.9pt}|p{56.9pt}|p{56.9pt}|p{56.9pt}|p{56.9pt}|p{56.9pt}|p{56.9pt}|p{56.9pt}|} \hline
## Inflammatory phenotype** & **eosinophilic** & **mixed granulocytic** & **neutrophilic** & **paucigranulocytic** & **Asthmatics without sputum result** & **Controls** (with sputum results) \\ \hline & **25** & **8** & **34** & **31** & **109** & **20
\\ \hline Female (\%) & 14 (56\%) & 6 (75\%) & 26 (76\%) & 27 (87\%) & 82 (75\%) & 12 (60\%) \\ \hline Age at questionnaire, years: mean (range) & 15.2 (12.7 - 17.9) & 15.7 (13.0 - 17.5) & 15.5 (12.0 - 17.8) & 15.6 (12.1 - 17.9) & 15.7 (12.2 - 18.0) & 15.7 (13.0 - 18.9) \\ \hline Asthma diagnosis confirmed by doctor & 17 (68\%) & 6 (75\%) & 16 (47\%) & 19 (61\%) & 83 (76\%) & - \\ \hline Age at asthma diagnosis, years: median (range) & 9, 1-13 & 5, 1-13 & 8, 1-16 & 12, 1-15 & 8, 1-17 & - \\ \hline
## Asthma severity in past 12 months*
& & & & & & - \\ \hline mild or moderate severe & 9 & 2 & 18 & 14 & 28 & \\ \hline
## Severe asthma
(\textgreater{}12 attacks in past 12 months) & 16 (64\%) & 6 (75\%) & 16 (47\%) & 17 (55\%) & 81 (74\%) & \\ \hline
## Asthma medication in past 12 months
& & & & & & \\ \hline none & 6 (24\%) & 2 (25\%) & 12 (35\%) & 10 (32\%) & 25 (23\%) & \\ \hline ICS (preventer inhaler) & 4 (16\%) & 2 (25\%) & 2 (6\%) & 3 (10\%) & 22 (20\%) & \\ \hline Bronchodilator (reliever inhaler) & 8 (32\%) & 5 (63\%) & 6 (18\%) & 12 (39\%) & 51 (47\%) & \\ \hline
## ACQ score (past week)
& & & & & & \\ \hline Median (IQR, range) & 0.5, 0 – 1.67, 0 – 2.67 & 1.0, 0 – 1.0, 0 – 2.5 & 1.1, 0.17 – 2.5 & 0.33, 0 – 1.5, 0 – 4 & 0.34, 0 – 1.5, 0 – 5 & 0.42, 0 – 1.6, 0 – 5 & - \\ \hline \end{tabular}
\begin{tabular}{l|l|l|l|l|l|l} Well controlled & 17 (74\%) & 5 (63\%) & 22 (65\%) & 22 (71\%) & 53 (74\%) & \\ (score\(<\)1.5) & & & & & & \\ \hline Not well controlled & 6 (26\%) & 3 (37\%) & 12 (35\%) & 9 (29\%) & 19 (26\%) & \\ (score\(\geq\)1.5) & & & & & & \\ \hline Not done & 2 & 0 & 0 & 0 & 37 & \\ \hline
## Lung function** & & & & & & \\ absolute values (L) \& & & & & & \\ GLI-2012 z-scores & n=17 & n=7 & n=27 & n=24 & n=63 & n=16 \\ \hline - FEV\({}_{1}\), mean (SD) & 2.54 (0.60) & 2.57 (1.00) & 2.53 (0.35) & 2.54 (0.38) & 2.67 (0.45) & 2.47 (0.63) \\ range & 1.81 - 3.98 & 1.73 - 4.02 & 1.95 - 3.14 & 2.04 - 3.38 & 1.68 - 4.06 & 1.57 - 3.72 \\ - FEV\({}_{1}\) z-score, mean & -0.40 (0.81) & -0.18 (1.35) & -0.29 (0.76) & -0.06 (0.70) & -0.19 (0.98) & -0.26 (1.04) \\ (SD) range & -1.48 - 1.66 & -1.58 - 1.89 & -1.50 - 1.03 & -1.23 - 1.30 & -2.78 - 2.23 & -1.97 - 1.60 \\ \hline - FVC, mean (SD) & 2.99 (0.55) & 3.55 (2.19) & 2.91 (0.35) & 2.92 (0.53) & 3.12 (0.58) & 2.89 (0.78) \\ range & 2.34 - 4.13 & 2.07 - 8.01 & 2.25 - 3.55 & 2.15 - 4.57 & 1.77 - 5.01 & 1.65 - 4.53 \\ \hline - FVC z-score, mean & -0.03 (0.88) & 1.22 (2.91) & -0.11 (0.78) & 0.17 (1.07) & 0.07 (1.04) & 0.11 (1.52) \\ (SD) range & -1.31 - 1.64 & -1.11 - 7.14 & -1.72 - 1.13 & -1.82 - 2.98 & -1.94 - 3.05 & -2.34 - 4.13 \\ \hline - FEV\({}_{1}\)/FVC, mean & 0.85 (0.09) & 0.79 (0.14) & 0.87 (0.06) & 0.88 (0.08) & 0.86 (0.09) & 0.87 (0.12) \\ (SD) range & 0.69 - 0.99 & 0.49 - 0.91 & 0.74 - 0.97 & 0.67 - 0.99 & 0.63 - 1.00 & 0.48 - 1.00 \\ - FEV/FVC z-score, & -0.55 (1.41) & -1.45 (1.38) & -0.34 (1.00) & -0.25 (1.21) & -0.35 (1.37) & -0.26 (1.46) \\ mean (SD) range & -2.69 - 1.98 & -4.25 - 0.04 & -2.13 - 1.46 & -2.90 - 1.78 & -3.14 - 2.51 & -3.92 - 1.93 \\ \hline \multicolumn{8}{l}{**FeNO level**} \\ \hline normal & 6 & 2 & 22 & 24 & 59 & 18 \\ \hline elevated & 17 (74\%) & 6 (75\%) & 12 (35\%) & 6 (20\%) & 43 (42\%) & 2 (10\%) \\ \hline not measured & 2 & 0 & 0 & 1 & 7 & 0 \\ \hline \multicolumn{8}{l}{**Skin prick test
\\ \hline
## positive
& & & & & & \\ \hline Not tested & 0 & 0 & 0 & 1 & 10 & 0 \\ \hline
## Blood eosinophils
& n=25 & n=8 & n=34 & n=31 & n=98 & n=20 \\ absolute values & 0.47 & 0.31 & 0.22 & 0.23 & 0.22 & 0.26 \\ (10\({}^{9}\)/L) median & (0.07 - 2.99) & (0.19 - 0.80) & (0.01 - 2.95) & (0 - 1.09) & (0.02 - 1.55) & (0.05 - 0.81) \\ \end{tabular}
## United Kingdom
\begin{tabular}{|l|l|l|l|l|l|l|} \hline
## Inflammatory phenotype** & **eosinophilic** & **mixed** & **neutrophilic** & **paucigranulocytic** & **Asthmatics** & **Controls** (with **without sputum** & **controls** (with **result**) \\ \hline & **23** & **2** & **6** & **45** & **100** & **29
\\ \hline Female (\%) & 14 (61\%) & 2 (100\%) & 5 (83\%) & 36 (80\%) & 74 (74\%) & 17 (59\%) \\ \hline Age at questionnaire, years: mean (range) & 25.9 (25.0 - 26.6) & 25.8 (25.6 - 26.1) & 26.0 (25.3 - 26.7) & 25.9 (24.9 - 26.9) & 25.9 (24.6 - 27.3) & 25.9 (24.7 - 27.3) \\ Asthma diagnosis confirmed by doctor & 22 (96\%) & 2 (100\%) & 6 (100\%) & 44 (98\%) & 97 (97\%) & - \\
## Asthma severity in past 12 months*
& & & & & - \\ \hline mild or moderate & 7 & 1 & 5 & 29 & 55 & \\ \hline severe & 16 (70\%) & 1 (50\%) & 1 (17\%) & 16 (36\%) & 45 (45\%) & \\
## Severe asthma
(\(>\)12 attacks in past 12 months) & 8 (35\%) & 1 (50\%) & 0 & 3 (7\%) & 15 (15\%) & \\ \hline
## Asthma medication in past 12 months
& & & & & - \\ \hline none & 1 (6\%) & 0 & 0 & 4 (9\%) & 22 (22\%) & \\ \hline ICS (preventer inhaler) & 17 (74\%) & 2 (100\%) & 5 (83\%) & 26 (58\%) & 44 (44\%) & \\ \hline Bronochloridator (reliever inhaler) & 22 (96\%) & 2 (100\%) & 6 (100\%) & 40 (89\%) & 75 (75\%) & \\ \hline
## ACQ score (past week)
& & & & & - \\ \hline Median (IQR, range) & 0.92 (0.50 - 1.17, 0 (0.83 - 1.17, 0 - 3) & 0.83 - 1.17) & 0.25 (0 - 0.67, 0 - 1.33) & 0.33 (0 - 1.17, 0 - 2.5) & 0.17 (0 - 0.83, 0 - 2.83) & \\ \hline Well controlled (score\(<\)1.5) & 19 (86\%) & 2 (100\%) & 6 (100\%) & 38 (86\%) & 89 (92\%) & \\ \hline \end{tabular}
\begin{tabular}{|l|l|l|l|l|l|l|} \hline Not well controlled & 3 (14\%) & 0 & 0 & 6 (14\%) & 8 (8\%) & \\ (score \(\geq\)1.5) & & & & & & \\ \hline Not done & 1 & 0 & 0 & 1 & 3 & \\ \hline
## Lung function
& & & & & & \\ absolute values (L) \& ALI-2012 z-scores & N=23 & N=2 & N=5 & N=44 & N=96 & N=29 \\ \hline - FEV1, mean (SD) & 3.70 (0.90) & 2.95 (0.95) & 3.77 (0.75) & 3.33 (0.78) & 3.50 (0.74) & 3.98 (0.90) \\ range & 2.39 - 5.45 & 2.28 - 3.62 & 2.97 - 4.62 & 1.62 - 5.29 & 2.36 - 5.61 & 2.59 - 6.32 \\ \hline - FEV1 z-score, mean (SD) range & -0.33 (0.91) & -0.88 (3.02) & -0.07 (1.60) & -0.56 (1.43) & -0.36 (1.00) & -0.15 (1.05) \\ (SD) range & -2.26 - 0.96 & -3.02 - 1.26 & -1.64 - 2.43 & -4.12 - 3.59 & -3.02 - 2.82 & -2.62 - 2.76 \\ \hline - FVC, mean (SD) & 4.75 (1.23) & 4.07 (1.24) & 4.53 (0.82) & 4.05 (0.95) & 4.27 (1.03) & 4.81 (1.31) \\ range & 3.33 - 7.78 & 3.19 - 4.95 & 3.65 - 5.69 & 1.80 - 6.34 & 2.78 - 7.45 & 3.31 - 8.11 \\ - FVC z-score, mean (SD) range & 0.31 (0.85) & 0.35 (0.33) & 0.02 (1.26) & -0.33 (1.32) & -0.13 (0.89) & -0.06 (1.10) \\ (SD) range & -1.62 - 1.96 & -2.00 - 2.70 & -1.61 - 1.67 & 4.52 - 3.74 & -2.03 - 1.65 & -2.12 - 3.12 \\ \hline - FEV1/FVC, mean (SD) range & 0.79 (0.08) & 0.72 (0.01) & 0.83 (0.04) & 0.83 (0.07) & 0.83 (0.08) & 0.84 (0.06) \\ (SD) range & 0.58 - 0.92 & 0.71 - 0.73 & 0.80 - 0.90 & 0.67 - 0.95 & 0.47 - 0.97 & 0.70 - 0.97 \\ \hline - FEV1/FVC z-score, & -0.88 (1.09) & -1.90 (0.11) & -0.33 (0.64) & -0.42 (1.00) & -0.34 (1.06) & -0.15 (0.91) \\ mean (SD) range & -3.18 - 1.00 & -1.97 - 1.82 & -0.89 - 0.73 & -2.73 - 1.71 & -4.05 - 2.20 & -2.11 - 1.96 \\ \hline
## Skin pick test
& 17 (94\%) & 2 (100\%) & 3 (50\%) & 27 (73\%) & 75 (84\%) & 9 (33\%) \\ \hline Not tested & 5 & 0 & 0 & 8 & 11 & 2 \\ \hline
## Blood eosinophils
& n=19 & n=2 & n=5 & n=34 & n=65 & n=26 \\ absolute values & 0.40 (0.11 - 0.81) & 0.22 (0.06 - 0.37) & 0.14 (0.09 - 0.56) & 0.15 (0.02 - 0.41) & 0.19 (0.02 - 0.83) & 0.11 (0.02 - 0.51) \\ (10\({}^{9}\)/L) median & & & & & & \\ (range) & & & & & \\ \hline \end{tabular}
## Online appendix 2: Comparison of sputum slide results, excluding low quality slides*
\begin{tabular}{|p{42.7pt}|p{42.7pt}|p{42.7pt}|p{42.7pt}|p{42.7pt}|p{42.7pt}|p{42.7pt}|p{42.7pt}|p{42.7pt}|p{42.7pt}|p{42.7pt}|p{42.7pt}|p{42.7pt}|} \hline
*c400 total squamous cells and \(\geq\)30% squamous cells. ** EA (eosinophilic or mixed); NEA (neutrophilic or paucigranulocytic)
#### Online supplementary information
Ethical approval for the study has been obtained from the LSHTM ethics committee (ref: 9776) and in all five study centres. Informed consent was obtained from all participants or their parents/carers before taking part.
ALSPAC: Ethical approval for the UK-arm of the study was obtained from the ALSPAC Ethics and Law Committee, and the Local Research Ethics Committees. Consent for biological samples has been collected in accordance with the Human Tissue Act. REDcap was used to collect the ALSPAC data ([http://projectredcap.org/resources/citations/](http://projectredcap.org/resources/citations/)). Informed consent for the use of data collected via questionnaires and clinics was obtained from participants following the recommendations of the ALSPAC Ethics and Law Committee at the time. The ALSPAC study website contains details of all the data that is available through a fully searchable data dictionary and variable search tool ([http://www.bristol.ac.uk/alspac/researchers/our-data/](http://www.bristol.ac.uk/alspac/researchers/our-data/))/. |
177527_file02 | ## Safety Analysis**:........................................................................................................................ **16
Adverse events........................................................................................................................................ 16
Table S12: Summary of adverse events up to Day 28 post-vaccination by study arm, and vaccine manufacturer, safety population........................................................................................................ 16
Table S13: Adverse events up to Day 28 post-vaccination by MedDRA coding (v20.0), study arm and vaccine manufacturer, safety population........................................................................................ 16
Table S14: Severity of adverse events up to Day 28 post-vaccination by study arm, and vaccine manufacturer, safety population........................................................................................................ 19
Table S15: Proportion of participants with at least one related event up to Day 28 post-vaccination, by study arm, and vaccine manufacturer, safety population........................................................................ 19
Table S16: Outcome of adverse events up to Day 28 post-vaccination, by study arm, and vaccine manufacturer, safety population........................................................................................................ 19
Serious Adverse Events........................................................................................ 20
Table S17: Summary of serious adverse events by study arm, and vaccine manufacturer, safety population........................................................................................................ 20
Table S18: Serious adverse events by MedDRA (v20.0) coding by study arm and vaccine manufacturer, safety population........................................................................................................ 20
Table S19: Outcome of serious adverse events, by study arm, and vaccine manufacturer, safety population........................................................................................................ 20
## Immunogenicity Analysis
Immunogenicity assessment
Viral stock preparation was done in C6/36 cells and titrated by plaque assay method. The attenuated yellow fever vaccine strain 17D is used as challenge strain for the neutralization assays. The yellow fever vaccine strain 17D was provided by the Institut Pasteur de Dakar vaccine production unit (reference 1927). Briefly, the yellow fever vaccine is prepared using various seed strains that were ultimately derived from the 17D strain of yellow fever virus cultured in chicken embryonated eggs. The vaccine was obtained lyophilized. For viral stock preparation, each vial was reconstituted with 5ml of buffer (NaCl 0,9%) and amplified in C636 cells. The passage of the virus stock is 2.
A defined virus concentration of 10\({}^{3}\) plaque forming units (pfu) per ml (dose test, DT) and diluted, heat-inactivated sera (10-fold in Leibovitz's medium containing 3% fetal calf serum, FCS, heated for 20 min at 60\({}^{\circ}\)C) were titrated in serial two-fold dilutions from 1:10 to 1:20480. 30 ml of each serum dilution and 30\(\mu\)l of virus were mixed and pre-incubated at 37\({}^{\circ}\)C for 1 hour. Calibration range was done with different doses of the challenge virus (DT, 50, 30, 10, 5 and 1% of the DT). Wells with cells alone were used as negative control and wells with undiluted virus as positive controls. In addition, a serum provided by NIBSC was used as international standard for the validation of the calibration range. After 1-hour incubation, 10\({}^{6}\) cells/ml of PS cells in L15-3 % FCS were then added to each well containing the mixture serum/virus and all control wells and incubated for 4 hours at 37\({}^{\circ}\)C before overlaying with 0.6% carboxy-methyl-cellulose and 3% FCS in L-15 Leibovitz's media. Plates were sealed and incubated for 4 to 5 days at 37\({}^{\circ}\)C for the development of cytopathic effect. Wells were washed in phosphate buffer saline and stained in amino black solution (0.1%) for 30 minutes at room temperature. Plates were rinsed with water and allowed to dry then infectious plaques visualized.
The test was considered valid if: there was no lysis plaques in the negative control wells; total lysis in the undiluted virus wells; and, linear lysis range in wells containing the different doses of the challenge virus (30-50 lysis plaques for the DT, 15-25 lysis plaques for the half dose and 3-5 lysis plaques for the 10% dose). Inhibition percentage of the DT for a serum was then obtained by comparing the results with the calibration range. Plaques were counted for each serum and antibody titer was determined as the antibody dilution that reduced observed lysis plaques by 90% and 50% compared to the number observed in the calibration range (PRNT\({}_{90}\) and PRNT\({}_{50}\)).
Seroconversion and geometric mean titers, per-protocol population
\begin{table}
\begin{tabular}{|c|c|c|c|c|c|c|c|c|} \hline \multirow{2}{*}{**Manufacturer**} & \multicolumn{3}{c|}{**Fractional dose**} & \multicolumn{3}{c|}{**Standard dose**} & \multicolumn{1}{c|}{**Difference - log**} & \multicolumn{1}{c|}{**Ratio - GMT**} \\ & \multicolumn{3}{c|}{**Fractional dose**} & \multicolumn{1}{c|}{**Standard dose**} & \multicolumn{1}{c|}{**GMT (Fractional – Standard)**} & \multicolumn{1}{c|}{**Ratio - GMT**} \\ & N & GMT & 95\% CI & N & GMT & 95\% CI & (95\% CI) & (95\% CI) \\ \hline Bio-Manguinhos & 117 & 3718.2 & 2676.0, 5166.3 & 118 & 4119.8 & 2895.4, 5862.1 & -0.045 (-0.253, 0.164) & 0.90 (0.56, 1.46) \\ \hline Chumakov IPVE & 118 & 5826.3 & 4152.9, 8174.1 & 118 & 5493.9 & 4045.0, 7461.9 & 0.026 (-0.172, 0.223) & 1.06 (0.67, 1.67) \\ \hline IPD & 119 & 4224.7 & 3170.7, 5629.0 & 119 & 2530.4 & 1787.6, 3581.8 & 0.223 (0.028, 0.417) & 1.67 (1.07, 2.61) \\ \hline Sanofi Pasteur & 120 & 5713.9 & 4290.7, 7609.1 & 120 & 4280.6 & 3105.3, 5900.7 & 0.125 (-0.060, 0.311) & 1.33 (0.87, 2.05) \\ \hline \end{tabular}
\end{table}
Table S4: Geometric mean titer by PRNT\({}_{50}\) in fractional vs.
Figure S2: Reverse cumulative distributions of geometric mean titers by PRNT50 at Day 10 for per-protocol population, by vaccine manufacturer and by vaccine dose
Figure S3: Reverse cumulative distributions of geometric mean titers by PRNT\({}_{50}\) at Day \(28\) for intent-to-treat population with baseline seropositivity to yellow fever, by vaccine manufacturer and by vaccine dose
Figure S4: Reverse cumulative distributions of geometric mean titers by PRNT\({}_{50}\) at Day 10 for intent-to-treat population, by vaccine manufacturer and by vaccine dose
Figure S5: Reverse cumulative distributions of geometric mean titers by PRNT\({}_{S0}\) at Day 365 for intent-to-treat population, by vaccine manufacturer and by vaccine dose
Figure S6: Geometric mean titer by PRNT\({}_{50}\) at various timepoints post-vaccination for ITT population, by vaccine manufacturer and by vaccine dose.
\begin{table}
\begin{tabular}{|l|c|c|c|c|c|c|c|c|c|} \hline \multirow{2}{*}{**Manufacturer**} & \multicolumn{2}{c|}{**Fractional dose**} & \multicolumn{2}{c|}{**Standard dose**} & \multicolumn{2}{c|}{**Difference - log**} & \multicolumn{2}{c|}{**Ratio - GMFI**} \\ \cline{2-9} & \multicolumn{2}{c|}{**Fractional dose**} & \multicolumn{2}{c|}{**Standard dose**} & \multicolumn{2}{c|}{**GMFI (Fractional – Standard)**} & \multicolumn{2}{c|}{**Ratio - GMFI**} \\ \cline{2-9} & N & GMFI & 95\% CI & N & GMFI & 95\% CI & (95\% CI) & (95\% CI) \\ \hline Bio-Manguinhos & 111 & 788 & 562, 1103 & 117 & 813 & 570, 1159 & -0.014 (-0.225, 0.198) & 0.97 (0.60, 1.58) \\ \hline Chumakov IPVE & 111 & 1175 & 832, 1658 & 114 & 1163 & 859.3, 1575 & 0.004 (-0.194, 0.202) & 1.01 (0.64, 1.59) \\ \hline IPD & 112 & 856 & 636, 1151 & 110 & 515 & 358, 742 & 0.220 (0.017, 0.423) & 1.66 (1.04, 2.65) \\ \hline Sanofi Pasteur & 113 & 1109 & 821, 1498 & 112 & 850 & 607, 1192 & 0.115 (-0.080, 0.311) & 1.30 (0.83, 2.04) \\ \hline \end{tabular}
\end{table}
Table S6: Geometric mean fold increase by PRNT\({}_{50}\) in fractional vs.
\begin{table}
\begin{tabular}{|l|c|c|c|c|c|c|c|c|c|} \hline \multirow{3}{*}{**Manufacturer**} & \multicolumn{2}{c|}{**Fractional dose**} & \multicolumn{2}{c|}{**Standard dose**} & \multicolumn{2}{c|}{**Difference - log**} & \multicolumn{2}{c|}{**Ratio - GMFI**} \\ & \multicolumn{2}{c|}{**Fractional dose**} & \multicolumn{2}{c|}{**Standard dose**} & \multicolumn{2}{c|}{**GMFI (Fractional – Standard)**} & \multicolumn{2}{c|}{**Ratio - GMFI**} \\ & N & GMFI & 95\% CI & N & GMFI & 95\% CI & (95\% CI) & (95\% CI) \\ \hline Bio-Manguinhos & 116 & 9.7 & 6.8, 14.0 & 119 & 9.0 & 6.3, 12.9 & 0.033 (-0.187, 0.252) & 1.08 (0.65, 1.79) \\ \hline Chumakov IPVE & 118 & 6.6 & 4.5, 9.5 & 119 & 10.4 & 7.3, 14.9 & -0.201 (-0.424, 0.022) & 0.63 (0.38, 1.05) \\ \hline IPD & 120 & 9.1 & 6.3, 13.2 & 117 & 15.5 & 10.3, 23.3 & -0.230 (-0.468, 0.007) & 0.59 (0.34, 1.02) \\ \hline Sanofi Pasteur & 120 & 14.0 & 9.7, 20.2 & 119 & 21.7 & 14.9, 31.4 & -0.189 (-0.414, 0.036) & 0.65 (0.39, 1.09) \\ \hline \end{tabular}
\end{table}
Table S10: Geometric mean fold increase in by PRNT\({}_{50}\) fractional vs.
## General disorders and administration site
## conditions
Chest pain 1 (0.8) 0 0 1 (0.8) 0 0 0 0 0 0 0 Fatigue 8 (6.7) 15 (12.5) 18 (15.1) 12 (10.0) 19 (15.8) 21 (17.5) 21 (17.5) 17 (14.2) Injection site discomfort 0 0 0 1 (0.8) 0 0 0 Injection site 0 0 0 0 0 0 1 (0.8) 0 Injection site reaction 1 (0.8) 0 0 0 0 0 0 0 Local reaction 1 (0.8) 1 (0.8) 1 (0.8) 1 (0.8) 0 0 0 1 (0.8) Malaise 0 0 0 1 (0.8) 0 0 0 0 Pyrexia 9 (7.5) 11 (9.2) 12 (10.1) 9 (7.5) 12 (10.0) 9 (7.5) 10 (8.3) 14 (11.7) Vaccination site discomfort 0 1 (0.8) 0 1 (0.8) 1 (0.8) 0 0 Vaccination site irritation 0 1 (0.8) 0 0 0 0 0 Vaccination site pain 1 (0.8) 0 0 0 0 1 (0.8) 0 Vaccination site anesthesia 0 0 0 0 0 0 1 (0.8) 0
## Infections and infestations
15 (12.5)
Abscess 0 1 (0.8) 0 0 0 0 0 0 0 1 (0.8) Accro dermatitis 0 0 0 1 (0.8) 0 0 0 0 Bacterial vaginosis 1 (0.8) 0 0 1 (0.8) 1 (0.8) 1 (0.8) 0 Dysentery 0 1 (0.8) 0 0 0 0 0 Eye infection, bacterial Folliculitis 0 0 0 0 1 (0.8) 0 0 0 0 Fungal skin infection Gastroenteritis 0 0 0 2 (1.7) 0 2 (1.7) 1 (0.8) 1 (0.8) Genitourinary tract infection Lower respiratory tract infection 0 0 0 1 (0.8) 1 (0.8) 0 0 0 Infectious 0 0 1 (0.8) 0 0 0 Pelvic inflammatory disease Pharyngitis 0 1 (0.8) 1 (0.8) 0 2 (1.7) 0 1 (0.8) Respiratory tract infection 3 (2.5) 2 (1.7) 4 (3.4) 6 (5.0) 6 (5.0) 2 (1.7) 1 (0.8) 3 (2.5) Respiratory tract infection, viral Rhinitis 0 0 1 (0.8) 0 0 0 0 0 Rhinitis 0 4 (3.3) 1 (0.8) 3 (2.5) 3 (2.5) 2 (1.7) 0 2 (1.7) Skin bacterial infection 0 0 1 (0.8) 0 0 0 1 (0.8) 0 Tinesa capitis Tinesa capitis Tinesa 1 (0.8) 1 (0.8) 1 (0.8) 0 1 (0.8) 2 (1.7) 2 (1.7) 1 (0.8) Upper respiratory tract infection 4 (3.3) 3 (2.5) 0 0 4 (3.3) 5 (4.2) 1 (0.8) 0 Urinary tract infection Viral rhinitis Viral upper respiratory tract infection Vulvovaginal candidiasis Wound sepsis Injury, poisoning, and procedural complaints Injury, poisoning, and procedural complaints Injury 0 0 0 0 0 0 0 0 0 1 (0.8)
\begin{tabular}{l c c c c c c c c} Road traffic accident & 0 & 0 & 0 & 0 & 0 & 0 & 1 (0.8) \\
## Metabolism and nutrition disorders
& 1 (0.8) & 0 & 0 & 0 & 0 & 1 (0.8) & 0 & 3 (2.5) \\ Abnormal loss of weight & 1 (0.8) & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ Decreased appetite & 0 & 0 & 0 & 0 & 0 & 1 (0.8) & 0 & 3 (2.5) \\
## Musculoskeletal and connective tissue disorders
& 20 (16.7) & 22 (18.3) & 20 (16.8) & 19 (15.8) & 21 (17.5) & 26 (21.7) & 19 (15.8) & 19 (15.8) \\ Arthritis & 4 (3.3) & 3 (2.5) & 4 (3.4) & 2 (1.7) & 4 (3.3) & 2 (1.7) & 4 (3.3) & 2 (1.7) \\ Back pain & 1 (0.8) & 1 (0.8) & 2 (1.7) & 2 (1.7) & 4 (3.3) & 2 (1.7) & 1 (0.8) & 1 (0.8) \\ Musculoskeletal chest & 1 (0.8) & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ pain & 1 (0.8) & 1 (0.8) & 2 (1.7) & 1 (0.8) & 0 & 0 & 1 (0.8) & 0 \\ Musculoskeletal pain & 15 (12.5) & 18 (15.0) & 14 (11.8) & 15 (12.5) & 14 (11.7) & 22 (18.3) & 14 (11.7) & 16 (13.3) \\
## Nervous system disorders
& 24 (20.0) & 29 (24.2) & 30 (25.2) & 36 (30.0) & 33 (27.5) & 25 (20.8) & 30 (25.0) & 29 (24.2) \\ Dizziness & 6 (5.0) & 4 (3.3) & 3 (2.5) & 4 (3.3) & 4 (3.3) & 5 (4.2) & 3 (2.5) & 2 (1.7) \\ Headache & 21 (17.5) & 26 (21.7) & 27 (22.7) & 30 (25.0) & 30 (25.0) & 22 (18.3) & 29 (24.2) & 28 (23.3) \\ Hypoesthesia & 0 & 0 & 0 & 0 & 0 & 0 & 1 (0.8) & 0 \\ Neuropathy peripheral & 0 & 0 & 0 & 1 (0.8) & 0 & 0 & 0 & 0 \\ Paresthesia & 0 & 1 (0.8) & 0 & 1 (0.8) & 0 & 1 (0.8) & 0 & 0 \\ Somnolence & 0 & 1 (0.8) & 0 & 0 & 0 & 0 & 0 & 0 \\
## Psychiatric disorders
& 0 & 0 & 0 & 0 & 0 & 0 & 2 (1.7) & 0 \\ Insomnia & 0 & 0 & 0 & 0 & 0 & 0 & 1 (0.8) & 0 \\ Libido decreased & 0 & 0 & 0 & 0 & 0 & 0 & 1 (0.8) & 0 \\
## Renal and urinary disorders
& 0 & 0 & 0 & 0 & 0 & 1 (0.8) & 0 & 0 \\ Dysuria & 0 & 0 & 0 & 0 & 0 & 1 (0.8) & 0 & 0 \\
## Reproductive system and breast disorders
& 0 & 2 (1.7) & 0 & 2 (1.7) & 0 & 1 (0.8) & 2 (1.7) & 1 (0.8) \\ Breast inflammation & 0 & 0 & 0 & 0 & 0 & 0 & 1 (0.8) & 0 \\ Dysfunctional uterine bleeding & 0 & 1 (0.8) & 0 & 0 & 0 & 0 & 0 & 0 \\ Dysmenorrhea & 0 & 0 & 0 & 1 (0.8) & 0 & 0 & 0 & 1 (0.8) \\ Erectile dysfunction & 0 & 1 (0.8) & 0 & 0 & 0 & 0 & 0 & 0 \\ Genital ulceration & 0 & 0 & 0 & 0 & 0 & 1 (0.8) & 1 (0.8) & 0 \\ Uterine hemorrhage & 0 & 0 & 0 & 1 (0.8) & 0 & 0 & 0 & 0 \\
## Respiratory, thoracic and mediastinal disorders
& 9 (7.5) & 5 (4.2) & 6 (5.0) & 7 (5.8) & 7 (5.8) & 9 (7.5) & 3 (2.5) & 10 (8.3) \\ Asthma & 0 & 0 & 1 (0.8) & 0 & 0 & 0 & 1 (0.8) \\ Cough & 4 (3.3) & 3 (2.5) & 2 (1.7) & 0 & 3 (2.5) & 7 (5.8) & 1 (0.8) & 3 (2.5) \\ Epistaxis & 0 & 0 & 0 & 1 (0.8) & 0 & 0 & 0 & 0 \\ Productive cough & 0 & 0 & 1 (0.8) & 0 & 0 & 0 & 0 & 0 \\ Rhinitis allergic & 0 & 1 (0.8) & 0 & 2 (1.7) & 1 (0.8) & 0 & 0 & 2 (1.7) \\ Rhinorrhea & 5 (4.2) & 1 (0.8) & 3 (2.5) & 3 (2.5) & 3 (2.5) & 1 (0.8) & 2 (1.7) & 4 (3.3) \\ Throat irritation & 0 & 0 & 0 & 0 & 0 & 1 (0.8) & 0 & 0 \\ Tonsillar inflammation & 0 & 0 & 0 & 1 (0.8) & 0 & 0 & 0 & 0 \\
## Skin and subcutaneous tissue disorders
& 3 (2.5) & 2 (1.7) & 5 (4.2) & 4 (3.3) & 3 (2.5) & 3 (2.5) & 3 (2.5) & 5 (4.2) \\ Dermatitis & 1 (0.8) & 0 & 1 (0.8) & 2 (1.7) & 0 & 0 & 0 & 2 (1.7) \\ Dermatitis allergic & 2 (1.7) & 0 & 2 (1.7) & 0 & 1 (0.8) & 2 (1.7) & 1 (0.8) & 0 \\ Dermatitis contact & 0 & 0 & 0 & 0 & 0 & 0 & 1 (0.8) & 0 \\ Iching scar & 0 & 1 (0.8) & 0 & 0 & 0 & 0 & 0 & 0 \\ Night sweats & 0 & 0 & 0 & 0 & 0 & 0 & 1 (0.8) & 0 \\ Pruritus & 0 & 1 (0.8) & 2 (1.7) & 0 & 0 & 1 (0.8) & 0 & 3 (2.5) \\ Pruritus generalized & 0 & 0 & 0 & 1 (0.8) & 0 & 0 & 0 & 0 \\ Skin irritation & 0 & 0 & 0 & 0 & 1 (0.8) & 0 & 0 & 0 \\ Skin lesion & 0 & 0 & 0 & 0 & 1 (0.8) & 0 & 0 & 0 \\
18 & & & & & & & & & \\ \end{tabular}
\begin{table}
\begin{tabular}{|l|c|c|c|c|c|c|c|c|} \hline \hline
## Severity** & \multicolumn{2}{c|}{**Bio-Manguinhos**} & \multicolumn{2}{c|}{**Chumakov IPVE**} & \multicolumn{2}{c|}{**IPD**} & \multicolumn{2}{c|}{**Sanofi Pasteur
\\ \hline n (\%) with \(\geq 1\) AE & Frac. & Standard & Frac. & Standard & Frac. & Standard & Frac. & Standard \\ N=120 & N=120 & N=119 & N=120 & N=120 & N=120 & N=120 & N=120 \\ \hline Mild & 57 (47.5) & 66 (55.0) & 65 (54.6) & 67 (55.8) & 73 (60.8) & 69 (57.5) & 54 (45.0) & 69 (57.5) \\ \hline Moderate & 4 (3.3) & 7 (5.8) & 8 (6.7) & 11 (9.2) & 9 (7.5) & 6 (5.0) & 10 (8.3) & 9 (7.5) \\ \hline Severe & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \hline Life Threatening & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ \hline \hline \end{tabular}
\end{table}
Table S15: Proportion of participants with at least one related event up to Day 28 post-vaccination, by study arm, and vaccine manufacturer, safety population
\begin{table}
\begin{tabular}{|p{113.8pt}|p{113.8pt}|p{113.8pt}|p{113.8pt}|p{113.8pt}|p{113.8pt}|p{113.8pt}|p{113.8pt}|p{113.8pt}|} \hline \multicolumn{1}{|c|}{**System Organ Class and**} & \multicolumn{1}{c}{**Bio-Manguinhos**} & \multicolumn{1}{c}{**Chumakov IPVE**} & \multicolumn{1}{c}{**IPD**} & \multicolumn{1}{c|}{**Sanofi Pasteur**} \\ \hline \multirow{2}{*}{n (\%) with \(\geq 1\) SAE} & Frac. N=120 & Standard N=120 & Frac. N=119 & Standard N=120 & Frac. N=120 & Standard N=120 & Frac. N=120 & Standard N=120 \\ \hline \multicolumn{1}{|c|}{n (\%) with \(\geq 1\) SAE} & 2 (1.7) & 1 (0.8) & 0 & 0 & 3 (2.5) & 2 (1.7) & 0 & 2 (1.7) \\ \hline \end{tabular}
\end{table}
Table S18: Serious adverse events by MedDRA (v20.0) coding by study arm and vaccine manufacturer, safety population |
177626_file02 | ## Instituto de Fisica & Observatorio do Valongo, Universidade Federal do Rio de Janeiro, Rio de Janeiro, RJ, Brazil
###### Contents
* I Antibody prevalence
* II Infection fatality rate
* III Uncertainty estimation
* IV IFR for the three EPICOVID19-BR rounds
* V Full numerical results
* VI.1.1
## I Antibody prevalence
The antibody presence in the population \(p_{a}\) was directly assessed via the EPICOVID19-BR serological survey, which adopted the One Step COVID-19 Test from Wondfo. The test was subjected to analysis of its specificity and sensitivity by different groups including the manufacturer. Specificity and sensitivity are in turn related directly to the false positive rate (FPR) and false negative rate (FNR), respectively. The EPICOVID19-BR team consolidated different analyses of this test and arrived at a FPR = 1.0% (95% CI: 0.3-2.2%) and FNR = 15.2% (95% CI: 12.2-18.6%).1
Footnote 1: Contributed equally
If both FPR and FNR were zero, each test outcome would be drawn from a simple Binomial distribution with probability \(p_{a}\). Therefore \(p_{a}\) would be distributed according to the conjugate-prior distribution, which for \(n_{\rm tot}\) tests with \(n_{\rm yes}\) positive detections, would be a Beta distribution \(\mathcal{B}[\alpha,\beta](p_{a})\) with \(\alpha=n_{\rm yes}+1\) and \(\beta=n_{\rm tot}-n_{\rm yes}+1\). A non-zero FPR and FNR can be taken into account with a simple change of variables \(p_{a}^{\rm obs}\to p_{a}^{\rm true}(1-{\rm FNR}-{\rm FPR})+{\rm FPR}\). The distribution for \(p_{a}^{\rm true}\) can then be computed numerically to arbitrary precision, but it can also be approximated to great accuracy by a Pearson type I distribution, sometimes referred to as the 4-parameter Beta distribution, which, in our case, can be simply thought of as a displaced Beta distribution:
\[\mathcal{B}[\alpha,\beta](p_{a}+p_{\rm min})\,, \tag{1}\]
Since this mathematically allows \(p_{a}<0\), it must be multiplied by a uniform (or top-hat) prior enforcing \(p_{a}\geq 0\), to wit \(\mathcal{U}(p_{a})\).
In order to combine the prevalence results in different cities and get results for a given state or for the whole country we proceed as follow. The combined prevalence is given by:
\[p_{a}^{\rm combined}=\frac{N_{a}}{{\rm TotPop}}=\frac{\sum_{{\rm city}\;i}p_{ a,i}{\rm pop}_{i}}{{\rm TotPop}}=\sum_{{\rm city}\;i}p_{a,i}{\rm fpop}_{i}. \tag{2}\]
In the above, \(N_{a}\) is the number of people with antibodies in the combination of \(N\) cities, TotPop is the total combined population, \(p_{a,i}\) and pop, is the prevalence and population in city \(i\), respectively, and \({\rm fpop}_{i}\) is the fraction of the total population considered in city \(i\). This means that the distribution for \(p_{a}^{\rm combined}\) is technically computed as a transformation of many variables \(p_{a,1},\ldots,p_{a,N}\) into one variable \(p_{a}^{\rm combined}\). This leads to the following challenging \(N\)-dimensional integral for the state \(s\):
\[\mathcal{L}(p_{a,s})\!=\!\mathcal{N}\!\int\!\!{\rm d}^{N}\!p_{a,j}\,\delta\! \left[p_{a,s}\!-\!\!\sum_{{\rm city}\;j}p_{a,j}{\rm fpop}_{j}\right]\!\prod_{ {\rm city}\;i}\mathcal{L}_{i}(p_{a,i}), \tag{3}\]
We have computed such integral for all states in which \(N\leq 4\) and found out that this exact integral can be accurately approximated once again by a displaced Beta distribution.
The displacement is exactly as above since it comes, after all, from the FPR and FNR, which is assumed to be the same in all cities as the same test was employed. Since both displacements are equal, we start by ignoring it and compute the variables \(\alpha\) and \(\beta\) in order to ensure that the combined distribution has the correct mean \(\mu\) and variance \(V\). These first 2 moments of the distribution define both parameters univocally:
\[\alpha=\frac{\mu}{V}\big{(}\!-\!V\!+\!\mu\!-\!\mu^{2}\big{)}\,,\quad\beta= \frac{1-\mu}{V}\big{(}\!-\!V\!+\!\mu\!-\!\mu^{2}\big{)}\,. \tag{4}\]
The combined \(\mu\) and \(V\) in turn are easily obtained using Eqs. and and the properties of the mean and variance of a sum of independent random variables. To wit,if \(\mu_{i}\) and \(V_{i}\) are the mean and variance of city \(i\), we get:
\[\mu=\sum_{\text{city }i}\mu_{i}\,\text{fpop}_{i}\,,\quad V=\sum_{\text{city }i}V_{i}\,\text{fpop}_{i}^{2}\,. \tag{5}\]
Note that since, once again, we must include the displacement and the prior \(\mathcal{U}(p_{a}^{\text{combined}})\), the above values of \(\mu\) and \(V\) are for the corresponding non-displaced Beta distribution only. The full posterior for \(p_{a}^{\text{combined}}\), including the displaced and prior, will have slightly different mean and variance. The displacement leaves the variance unchanged but reduces the mean by \(p_{\text{min}}\). The inclusion of the prior, which removes the negative tail of the distribution, raises the mean while lowering the variance. So in order to improve the approximation in the cases where the prior affects the final distribution (this is the case for those states with few positive results, effectively irrelevant for the whole country analysis), we iterate the process one more time and adjust \(\mu\) and \(V\) slightly to ensure the final distribution has approximately the correct mean and variance.
\[\lambda=\int_{p_{\text{min}}}^{1}\mathcal{B}[\alpha,\beta](p)\text{d}p\,, \tag{6}\]
The resulting approximation is very good, and in particular it leads to medians (95% confidence interval widths) which differ on average from the exact result by a relative amount of just \(\simeq 1\%\) (\(\simeq 3\%\)). Moreover, there are no severe outlier cases for this approximation, and for the whole range of states and rounds the largest discrepancy of medians was 7%. shows the excellent performance of the Beta distribution approximation.
## II Infection fatality rate
In order to estimate the IFR we need to relate the cumulative number \(n_{+}(t)\) of COVID-19 cases to the cumulative number \(n_{a}(t)\) of patients with SARS-CoV-2 antibodies and the cumulative number \(n_{d}(t)\) of non-survivors. To this end we need to estimate the average time \(\tau_{ca}\) from contagion to antibody presence and the average time \(\tau_{cd}\) from contagion to death, and then compute the time-delay between antibodies and death \(\tau_{ad}\simeq\tau_{sd}-\tau_{sa}\simeq\tau_{cd}-\tau_{ca}\).
We obtain \(\tau_{ca}\) from the mean of the convolution \(\text{d}f_{ca}/\text{d}t\) of the distributions of the time from contagion to symptoms onset \(\text{d}f_{cs}/\text{d}t\) and from symptoms onset to antiviral immunoglobulin G (IgG) and/or M (IgM) presence \(\text{d}f_{sa}/\text{d}t\):
\[\frac{\text{d}f_{ca}(t)}{\text{d}t} =\int_{0}^{t}\text{d}\bar{t}\;\frac{\text{d}f_{sa}(\bar{t})}{ \text{d}\bar{t}}\;\frac{\text{d}f_{cs}}{\text{d}t}(t-\bar{t})\,, \tag{7}\] \[f_{ca}(t) =\int_{0}^{t}\text{d}\bar{t}\;\frac{\text{d}f_{ca}(\bar{t})}{ \text{d}\bar{t}}\simeq H(t-\tau_{ca})\,, \tag{8}\]
The distribution \(\text{d}f_{sa}/\text{d}t\) is modeled empirically, while \(\text{d}f_{cs}/\text{d}t\) according to a lognormal template. The means \(\tau_{ca}\), \(\tau_{cs}\) and \(\tau_{sa}\) relative to \(\text{d}f_{ca}/\text{d}t\), \(\text{d}f_{cs}/\text{d}t\) and \(\text{d}f_{sa}/\text{d}t\) are reported in Table 2 of the main text. Note that \(\tau_{ca}\simeq\tau_{cs}+\tau_{sa}\). The functions \(f_{ca}(t)\) and \(H(t-\tau_{ca})\) are shown in \(\tau_{sd}\) is in agreement with the average time from symptoms onset to death relative to other countries.
Similarly, we obtain \(\tau_{cd}\) from the mean of the convolution \(\text{d}f_{cd}/\text{d}t\) of the distributions of the time from contagion to symptoms onset \(\text{d}f_{cs}/\text{d}t\) and from symptoms onset to death \(\text{d}f_{sd}/\text{d}t\):
\[\frac{\text{d}f_{cd}(t)}{\text{d}t} =\int_{0}^{t}\text{d}\bar{t}\;\frac{\text{d}f_{sd}(\bar{t})}{ \text{d}\bar{t}}\;\frac{\text{d}f_{cs}}{\text{d}t}(t-\bar{t})\,, \tag{9}\] \[f_{cd}(t) =\int_{0}^{t}\text{d}\bar{t}\;\frac{\text{d}f_{cd}(\bar{t})}{ \text{d}\bar{t}}\simeq H(t-\tau_{cd})\,. \tag{10}\]
The distribution \(\text{d}f_{sd}/\text{d}t\) is modeled empirically using the data from the SIVEP-Gripe dataset at the Brazilian and state levels as described below. Note that \(\tau_{cd}\simeq\tau_{cs}+\tau_{sd}\)
_Top_: Beta distribution approximation of Eq. for a single city, assuming 5 positive results out of 250 tests and the FNR and FPR discussed in the text. The exact numerical distribution is the solid line in orange; the Beta approximation is the dashed line in black. There is no discernible difference. _Bottom_: Beta distribution approximation of Eqs. and for the states AC, AL and PE in Round 1. The exact numerical distribution is the solid line in orange; the Beta approximation is the dashed line in black. There is only a small difference in the cases where the maximum likelihood is very small (\(p_{a}<0.015\)), otherwise the approximation is indistinguishable.
The data from SIVEP-Gripe is biased towards cases with severe symptoms. Indeed, there is a significant number of cases that are hospitalized when symptoms are notified (see Figure 3, top panel). In order to take this into account we introduce a delay parameter \(\tau_{\Delta}\) (see Table 2 of the main text) which models the time that a patient takes on average to go from symptoms onset to severe symptoms:
\[\frac{\mathrm{d}f_{sd}}{\mathrm{d}t}(t)=\int_{0}^{t}\!\!\mathrm{d}\bar{t}\, \frac{\mathrm{d}f_{sd}^{\mathrm{sivep}}(\bar{t})}{\mathrm{d}\bar{t}}\,\frac{ \mathrm{d}f_{\Delta}}{\mathrm{d}t}(t-\bar{t})\simeq\frac{\mathrm{d}f_{sd}^{ \mathrm{sivep}}}{\mathrm{d}t}(t-\tau_{\Delta}), \tag{11}\]
We estimate \(\tau_{\Delta}=2\) days. This means that \(\tau_{sd}=\tau_{sd}^{\mathrm{sivep}}+\tau_{\Delta}\). The distribution \(\mathrm{d}f_{sd}^{\mathrm{sivep}}/\mathrm{d}t\) at the Brazilian level is shown in (bottom panel). In the computation of the IFR we will adopt the median of \(\mathrm{d}f_{sd}^{\mathrm{sivep}}/\mathrm{d}t\) as a robust measure of \(\tau_{sd}^{\mathrm{sivep}}\).
We can now relate the cumulative number \(n_{+}(t)\) of COVID-19 cases to the cumulative number \(n_{a}(t)\) of patients with SARS-CoV-2 antibodies and the cumulative number \(n_{d}(t)\) of non-survivors:
\[n_{a}(t) =\int_{t_{0}}^{t}\!\mathrm{d}\bar{t}\,\frac{\mathrm{d}n_{+}(\bar{ t})}{\mathrm{d}\bar{t}}f_{ca}(t-\bar{t})\simeq n_{+}(t-\tau_{ca})\,, \tag{12}\] \[n_{d}(t) =\mathrm{IFR}\int_{t_{0}}^{t}\!\mathrm{d}\bar{t}\,\frac{\mathrm{d }n_{+}(\bar{t})}{\mathrm{d}\bar{t}}f_{cd}(t-\bar{t})\simeq\mathrm{IFR}\,n_{+}( t-\tau_{cd}), \tag{13}\]
The number of fatalities is obtained via the public Painel Coronavirus dataset. shows the new deaths \(\mathrm{d}n_{d}/\mathrm{d}t\) for the 133 cities that entered the EPICOVID19-BR survey. From \(\mathrm{d}n_{d}/\mathrm{d}t\) we can compute the cumulative number of deaths \(n_{d}(t)\).
We can now use the previous two equations to compute the IFR:
\[\mathrm{IFR} =\frac{n_{d}(t)}{n_{+}(t-\tau_{cd})}=\frac{n_{d}(\bar{t}+\tau_{ cd}-\tau_{ca})}{n_{a}(\bar{t})}\] \[\simeq\frac{n_{d}(\bar{t}+\tau_{sd}-\tau_{sa})}{n_{a}(\bar{t})}= \frac{p_{d}(\bar{t}+\tau_{ad})}{p_{a}(\bar{t})}, \tag{14}\]
where \(\bar{t}\) is the time relative to the measurement of \(n_{a}\) and in the last equation we divided numerator and denominator by the number \(n_{\mathrm{pop}}\) of inhabitants according to the
New deaths by COVID-19 for the 133 cities that entered the EPICOVID19-BR survey—the windows mark its three phases. From Painel Coronavirus data of July 17, 2020.
_Top_: distribution of times from symptoms onset to hospitalization. _Middle_: distribution of times from hospitalization to death. _Bottom_: distribution of times from symptoms onset to death. The means are given in the Table 2 of the main text. From SIVEP-Gripe data of June 16, 2020.
Cumulative probability distribution of IgG and/or IgM presence as a function of days after contagion.
2019 official population values,\(p_{d}=n_{d}/n_{\rm pop}\). As explained earlier, we estimate \(p_{a}\) using EPICOVID19-BR data and \(p_{d}\) using the Painel Coronavirus data shown in We smooth the Painel Coronavirus data according to a 7-day moving average that assigns to the time \(t_{0}\) the average value of deaths in the interval \([t_{0},t_{0}+6\) days]. Indeed, for many reasons, but mostly because of weekends, deaths that happen at the time \(t_{0}\) are reported at a later time that we estimate according to a flat distribution in the above mentioned interval.
As discussed in the main text, because of fading IgG levels, we consider a detectability window \(T\) and thus the number of fatalities relative only to such a window. Specifically, we limit the number of deaths between the delayed time \(\tilde{t}+\tau_{ad}\) and \(T\) days earlier. We treat \(T\) as a nuisance parameter which takes values in the interval \(\) days.
We estimate the IFR at the state and Brazilian level. This means that in Eq. \(n_{d}\), \(\tau_{sd}\) and \(n_{\rm pop}\) are calculated accordingly.
## III Uncertainty estimation
Our results are given in terms of the maxima of the probability distributions and highest density intervals. The full probability distribution of \(p_{a}\) was already discussed in Section I.
Regarding \(p_{d}\), we estimate the error by propagating the uncertainty on \(n_{d}\) due to the uncertainty on \(\tau_{sd}\). We estimate the error on \(\tau_{sd}\) by adding in quadrature the uncertainty on \(\tau_{\Delta}\) and the uncertainty on \(\tau_{sd}^{\rm aivep}\). We estimate the former as \(\sigma_{\Delta}=1\) day and the latter via bootstrapping from the empirical distribution. Systematic uncertainties are discussed in the main text.
Regarding the IFR, we find that the relative error on \(p_{d}\) is smaller than the one on \(p_{a}\) by a factor between 3.5 to 5 depending on the survey round. We can therefore approximate \(p_{d}\) as a fixed variable in Eq.. We then take into account the full distribution of IFR due to the uncertainties in \(p_{a}\). The distribution on the IFR is thus the one of the inverse of a truncated Beta distribution, the PDF of which can be written in closed form as:
\[\frac{p_{d}\,\Gamma(\alpha+\beta)\left(\frac{p_{d}}{x}+p_{\rm min}\right)^{ \alpha}\left(1-p_{\rm min}-\frac{p_{d}}{x}\right)^{\beta}}{\Gamma(\alpha) \Gamma(\beta)(p_{d}+p_{\rm min}x)\big{[}p_{d}-(1-p_{\rm min})x\big{]}\big{(}I_ {p_{\rm min}}[\alpha,\beta]-1\big{)}} \tag{15}\]
Here, \(x\) is the free variable, in our case the IFR, \(I\) is the regularized incomplete Beta function, and \(\Gamma\) is the gamma function.
As discussed earlier and in the main text, because of fading IgG levels, we only consider fatalities between the delayed time \(\tilde{t}+\tau_{ad}\) and \(T\) days earlier. The resulting value of the IFR correlates with \(T\) and the fact that \(T\) is not precisely known could introduce an important bias in the analysis. In order to robustly overcome this issue we treat \(T\) as a nuisance parameter to be integrated over. Specifically, we adopt a broad flat prior \(T\in\) days so that the marginalized distribution on the IFR is:
\[\mathcal{P}_{\rm IFR}\propto\int_{40\,{\rm days}}^{80\,{\rm days}}\widetilde{ \mathcal{P}}_{\rm IFR}\,{\rm d}T\,, \tag{16}\]
Finally, as the error budget is driven by the uncertainty on \(p_{a}\) and the determinations of \(p_{a}\) during the three rounds are statistically independent, we can combine the rounds by simply multiplying the likelihoods. This combination allows for a more precise estimate of the average IFR over all rounds. Clearly, this ignores possible changes of the IFR during the course of the 5 weeks between rounds 1 and 3.
## IV IFR for the three epicovid19-br rounds
Brazil is divided geopolitically into 5 macroregions, the 27 states of which are:
* North: Acre (AC), Amapa (AP), Amazonas (AM), Para (PA), Rondonia (RO), Roraima (RR), Tocantins (TO);
* Northeast: Alagoas (AL), Bahia (BA), Ceara (CE), Maranhao (MA), Paraiba (PB), Pernambuco (PE), Piaui (PI), Rio Grande do Norte (RN), Sergipe (SE);
* Central-West: Distrito Federal (DF), Goias (GO), Mato Grosso (MT), Mato Grosso do Sul (MS);
* Southeast: Espirito Santo (ES), Minas Gerais (MG), Rio de Janeiro (RJ), Sao Paulo (SP);
* South: Parana (PR), Rio Grande do Sul (RS), Santa Catarina (SC).
Separate IFR estimates for each of the 3 rounds for each state (maximum posterior and 95% CI). The lower statistics leads to larger uncertainties. |
178699_file02 | ## ABSTRACT
& & & \\ Structured summary & 2 & Provide a structured summary including, as applicable: background; objectives; data sources; study eligibility criteria, participants, and interventions; study appraisal and synthesis methods; results; limitations; conclusions and implications of key findings; systematic review registration number. & 2 \\ \hline
## INTRODUCTION
& & \\ Rationale & 3 & Describe the rationale for the review in the context of what is already known. & 3 \\ \hline Objectives & 4 & Provide an explicit statement of questions being addressed with reference to participants, interventions, comparisons, outcomes, and study design (PICOS). & 3 \\ \hline
## METHODS
& & & \\ Protocol and registration & 5 & Indicate if a review protocol exists, if and where it can be accessed (e.g., Web address), and, if available, provide registration information including registration number. & 5 \\ \hline Eligibility criteria & 6 & Specify study characteristics (e.g., IPCOS, length of follow-up) and report characteristics (e.g., years considered, language, publication status) used as criteria for eligibility, giving rationale. & 5 \\ \hline Information sources & 7 & Describe all information sources (e.g., databases with dates of coverage, contact with study authors to identify additional studies) in the search and date last searched. & 5 \\ \hline Search & 8 & Present full electronic search strategy for at least one database, including any limits used, such that it could be repeated. & 5 \\ \hline Study selection & 9 & State the process for selecting studies (i.e., screening, eligibility, included in systematic review, and, if applicable, included in the meta-analysis). & 5 \\ \hline Data collection process & 10 & Describe method of data extraction from reports (e.g., piloted forms, independently, in duplicate) and any processes for obtaining and confirming data from investigators. & 6 \\ \hline Data items & 11 & List and define all variables for which data were sought (e.g., PICOS, funding sources) and any assumptions and simplifications made. & 6 \\ \hline Risk of bias in individual studies & 12 & Describe methods used for assessing risk of bias of individual studies (including specification of whether this was done at the study or outcome level), and how this information is to be used in any data synthesis. & 7 \\ \hline Summary measures & 13 & State the principal summary measures (e.g., risk ratio, difference in means). & 7-8 \\ \hline Synthesis of results & 14 & Describe the methods of handling data and combining results of studies, if done, including measures of consistency (e.g., F) for each meta-analysis. & 7 \\ \hline \hline \end{tabular}
PRISMA 2009 Checklist
SactionDate:
# # CheckingItem:
Reported:
on page # 1
Risk of bias across studies
15
Specify any assessment of risk of bias that may affect the cumulative evidence (e.g., publication bias, selective reporting within studies).
Additional analyses
16
Describe methods of additional analyses (e.g., sensitivity or subgroup analyses, meta-regression), if done, indicating which were pre-specified.
RESULTS
Study selection
17
Give numbers of studies screened, assessed for eligibility, and included in the review, with reasons for exclusions at each stage, ideally with a flow diagram.
Study characteristics
18
For each study, present characteristics for which data were extracted (e.g., study size, PICOS, follow-up period) and provide the citations.
Risk of bias within studies
19
Present data on risk of bias of each study and, if available, any outcome level assessment (see item 12),
Results of individual studies
20
For all outcomes considered (benefits or harms), present, for each study: (a) simple summary data for each intervention group (b) effect estimates and confidence intervals, ideally with a forest plot.
figure3
Synthesis of results
21
Present results of each meta-analysis done, including confidence intervals and measures of consistency.
12
Risk of bias across studies
22
Present results of any assessment of risk of bias across studies (see item 15).
Additional analysis
23
Give results of additional analyses, if done (e.g., sensitivity or subgroup analyses, meta-regression [see item 16]).
12
## DISCUSSION
Summary of evidence
24
Summarize the main findings including the strength of evidence for each main outcome; consider their relevance to key groups (e.g., healthcare providers, users, and policy makers).
Limitations
25
Discuss limitations at study and outcome level (e.g., risk of bias), and at review-level (e.g., incomplete retrieval of identified research, reporting bias).
Conclusions
26
Provide a general interpretation of the results in the context of other evidence, and implications for future research.
# Figure S8 NLME model derived parameters versus covariates for final model.
Plot of model-predicted viral area under the curve from day 0-28 of symptom onset; area under the viral load curve AUC, peak viral load and viral elimination half-life compared with sex, age and disease severity |
179473_file02 | ### Google search data
Google searches for 'church + churches', 'bar + bars', 'park + parks', 'grocery', and 'gym + gyms' were monitored using Google Trends for all 50 US states, D.C., and nationally from January 1, 2010 to October 1, 2020 and were normalized by the number of searches per 10,000,000 searches over the time period. Data were downloaded using the Trends Application Programming Interface for health. To examine increases in searches for churches in the month following the declaration of emergency on March 13, 2020 we compare search volumes for Sundays from March 13 to April 13 to Sundays in March 13 to April 13 from 2010-2019. This approximates a counterfactual scenario to account for the Catholic observance of Lent that occurs around this period. To assess potential differences in search behaviors for the first six months of the epidemic, we calculate the coefficient of variation (search volume standard deviation divided by mean search volume) for January to September for all years.
### SARS-CoV-2 case data
SARS-CoV-2 incidence data at the county level were downloaded from the COVID-19 Data Repository by the Center for Systems Science and Engineering at Johns Hopkins University at the county level beginning in February, 2020. We join SafeGraph movement data with case counts at the county level and to assess movement in response to cases, we distinguish a _focal county_ to _visiting counties_. That is, for each venue type (church, bar, park, grocery, gym), and each unique county represented by that venue type (this is the focal county) we calculate the total number of cases in that county for that week. We keep this as well as total cases divided by the population of that county. Next we calculate the total cases for each represented visiting counties to venues represented. Finally, we calculate the mean number of unique visiting counties by week and county.
With these data we calculate two metrics, one is the proportion of visiting counties which have more cases than the focal county being visited, and the other is the raw difference in cases between the focal and visiting counties. For the latter we calculate the 5th, 25th, 50th, 75th, and 95th quantiles of numbers of cases. We can then compare these two metrics by state with observed incidence in that state. To quantify any associations between the proportion of visiting counties larger than focal counties, we take the cross-wavelet of the two time series and see where the power is significant and the relative phase angle between the two.
Included as supplementary materials are plots of proportions of visiting counties with more cases than the focal county and differences in cases between visiting and focal counties for all 50 US states and D.C., and cross-wavelet plots for churches, parks, gyms, groceries, and bars and cases for all 50 US states and D.C..
## Mobility data correlates
We used the social, demographic, and economical variables compiled by White & Laurent Hebert-Dufresne to examine potential correlates for the mobility data. We found that none of these variables strongly correlated with either percentage decreases in visits or percent change in distance traveled (results not shown). However, increases in state-level "tightness" was correlated with larger decreases in church visits and farther distanced traveled (Fig. S1). Tight cultures are typically defined as those with strong social norms and little tolerance for deviance.
## Mathematical analysis of final outbreak size
The mathematical simplicity of the classic SIR model, on which our model is based, allows for a number of more detailed analyses of the role of \(X\) and \(Y\) on the final outbreak size.
\[R(\infty)=(1-X)R_{o}(\infty)+XR_{c}(\infty)\] (S1)
We assume here that \(t_{c}=0\), and that \(S_{o}\approx 1\), \(I_{o}\ll 1\), and \(R_{o}=0\). These assumptions serve as a natural motivating example while allowing for a less cumbersome mathematical analysis. In this case, \(R_{o}(t_{c})\) becomes 0 and so Eq. S1 simplifies to \((1-X)R_{o}(\infty)\). therefore for notational convenience we simply write \(R\) and \(S\) to denote the open compartments, since closed compartments will always be empty.
Note that after redistribution, the population sizes for open compartments are no longer normalized to 1. Therefore to help prevent confusion we let \(r/s(t)\) be the proportion of recovered/susceptible individuals. After redistribution the population size in open compartments is \(1+\frac{XY}{1-X}=:P\), so \(s(t)=S(t)/P\) and \(r(t)=R(t)/P\).
By Eq.
\[r(\infty) =1-s(\infty)\] \[=1-s\exp(-R_{0}(r(\infty)-r)\] \[=1-\exp(-R_{0}r(\infty))),\] (S2)
Note the reproductive number \(R_{0}\) here is defined \(\lambda P\). This transcendental equation can then be solved for \(r(\infty)\) with respect to a particular set of parameters though numerical means or using the Lambert W function. Following Appendix A of Ma & Earn and elsewhere, \(s(\infty)=-\frac{1}{R_{0}}W(-R_{0}e^{-R_{0}})\), where \(W\) is the principal branch of the Lambert W function.
\[R(\infty) =(1-X)P\left(1+\frac{W(-R_{0}e^{-R_{0}})}{R_{0}}\right)\] \[=(1-X+XY)\left(1+\frac{W(-R_{0}e^{-R_{0}})}{R_{0}}\right)\] (S3)
### Finding critical \(Y\) for a given \(\lambda\)
We first show how Eq. S2 can be used to find the value of \(Y\) past which, for any \(\lambda\), any choice of \(X>0\) will cause a worse final outbreak than compared to \(X=0\); i.e. critical Y.
Let \(\beta\) be the initial infectiousness \(\lambda(1+\frac{XY}{1-X})\), and as above we use \(R\) to denote the open compartment.
We now turn to finding the value of \(X\) which minimizes (S1) for a given \(Y\) and \(\lambda\geq 1\) (when \(\lambda<1\), \(X=0\) is clearly as optimal as anything else). When \(\lambda\geq 1\), one can see from in the main text that \(R(\infty)\) as a function of \(X\) has either a single intermediate peak higher values of \(Y\), or is monotone decreasing for lower values of \(Y\). This pervasive downward parabolic shape arises from the fact that \(R(\infty)\) is the product of the linearly decreasing, positive function \(f(X)=1-X+XY\), and the sigmoidal, positive function \(g(X)=1+(W(-R_{0}e^{-R_{0}}))/R_{0}\), where \(\frac{dg}{dX}\) approaches 0 as \(X\) approaches 1. This guarantees that \(R(\infty)\) is maximized at one of the extreme values \(X=0\) or \(X=1\).
While Eq. (S3) is not defined at \(X=1\), we can obtain a right-hand limit.
\[R(\infty) =(1+e^{-R_{0}})P(1-X)\] \[=1-X+XY+e^{-R_{0}}(1-X+XY)\] \[\to Y.\]
This result makes sense, since we would expect that \(r(\infty)\) be equal to 1 when \(R_{0}\to\infty\), so plugging this into Eq. (S2) and simplifying gives \(R(\infty)=Y\) for \(X=1\).
This leads to the section's main result, which is summarized in Figure S2.
\[\operatorname*{arg\,min}_{X}R(\infty)=\begin{cases}0&\text{if }Y>\left(1+\frac{W(-\lambdae^{-\lambda})}{\lambda}\right)\\ 1&\text{otherwise.}\end{cases}\] (S7)
While this is in closed form, \(W\) cannot be expressed with elementary functions and hence poses similar interpretability issues to practitioners as implicit solutions or numerical approximations. Thankfully, a number of useful approximations for \(W\) exist. For example, here we can use the crude estimate \(W(x)<x\) for \(-1/e\leq x<0\) to obtain the bound \(Y>1-e^{-\lambda}\), which serves as sufficient criteria to be certain that no closure is the best option.
|
180844_file03 | #### Validation of inferences from Eswatini
To validate our inferences on Eswatini surveillance data, we applied our algorithm to simulated data generated using the median posterior parameter estimates inferred from the surveillance data and evaluated our ability to recover known networks and parameter values. We did this by simulating under and inferring under the same inference setting, for all five inference settings.
The goal of these exercises was to understand the potential limits of the accuracy of our inferences on the Eswatini surveillance data, where the true network and parameters were unknown. As with the simple test case, we measured the accuracy of classifying cases as imported or locally acquired, inferring transmission linkages, identifying the correct outbreak for each locally acquired case, and estimating \(R_{c}\).
For this exercise, we simulated transmission networks and corresponding epidemiological data (e.g., household location, timing of clinical presentation, etc.) using a branching process model for which generative processes for spatial, temporal, and travel-history data mirrored the assumptions used in the formulation of our likelihood. To simulate data using the branching process, the maximum number of cases (i.e., treated \(P\). _falciparum_ infections) and \(R_{c}\) were first specified. We then calculated the maximum number of infections based on the probability of treatment given symptoms (1.0), the probability of treatment given no symptoms (0.42), and the probability of symptoms (0.87). Each probability was calculated empirically from the Eswatini data set. The number of imported infections was equal to the product of the maximum number of infections and the importation proportion (i.e., 1 - \(R_{c}\)). We uniformly distributed the imported infections over a temporal window consistent with that of the Eswatini data set (1361 days), and we randomly sampled the spatial coordinates of these imported infections according to population density estimates from WorldPop. While the number of treated _P. falciparum_ infections was less than the specified maximum number of cases, we sampled the number of offspring from each node according to a Poisson distribution with a mean of \(R_{c}\). For each offspring, the timing and location of detection were sampled relative to the timing and location of detection of the parent using the spatial and temporal kernels formulated in the likelihood. Travel histories for imported and locally acquired cases were Bernoulli trials with probabilities of \(\tau_{s}\) and \(\tau_{l}\), respectively, the symptom status of each case was a Bernoulli trial with the probability of symptoms, and the treatment status of each was a Bernoulli trial with either the probability of treatment given symptoms or the probability of treatment given no symptoms. Each simulated data set was generated to approximate characteristics of the Eswatini surveillance data along with inferred parameters from the model. Specifically, the number of nodes in the simulated data approximated the total number of cases in the Eswatini surveillance data, and we set the proportion of imported cases (\(p_{i}\)), the diffusion coefficient (\(D\)), and the parameters that govern the accuracies of the travel history (\(\tau_{s}\) and \(\tau_{l}\)) to their median values from the posterior distribution. Similarly, under inference settings where the accuracy of the travel history was not estimated, we assigned \(\tau_{s}=1\) and \(\tau_{l}=0\), implying perfectly accurate travel histories. To match the observation from surveillance data that individuals who reported travel tended to be located in metropolitan areas, we distributed the imported cases spatially proportional to gridded population density estimates from WorldPop.
#### Simulation Sweep
To identify the epidemiological parameters that affect the accuracy of reconstructing transmission networks using routinely collected surveillance data, we performed a simulation sweep in which we varied the following epidemiological parameters: the diffusion coefficient, the proportion of imported infections, the temporal window over which imported infections were distributed, the degree of spatial clustering among imported infections, \(\tau_{\text{s}}\), and \(\tau_{\text{l}}\). We sampled 2,000 values for each epidemiological parameter using a Sobol design (S2 Table). We then parameterized a branching process model with each parameter set to generate a total of 2,000 simulated data sets, each comprising a transmission network of 200 nodes. The number of nodes in each simulated data set was less than the number of nodes in the Eswatini surveillance data and was selected to reduce computational burden. Nevertheless, the relative epidemiological features of the transmission network should affect the accuracy of network reconstruction more so than the size of the network itself. Therefore, we expect that the results of this simulation sweep should generalize to networks of various sizes.
We applied our inference algorithm under three inference settings to each simulated data set and measured the accuracy of reconstructing transmission networks. The three inference settings used: spatial and temporal data while estimating the accuracy of the travel history (default setting); spatial and temporal data while believing the travel history; and spatial and temporal data alone (S1 Table). We chose to use those inference settings, because they included each of the three assumptions about travel-history data. As with previous validation exercises, we measured the accuracy of classifying cases as imported or locally acquired, inferring transmission linkages, identifying the correct outbreak of each locally acquired case, and estimating \(R_{c}\). We then examined how each of these accuracy metrics varied as a function of the epidemiological parameters.
## Results
### Validation using a simple test case
We first validated our approach on three small, simulated networks of twenty nodes. Although these networks varied in their proportion of imported cases, the local transmission chains were arranged to ensure that there was sufficient spatiotemporal separation between transmission chains, and we simulated perfect travel histories and complete observation of cases, providing idealized test cases to validate our inference algorithm. We measured the performance of our inference algorithm in terms of its ability to reconstruct different features of the transmission network and correctly estimate \(R_{c}\). As the proportion of imported cases decreased from 85% to 5%, we found that the ability of the algorithm to correctly classify cases as imported or locally acquired improved (Fig S2). For example, when we used the default inference setting, classification accuracy improved from 85.7% (95% Credible Interval: 85.7 - 85.7%) to 100% (100 - 100%). As classification accuracy improved, our estimates of \(R_{c}\) also improved, with all five inference settings yielding accurate estimates when imported cases comprised only 5% of total cases (Fig S2C). Similarly, the ability to identify the correct parent of each locally acquired case and assign it to the correct outbreak depended on the extent of local transmission in the network. When 85% of the cases were imported, performance was variable across inference settings (Fig S2A). Using spatial data and either estimating or ignoring the travel histories, the algorithm identified a local optimum in the likelihood and consequently classified all locally acquired cases as imported, leading to highly inaccurate transmission network inferences.
* Believing the travel history, regardless of whether spatial data was included, enabled us to perfectly reconstruct the transmission network, because the travel-history data was simulated to be perfectly accurate, allowing for correct classification of cases as imported or locally acquired.
* 94.7%) under the default inference settings to 63.2% (47.4
- 78.9%) using temporal data and estimating the accuracy of the travel history (Fig S2C). In terms of identifying the outbreak to which a case belongs, the algorithm was accurate under all inference settings, since there was only one outbreak (Fig S2C).
*_S2 Fig. Inference accuracies for three simulated transmission networks with (A) 85%, (B) 50%, and (C) 5% of cases as imported. Case classification refers to proportion of cases that are correctly classified as imported vs. locally acquired. Transmission linkage denotes the proportion of locally acquired cases for which the true parent is correctly identified, Outbreak is the proportion of locally acquired cases for which the inferred parent belongs to the correct outbreak, and \(R_{c}\) is the estimated reproduction number under control. Square points signify the median posterior value, and bars are the 95% credible intervals. The gray line indicates the true value of \(R_{c}\)._* **S3 Fig. Likelihood profile of the diffusion coefficient conditioning on the true network.** _The likelihood profile for two inference settings that incorporate spatial data are shown as a function of the diffusion coefficient. The green line corresponds to the default inference setting, the purple line corresponds to the setting in which spatial and temporal data are used and the travel history is believed, and the blue line corresponds to the setting in which spatial and temporal data are used and the travel history was ignored. Black bars denote the true value of the diffusion coefficient, dark grey shapes denote the region with the maximum likelihood, and light grey shapes denote the region within 10 log likelihood units of the maximum likelihood._
### Convergence of Posterior Transmission Network Inferences* _S4 Fig. Comparison of individual-level importation probabilities on Eswatini data under default settings. Pairwise scatter plots of importation probabilities are shown for each pairing of the 5 independent replicates to assess convergence. The correlation between importation probabilities for each pair of replicates is reported in red._*_S5 Fig. Comparison of transmission linkage probabilities on Eswatini data under default settings. Pairwise scatter plots of the probability of each transmission linkage are shown for each pairing of the 5 independent replicates to assess convergence. The correlation between transmission linkage probabilities for each pair of replicates is reported in red._*_S6 Fig. Comparison of individual-level R\({}_{c}\) estimates on Eswatini data under default settings._
*_Pairwise scatter plots of individual-level R\({}_{c}\) are show for each pairing of the five independent replicates to assess convergence. The correlation between individual-level R\({}_{c}\) values is reported in red._
### Analytical Solution for the Posterior Distribution of ts and ts
We specified a Bernoulli likelihood and a beta-distributed prior on ts and ts. Therefore, the posterior distributions of ts and ts satisfy a conjugate-prior relationship and can be solved analytically as beta distributions.
The prior distribution for ts is a beta distribution with hyperparameters as 12 and = 3, and the prior distribution for ts is a beta distribution with hyperparameters a1 = 3 and b1 = 12.
Following the conjugate-prior relationship, the posterior distribution for ts is calculated as a beta distribution with hyperparameters,
\[\hat{\alpha}_{s}=\alpha_{s}+\sum_{nfounders}\mathbb{I}(report\ travel)\quad(S1)\]
The summation in eq. (S1) is the number of cases that reported travel and are inferred by the algorithm to be imported cases. Similarly, the second term in eq. (S2) is the number of cases inferred by the algorithm to be imported cases that did not report travel.
\[\hat{\alpha}_{l}=\alpha_{l}+\sum_{nlocal}\mathbb{I}(report\ travel)\quad(S3)\]
* 297* imported, which was sufficient to shift the posterior distribution of \(\tau_{s}\) away from the prior distribution (S7 Fig). Using the latter, we only estimated 0.13% of cases as imported. This small number of imported cases implied that the posterior distribution of \(\tau_{s}\) resembled the prior distribution (S8 Fig).
* The derivation of the analytical solution of \(\tau_{s}\) explains our inability to correctly estimate this parameter from simulated data. Using the spatial and temporal data and estimating the accuracy of the travel history, the true value of \(\tau_{s}\) was 0.61, and 5.2% of all cases in the simulated data set were imported. However, applying the MC3 algorithm to this simulated data set, we inferred only \(\sim\)1% of all cases to be imported. Consequently, we do not estimate a sufficient number of imported cases to shift the posterior distribution of \(\tau_{s}\) away from the prior distribution and correctly estimate this parameter (S9 Fig).
* _S7 Fig. Comparison of the prior and posteriors of \(\tau_{s}\) and \(\eta\) from the Eswatini surveillance data using spatial and temporal data and estimating the accuracy of the travel history. The prior (gray shape), the analytical posterior distribution (black line), and the numerical posterior distribution from MC3 (green histogram) are plotted for \(\tau_{s}\) and \(\eta\)._*_S8 Fig. Comparison of the prior and posteriors of \(\pi\)s and \(\pi\) from the Eswatini surveillance data using temporal data and estimating the accuracy of the travel history. The prior (gray shape), the analytical posterior distribution (black line), and the numerical posterior distribution from MC3 (pink histogram) are plotted for \(\pi\)s and \(\pi\)._* **S9 Fig. Comparison of the prior and posteriors of \(\tau_{s}\) from simulated data using spatial and temporal data and estimating the accuracy of the travel history.** The prior (gray shape), the analytical posterior distribution (black line), and the numerical posterior distribution from MC3. (green histogram) are plotted for \(\tau_{s}\).
* **Simulation Sweep***_S10 Fig. Univariate relationships between accuracy metrics and simulation parameters using spatial and temporal data and estimating the accuracy of the travel history. Scatterplots of the relationship between five accuracy metrics and the simulation parameters are reported._
*_Imported classification refers to the proportion of imported cases that are correct classified as imported, local classification refers to the proportion of locally acquired cases that are correctly classified as locally acquired, and case classification refers to the proportion of all cases that _are correctly classified as imported or locally acquired. Transmission linkage is the proportion of locally acquired cases for which the true parent is correctly identified, and outbreak is the proportion of locally acquired cases for which the inferred parent belongs to the same outbreak._
* _classified as imported or locally acquired. Transmission linkage is the proportion of locally acquired cases for which the true parent is correctly identified, and outbreak is the proportion of locally acquired cases for which the inferred parent belongs to the same outbreak._*_S12 Fig. Univariate relationships between accuracy metrics and simulation parameters using spatial and temporal data only._ Scatterplots of the relationship between five accuracy metrics and the simulation parameters are reported._ Imported classification refers to the proportion of imported cases that are correct classified as imported, local classification refers to the proportion of locally acquired cases that are correctly classified as locally acquired, and case classification refers to the proportion of all cases that are correctly classified as imported or *_true parent is correctly identified, and outbreak is the proportion of locally acquired cases for which the inferred parent belongs to the same outbreak._
* _Uncertainty in Higher-Order Summaries of the Network_
* _The credible intervals for higher-order summaries of the network, including case classification and_ R__c_, are narrow, because the calculation of these higher-order summaries requires that we apply a binary condition to each node in the network (e.g., "Was the node inferred to be imported or locally acquired?", "Was the inferred parent the true parent?", etc.) In doing so, we compressed or reduced much of the uncertainty inherent to the inferred network. Because the estimates of_ R__c_ depend only upon the case classification, we obtained narrow credible intervals for_ R__c_.
* _To consider this further, we took the posterior distributions from the "Validation of inferences from Eswatini" analysis and compared the log-likelihoods that each case was imported or locally acquired. For each of the three inference settings examined (S13-S15 Figs), the log-likelihood that each case was locally acquired was generally higher, because, in each simulated network, there were 775 cases over 1361 days. This ensured that there was generally a plausible observed parent that occurred within one serial interval prior to each case. The log-likelihood that a case was imported was higher for asymptomatic cases than symptomatic cases, because the serial interval distribution was more diffuse for asymptomatic cases. Although this effect is sensitive to our assumption about the different serial interval distribution for symptomatic and asymptomatic cases, the calculation of the serial interval distributions was informed by empirical data collected in Zanzibar and modeled asexual parasite densities obtained from a validated, within-host model of_ P. falciparum infection_.
*_S13 Fig. Likelihoods of case classification simulated nodes using spatial and temporal data and estimating the accuracy of the travel history. The log likelihoods that each node is locally acquired (navy) or imported (maroon) is calculated for each network from the posterior distribution. Points are the median estimate across the full posterior distribution, and segments are the 95% credible intervals. The gray line is the posterior probability that each node was imported, and the nodes are ordered by increasing posterior probability of importation._* _S14 Fig. Likelihoods of case classification simulated nodes using spatial and temporal data only. The log likelihoods that each node is locally acquired (navy) or imported (maroon) is calculated for each network from the posterior distribution. Points are the median estimate across the full posterior distribution, and segments are the 95% credible intervals. The gray line is the posterior probability that each node was imported, and the nodes are ordered by increasing posterior probability of importation._
* Routledge, I. _et al._ Tracking progress towards malaria elimination in China: Individual-level estimates of transmission and its spatiotemporal variation using a diffusion network approach. _PLoS Comput Biol_**16**, e1007707.
* Routledge, I. _et al._ Estimating spatiotemporally varying malaria reproduction numbers in a near elimination setting. _Nat Commun_**9**, 2476.
* Wood, S. N. _Generalized additive models: an introduction with R_. (Chapman & Hall/CRC, 2006).
* R Development Core Team. _R: A Language and Environment for Statistical Computing_. (R Foundation for Statistical Computing, 2017).
* Smithson, M. & Verkuilen, J. A better lemon squeezer? Maximum-likelihood regression with beta-distributed dependent variables. _Psychological Methods_**11**, 54-71.
* WorldPop, & Bondarenko, Maksym. Individual Countries 1km UN Adjusted Population Density. doi:10.5258/SOTON/WP00675.
* Tatem, A. J. WorldPop, open data for spatial demography. _Sci Data_**4**, 170004.
* Baddeley, A., Rubak, E. & Turner, R. _Spatial point patterns: methodology and applications with R_. (CRC Press, Taylor & Francis Group, 2016).
* King, A. A., Nguyen, D. & Ionides, E. L. Statistical Inference for Partially Observed Markov Processes via the \(R\) Package **pomp**. _J. Stat. Soft._**69**,.
* Huber, J. H., Johnston, G. L., Greenhouse, B., Smith, D. L. & Perkins, T. A. Quantitative, model-based estimates of variability in the generation and serial intervals of Plasmodium falciparum malaria. _Malaria Journal_**15**,. |
181628_file04 | ## Loading required package: ggplot2
## rstan (Version 2.21.2, GitHub: 2e1f913d3ca3)
## For execution on a local, multicore CPU with excess RAM we recommend calling
## options(mc.cores = parallel::detectCores()).
## To avoid recompilation of unchanged Stan programs, we recommend calling
## rstan_options(auto_write = TRUE) library(StanHeaders) library(bayesplot)
## This is bayesplot version 1.7.2
## - Online documentation and vignettes at mc-stan.org/bayesplot
## - bayesplot theme set to bayesplot::theme_default()
## * Does_not_ affect other ggplot2 plots
See?bayesplot_theme_set for details on theme setting library(ggplot2) library(gridExtra) library(HardyWeinberg)
## Loading required package: mice
## Attaching package:'mice'
## The following objects are masked from 'package:base':
## cbind, rbind
## Loading required package: Rsolnp version
## function (pkg = "mice")
# lib<-dirname(system.file(package=pkg))
# d<-packageDescription(pkg)
# return(paste(d$Package,d$Version,d$Date,lib))
# }
#<bytecode:0x7ff2b9c7bd08>
# <environment:namespace:mice> sessionInfo()
# R version 4.0.2
# Platform:x86_64-apple-darwin17.0 (64-bit)
# Running under:macOS Catalina 10.15.2
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# en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
# # attached base packages:
# stats graphics grDevices utils datasets methods base
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# HardyWeinberg_1.6.8 Rsolnp_1.16 mice_3.10.0
# gridExtra_2.3 bayesplot_1.7.2 rstan_2.21.2
# ggplot2_3.3.2 StanHeaders_2.21.0-5
# #
# loaded via a namespace (and not attached):
# tidyselect_1.1.0 xfun_0.15 purrr_0.3.4 lattice_0.20-41
# V8_3.2.0 colorspace_1.4-1 vctrs_0.3.2 generics_0.0.2
# htmltools_0.5.0 stats4_4.0.2 loo_2.3.1 yam1_2.2.1
# rlang_0.4.7 pkgbuild_1.1.0 pillar_1.4.6 glue_1.4.1
# withr_2.2.0 matrixStats_0.56.0 lifecycle_0.2.0 plyr_1.8.6
# stringr_1.4.0 munsell_0.5.0 gtable_0.3.0 codetools_0.2-16
# evaluate_0.14 inline_0.3.15 knitr_1.29 callr_3.4.3
# ps_1.3.3 curl_4.3 parallel_4.0.2 fansi_0.4.1
# broom_0.7.0 Rcpp_1.0.5.1 scales_1.1.1 backports_1.1.8
# RcppParallel_5.0.2 jsonlite_1.7.0 truncnorm_1.0-8 digest_0.6.25
# stringi_1.4.6 processx_3.4.3 dplyr_1.0.0 grid_4.0.2
# cli_2.0.2 tools_4.0.2 magritr_1.5 tibble_3.0.3
# crayon_1.3.4 tidyr_1.1.0 pkgconfig_2.0.3 ellipsis_0.3.1
# prettyunits_1.1.1 ggriddges_0.5.2 assertthat_0.2.1 rmarkdown_2.3
# R6_2.4.1 compiler_4.0.2
## Data
#### parasite counts
para_dat = readr::read_csv('Data/Parasite_counts.csv')
## Parsed with column specification:
# Hb = col_double(),
# ^Age in years' = col_double(),
# ^Parasite/uL^ = col_double(),
# ^Gamet/uL^ = col_double(),
# Parasitaemia = col_double(),
# PCR = col_character()
# )
para_dat$PCR[grep('homozygous', para_dat$PCR,ignore.case = T)] = 0 para_dat$PCR[grep('hetero', para_dat$PCR,ignore.case = T)] = 1 para_dat$PCR[grep('WT', para_dat$PCR, ignore.case = T)] = 2 para_dat$PCR = as.numeric(para_dat$PCR) table(para_dat$PCR)
012
625570
par(las = 1) hist(log10(para_dat$Parasitaemia))mod = glm(PCR - log10para, family='binomial', weights = rep(2, nrow(para_dat)), data = data.frame(PCR = para_dat$PCR/2, log10para=log10(para_dat$Parasitaemia))) summary(mod)
## Call:
## glm(formula = PCR - log10para, family = "binomial", data = data.frame(PCR = para_dat$PCR/2,
## log10para = log10(para_dat$Parasitaemia)), weights = rep(2,
## nrow(para_dat)))
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -3.8097 0.3172 0.3474 0.3751 0.4900
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.8483 1.1017 1.678 0.0934.
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1'' 1
## (Dispersion parameter for binomial family taken to be 1)
## Null deviance: 261.12 on 600 degrees of freedom
## Residual deviance: 259.00 on 599 degrees of freedom
## AIC: 297.66
Number of Fisher Scoring iterations: 6 wilcox.test(para_dat$Parasitaemia[para_dat$PCR==0], para_dat$Parasitaemia[para_dat$PCR>=1])
## Wilcoxon rank sum test with continuity correction
## data: para_dat$Parasitaemia[para_dat$PCR == 0] and para_dat$Parasitaemia[para_dat$PCR >= 1]
## W = 1117, p-value = 0.1147
## alternative hypothesis: true location shift is not equal to 0
### Hb exclusion criteria
pcr_before = readr::read_csv('Data/PCR_data_before_cutoff.csv')
## Parsed with column specification:
## cols(
## Sex = col_character(),
## Hb = col_double(),
## PCR = col_character()
## )
pcr_after = readr::read_csv('Data/PCR_data_after_cutoff.csv')
## Parsed with column specification:
## cols(
## Sex = col_character(),
## Hb = col_double(),
## PCR = col_character()
## )
table(pcr_after$Sex, pcr_after$PCR)
## Heterozygous Homozygous WT
## F 7 0 103
## M 2 3 186
table(pcr_before$Sex, pcr_before$PCR)
## Heterozygous (563C>C/T) Homozygous (563C>T) unable to amplify WT
## Female 23 3 2 314
# (Intercept) 2.0065 1.3222 1.518 0.129
## Hb 0.1022 0.1059 0.965 0.334
## (Dispersion parameter for binomial family taken to be 1)
## Null deviance: 220.23 on 456 degrees of freedom
## Residual deviance: 219.31 on 455 degrees of freedom
## (5 observations deleted due to missingness)
## AIC: 255.19
Number of Fisher Scoring iterations: 6 mod = glm(PCR - Hb, family='binomial', weights = rep(2, nrow(pcr_after)), data = data.frame(PCR = as.numeric(pcr_after$PCR)/2, Hb=pcr_after$Hb)) summary(mod)
## Call:
glm(formula = PCR - Hb, family = "binomial", data = data.frame(PCR = as.numeric(pcr_after$PCR)/2, ## Hb = pcr_after$Hb), weights = rep(2, nrow(pcr_after)))
## Deviance Residuals:
## Min 1Q Median 3Q Max
## -3.7679 0.2503 0.3037 0.3489 0.5730
## Coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 1.3754 1.3816 0.996 0.319
## Hb 0.2166 0.1336 1.622 0.105
## (Dispersion parameter for binomial family taken to be 1)
## Null deviance: 115.44 on 300 degrees of freedom
## Residual deviance: 112.62 on 299 degrees of freedom
## AIC: 129.1
## Number of Fisher Scoring iterations: 6
a_bad_at = rbind(pcr_after, pcr_before) a_bad_at$Sex[awab_dat$Sex %in% c('F','Female')] = 'F' a_bad_at$Sex[awab_dat$Sex %in% c('M','Male')] = 'M' table(a_bad_at$Sex)
## F M
## 456 307
## a_bad_at = a_bad_at[!is.na(awab_dat$PCR), ]
A_bad_study A_bad_at = list(Nmales_controls_hemi = 28, Nmales_controls_total = 314+28, Nmales_vivaxcases_hemi = 5, Nmales_vivaxcases_total = 5+299, Mfemales_controls_homo = 2,Nfemales_controls_het = 50, Nfemales_controls_total = 305+50+2, Nfemales_vivaxcases_homo = 3, Nfemales_vivaxcases_het = 32, Nfemales_vivaxcases_total = 425+32+3)
_# Combined data__# Leslie + Bouma + Awab_ Combineddata = list(Nmales_controls_hemi=31+25+Awabdata$Nmales_controls_hemi, Nmales_controls_total=285+31+214+25+Awabdata$Nmales_controls_total, Nmales_vivaxcases_hemi=20+Awabdata$Nmales_vivaxcases_hemi, Nmales_vivaxcases_total=155+2+Awabdata$Nmales_vivaxcases_total, Nfemales_controls_homo=20+Awabdata$Nfemales_controls_homo, Nfemales_controls_het=26+0+Awabdata$Nfemales_controls_het, Nfemales_controls_total=126+26+2+Awabdata$Nfemales_controls_total, Nfemales_vivaxcases_homo=0+Awabdata$Nfemales_vivaxcases_homo, Nfemales_vivaxcases_het=6+Awabdata$Nfemales_vivaxcases_het, Nfemales_vivaxcases_total=72+6+Awabdata$Nfemales_vivaxcases_total)
datAwab = data.frame(sex = c(rep('male', Awabdata$Nmales_controls_total+ Awabdata$Nmales_vivaxcases_total), rep('female', Awabdata$Nfemales_controls_total+ Awabdata$Nfemales_vivaxcases_total)), GpD = c(rep('hemi/homo',Awabdata$Nmales_controls_hemi), rep('Normal',Awabdata$Nmales_controls_total- Awabdata$Nmales_controls_hemi), rep('hemi/homo',Awabdata$Nmales_vivaxcases_hemi), rep('Normal',Awabdata$Nmales_vivaxcases_total- Awabdata$Nmales_vivaxcases_hemi), rep('hemi/homo',Awabdata$Nfemales_controls_homo), rep('Het',Awabdata$Nfemales_controls_het), rep('Normal',Awabdata$Nfemales_controls_total- Awabdata$Nfemales_controls_homo- Awabdata$Nfemales_controls_het), rep('hemi/homo',Awabdata$Nfemales_vivaxcases_homo), rep('Het',Awabdata$Nfemales_vivaxcases_het), rep('Normal',Awabdata$Nfemales_vivaxcases_total- Awabdata$Nfemales_vivaxcases_homo- Awabdata$Nfemales_vivaxcases_het)), Status = c(rep('Healthy',Awabdata$Nmales_controls_total), rep('Vivav',Awabdata$Nmales_vivaxcases_total), rep('Healthy',Awabdata$Nfemales_controls_total), rep('Vivav',Awabdata$Nfemales_vivaxcases_total)))
datCombined = data.frame(sex = c(rep('male', Combineddata$Nmales_controls_total+ Combineddata$Nmales_vivaxcases_total), rep('female', Combineddata$Nfemales_controls_total+ Combineddata$Nfemales_vivaxcases_total)), G6PD = c(rep('hemi/homo',Combineddata$Nmales_controls_hemi),rep('Normal',Combineddata$Nmales_controls_total- Combineddata$Nmales_controls_hemi), rep('hemi/homo',Combineddata$Nmales_vivaxcases_hemi), rep('Normal',Combineddata$Nmales_vivaxcases_total- Combineddata$Nmales_vivaxcases_hemi), rep('hemi/homo',Combineddata$Nfemales_controls_homo), rep('Het',Combineddata$Nfemales_controls_het), rep('Normal',Combineddata$Nfemales_controls_total- Combineddata$Nfemales_controls_homo- Combineddata$Nfemales_controls_het), rep('hemi/homo',Combineddata$Nfemales_vivaxcases_homo), rep('Het',Combineddata$Nfemales_vivaxcases_het), rep('Normal',Combineddata$Nfemales_vivaxcases_total- Combineddata$Nfemales_vivaxcases_homo- Combineddata$Nfemales_vivaxcases_het)), Status = c(rep('Healthy',Combineddata$Nmales_controls_total), rep('Vivax',Combineddata$Nmales_vivaxcases_total), rep('Healthy',Combineddata$Nfemales_controls_total), rep('Vivax',Combineddata$Nfemales_vivaxcases_total))) writeLines('In Awab's data, the breakdown is as follows:\n')
## In Awab's data, the breakdown is as follows:
knitr::kable(table(datAwab$sex,datAwab$66PD,datAwab$Status))
\begin{tabular}{l l l r} \hline \hline Var1 & Var2 & Var3 & Freq \\ \hline female & hemi/homo & Healthy & 2 \\ male & hemi/homo & Healthy & 28 \\ female & Het & Healthy & 50 \\ male & Het & Healthy & 0 \\ female & Normal & Healthy & 305 \\ male & Normal & Healthy & 314 \\ female & hemi/homo & Vivax & 3 \\ male & hemi/homo & Vivax & 5 \\ female & Het & Vivax & 32 \\ male & Het & Vivax & 0 \\ female & Normal & Vivax & 425 \\ male & Normal & Vivax & 299 \\ \hline \hline \end{tabular}
\end{table}
writeLines('In the combined data, the breakdown is as follows:\n')
In the combined data, the breakdown is as follows: knitr::kable(table(datCombined$sex,datCombined$GGPD,datCombined$Status))
## Testing Hardy-Weinberg
Awab_controls = c(A = Awabdata$Nmales_controls_hemi, B = Awabdata$Nmales_controls_total- Awabdata$Nmales_controls_hemi, AA = Awabdata$Nfemales_controls_homo, AB = Awabdata$Nfemales_controls_het, BB = Awabdata$Nfemales_controls_total- Awabdata$Nfemales_controls_homo- Awabdata$Nfemales_controls_het )
All_controls = c(A = Combineddata$Nmales_controls_hemi, B = Combineddata$Nmales_controls_total- Combineddata$Nmales_controls_hemi, AA = Combineddata$Nfemales_controls_homo, AB = Combineddata$Nfemales_controls_het, BB = Combineddata$Nfemales_controls_total- Combineddata$Nfemales_controls_homo- Combineddata$Nfemales_controls_het )
HWExact(Awab_controls,x.linked=TRUE,verbose=TRUE)
## Grafelman-Weir exact test for Hardy-Weinberg equilibrium on the X-chromosome
## using SELOME p-value
## Sample probability 0.02651387 p-value = 0.9436494
HWExact(All_controls,x.linked=TRUE,verbose=TRUE)
## Grafelman-Weir exact test for Hardy-Weinberg equilibrium on the X-chromosome
## using SELOME p-value
## Sample probability 0.008872498 p-value = 0.5968529
### Stan model
The assumptions in the model:
* Hardy-Weinberg equilibrium holds in the Pashtun group (there is no evidence that this assumption does not hold in the controls)
* The protective effect is the same in hemizygous deficient males as it is in homozygous deficient females
# stan model code
GGPD_effect = "
data { int<lower=O> Nmales_controls_hemi; // #males hemizygous deficientint<lower=0> Nmales_controls_total; int<lower=0> Nfemales_controls_homo; int<lower=0> Nfemales_controls_het; int<lower=0> Nfemales_controls_het; int<lower=0> Nfemales_controls_total; int<lower=0> Nmales_vivaxcases_hemi; int<lower=0> Nmales_vivaxcases_total; int<lower=0> Nfemales_vivaxcases_homo; int<lower=0> Nfemales_vivaxcases_het; int<lower=0> Nfemales_vivaxcases_total; int<lower=0> Nfemales_vivaxcases_total; int<lower=0> Nfemales_vivaxcases_total; real p_1; // Prior beta model of prevalence p real p_2; // Prior beta model of prevalence p } transformed data { int female_controls; int female_cases; female_controls = Nfemales_controls_homo; female_controls = Nfemales_controls_het; female_controls = Nfemales_controls_total-Nfemales_controls_het-Nfemales_controls_homo; female_cases = Nfemales_vivaxcases_homo; female_cases = Nfemales_vivaxcases_het; female_cases = Nfemales_vivaxcases_total-Nfemales_vivaxcases_het-Nfemales_vivaxcases_homo; } parameters { real<lower=0,upper=1> p; // allele frequency real<lower=0,upper=1> alpha; // protective effect in fully deficits: hemi or homo-zygous real<lower=0,upper=1> beta; // protective effect in heterozygous deficients } transformed parameters { // For ease of model interpretation (these are the quantities we are interested in) real one_minus_alpha = 1-alpha; vector theta_females_controls; vector theta_females_cases; theta_females_controls = p^2; theta_females_controls = 2*p*(1-p); theta_females_controls = 1 - 2*p*(1-p) - p^2; theta_females_cases = alpha * p^2; theta_females_cases = beta * 2*p*(1-p); theta_females_cases = 1 - (beta*2*p*(1-p)) - (alpha*p^2); } model { // Prior p - beta(p_1, p_2); alpha - uniform; beta - uniform; // Multinomial likelihood for females and binomial likelihood for males // Healthy individuals - controls : gives estimate for p Nmales_controls_hemi - binomial(Nmales_controls_total, p);female_controls - multinomial(theta_females_controls); //Vivax individuals: gives estimate for alpha and beta Nmales_vivaxcases_hemi - binomial(Nmales_vivaxcases_total, alpha*p); female_cases - multinomial(theta_females_cases); } " GGPD_effect_stan = stan_model(model_code = GGPD_effect)
#_Awab's dataoptions(mc.cores = 4) set.seed
writeLines(sprintf('In Awab data, we have %s controls (%s males and %s females) and %s vivax cases (%s in Awabdata$Nmales_controls_total+Awabdata$Nfemales_controls_total, Awabdata$Nmales_controls_total,Awabdata$Nfemales_controls_total, Awabdata$Nmales_vivaxcases_total+Awabdata$Nfemales_vivaxcases_total, Awabdata$Nmales_vivaxcases_total,Awabdata$Nfemales_vivaxcases_total))
In Awab data, we have 699 controls (342 males and 357 females) and 764 vivax cases (304 males and 460 males)
Just Awab data mod_awab=sampling(GGPD_effect_stan, data=c(Awabdata, p_1 = 2, p_2 = 18), iter = 10^6, thin = 2*10^2, chains=4)
theta1=extract(mod_awab) knitr::kable(round(100*sapply(thetas1, quantile, probs = c(0.025,.5,.975)),1)[,1:5])
writeLines(sprintf('In the combined dataset, we have %s controls (%s males and %s females) and %s vivax combineddata$Nmales_controls_total+Combineddata$Nfemales_controls_total, Combineddata$Nmales_controls_total, Combineddata$Nmales_vivaxcases_total+Combineddata$Nfemales_vivaxcases_total, Combineddata$Nmales_vivaxcases_total,Combineddata$Nfemales_vivaxcases_total))
In the combined dataset, we have 1408 controls (897 males and 511 females) and 999 vivax cases (461 males)
#_Meta-analysis:Awab+Leslie+Boura_ mod_combined=sampling(GGPD_effect_stan, data=c(Combineddata, p_1 = 2, p_2 = 18), iter = 10^6, thin = 2*10^2, chains=4)
theta2=extract(mod_combined) knitr::kable(round(100*sapply(thetas2, quantile, probs = c(0.025,.5,.975)),1)[,1:5])
\begin{tabular}{l r r r r r} \hline & p & alpha & beta & one\_minus\_alpha & one\_minus\_beta \\ \hline
2.5\% & 6.3 & 14.9 & 33.4 & 38.6 & 28.3 \\
50\% & 7.8 & 32.4 & 49.3 & 67.6 & 50.7 \\
97.5\% & 9.5 & 61.4 & 71.7 & 85.1 & 66.6 \\ \hline \end{tabular}
writeLines(sprintf('In the combined dataset, we have %s controls (%s males and %s females) and %s vivax combineddata$Nmales_controls_total+Combineddata$Nfemales_controls_total, Combineddata$Nmales_controls_total, Combineddata$Nmales_controls_total, Combineddata$Nmales_vivaxcases_total+Combineddata$Nfemales_vivaxcases_total, Combineddata$Nmales_vivaxcases_total, Combineddata$Nmales_vivaxcases_total,Combineddata$Nfemales_vivaxcases_total))
In the combined dataset, we have 1408 controls (897 males and 511 females) and 999 vivax cases (461 males)
#_Meta-analysis:Awab+Leslie+Boura_ mod_combined=sampling(GGPD_effect_stan, data=c(Combineddata, p_1 = 2, p_2 = 18), iter = 10^6, thin = 2*10^2, chains=4)
theta3=extract(mod_combined) knitr::kable(round(100*sapply(thetas2, quantile, probs = c(0.025,.5,.975)),1)[,1:5])Check model convergence
traceplot(mod_awab)
```
## 'pars' not specified. Showing first 10 parameters by default.
``` traceplot(mod_combined)
## Results
writeLines(sprintf('The allele frequency in the Pasthun ethnic group is %s (95%% CI %s-%s) (using Awab & round(100*mean(thetas1%p), 1), round(100*quantile(thetas1%p,probs = 0.025), 1), round(100*quantile(thetas1%p,probs = 0.975), 1)))
The allele frequency in the Pasthun ethnic group is 7.8 (95% CI 6.3-9.5) (using Awab data only) writeLines(sprintf('The allele frequency in the Pasthun ethnic group is %s (95% CI %s-%s) (meta-analysis: round(100*mean(thetas2%p), 1), round(100*quantile(thetas2%p,probs = 0.025), 1),round(100*quantile(thetas2$p,probs = 0.975), 1)))
The allele frequency in the Pashtun ethnic group is 8.8 (95% CI 7.6-10.1) (meta-analysis) writeLines(sprintf('The protective effect in hemi/homo-zygotes is %s%% (credible interval %s-%s) (using round(100*(1-mean(thetas1$alpha))), round(100*(1-quantile(thetas1$alpha,probs = 0.975))), round(100*(1-quantile(thetas1$alpha,probs = 0.025)))))
The protective effect in hemi/homo-zygotes is 66% (credible interval 39-85) (using Awab data only) writeLines(sprintf('The protective effect in hemi/homo-zygotes is %s%% (credible interval %s-%s) (meta-% round(100*(1-mean(thetas2$alpha))), round(100*(1-quantile(thetas2$alpha,probs = 0.975))), round(100*(1-quantile(thetas2$alpha,probs = 0.025)))))
The protective effect in hemi/homo-zygotes is 75% (credible interval 58-88) (meta-analysis) writeLines(sprintf('The protective effect in heterozygotes is %s%% (credible interval %s-%s) (using Awab round(100*(1-mean(thetas1$beta))), round(100*(1-quantile(thetas1$beta,probs = 0.975))), round(100*(1-quantile(thetas1$beta,probs = 0.025)))))
The protective effect in heterozygotes is 54% (credible interval 38-68) (meta-analysis) writeLines(sprintf('The ratio of effect between hemi to hets is %s (credible interval %s to %s) (using a round((mean((1-thetas1$beta)/(1-thetas1$alpha))),2), round((quantile((1-thetas1$beta)/(1-thetas1$alpha),probs = 0.975)),2), round((quantile((1-thetas1$beta)/(1-thetas1$alpha),probs = 0.025)),2)))
The ratio of effect between hemi to hets is 0.78 (credible interval 1.3 to 0.43) (using Awab data only) writeLines(sprintf('The protective effect in heterozygotes is %s (credible interval %s-%s) (meta-analysis) round((mean((1-thetas2$beta)/(1-thetas2$alpha))),2), round(quantile((1-thetas2$beta)/(1-thetas2$alpha),probs = 0.975)),2), round(quantile((1-thetas2$beta)/(1-thetas2$alpha),probs = 0.025)),2)))
The protective effect in heterozygotes is 0.73 (credible interval 1-0.5) (meta-analysis) writeLines(sprintf('The posterior probability that the effect is greater in hemi/homo-zygous deficits) round(mean(thetas1$beta > theta1$alpha),2)))
The posterior probability that the effect is greater in hemi/homo-zygous deficits is 0.88 (using Awab ruleLines(sprintf('The posterior probability that the effect is greater in hemi/homo-zygous deficits) round(mean(thetas2$beta > theta2$alpha),2)))
The posterior probability that the effect is greater in hemi/homo-zygous deficits is 0.98 (meta-analysis)
in paper ind = names(mod_combined) %in% c('alpha','beta') names(mod_combined)[ind] = c(' hemi/homo-zygous','heterozygous')
ind = names(mod_awab)%in%c('alpha','beta') names(mod_awab)[ind] = c('hemi/homo-zygous','heterozygous')
x = 100 - 100*as.matrix(mod_combined, pars = c('hemi/homo-zygous','heterozygous')) p1 = mcmc_intervals(x, point_est='median', prob_outer = 0.95) + scale_x_continuous(name = 'Reduction in prevalence of clinical vivax malaria (%)', limits = c) + theme(text=element_text(size=17), axis.line.y = element_blank(), axis.ticks.y = element_blank(), plot.title = element_text(size=34,hjust=0.5))# + ggtitle('Meta-analysis')
## Scale for 'x' is already present.
## replace the existing scale.
p1
### hemi/homo-zygous
\begin{tabular}{c c c c c} \hline \hline \(0\) & \(25\) & \(50\) & \(75\) & \(100\) \\ \hline \hline \end{tabular}
Reduction in prevalence of clinical vivax malaria (%)
x = as.matrix(mod_awab, pars = c('hemi/homo-zygous','heterozygous')) p2 = mcmc_intervals(x) + scale_x_continuous(name = 'Proportion presenting with clinical vivax malaria relative to GGPD normals, limits = c) + theme(axis.text=element_text(size=15), axis.line.y = element_blank(), axis.ticks.y = element_blank(), plot.title = element_text(size=24,hjust=0.5)) + ggtitle('Awab data only')
## Scale for 'x' is already present.
Awab data only
## hemi/homo-zygous
## heterozygous
\begin{tabular}{l l l l} \hline
0.00 & 0.25 & 0.50 & 0.75 & 1.00 \\ Proportion presenting with clinical vivax malaria relative to G6PD normals & Make a plot for the paper with both results. \\ grid.arrange(p2, p1, mrow = 2) & & \\ \end{tabular}
Awab data only
## hemi/homo-zygous heterozygous
\begin{tabular}{c c c c} \hline
0.00 & 0.25 & 0.50 & 0.75 & 1.00 \\ & & Proportion presenting with clinical vivax malaria relative to G6PD normals \\
## hemi/homo-zygous
& & & \\ \end{tabular}
heterozygous
\begin{tabular}{c c c} \hline
0 & 25 & 50 & 75 & 100 \\ & & Reduction in prevalence of clinical vivax malaria (\%) \\ \hline
0 & 25 & 50 & 75 & 100 \\ & & Reduction in prevalence of clinical vivax malaria (\%) \\ \hline \end{tabular} |
181990_file02 | ### Population structure of demographic-classes derivation (Table 2 in Main Text)
In April, 2020, 40.7% of the population in informal IDP camps in Northern Syria was aged 0-12, 53.4% aged 13-50, and 5.9% aged 51+. To estimate the proportion of each age group with comorbidities, we calculated the weighted average age-specific comorbidity prevalence of the 4 most common comorbidities in the Syrian refugee populations in Jordan and Lebanon: hypertension, cardiovascular disease, diabetes, and chronic respiratory disease. We standardized these weighted averages to the age structure of IDPs in Northern Syria and estimated that 11.7% of people aged 13-50 have comorbidities, while 62.9% of people aged 51+ have comorbidities.
### Derivation of transmissibility parameters
The probability of infection if there is a contact between a susceptible and an infected person depends on the stage of the disease, denoted \(\tau\beta_{\text{P}}\), \(\tau\beta_{\text{A}}\), \(\tau\beta_{\text{I}}\) or \(\tau\beta_{\text{H}}\) depending upon whether the infected individual is in the presymptomatic (\(P_{i}\)), symptomatic (\(I_{i}\)), asymptomatic (\(A_{i}\)), or hospitalized compartment (\(H_{i}\)), respectively. We estimated these parameters in two steps. In the following section, we estimate the \(\beta_{\text{X}}\) parameters (\(\text{X}\in\{\text{P},\text{A},\text{I},\text{H}\}\)) which represent the relative transmissibility of each stage with respect to the maximum transmissibility \(\tau\). After this calculation, we present our estimate for the maximum transmissibility parameter \(\tau\).
#### Relative transmissibilities \(\beta\) (Table 1 in Main Text)
We start by considering the transmissibility of the presymptomatic stage for those individuals who become symptomatic as a reference (\(\beta_{\text{P}\rightarrow\text{I}}=1\)), since the probability of infection from contact with an individual at this epidemiological stage is highest. Next, we set the contribution of each epidemiological stage to infectivity as proportional to \(\beta_{\text{X}}/\gamma_{\text{X}}\), with \(1/\gamma_{\text{X}}\) the duration of stage X. Following He et al, we estimate the proportion of infectivity in individuals who go on to develop symptoms that occurs at the presymptomatic stage (\(\text{X}\in\{\text{P}\}\)) as the area under the infectivity curve prior to symptom onset, \(AUC_{\text{P}}\), and the proportion of infectivity that occurs at symptomatic stages (\(\text{X}\in\{\text{I},\text{H}\}\)) as the area under the infectivity curve after symptom onset, \(1-AUC_{\text{P}}\):
\[\frac{AUC_{\text{P}}}{(1-AUC_{\text{P}})}\approx\frac{\frac{\beta_{\text{P} \rightarrow\text{I}}}{\beta_{\text{P}}}}{\frac{\beta_{\text{I}}}{\gamma_{\text {I}}}+\frac{\beta_{\text{H}}}{\gamma_{\text{H}}}} \tag{1}\]
We then considered the quantity \(\rho_{\text{HI}}\), the ratio of the viral culture positive test rate in hospitalized patients 7-16 days since start of symptoms to the positive test rate in patients 0-6 days since start of symptoms from van Kampen et al.. Similarly, the relative risk of asymptomatic transmission to symptomatic transmission according to Byambasuren et al. is expressed as \(\rho_{\text{AI}}\):
\[\beta_{\text{A}}=\rho_{\text{AI}}\beta_{\text{I}} \tag{2}\]
\[\beta_{\text{H}}=\rho_{\text{HI}}\beta_{\text{I}} \tag{3}\]
Considering these relationships we rewrite Eq. 1 to obtain the desired parameters:\[\beta_{\rm I}=\frac{\beta_{\rm P\to I}\gamma_{\rm I}\gamma_{\rm H}(1-AUC_{\rm P})}{ AUC_{\rm P}\delta_{\rm P}(\gamma_{\rm H}+\rho_{\rm HI}\gamma_{\rm I})} \tag{4}\]
\[\beta_{\rm A}=\frac{\rho_{\rm AI}\beta_{\rm P\to I}\gamma_{\rm I}\gamma_{\rm H} (1-AUC_{\rm P})}{AUC_{\rm P}\delta_{\rm P}(\gamma_{\rm H}+\rho_{\rm HI}\gamma_{ \rm I})} \tag{5}\]
\[\beta_{\rm H}=\frac{\rho_{\rm HI}\beta_{\rm P\to I}\gamma_{\rm I}\gamma_{\rm H} (1-AUC_{\rm P})}{AUC_{\rm P}\delta_{\rm P}(\gamma_{\rm H}+\rho_{\rm HI}\gamma_{ \rm I})}. \tag{6}\]
The values of \(AUC_{\rm P}\), \(\rho_{\rm AI}\) and \(\rho_{\rm HI}\) are presented in Table 1, and the values of \(\beta_{\rm X}\) in Main Text. Noting that the starting point for these derivations is the transmissibility of individuals in the presymptomatic stage who go on to develop symptoms (\(\beta_{\rm P\to I}=1\)), we need to go back and derive the transmissibility of all presymptomatic individuals (\(\beta_{\rm P}\)), taking those that will be asymptomatic into account. We assumed that the relative transmissibility of presymptomatic individuals who will become asymptomatic to those that will become symptomatic, is equal to the relative transmissibility of asymptomatic to symptomatic individuals (\(\rho_{\rm AI}\)). With the proportion of presymptomatic cases that will become developed symptoms \(f\) (encoded in in Eqs. 24-32 in Main Text), we compute the mean transmissibility of all presymptomatic individuals as:
\[\beta_{\rm P}=f\beta_{\rm P\to I}+(1-f)\rho_{\rm AI}\beta_{\rm P\to I}. \tag{7}\]
#### Maximum transmissibility parameter \(\tau\)
In the following, to simplify the notation we define \(\kappa_{i}=(l_{i}\gamma_{\rm I}+h_{i}\eta+g_{i}\alpha)\). To estimate the probability of infection if there is a contact between a susceptible and an infected individual (parameter \(\tau\)) we proceed as follows. We start by considering the subsystem containing the infected population:
\[\dot{E}_{i}=\lambda_{i}S_{i}-\delta_{\rm E}E_{i} \tag{8}\]
\[\dot{P}_{i}=\delta_{\rm E}E_{i}-\delta_{\rm P}P_{i} \tag{9}\]
\[\dot{A}_{i}=(1-f)\delta_{\rm P}P_{i}-\gamma_{\rm A}A_{i} \tag{10}\]
\[\dot{I}_{i}=f\delta_{\rm P}P_{i}-\kappa_{i}I_{i} \tag{11}\]
\[\dot{H}_{i}=h_{i}\eta I_{i}-\gamma_{\rm H}H_{i}. \tag{12}\]
For the sake of simplifying the notation, let us consider the following ordering of the variables in the vector \(x=(E_{1},...,E_{\rm M},P_{1},...,P_{\rm M},A_{1},...,A_{\rm M},I_{1},...,I_{ \rm M},H_{1},...,H_{\rm M})\), with \(M\) the number of population classes. We are interested in the parameterization of the null model, which will serve as a baseline to estimate the parameter \(\tau\), which is initially unknown, but does not change when interventions are introduced. Considering the contacts matrix for the null model (Eq. 9 in Main Text), the rate of exposure becomes
\[\lambda_{i}=\frac{\tau}{N}\sum_{j=1}^{M}c_{i}\left(\beta_{\rm P}P_{j}+\beta_{ \rm A}A_{j}+\beta_{\rm I}I_{j}+\beta_{\rm H}H_{j}\right). \tag{13}\]
\begin{table}
\begin{tabular}{|c|c|c|c|c|} \hline Parameter & Description & Value & Distribution & Reference \\ \hline \hline \(AUC_{\rm P}\) & \begin{tabular}{c} Presymptomatic area under \\ infectivity curve \\ \end{tabular} & 0.44 (95\% CI:.30-.57) & Gaussian & \\ \hline \(\rho_{\rm AI}\) & \begin{tabular}{c} Ratio of asymptomatic to \\ symptomatic infectiousness \\ \end{tabular} & 0.58 (95\% CI:.34-.99) & Lognormal & \\ \hline \(\rho_{\rm HI}\) &
\begin{tabular}{c} Ratio of hospitalized to \\ symptomatic infectiousness \\ \end{tabular} & 0.48 & - & \\ \hline \end{tabular}
\end{table}
Table 1: **Relative transmissibility parameters.**In the following, we use bold symbols for vectors and matrices, and the symbols \(\odot\) and \(\odot\) for the element-wise multiplication and division, respectively.
\[\mathbf{\Sigma}=\begin{bmatrix}-\delta_{\mathrm{E}}\mathbf{I}&\mathbf{0}&\mathbf{0}&\mathbf{0}& \mathbf{0}\\ \delta_{\mathrm{E}}\mathbf{I}&-\delta_{\mathrm{P}}\mathbf{I}&\mathbf{0}&\mathbf{0}&\mathbf{0}\\ \mathbf{0}&(1-f)\delta_{\mathrm{P}}\mathbf{I}&-\gamma_{\mathrm{A}}\mathbf{I}&\mathbf{0}&\mathbf{0} \\ \mathbf{0}&f\delta_{\mathrm{P}}\mathbf{I}&\mathbf{0}&-\mathrm{diag}(\mathbf{\kappa})\mathbf{I}&\mathbf{ 0}\\ \mathbf{0}&\mathbf{0}&\mathbf{0}&\eta\mathrm{diag}(\mathbf{h})\mathbf{I}&-\gamma_{\mathrm{H}}\mathbf{I} \end{bmatrix} \tag{15}\]
Where \(\mathbf{I}\) and \(\mathbf{0}\) are the identity and null matrices of size \(M\), and \(\mathbf{\kappa}=\mathbf{l}\gamma_{I}+\mathbf{h}\eta+\mathbf{g}\alpha\).
\[\mathbf{\Sigma^{-1}}=\begin{bmatrix}-\frac{1}{\delta_{\mathrm{E}}}\mathbf{I}&\mathbf{0}& \mathbf{0}&\mathbf{0}&\mathbf{0}\\ -\frac{1}{\delta_{\mathrm{P}}}\mathbf{I}&-\frac{1}{\delta_{\mathrm{P}}}\mathbf{I}&\mathbf{ 0}&\mathbf{0}&\mathbf{0}\\ -\frac{(1-f)}{\gamma_{\mathrm{A}}}\mathbf{I}&-\frac{(1-f)}{\gamma_{\mathrm{A}}}\mathbf{ I}&-\frac{1}{\gamma_{\mathrm{A}}}\mathbf{I}&\mathbf{0}&\mathbf{0}\\ -f\mathrm{diag}(\mathbf{\kappa}^{-1})\mathbf{I}&-f\mathrm{diag}(\mathbf{\kappa}^{-1})\mathbf{I }&\mathbf{0}&-\mathrm{diag}(\mathbf{\kappa}^{-1})\mathbf{I}&\mathbf{0}\\ -\frac{f\eta}{\gamma_{\mathrm{H}}}\mathrm{diag}(\mathbf{h}\odot\mathbf{\kappa})\mathbf{I}& -\frac{f\eta}{\gamma_{\mathrm{H}}}\mathrm{diag}(\mathbf{h}\odot\mathbf{\kappa})\mathbf{I}& 0&-\frac{\eta}{\gamma_{\mathrm{H}}}\mathrm{diag}(\mathbf{h}\odot\mathbf{\kappa})\mathbf{I }&-\frac{1}{\gamma_{\mathrm{H}}}\mathbf{I}\end{bmatrix} \tag{16}\]
The NGM with large domain can now be found by \(\mathbf{K_{\mathrm{L}}}=-\mathbf{T}\mathbf{\Sigma}^{-1}\). However, since we know that each individual who gets infected becomes exposed (\(E\) compartment), we focus on the NGM with small domain, \(\mathbf{K_{\mathrm{S}}}\), which only consists of the \(E\) compartment. We do this by removing the rows that correspond to the other compartments from \(T\) and the columns from \(\Sigma^{-1}\). We then find:
\[\mathbf{K_{\mathrm{S}}}=\tau\left[\frac{1}{\delta_{P}}\mathbf{\Theta}_{\mathrm{P}}+ \frac{(1-f)}{\gamma_{A}}\mathbf{\Theta}_{\mathrm{A}}+f\mathrm{diag}\left(\mathbf{h}^{- 1}\right)\mathbf{\Theta}_{\mathrm{I}}+\frac{f\eta}{\gamma_{\mathrm{H}}}\mathrm{ diag}(\mathbf{h}\odot\mathbf{\kappa})\mathbf{\Theta}_{\mathrm{H}}\right]. \tag{17}\]
The reproduction number is related to the dominant eigenvalue of \(\mathbf{K_{\mathrm{S}}}\), i.e. \(R_{0}=|\lambda_{1}|\), and \(\tau\) is estimated from the real dominant eigenvalue of \(\tilde{K}_{\mathrm{S}}=K_{\mathrm{S}}/\tau\). Considering the null model parameters (\(\tilde{\lambda}_{1}^{0}\)), we have the expression:
\[\tau=\frac{R_{0}}{|\tilde{\lambda}_{1}^{0}|}. \tag{18}\]
### Epidemiological severity proportions (Table 4 in Main Text)
In the Main Text, we presented the proportions in which clinical symptomatic individuals resolve into critical (\(q_{i}^{D}\)), severe (\(q_{i}^{\mathrm{H}}\)) and recovered (\(q_{i}^{R}\)) cases. We assigned the fractions of symptomatic cases in children aged \(<\)13 that would become severe and critical from the fractions of symptomatic cases in children aged \(<\)11 that were severe and critical in China. We assigned the class-specific fractions of symptomatic cases in adults that would become severe and critical based on age and comorbidity-specific fractions of symptomatic cases with known outcomes that required hospitalization, without and with ICU admission, respectively in the United States. To account for poorer health among Syrian adults compared to their similarly aged peers in developed countries, estimates for US adults aged 19-64 were used for Syrian adults aged 13-50, while estimates for US adults aged 65+ were used for Syrian adults aged 51+.
Since the rates at which these individuals progress are different (\(\eta\) for \(H\), \(\alpha\) for \(D\) and \(\gamma_{\rm I}\) for \(R\)) we introduced three parameters, \(h_{i}\), \(g_{i}\) and \(l_{i}\), to distribute individuals according to the desired proportions following the equations:
\[q_{i}^{\rm H}=h_{i}\eta\kappa_{i}^{-1} \tag{19}\]
\[q_{i}^{D}=g_{i}\alpha\kappa_{i}^{-1} \tag{20}\]
\[q_{i}^{R}=1-q_{i}^{\rm H}-q_{i}^{D}=l_{i}\gamma_{\rm I}\kappa_{i}^{-1}, \tag{21}\]
where \(\kappa_{i}=h_{i}\eta+g_{i}\alpha+l_{i}\gamma_{\rm I}.\) The system has three unknowns and three equations but one equation linearly depends on the other two, hence we introduce the constraint \(l_{i}=1-h_{i}-g_{i}\) to solve the system as:
\[h_{i}=\frac{\alpha q_{i}^{H}}{\eta q_{i}^{D}}g_{i}, \tag{22}\]
\[g_{i}=\gamma_{I}\left(\frac{\alpha}{q_{i}^{D}}+\frac{\gamma_{I}\alpha q_{i}^{H }}{\eta q_{i}^{D}}+\gamma_{I}-\frac{\alpha q_{i}^{H}}{q_{i}^{D}}-\alpha\right) ^{-1}. \tag{23}\]
## 2 Parameterization of the interventions (Table 5 in Main Text)
### Safety zone
We considered the existence of a safety zone to protect a certain fraction, \(f_{\rm S}\), of the population, mostly those more vulnerable. In practice, this involves dividing the camp in two areas, a "green" zone (denoted g) for the protected population and an "orange" zone (o) for the exposed population, and dividing each demographic-class into two behaviour-classes for each respective zone. These two populations interact via a buffer zone, under controlled conditions where we assumed transmissivity is reduced by 80%, encoded in the parameter \(\xi_{ij}=0.2\). Each individual in the green zone can interact with a limited number (\(c_{\rm visit}\)) of family members (hereafter "visitors") from the orange zone per day. In some interventions we considered that individuals visiting the buffer zone will have a health check (e.g. temperature measurement), aimed at excluding symptomatic individuals. When the health check is applied, the probability of transmission by individuals in the \(I\) or \(H\) compartments from one zone to susceptible individuals from a different zone is set to zero (see parameters \(\zeta_{\rm I}\) and \(\zeta_{\rm H}\) in Eq. 10 in Main Text). In the following, we derive the values of parameters \(\epsilon_{ij}\) and \(\omega_{ij}\), modifying the rate at which individuals become exposed (see Eq. 10 in Main Text).
Although setting up a safety zone implies a reduction in the number of contacts between classes of the green zone and the orange zone, the mean number of contacts that each individual has per day, \(c_{i}\), is conserved. Therefore we need to estimate how contacts will be redistributed from individuals from a different zone to individuals living in the same zone. We model this redistribution of contacts with the parameter \(\epsilon_{ij}\):
\[\epsilon_{ij} = \vartheta c_{\rm visit}/c_{i}\quad(i,j\text{ in different zones})\] \[\epsilon_{ij} = 1-\vartheta c_{\rm visit}/c_{i}\quad(i,j\text{ in same zone}).\]
We define \(\vartheta\) as1
Footnote 1: If \(c_{\rm visit}\) is large enough ( ( \(c_{\rm visit}\approx 15\) contacts per day), \(\vartheta\) should saturate, because every member of the orange zone would eventually visit the buffer zone, following the expression:
\[\vartheta=\begin{cases}1&\text{if }i\in\text{g}\\ f_{\rm o,visit}\,\,\text{if }i\in\text{o}\end{cases}\]
with the Heaviside function \(\Theta(f_{\rm o,visit}-1)=1\) if \(f_{\rm o,visit}\geq 1\). We chose values well below this saturation threshold (a maximum of 10 contacts per week, i.e. 1.42 contacts per day).
If we assume that visitors are always different, the quantity \(f_{\rm o,visit}=c_{\rm visit}\frac{N_{\rm s}}{N_{\rm o}}\) is the fraction of the orange population that visits the buffer zone.
Next, we estimate how the probability of interaction between a member of class \(i\) and class \(j\) is modified with respect to the null model, depending on the zones from which class \(i\) and class \(j\) are drawn. Suppose classes \(i\) and \(j\) are separated from the rest of the camp's population and confined within a restricted zone. The probability that an individual of class \(i\) randomly encounters an individual of class \(j\) would now be higher than in a well-mixed population where interaction with individuals belonging to other classes is not restricted. This modification of relative probability of interaction is encoded in the parameter \(\omega_{ij}\) (see Eq. 10 in Main Text). More specifically, the proportion \(N_{i}/N\) of individuals of class \(i\) in the null model becomes \(N_{i}/N_{\rm X}\) with \(N_{\rm X}\) the total number of individuals in zone \(X=\{\rm o,g\}\). This yields the following values for \(\omega_{ij}\):
\[\omega_{ij} = \left(\frac{N_{i}}{N_{\rm X}}\right)/\left(\frac{N}{N_{\rm s}} \right)=\frac{N}{N_{\rm X}}\quad(i,j\mbox{ in same zone }X)\] \[\omega_{ij} = \left(\frac{N_{i}}{N_{\rm Y}}\right)/\left(\frac{N}{N_{i}} \right)=\frac{N}{N_{\rm Y}}\quad(i\in X\mbox{ and }j\in Y).\]
Following this parameterization, we explore different scenarios, summarized in Table 2, for allocating members of each population class to the safety, or "green" zone, and the exposed, or "orange" zone. In one scenario, we only place individuals in age group 3 (\(>\)50) in the green zone, while in another we place all vulnerable individuals, age group 3 and age group 2 with comorbidities, in the green zone. In 3 additional scenarios, after all vulnerable individuals are allocated to the green zone, we set the green zone's capacity to a certain percentage of the camp's population (20%, 25%, 30%), and allocate its remainder to non-vulnerable family members, who by necessity are either children \(<\)13 in age group 1 or healthy younger adults in age group 2. In accordance with camp managers' expectations that many vulnerable individuals will have non-vulnerable spouses, while fewer vulnerable individuals will have young children, in these scenarios we allocate 40% of the remainder of the green zone to children and 60% of the remainder of the green zone to younger adults without comorbidities. We also consider a baseline scenario in which there is no green zone.
\begin{table}
\begin{tabular}{|c|c|c|c|c|c|c|c|c|} \hline Scenario & Age 1, orange & Age 1, green & Age 2 no comorbidities, orange & Age 2 no competing cities, green & Age 2 comorbidities, orange & Age 2 comorbidities, green & Age 3 no green & Age 3 comorbidities, green \\ \hline \hline Only age 3 &.407 & 0 &.471 & 0 &.0626 & 0 &.022 &.0373 \\ in green zone & & & & & & & & \\ \hline Age 3 + age 2 with comorbidities in green zone &.407 & 0 &.471 & 0 & 0 &.0626 &.022 &.0373 \\ \hline \begin{tabular}{c} 20\% green zone \\ capacity \\ \end{tabular} &.376 &.0312 &.424 &.0469 & 0 &.0626 &.022 &.0373 \\ \hline \begin{tabular}{c} 25\% green zone \\ capacity \\ \end{tabular} &.356 &.0512 &.394 &.0769 & 0 &.0626 &.022 &.0373 \\ \hline
\begin{tabular}{c} 30\% green zone \\ capacity \\ \end{tabular} &.336 &.0712 &.364 &.107 & 0 &.0626 &.022 &.0373 \\ \hline \end{tabular}
\end{table}
Table 2: **Fraction of population in each zone by safety zone scenario and behaviour-class.** Behaviour-classes that are not considered in a given scenario have a proportion equal to zero.
### Self-isolation and evacuation
To implement self-isolation we start by expanding our model (Eqs 24-32 in Main Text) to consider a new compartment for each demographic-class. To model the fact that symptomatic individuals require some time to recognize their symptoms and to self-isolate, we split the symptomatic compartment in two: symptomatic prior to identification, \(O_{i}\), and symptomatic following identification, \(I_{i}\). Following these considerations, the structure of the model is represented in Fig. 1, which follows the equations:
\[\dot{S}_{i}=-\lambda_{i}S_{i} \tag{24}\] \[\dot{E}_{i}=\lambda_{i}S_{i}-\delta_{\mathrm{E}}E_{i}\] \[\dot{P}_{i}=\delta_{\mathrm{E}}E_{i}-\delta_{\mathrm{P}}P_{i}\] \[\dot{A}_{i}=(1-f)\delta_{\mathrm{P}}P_{i}-\gamma_{\mathrm{A}}A_{i}\] \[\dot{O}_{i}=f\delta_{\mathrm{P}}P_{i}-(l_{i}\gamma_{I}+h_{i} \delta_{\mathrm{O}}+g_{i}\alpha)O_{i}\] \[\dot{I}_{i}=\delta_{\mathrm{O}}O_{i}-(l_{i}\gamma_{I}+h_{i} \eta^{\prime}+g_{i}\alpha)I_{i}\] \[\dot{H}_{i}=h_{i}(\eta^{\prime}I_{i}+\delta_{\mathrm{O}}O_{i})- \gamma_{\mathrm{H}}H_{i}\] \[\dot{R}_{i}=\gamma_{\mathrm{A}}A_{i}+l_{i}\gamma_{\mathrm{I}}(I_ {i}+O_{i})+(1-\sigma)\gamma_{\mathrm{H}}H_{i}\] \[\dot{D}_{i}=g_{i}\alpha(I_{i}+O_{i})+\sigma\gamma_{\mathrm{H}}H_{i} \tag{32}\]
The duration for which an individual spends in the clinical symptomatic compartment, \(1/\eta^{\prime}\), is then calculated as the difference between the symptomatic period if there is no isolation, \(1/\eta\), and the duration spent in the symptom onset compartment (\(1/\delta_{\mathrm{O}}\)). The remaining parameters determining the rate of change of individuals at \(O_{i}\), namely the rate of progression towards recovery or death (\(\gamma_{i}\) or \(\alpha\), respectively), as well as the relative transmissibility, \(\beta_{\mathrm{I}}\), remain the same as those of the symptomatic compartment, \(I_{i}\).
The second modification required is a delineation between the isolated and non-isolated population within the clinical symptomatic compartment after identification of symptoms (\(I_{i}\)). This does not entail the creation of a new compartment, but rather the identification of the number of individuals in each class in isolation (\(\tilde{I}_{i}\)).
**Diagram of the model including the self-isolation intervention. The model considers an additional symptom onset compartment (O).**simulation. Next, we consider the isolation capacity of the camp (\(\tilde{N}\)), and we assume that, when the infectious population exceeds this capacity, the number of isolated individuals for each class is proportional to the number of clinical symptomatic individuals in the class, i.e. \(\tilde{I}_{i}=\tilde{N}I_{i}/N_{\text{I}}\). Once this is ascertained, we can encode the different contact rates of these two subpopulations (isolated and not isolated) with other classes in \(\lambda_{i}\). Similar reasoning can be followed regarding the modelization of carers. We do not create a new class since carers are exclusively composed of younger adults with no comorbidities and thus have identical epidemiological parameters to this demographic-class; we only need to modify carers' rate of exposure. Therefore, we can proceed by encoding this intervention in \(\lambda_{i}\) with the parameters \(\epsilon_{ij}\) and \(\omega_{ij}\) (see Eq 10 in Main Text).
Let us start by considering the rate of exposure of younger adults with no comorbidities, hereafter indexed \(k\). If this class has \(N_{\text{care}}\) carers, each isolated individual requires \(c_{\text{care}}\) contacts per day with them, and each class \(j\) has \(\tilde{I}_{j}\) isolated individuals, the mean number of contacts that each carer has per day with individuals in isolation is \(\tilde{c}_{k}=c_{\text{care}}\sum_{j}\tilde{I}_{j}/N_{\text{care}}\). In our simulations, each isolated individual receives one visit per day, i.e. \(c_{\text{care}}=1\). We envisage these interactions occuring in what we call buffer zones, namely open spaces in which carers and isolated individuals maintain a distance and wear masks, reducing the transmissibility by 80% (\(\xi=0.2\)).
\[\lambda_{k}=\tau\sum_{j}\underbrace{\xi_{ij}\beta_{\text{l}}\tilde{c}_{k} \tilde{P}(k\to j)}_{\text{isolated}}+\underbrace{c_{k}\left(\frac{N_{j}- \tilde{I}_{j}}{N}\right)\left(\frac{\beta_{\text{P}}P_{j}+\beta_{\text{A}}A_{j }+\beta_{\text{l}}O_{j}+\beta_{\text{l}}\Theta(N_{\text{I}}-\tilde{N})(I_{j}- \tilde{I}_{j})+\beta_{\text{H}}H_{j}}{N_{j}-\tilde{I}_{j}}\right)}_{\text{not isolated}}, \tag{33}\]
For the not-isolated term, we maintain the well-mixed population assumption explained in the Main Text, with the incorporation of a Heaviside function, \(\Theta(N_{\text{I}}-\tilde{N})\), which activates interaction with clinical symptomatic individuals when their number \(N_{\text{I}}\) exceeds the isolation capacity \(\tilde{N}\). We set the probability of interacting with symptomatic non-isolated individuals in class \(j\) proportional to their fraction of the class' population, \((I_{j}-\tilde{I}_{j})/(N_{j}-\tilde{I}_{j})\). For the isolated term however, the well-mixed assumption is no longer valid, because by definition, those fulfilling their roles as carers will interact with isolated individuals, hence \(\tilde{P}(k\to j)=1\). This yields the following expression for the subpopulation of carers:
\[\lambda_{k}^{\text{care}}=\tau\sum_{j}\underbrace{\xi_{ij}\beta_{\text{l}} \tilde{c}_{k}}_{\text{isolated}}+\underbrace{c_{k}\left(\frac{N_{j}-\tilde{I }_{j}}{N}\right)\left(\frac{\beta_{\text{P}}P_{j}+\beta_{\text{A}}A_{j}+\beta_ {\text{l}}O_{j}+\beta_{\text{l}}\Theta(N_{\text{I}}-\tilde{N})(I_{j}-\tilde{I }_{j})+\beta_{\text{H}}H_{j}}{N_{j}-\tilde{I}_{j}}\right)}_{\text{not isolated}}. \tag{34}\]
Note that the mean number of contacts per day that carers have with the rest of the population, \(c_{k}\), is not reduced since we do not make additional assumptions about carers' behavioural changes outside of their role as carers.
Younger adults without comorbidities who do not serve as carers will not interact with isolated individuals (i.e. \(\tilde{P}(k\to j)=0\)), and hence their rate of exposure becomes:
\[\lambda_{k}^{\text{care}}=\underbrace{c_{k}\left(\frac{N_{j}-\tilde{I}_{j}}{ N}\right)\left(\frac{\beta_{\text{P}}P_{j}+\beta_{\text{A}}A_{j}+\beta_{\text{l}} O_{j}+\beta_{\text{l}}\Theta(N_{\text{I}}-\tilde{N})(I_{j}-\tilde{I}_{j})+ \beta_{\text{H}}H_{j}}{N_{j}-\tilde{I}_{j}}\right)}_{\text{not isolated}}. \tag{35}\]
The total rate of exposure of younger adults without comorbidities, then becomes:
\[\lambda_{k}=\frac{N_{\text{care}}}{N_{k}}\lambda_{k}^{\text{care}}+\left( \frac{N_{k}-N_{\text{care}}}{N_{k}}\right)\lambda_{k}^{\text{care}}, \tag{36}\]
which can be made explicit and simplified to yield:
\[\lambda_{k}=\tau\sum_{j}\underbrace{\xi_{ij}\beta_{\text{l}}c_{\text{care}} \frac{\tilde{I}_{j}}{N_{k}}}_{\text{isolated}}+\underbrace{c_{k}\left(\frac{ \beta_{\text{P}}P_{j}+\beta_{\text{A}}A_{j}+\beta_{\text{l}}O_{j}+\beta_{\text {l}}\Theta(N_{\text{I}}-\tilde{N})(I_{j}-\tilde{I}_{j})+\beta_{\text{H}}H_{j}}{ N}\right)}_{\text{not isolated}}. \tag{37}\]
We can express this equation following the parameterization presented in Eq. 10 in the Main Text where \(\epsilon_{ij}=(c_{\text{care}}/c_{i})(\tilde{I}_{j}/N_{i})\) and \(\omega_{ij}=N/N_{j}\) for \(j\in\) isolated individuals in class \(j\), while \(\epsilon_{ij}=1\) and \(\omega_{ij}=1\) for individuals in class \(j\) who are not isolated. The rate of exposure of the remaining classes (not younger adults without comorbidities, \(i\neq k\)) corresponds to the second term in the r.h.s of Eq. 37:
\[\lambda_{i}=\tau\sum_{j}\underbrace{c_{i}\frac{\beta_{\text{P}}P_{j}+\beta_{ \text{A}}A_{j}+\beta_{\text{I}}O_{j}+\beta_{\text{I}}\Theta(N_{\text{I}}- \tilde{N})(I_{j}-\tilde{I}_{j})+\beta_{\text{H}}H_{j}}{N}}_{\text{not isolated}}. \tag{38}\]
We should note that Eq. 37 does not depend on the number of carers, \(N_{\text{care}}\), since we assume that the rate of exposure of carers is evenly distributed among all individuals in the class of healthy younger adults. If this assumption were not made, a specific class of carers could be created and the variable \(N_{\text{care}}\) maintained explicit as in Eq. 34.
**Self-isolation.** IFR (left), and fraction of the population that recovers (right) as a function of the number of isolation tents available in the camp.
**Time to self-isolation.** Probability of an outbreak (top left), fraction of the population dying (top middle), time until peak symptomatic cases (top right), IFR (bottom left), and fraction of the population that recovers (bottom middle) as a function of the time that individuals require to recognize their symptoms and self-isolate.
**Evacuation.** Probability of an outbreak (top left), fraction of the population dying (top middle), time until peak symptomatic cases (top right), IFR (bottom left), and fraction of the population that recovers (bottom middle), as a function of whether individuals requiring hospitalization are evacuated to isolation centers.
**Health-checks in the buffer zone.** Probability of an outbreak (top left), fraction of the population dying (top middle), time until peak symptomatic cases (top right), IFR (bottom left), and fraction of the population that recovers (bottom middle), as a function of whether health-checks are implemented in the buffer zone between the safety and exposed zones. Scenarios with 10 or 2 contacts in the buffer zone per person in the safety zone per week are plotted. All figures consider the scenario in which 20% of the camp’s population is allocated to the safety zone.
**Effects of the safety zone on outcomes by population class.** Probability of an outbreak (top), and proportion that dies in each population class (bottom) when no interventions are implemented (Mixed), compared to protection of older adults in the safety zone with 2 contacts in the buffer zone per week (Safety zone). The fraction of deaths in the safety zone for the older population is significantly lower.
**Population moving to the safety zone.** Probability of an outbreak (top left), fraction of the population dying (top middle), time until peak symptomatic cases (top right), IFR (bottom left), and fraction of the population that recovers (bottom middle) as a function of the safety zone allocation scenario (see Table 2). All figures consider the scenario with 2 contacts in the buffer per person in the safety zone per week.
**Number of contacts in the buffer zone.** IFR (left), and fraction of the population that recovers (right) as a function of the number of contacts that each individual in the safety zone has in the buffer zone per week. All figures consider the scenario in which 20% of the camp’s population is allocated to the safety zone.
**Efficacy of the safety zone for different population sizes.** Probability of an outbreak (top left), fraction of the population dying (top middle), time until peak symptomatic cases (top right), IFR (bottom left), and fraction of the population that recovers (bottom middle) as a function of the total population size. The figures consider scenarios with no interventions (null), and with a safety zone comprising 20% of the camp’s population with 2 contacts in the buffer zone per person in the safety zone per week (safety 2).
**Lockdown of the safety zone.** Probability of an outbreak (top left), fraction of the population dying (top middle), time until peak symptomatic cases (top right), IFR (bottom left), and fraction of the population that recovers (bottom middle) as a function of the reduction in the number of contacts permitted in the buffer zone from a baseline of 2 per person in the safety zone per week. All figures consider the scenario in which 20% of the camp’s population is allocated to the safety zone.
**Combined interventions.** IFR (top), and fraction of the population that recovers (bottom) for different combinations of interventions. \(\text{Evac}=\text{evacuation}\) of severely symptomatic, \(\text{self}=\text{self-distancing}\), \(\text{tents}=\text{number of available self-isolation}\)tents, \(\text{safety}=\text{safety zone}\), \(\text{lock}=\text{lockdown}\) of the buffer zone. For combinations of interventions including a safety zone, we distinguish between the population living in the green zone, in the orange zone and the whole population. The increase in the IFR for the green zone is explained by the discretization of the possible values that the IFR can take when the number of cases is very low (see Supplementary Table 3).
\begin{table}
\begin{tabular}{|l|r|r|r|} \hline Intervention & \(<\)20 cases & Total & \% of total \\ \hline \hline safety & 36 & 1908 & 1.9 \\ \hline safety + evac & 48 & 1894 & 2.5 \\ \hline safety + lock 50\% & 40 & 1454 & 2.8 \\ \hline safety + self 20\% & 56 & 1582 & 3.5 \\ \hline safety + 50 tents & 29 & 1827 & 1.6 \\ \hline safety + self 50\% & 187 & 719 & 26 \\ \hline safety + 50 tents + lock 50\% & 50 & 1349 & 3.7 \\ \hline safety + 50 tents + evac & 47 & 1804 & 2.6 \\ \hline safety + 50 tents + self 20\% & 90 & 1421 & 6.3 \\ \hline safety + 50 tents + self 50\% & 199 & 486 & 41 \\ \hline safety + 50 tents + evac + lock 50\% + self 20\% & 113 & 991 & 11 \\ \hline safety + 50 tents + evac + lock 50\% + self 50\% & 129 & 275 & 47 \\ \hline safety + 50 tents + evac + lock 90\% + self 50\% & 38 & 82 & 46 \\ \hline \end{tabular}
\end{table}
Table 3: **Efficacy of the safety zone in combination with other interventions.**\(<\)20 cases = number of outbreaks in the green zone with fewer than 20 cases recorded. Total = total number of simulations where an outbreak in the green zone occurs (at least one death). % of total = percent of outbreaks where fewer than 20 cases are recorded. N = 500 simulations for each combination of interventions. For the most effective combinations, the majority of simulations where an outbreak occurs in the green zone see fewer than 20 cases.
**Critical number of exposed individuals.** (Left) Reducing the number of contacts reduces the maximum number of individuals simultaneously exposed while increasing the time until symptomatic cases peak. When the reduction goes beyond 60%, there are abrupt drops in the time until cases peak and the fraction of the population dying, suggesting there is a critical number of individuals who must be exposed, under which outbreaks die out before spreading widely throughout the population. Above this threshold, the virus becomes established in the population over a longer period of time, increasing mortality. (Right) Fraction of the simulations which do not achieve the critical number of exposed individuals (that we set to 2% of the population). The abrupt transition between 50 and 70% reductions in contacts is apparent.
\begin{table}
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|c|} \hline Simul. & Experim. & Structure & Npop & Evac. & N.
40 & & & & & & & & & & 0.5 & & \\ \hline
41 & & G. Lockdown & Shield (20\%) & 2000 & No & 0 & 0 & 2/7 & Yes &
\begin{tabular}{c} 0.5 \\ 0.9 \\ \end{tabular} & No & D \\ \hline
2 & \\ \hline \end{tabular}
\end{table}
Table 5: **List of simulations performed (II).** Npop = Population size. Evac. = Is people requiring hospitalization evacuated? N. tents = Number self-isolation tents per camp. Onset = Mean time that an individual takes to self-isolate from onset of symptoms. Contacts = Number of contacts per day between populations shielded. Tcheck = Are temperature checks performed? Lock = Is lockdown applied after first symptomatic case is identified? self = Fraction of contacts remaining after self-distancing is implemented. H-fate = Final compartment for hospitalized people. MF = Mean field. Shield = Population shielded. age3 = elderly population. age2 = adults with comorbidities and spouses. (20-30%) = kids from adults shielded up to x% of total population.
|
181990_file03 | ### Population structure of demographic-classes derivation (Table 2 in Main Text)
In April, 2020, 40.7% of the population in informal IDP camps in Northern Syria was aged 0-12, 53.4% aged 13-50, and 5.9% aged 51+. To estimate the proportion of each age group with comorbidities, we calculated the weighted average age-specific comorbidity prevalence of the 4 most common comorbidities in the Syrian refugee populations in Jordan and Lebanon: hypertension, cardiovascular disease, diabetes, and chronic respiratory disease. We standardized these weighted averages to the age structure of IDPs in Northern Syria and estimated that 11.7% of people aged 13-50 have comorbidities, while 62.9% of people aged 51+ have comorbidities.
### Derivation of transmissibility parameters
The probability of infection if there is a contact between a susceptible and an infected person depends on the stage of the disease, denoted \(\tau\beta_{\text{P}}\), \(\tau\beta_{\text{A}}\), \(\tau\beta_{\text{I}}\) or \(\tau\beta_{\text{H}}\) depending upon whether the infected individual is in the presymptomatic (\(P_{i}\)), symptomatic (\(I_{i}\)), asymptomatic (\(A_{i}\)), or hospitalized compartment (\(H_{i}\)), respectively. We estimated these parameters in two steps. In the following section, we estimate the \(\beta_{\text{X}}\) parameters (\(\text{X}\in\{\text{P},\text{A},\text{I},\text{H}\}\)) which represent the relative transmissibility of each stage with respect to the maximum transmissibility \(\tau\). After this calculation, we present our estimate for the maximum transmissibility parameter \(\tau\).
#### Relative transmissibilities \(\beta\) (Table 1 in Main Text)
We start by considering the transmissibility of the presymptomatic stage for those individuals who become symptomatic as a reference (\(\beta_{\text{P}\rightarrow\text{I}}=1\)), since the probability of infection from contact with an individual at this epidemiological stage is highest. Next, we set the contribution of each epidemiological stage to infectivity as proportional to \(\beta_{\text{X}}/\gamma_{\text{X}}\), with \(1/\gamma_{\text{X}}\) the duration of stage X. Following He et al, we estimate the proportion of infectivity in individuals who go on to develop symptoms that occurs at the presymptomatic stage (\(\text{X}\in\{\text{P}\}\)) as the area under the infectivity curve prior to symptom onset, \(AUC_{\text{P}}\), and the proportion of infectivity that occurs at symptomatic stages (\(\text{X}\in\{\text{I},\text{H}\}\)) as the area under the infectivity curve after symptom onset, \(1-AUC_{\text{P}}\):
\[\frac{AUC_{\text{P}}}{(1-AUC_{\text{P}})}\approx\frac{\frac{\beta_{\text{P} \rightarrow\text{I}}}{\beta_{\text{P}}}}{\frac{\beta_{\text{I}}}{\gamma_{\text {I}}}+\frac{\beta_{\text{H}}}{\gamma_{\text{H}}}} \tag{1}\]
We then considered the quantity \(\rho_{\text{HI}}\), the ratio of the viral culture positive test rate in hospitalized patients 7-16 days since start of symptoms to the positive test rate in patients 0-6 days since start of symptoms from van Kampen et al.. Similarly, the relative risk of asymptomatic transmission to symptomatic transmission according to Byambasuren et al. is expressed as \(\rho_{\text{AI}}\):
\[\beta_{\text{A}}=\rho_{\text{AI}}\beta_{\text{I}} \tag{2}\]
\[\beta_{\text{H}}=\rho_{\text{HI}}\beta_{\text{I}} \tag{3}\]
Considering these relationships we rewrite Eq. 1 to obtain the desired parameters:\[\beta_{\rm I}=\frac{\beta_{\rm P\to I}\gamma_{\rm I}\gamma_{\rm H}(1-AUC_{\rm P})}{ AUC_{\rm P}\delta_{\rm P}(\gamma_{\rm H}+\rho_{\rm HI}\gamma_{\rm I})} \tag{4}\]
\[\beta_{\rm A}=\frac{\rho_{\rm AI}\beta_{\rm P\to I}\gamma_{\rm I}\gamma_{\rm H} (1-AUC_{\rm P})}{AUC_{\rm P}\delta_{\rm P}(\gamma_{\rm H}+\rho_{\rm HI}\gamma_{ \rm I})} \tag{5}\]
\[\beta_{\rm H}=\frac{\rho_{\rm HI}\beta_{\rm P\to I}\gamma_{\rm I}\gamma_{\rm H} (1-AUC_{\rm P})}{AUC_{\rm P}\delta_{\rm P}(\gamma_{\rm H}+\rho_{\rm HI}\gamma_{ \rm I})}. \tag{6}\]
The values of \(AUC_{\rm P}\), \(\rho_{\rm AI}\) and \(\rho_{\rm HI}\) are presented in Table 1, and the values of \(\beta_{\rm X}\) in Main Text. Noting that the starting point for these derivations is the transmissibility of individuals in the presymptomatic stage who go on to develop symptoms (\(\beta_{\rm P\to I}=1\)), we need to go back and derive the transmissibility of all presymptomatic individuals (\(\beta_{\rm P}\)), taking those that will be asymptomatic into account. We assumed that the relative transmissibility of presymptomatic individuals who will become asymptomatic to those that will become symptomatic, is equal to the relative transmissibility of asymptomatic to symptomatic individuals (\(\rho_{\rm AI}\)). With the proportion of presymptomatic cases that will become developed symptoms \(f\) (encoded in in Eqs. 1-8 in Main Text), we compute the mean transmissibility of all presymptomatic individuals as:
\[\beta_{\rm P}=f\beta_{\rm P\to I}+(1-f)\rho_{\rm AI}\beta_{\rm P\to I}. \tag{7}\]
#### Maximum transmissibility parameter \(\tau\)
In the following, to simplify the notation we define \(\kappa_{i}=(l_{i}\gamma_{\rm I}+h_{i}\eta+g_{i}\alpha)\). To estimate the probability of infection if there is a contact between a susceptible and an infected individual (parameter \(\tau\)) we proceed as follows. We start by considering the subsystem containing the infected population:
\[\dot{E}_{i}=\lambda_{i}S_{i}-\delta_{\rm E}E_{i} \tag{8}\]
\[\dot{P}_{i}=\delta_{\rm E}E_{i}-\delta_{\rm P}P_{i} \tag{9}\]
\[\dot{A}_{i}=(1-f)\delta_{\rm P}P_{i}-\gamma_{\rm A}A_{i} \tag{10}\]
\[\dot{I}_{i}=f\delta_{\rm P}P_{i}-\kappa_{i}I_{i} \tag{11}\]
\[\dot{H}_{i}=h_{i}\eta I_{i}-\gamma_{\rm H}H_{i}. \tag{12}\]
For the sake of simplifying the notation, let us consider the following ordering of the variables in the vector \(x=(E_{1},...,E_{\rm M},P_{1},...,P_{\rm M},A_{1},...,A_{\rm M},I_{1},...,I_{\rm M },H_{1},...,H_{\rm M})\), with \(M\) the number of population classes. We are interested in the parameterization of the null model, which will serve as a baseline to estimate the parameter \(\tau\), which is initially unknown, but does not change when interventions are introduced. Considering the contacts matrix for the null model (Eq. 9 in Main Text), the rate of exposure becomes
\[\lambda_{i}=\frac{\tau}{N}\sum_{j=1}^{M}c_{i}\left(\beta_{\rm P}P_{j}+\beta_{ \rm A}A_{j}+\beta_{\rm I}I_{j}+\beta_{\rm H}H_{j}\right). \tag{13}\]
\begin{table}
\begin{tabular}{|c|c|c|c|c|} \hline Parameter & Description & Value & Distribution & Reference \\ \hline \hline \(AUC_{\rm P}\) & \begin{tabular}{c} Presymptomatic area under \\ infectivity curve \\ \end{tabular} & 0.44 (95\% CI:.30–.57) & Gaussian & \\ \hline \(\rho_{\rm AI}\) & \begin{tabular}{c} Ratio of asymptomatic to \\ symptomatic infectiousness \\ \end{tabular} & 0.58 (95\% CI:.34–.99) & Lognormal & \\ \hline \(\rho_{\rm HI}\) &
\begin{tabular}{c} Ratio of hospitalized to \\ symptomatic infectiousness \\ \end{tabular} & 0.48 & - & \\ \hline \end{tabular}
\end{table}
Table 1: **Relative transmissibility parameters.**In the following, we use bold symbols for vectors and matrices, and the symbols \(\odot\) and \(\odot\) for the element-wise multiplication and division, respectively.
\[\mathbf{\Sigma}=\begin{bmatrix}-\delta_{\mathrm{E}}\mathbf{I}&\mathbf{0}&\mathbf{0}&\mathbf{0}& \mathbf{0}\\ \delta_{\mathrm{E}}\mathbf{I}&-\delta_{\mathrm{P}}\mathbf{I}&\mathbf{0}&\mathbf{0}&\mathbf{0}\\ \mathbf{0}&(1-f)\delta_{\mathrm{P}}\mathbf{I}&-\gamma_{\mathrm{A}}\mathbf{I}&\mathbf{0}&\mathbf{0} \\ \mathbf{0}&f\delta_{\mathrm{P}}\mathbf{I}&\mathbf{0}&-\mathrm{diag}(\mathbf{\kappa})\mathbf{I}&\mathbf{ 0}\\ \mathbf{0}&\mathbf{0}&\mathbf{0}&\eta\mathrm{diag}(\mathbf{h})\mathbf{I}&-\gamma_{\mathrm{H}}\mathbf{I} \end{bmatrix} \tag{15}\]
Where \(\mathbf{I}\) and \(\mathbf{0}\) are the identity and null matrices of size \(M\), and \(\mathbf{\kappa}=\mathbf{l}\gamma_{I}+\mathbf{h}\eta+\mathbf{g}\alpha\).
\[\mathbf{\Sigma^{-1}}=\begin{bmatrix}-\frac{1}{\delta_{\mathrm{E}}}\mathbf{I}&\mathbf{0}& \mathbf{0}&\mathbf{0}&\mathbf{0}\\ -\frac{1}{\delta_{\mathrm{P}}}\mathbf{I}&-\frac{1}{\delta_{\mathrm{P}}}\mathbf{I}&\mathbf{ 0}&\mathbf{0}&\mathbf{0}\\ -\frac{(1-f)}{\gamma_{\mathrm{A}}}\mathbf{I}&-\frac{(1-f)}{\gamma_{\mathrm{A}}}\mathbf{ I}&-\frac{1}{\gamma_{\mathrm{A}}}\mathbf{I}&\mathbf{0}&\mathbf{0}\\ -f\mathrm{diag}(\mathbf{\kappa}^{-1})\mathbf{I}&-f\mathrm{diag}(\mathbf{\kappa}^{-1})\mathbf{I }&\mathbf{0}&-\mathrm{diag}(\mathbf{\kappa}^{-1})\mathbf{I}&\mathbf{0}\\ -\frac{f\eta}{\gamma_{\mathrm{H}}}\mathrm{diag}(\mathbf{h}\odot\mathbf{\kappa})\mathbf{I}& -\frac{f\eta}{\gamma_{\mathrm{H}}}\mathrm{diag}(\mathbf{h}\odot\mathbf{\kappa})\mathbf{I}& 0&-\frac{\eta}{\gamma_{\mathrm{H}}}\mathrm{diag}(\mathbf{h}\odot\mathbf{\kappa})\mathbf{I }&-\frac{1}{\gamma_{\mathrm{H}}}\mathbf{I}\end{bmatrix} \tag{16}\]
The NGM with large domain can now be found by \(\mathbf{K_{\mathrm{L}}}=-\mathbf{T}\mathbf{\Sigma}^{-1}\). However, since we know that each individual who gets infected becomes exposed (\(E\) compartment), we focus on the NGM with small domain, \(\mathbf{K_{\mathrm{S}}}\), which only consists of the \(E\) compartment. We do this by removing the rows that correspond to the other compartments from \(T\) and the columns from \(\Sigma^{-1}\). We then find:
\[\mathbf{K_{\mathrm{S}}}=\tau\left[\frac{1}{\delta_{P}}\mathbf{\Theta}_{\mathrm{P}}+ \frac{(1-f)}{\gamma_{A}}\mathbf{\Theta}_{\mathrm{A}}+f\mathrm{diag}\left(\mathbf{h}^{- 1}\right)\mathbf{\Theta}_{\mathrm{I}}+\frac{f\eta}{\gamma_{\mathrm{H}}}\mathrm{ diag}(\mathbf{h}\odot\mathbf{\kappa})\mathbf{\Theta}_{\mathrm{H}}\right]. \tag{17}\]
The reproduction number is related to the dominant eigenvalue of \(\mathbf{K_{\mathrm{S}}}\), i.e. \(R_{0}=|\lambda_{1}|\), and \(\tau\) is estimated from the real dominant eigenvalue of \(\tilde{K}_{\mathrm{S}}=K_{\mathrm{S}}/\tau\). Considering the null model parameters (\(\tilde{\lambda}_{1}^{0}\)), we have the expression:
\[\tau=\frac{R_{0}}{|\tilde{\lambda}_{1}^{0}|}. \tag{18}\]
### Epidemiological severity proportions (Table 4 in Main Text)
In the Main Text, we presented the proportions in which clinical symptomatic individuals resolve into critical (\(q_{i}^{D}\)), severe (\(q_{i}^{\mathrm{H}}\)) and recovered (\(q_{i}^{R}\)) cases. We assigned the fractions of symptomatic cases in children aged \(<\)13 that would become severe and critical from the fractions of symptomatic cases in children aged \(<\)11 that were severe and critical in China. We assigned the class-specific fractions of symptomatic cases in adults that would become severe and critical based on age and comorbidity-specific fractions of symptomatic cases with known outcomes that required hospitalization, without and with ICU admission, respectively in the United States. To account for poorer health among Syrian adults compared to their similarly aged peers in developed countries, estimates for US adults aged 19-64 were used for Syrian adults aged 13-50, while estimates for US adults aged 65+ were used for Syrian adults aged 51+.
Since the rates at which these individuals progress are different (\(\eta\) for \(H\), \(\alpha\) for \(D\) and \(\gamma_{\rm I}\) for \(R\)) we introduced three parameters, \(h_{i}\), \(g_{i}\) and \(l_{i}\), to distribute individuals according to the desired proportions following the equations:
\[q_{i}^{\rm H}=h_{i}\eta\kappa_{i}^{-1} \tag{19}\]
\[q_{i}^{D}=g_{i}\alpha\kappa_{i}^{-1} \tag{20}\]
\[q_{i}^{R}=1-q_{i}^{\rm H}-q_{i}^{D}=l_{i}\gamma_{\rm I}\kappa_{i}^{-1}, \tag{21}\]
where \(\kappa_{i}=h_{i}\eta+g_{i}\alpha+l_{i}\gamma_{\rm I}.\) The system has three unknowns and three equations but one equation linearly depends on the other two, hence we introduce the constraint \(l_{i}=1-h_{i}-g_{i}\) to solve the system as:
\[h_{i}=\frac{\alpha q_{i}^{H}}{\eta q_{i}^{L}}g_{i}, \tag{22}\]
\[g_{i}=\gamma_{I}\left(\frac{\alpha}{q_{i}^{D}}+\frac{\gamma_{I}\alpha q_{i}^{H }}{\eta q_{i}^{D}}+\gamma_{I}-\frac{\alpha q_{i}^{H}}{q_{i}^{D}}-\alpha\right) ^{-1}. \tag{23}\]
## 2 Parameterization of the interventions (Table 5 in Main Text)
### Safety zone
We considered the existence of a safety zone to protect a certain fraction, \(f_{\rm S}\), of the population, mostly those more vulnerable. In practice, this involves dividing the camp in two areas, a "green" zone (denoted g) for the protected population and an "orange" zone (o) for the exposed population, and dividing each demographic-class into two behaviour-classes for each respective zone. These two populations interact via a buffer zone, under controlled conditions where we assumed transmissivity is reduced by 80%, encoded in the parameter \(\xi_{ij}=0.2\). Each individual in the green zone can interact with a limited number (\(c_{\rm visit}\)) of family members (hereafter "visitors") from the orange zone per day. In some interventions we considered that individuals visiting the buffer zone will have a health check (e.g. temperature measurement), aimed at excluding symptomatic individuals. When the health check is applied, the probability of transmission by individuals in the \(I\) or \(H\) compartments from one zone to susceptible individuals from a different zone is set to zero (see parameters \(\zeta_{\rm I}\) and \(\zeta_{\rm H}\) in Eq. 24 in Main Text). In the following, we derive the values of parameters \(\epsilon_{ij}\) and \(\omega_{ij}\), modifying the rate at which individuals become exposed (see Eq. 24 in Main Text).
Although setting up a safety zone implies a reduction in the number of contacts between classes of the green zone and the orange zone, the mean number of contacts that each individual has per day, \(c_{i}\), is conserved. Therefore we need to estimate how contacts will be redistributed from individuals from a different zone to individuals living in the same zone. We model this redistribution of contacts with the parameter \(\epsilon_{ij}\):
\[\epsilon_{ij} = \vartheta c_{\rm visit}/c_{i}\quad(i,j\text{ in different zones})\] \[\epsilon_{ij} = 1-\vartheta c_{\rm visit}/c_{i}\quad(i,j\text{ in same zone}).\]
We define \(\vartheta\) as1
Footnote 1: If \(c_{\rm visit}\) is large enough ( ( \(c_{\rm visit}\approx 15\) contacts per day), \(\vartheta\) should saturate, because every member of the orange zone would eventually visit the buffer zone, following the expression:
\[\vartheta=\begin{cases}1&\text{if }i\in\text{g}\\ f_{\rm o,visit}\quad\text{if }i\in\text{o}\end{cases}\]
with the Heaviside function \(\Theta(f_{\rm o,visit}-1)=1\) if \(f_{\rm o,visit}\geq 1\). We chose values well below this saturation threshold (a maximum of 10 contacts per week, i.e. 1.42 contacts per day).
If we assume that visitors are always different, the quantity \(f_{\rm o,visit}=c_{\rm visit}\frac{N_{\rm s}}{N_{\rm o}}\) is the fraction of the orange population that visits the buffer zone.
Next, we estimate how the probability of interaction between a member of class \(i\) and class \(j\) is modified with respect to the null model, depending on the zones from which class \(i\) and class \(j\) are drawn. Suppose classes \(i\) and \(j\) are separated from the rest of the camp's population and confined within a restricted zone. The probability that an individual of class \(i\) randomly encounters an individual of class \(j\) would now be higher than in a well-mixed population where interaction with individuals belonging to other classes is not restricted. This modification of relative probability of interaction is encoded in the parameter \(\omega_{ij}\) (see Eq. 24 in Main Text). More specifically, the proportion \(N_{i}/N\) of individuals of class \(i\) in the null model becomes \(N_{i}/N_{\rm X}\) with \(N_{\rm X}\) the total number of individuals in zone \(X=\{\rm o,g\}\). This yields the following values for \(\omega_{ij}\):
\[\omega_{ij} = \left(\frac{N_{i}}{N_{\rm X}}\right)/\left(\frac{N}{N_{\rm s}} \right)=\frac{N}{N_{\rm X}}\quad(i,j\mbox{ in same zone }X)\] \[\omega_{ij} = \left(\frac{N_{i}}{N_{\rm Y}}\right)/\left(\frac{N}{N_{i}} \right)=\frac{N}{N_{\rm Y}}\quad(i\in X\mbox{ and }j\in Y).\]
Following this parameterization, we explore different scenarios, summarized in Table 2, for allocating members of each population class to the safety, or "green" zone, and the exposed, or "orange" zone. In one scenario, we only place individuals in age group 3 (\(>\)50) in the green zone, while in another we place all vulnerable individuals, age group 3 and age group 2 with comorbidities, in the green zone. In 3 additional scenarios, after all vulnerable individuals are allocated to the green zone, we set the green zone's capacity to a certain percentage of the camp's population (20%, 25%, 30%), and allocate its remainder to non-vulnerable family members, who by necessity are either children \(<\)13 in age group 1 or healthy younger adults in age group 2. In accordance with camp managers' expectations that many vulnerable individuals will have non-vulnerable spouses, while fewer vulnerable individuals will have young children, in these scenarios we allocate 40% of the remainder of the green zone to children and 60% of the remainder of the green zone to younger adults without comorbidities. We also consider a baseline scenario in which there is no green zone.
\begin{table}
\begin{tabular}{|c|c|c|c|c|c|c|c|c|} \hline Scenario & Age 1, orange & Age 1, green & Age 2 no comorbidities, orange & Age 2 no competities, green & Age 2 comorbidities, orange & Age 2 comorbidities, green & Age 3 no competities, green & Age 3 comorbidities, green \\ \hline \hline Only age 3 &.407 & 0 &.471 & 0 &.0626 & 0 &.022 &.0373 \\ in green zone & & & & & & & & \\ \hline Age 3 + age 2 with comorbidities in green zone &.407 & 0 &.471 & 0 & 0 &.0626 &.022 &.0373 \\ \hline \hline \(20\%\) green zone &.376 &.0312 &.424 &.0469 & 0 &.0626 &.022 &.0373 \\ \hline \(25\%\) green zone &.356 &.0512 &.394 &.0769 & 0 &.0626 &.022 &.0373 \\ \hline \(30\%\) green zone capacity &.336 &.0712 &.364 &.107 & 0 &.0626 &.022 &.0373 \\ \hline \(30\%\) green zone capacity & & & & & & & & \\ \hline \end{tabular}
\end{table}
Table 2: **Fraction of population in each zone by safety zone scenario and behaviour-class.** Behaviour-classes that are not considered in a given scenario have a proportion equal to zero.
### Self-isolation and evacuation
To implement self-isolation it is required a delineation between the isolated and non-isolated population within the clinical symptomatic compartment after identification of symptoms (\(I_{i}\)). This does not entail the creation of a new compartment, but rather the estimation of the number of individuals in each class in isolation (\(\tilde{I}_{i}\)). We first compute the total number of infected individuals across every class, \(N_{\text{I}}=\sum_{i}I_{i}\), at each integration step in the simulation. Next, we consider the isolation capacity of the camp (\(\tilde{N}\)), and we assume that, when the infectious population exceeds this capacity, the number of isolated individuals for each class is proportional to the number of clinical symptomatic individuals in the class, i.e. \(\tilde{I}_{i}=\tilde{N}I_{i}/N_{\text{I}}\). Once this is ascertained, we can encode the different contact rates of these two subpopulations (isolated and not isolated) with other classes in \(\lambda_{i}\). Similar reasoning can be followed regarding the modelization of carers. We do not create a new class since carers are exclusively composed of younger adults with no comorbidities and thus have identical epidemiological parameters to this demographic-class; we only need to modify carers' rate of exposure. Therefore, we can proceed by encoding this intervention in \(\lambda_{i}\) with the parameters \(\epsilon_{ij}\) and \(\omega_{ij}\).
Let us start by considering the rate of exposure of younger adults with no comorbidities, hereafter indexed \(k\). The general expression of \(\lambda_{k}\) presented in the Main Text is:
\[\lambda_{k}=\sum_{j=1}^{n}\tau\xi_{kj}c_{k}\epsilon_{kj}\omega_{kj}\frac{N_{j }}{N}\left(\frac{\beta_{\text{P}}P_{j}+\beta_{\text{A}}A_{j}+\zeta_{\text{I}} \beta_{\text{I}}I_{j}+\zeta_{\text{H}}\beta_{\text{H}}H_{j}}{N_{j}}\right). \tag{24}\]
If we have \(N_{\text{care}}\) carers, the expression of \(\lambda_{k}\) can be split in two contributions:
\[\lambda_{k}=\frac{N_{\text{care}}}{N_{k}}\lambda_{k}^{\text{care}}+\left(\frac {N_{k}-N_{\text{care}}}{N_{k}}\right)\lambda_{k}^{\overline{\text{care}}} \tag{25}\]
of the equation is the contribution from carers, and the second term from the remaining population of the class. We can proceed similarly now splitting \(\lambda_{k}^{\text{care}}\) in two, one term to model the interaction with the \(\tilde{I}_{j}\) isolated individuals and another term to account for the interaction with the \(I_{j}-\tilde{I}_{j}\) not-isolated individuals (if the total number of symptomatic individuals \(N_{\text{I}}\) exceeds the capacity of the camp \(\tilde{N}\)):
\[\lambda_{k}^{\text{care}}=\tau\sum_{j=1}^{n}\underbrace{\tilde{\xi}_{kj} \tilde{c}_{k}\tilde{\epsilon}_{kj}\tilde{\omega}_{kj}\frac{N_{j}}{N}\frac{ \tilde{\zeta}_{\text{I}}\tilde{\beta}_{\text{I}}\tilde{I}_{j}}{N_{j}}}_{\text {isolated}}+\underbrace{\xi_{kj}c_{k}\epsilon_{kj}\omega_{kj}\frac{N_{j}}{N} \left(\frac{\beta_{\text{P}}P_{j}+\beta_{\text{A}}A_{j}+\zeta_{\text{I}}\beta _{\text{I}}(I_{j}-\tilde{I}_{j})+\zeta_{\text{H}}\beta_{\text{H}}H_{j}}{N_{j} }\right)}_{\text{not isolated}}. \tag{26}\]
24. The split presented in Eq. 26 is valid under the well-mixed assumption. However, this assumption does not hold for the isolated population, which is confined under very particular conditions. More specifically, we should re-estimate the term highlighted as \(\tilde{P}(k\to j)\) which is the probability of interaction of the population of carers with isolated individuals (because, by definition, those fulfilling their roles as carers will interact with isolated individuals), and hence \(\tilde{P}(k\to j)=1\).
Therefore, for the isolated term, we should just estimate the coefficients \(\tilde{\xi}_{kj}\) and \(\tilde{c}_{k}\). To estimate \(\tilde{c}_{k}\) we note that, if the class has \(N_{\text{care}}\) carers, each isolated individual requires \(c_{\text{care}}\) contacts per day with them, and each class \(j\) has \(\tilde{I}_{j}\) isolated individuals, the mean number of contacts that each carer has per day with individuals in isolation is \(\tilde{c}_{k}=c_{\text{care}}\sum_{j}\tilde{I}_{j}/N_{\text{care}}\). In our simulations, each isolated individual receives one visit per day, i.e. \(c_{\text{care}}=1\). Finally, since we envisage these interactions occuring in what we call buffer zones, namely open spaces in which carers and isolated individuals maintain a distance and wear masks, reducing the transmissibility by 80%, we consider that \(\tilde{\xi}_{ij}=0.2\).
For the not-isolated term, we maintain the well-mixed population assumption explained in the Main Text, with the incorporation of a Heaviside function, \(\zeta_{I}=\Theta(N_{\text{I}}-\tilde{N})\), which activates interaction with clinical symptomatic individuals when their number \(N_{\text{I}}\) exceeds the isolation capacity \(\tilde{N}\). We should also readjust the probability of interacting with symptomatic non-isolated individuals in class \(j\) to be proportional to their fraction of the class' population, \((I_{j}-\tilde{I}_{j})/(N_{j}-\tilde{I}_{j})\). This yields the following expression for the subpopulation of carers:\[\lambda_{k}^{\rm care}=\tau\sum_{j}\underbrace{\xi_{ij}\beta_{\rm l}\tilde{\epsilon} _{k}}_{\rm isolated}+\underbrace{c_{k}\left(\frac{N_{j}-\tilde{I}_{j}}{N} \right)\left(\frac{\beta_{\rm P}P_{j}+\beta_{\rm A}A_{j}+\beta_{\rm l}\Theta(N_ {\rm I}-\tilde{N})(I_{j}-\tilde{I}_{j})+\beta_{\rm H}H_{j}}{N_{j}-\tilde{I}_{j }}\right)}_{\rm not\ isolated}. \tag{27}\]
Note that the mean number of contacts per day that carers have with the rest of the population, \(c_{k}\), is not reduced since we do not make additional assumptions about carers' behavioural changes outside of their role as carers.
Younger adults without comorbidities who do not serve as carers will not interact with isolated individuals (i.e. \(\tilde{P}(k\to j)=0\)), and hence their rate of exposure becomes:
\[\lambda_{k}^{\rm\overline{\rm care}}=\underbrace{c_{k}\left(\frac{N_{j}- \tilde{I}_{j}}{N}\right)\left(\frac{\beta_{\rm P}P_{j}+\beta_{\rm A}A_{j}+ \beta_{\rm l}\Theta(N_{\rm I}-\tilde{N})(I_{j}-\tilde{I}_{j})+\beta_{\rm H}H_ {j}}{N_{j}-\tilde{I}_{j}}\right)}_{\rm not\ isolated}. \tag{28}\]
Inserting Eqs. 27 and 28 into Eq. 25 yields:
\[\lambda_{k}=\tau\sum_{j}\underbrace{\xi_{ij}\beta_{\rm l}c_{\rm care}\frac{ \tilde{I}_{j}}{N_{k}}}_{\rm isolated}+\underbrace{c_{k}\left(\frac{\beta_{\rm P }P_{j}+\beta_{\rm A}A_{j}+\beta_{\rm l}\Theta(N_{\rm I}-\tilde{N})(I_{j}- \tilde{I}_{j})+\beta_{\rm H}H_{j}}{N}\right)}_{\rm not\ isolated}. \tag{29}\]
We can express this equation following the parameterization presented in Eq. 24 making \(\tilde{\xi}_{ij}=0.2\), \(\tilde{\epsilon}_{ij}=(c_{\rm care}/c_{i})(\tilde{I}_{j}/N_{i})\), \(\tilde{\omega}_{ij}=N/N_{j}\) and \(\tilde{\zeta}_{\rm l}\tilde{\beta}_{\rm l}=1\) for \(j\in\) isolated individuals in class \(j\), while \(\xi=1\),\(\epsilon_{ij}=1\), \(\omega_{ij}=1\) and \(\zeta_{\rm I}=\Theta(N_{\rm I}-\tilde{N})\) for \(j\in\) individuals in class \(j\) who are not isolated. The rate of exposure of the remaining classes (not younger adults without comorbidities, \(i\neq k\)) corresponds to the second term in the r.h.s of Eq. 29:
\[\lambda_{i}=\tau\sum_{j}\underbrace{c_{i}\frac{\beta_{\rm P}P_{j}+\beta_{\rm A }A_{j}+\beta_{\rm l}\Theta(N_{\rm I}-\tilde{N})(I_{j}-\tilde{I}_{j})+\beta_{ \rm H}H_{j}}{N}}_{\rm not\ isolated}. \tag{30}\]
We should note that Eq. 29 does not depend on the number of carers, \(N_{\rm care}\), since we assume that the rate of exposure of carers is evenly distributed among all individuals in the class of healthy younger adults. If this assumption were not made, a specific class of carers could be created and the variable \(N_{\rm care}\) maintained explicit.
**Evacuation.** Probability of an outbreak (top left), fraction of the population dying (top middle), time until peak symptomatic cases (top right), IFR (bottom left), and fraction of the population that recovers (bottom middle), as a function of whether individuals requiring hospitalization are evacuated to isolation centers.
**Self-isolation.** IFR (left), and fraction of the population that recovers (right) as a function of the number of isolation tends available in the camp.
**Health-checks in the buffer zone.** Probability of an outbreak (top left), fraction of the population dying (top middle), time until peak symptomatic cases (top right), IFR (bottom left), and fraction of the population that recovers (bottom middle), as a function of whether health-checks are implemented in the buffer zone between the safety and exposed zones. Scenarios with 10 or 2 contacts in the buffer zone per person in the safety zone per week are plotted. All figures consider the scenario in which 20% of the camp’s population is allocated to the safety zone. Note that the mean of an outcome for the whole population is not the weighted mean of the exposed and safety zones, since outcomes are computed considering simulations in which at least one death was observed in the population class inhabiting the zone, i.e. the number of simulations considered to compute each mean may be different. This explains for example why there is a reduction in the mean time until symptomatic cases peak when moving from 2 contacts per week without health checks to considering health checks for the whole population, despite there being an increase in the safety zone.
**Effects of the safety zone on outcomes by population class.** Probability of an outbreak (top), and proportion that dies in each population class (bottom) when no interventions are implemented (Mixed), compared to protection of older adults in the safety zone with 2 contacts in the buffer zone per week (Safety zone). The fraction of deaths in the safety zone for the older population is significantly lower.
**Population moving to the safety zone.** Probability of an outbreak (top left), fraction of the population dying (top middle), time until peak symptomatic cases (top right), IFR (bottom left), and fraction of the population that recovers (bottom middle) as a function of the safety zone allocation scenario (see Table 2). All figures consider the scenario with 2 contacts in the buffer per person in the safety zone per week.
**Number of contacts in the buffer zone.** IFR (left), and fraction of the population that recovers (right) as a function of the number of contacts that each individual in the safety zone has in the buffer zone per week. All figures consider the scenario in which 20% of the camp’s population is allocated to the safety zone.
**Efficacy of the safety zone for different population sizes.** Probability of an outbreak (top left), fraction of the population dying (top middle), time until peak symptomatic cases (top right), IFR (bottom left), and fraction of the population that recovers (bottom middle) as a function of the total population size. The figures consider scenarios with no interventions (null), and with a safety zone comprising 20% of the camp’s population with 2 contacts in the buffer zone per person in the safety zone per week (safety 2).
**Lockdown of the safety zone.** Probability of an outbreak (top left), fraction of the population dying (top middle), time until peak symptomatic cases (top right), IFR (bottom left), and fraction of the population that recovers (bottom middle) as a function of the reduction in the number of contacts permitted in the buffer zone from a baseline of 2 per person in the safety zone per week. All figures consider the scenario in which 20% of the camp’s population is allocated to the safety zone.
**Combined interventions.** IFR (top), and fraction of the population that recovers (bottom) for different combinations of interventions. \(\text{Evac}=\text{evacuation}\) of severely symptomatic, \(\text{self}=\text{self-distancing}\), \(\text{tents}=\text{number of available self-isolation}\)tents, \(\text{safety}=\text{safety zone}\), \(\text{lock}=\text{lockdown}\) of the buffer zone. For combinations of interventions including a safety zone, we distinguish between the population living in the green zone, in the orange zone and the whole population. The increase in the IFR for the green zone is explained by the discretization of the possible values that the IFR can take when the number of cases is very low (see Supplementary Table 3).
\begin{table}
\begin{tabular}{|l|r|r|r|} \hline Intervention & \(<\)20 cases & Total & \% of total \\ \hline \hline safety & 36 & 1908 & 1.9 \\ \hline safety + evac & 48 & 1894 & 2.5 \\ \hline safety + lock 50\% & 40 & 1454 & 2.8 \\ \hline safety + self 20\% & 56 & 1582 & 3.5 \\ \hline safety + 50 tents & 37 & 1330 & 2.8 \\ \hline safety + self 50\% & 187 & 719 & 26 \\ \hline safety + 50 tents + lock 50\% & 58 & 1021 & 5.7 \\ \hline safety + 50 tents + evac & 44 & 1245 & 3.5 \\ \hline safety + 50 tents + self 20\% & 78 & 907 & 8.6 \\ \hline safety + 50 tents + self 50\% & 57 & 71 & 80 \\ \hline safety + 50 tents + evac + lock 50\% + self 20\% & 108 & 594 & 18 \\ \hline safety + 50 tents + evac + lock 50\% + self 50\% & 42 & 44 & 95 \\ \hline safety + 50 tents + evac + lock 90\% + self 50\% & 14 & 15 & 93 \\ \hline \end{tabular}
\end{table}
Table 3: **Efficacy of the safety zone in combination with other interventions.**\(<\)20 cases = number of outbreaks in the green zone with fewer than 20 cases recorded. Total = total number of simulations where an outbreak in the green zone occurs (at least one death). % of total = percent of outbreaks where fewer than 20 cases are recorded. N = 2500 simulations for each combination of interventions. For the most effective combinations, the majority of simulations where an outbreak occurs in the green zone see fewer than 20 cases.
**Critical number of exposed individuals.** (Left) Reducing the number of contacts reduces the maximum number of individuals simultaneously exposed while increasing the time until symptomatic cases peak. When the reduction goes beyond 60%, there are abrupt drops in the time until cases peak and the fraction of the population dying, suggesting there is a critical number of individuals who must be exposed, under which outbreaks die out before spreading widely throughout the population. Above this threshold, the virus becomes established in the population over a longer period of time, increasing mortality. (Right) Fraction of the simulations which do not achieve the critical number of exposed individuals (that we set to 2% of the population). The abrupt transition between 50 and 70% reductions in contacts is apparent.
## 4 Appendix: List of Experiments
\begin{table}
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|} \hline Simul. & Experim. & Structure & Npop & Evac. & N.Tents & Contacts & Tcheck & lock & self & H-fate \\ \hline \hline
1 & & & Null Mixed & & & & MF & No & & & D \\ \hline
2 & & & Null Mixed & & & & MF & No & & & R \\ \hline
3 & A.
4 & and limits & & Shield (20\%) & & & & & & Yes & & & R \\ \hline
5 & & & & & & & 10/7 & & & & & D \\ \hline
6 & & & & & & & & 10 & & & & R \\ \hline
7 & & & & & & & & & & & & \\ \hline
8 & & & & & & & & & & & & \\ \hline
9 & & & & & & & & & & & & \\ \hline
10 & & & Null Mixed & & & & & & & & & \\ \hline
11 & & & & & & & & 250 & & & & \\ \hline
12 & & & & & & & 500 & & & & & \\ \hline
13 & B.
14 & individual tents & & & & & & & & & & & \\ \hline
15 & & & & & & & & & & & \\ \hline
16 & & & & & & & & & & & \\ \hline
17 & & & Shield (20\%) & & & & & & & & & \\ \hline
18 & & & & & & & & 250 & & & & \\ \hline
19 & & & & & & & & 500 & & & & \\ \hline
20 & & & & & & & & & & & \\ \hline
21 & & & Shield (age3) & & & & & & & & & \\ \hline
22 & & & Shield (age2) & & & & & & & & & \\ \hline
23 & & & Shield (20\%) & 2000 & No & 0 & 2/7 & Yes & No & No & D \\ \hline
24 & & & Shield (25\%) & & & & & & & & \\ \hline
25 & & & Shield (30\%) & & & & & & & & \\ \hline
26 & & & Null Mixed & 500 & & & & MF & No & & \\ \hline
27 & & & & & 1000 & & & & & & \\ \hline
28 & & size & & & 500 & & & & 2/7 & Yes & No & No & D \\ \hline
29 & & & & & 1000 & & & & & & \\ \hline
30 & & & & & & & & & & & \\ \hline
31 & & E.
32 & & testing & & & & & & & & & \\ \hline
33 & & & & & & & & & & & \\ \hline \end{tabular}
\end{table}
Table 4: **List of simulations performed.** Npop = Population size. Evac. = Is people requiring hospitalization evacuated? N. tents = Number self-isolation tents per camp. Contacts = Number of contacts per day between populations shielded. Tcheck = Are temperature checks performed? Lock = Is lockdown applied after first symptomatic case is identified? self = Fraction of contacts remaining after self-distancing is implemented. H-fate = Final compartment for hospitalized people. MF = Mean field. Shield = Population shielded. age3 = elderly population. age2 = adults with comorbidities and spouses. (20-30%) = kids from adults shielded up to x% of total population.
\begin{table}
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|} \hline Simul. & Experim. & Structure & Npop & Evac. & N.
2 & \\ \hline \end{tabular}
\end{table}
Table 5: **List of simulations performed (II).** Npop = Population size. Evac. = Is people requiring hospitalization evacuated? N. tents = Number self-isolation tents per camp. Contacts = Number of contacts per day between populations shielded. Tcheck = Are temperature checks performed? Lock = Is lockdown applied after first symptomatic case is identified? self = Fraction of contacts remaining after self-distancing is implemented. H-fate = Final compartment for hospitalized people. MF = Mean field. Shield = Population shielded. age3 = elderly population. age2 = adults with comorbidities and spouses. (20-30%) = kids from adults shielded up to x% of total population.
|
182824_file02 | ### Droplet transfer to surfaces
In the continuous stirred tank reactor (CSTR), a canonical system in chemical engineering, the relative rate of chemical reaction to convection is prescribed by the dimensionless Damkoller number. In the context of airborne disease transmission, we consider the'reaction' corresponding to aerosol-borne virion removal from a well-mixed room, and so define \(\text{Da}=\lambda_{c}/\lambda_{a}\) in terms of the concentration relaxation rate \(\lambda_{c}(r)\) and the air change rate \(\lambda_{a}\).
\[\text{Da}=\text{Da}_{\text{b}}+\text{Da}_{s}=\frac{(\lambda_{o}+\lambda_{f})V}{ Q}+\frac{hA}{Q}. \tag{1}\]
Bulk disinfection of the air may arise through viral deactivation at a rate \(\lambda_{c}(r)\) or air filtration at a rate \(\lambda_{f}(r)=p_{f}(r)\lambda_{r}\). Wedenote by \(h\) the virion mass-transfer coefficient from the bulk to the surfaces, which necessarily has the units of velocity.
In the field of aerosol science, it is customary to refer to the dimensionless droplet mass-transfer coefficient as the 'deposition efficiency', \(\eta=hA/Q\), and to relate it to various particle transport resistances. Such resistances are expressed in dimensionless form in terms Stokes numbers, each of which represents the ratio of two particle speeds. There are three potentially relevant resistances to drop mass-transfer from the bulk air to surfaces: gravitational settling, diffusion and surface deposition. We thus express the efficiency of droplet deposition from the bulk in terms of three Stokes numbers:
\[\eta^{-1}=(\mathrm{St}_{g}+\mathrm{St}_{d})^{-1}+\mathrm{St}_{dep}^{-1}. \tag{2}\]
We note that the droplet deposition efficiency \(\eta\) is equivalent to the 'particle loss-rate coefficient', \(\beta\), customarily defined for particulate aerosols in indoor air
The gravitational Stokes number, \(St_{g}=v_{s}/v_{a}\), prescribes the relative magnitudes of the Stokes settling speed, \(v_{s}=2\rho_{d}gr^{2}/9\mu_{a}\) and the ambient air flow, \(v_{a}=Q/A=\lambda_{a}L\). We note that inertial corrections to Stokes law only become important for droplets with \(r>100\mu\)m, and so are not relevant for aerosols. For the largest respirable droplets (\(r=5\mu\)m) with poor, natural ventilation (0.35 ACH) in a typical room (\(H=2.7\)m), settling dominates convection since \(\mathrm{St}_{g}=12\gg 1\). Conversely, for smaller droplets (\(r=0.5\mu\)m) with hospitalized ventilation (25 ACH), settling can be neglected since \(\mathrm{St}_{g}=0.0017\ll 1\). Drops with radius exceeding a critical values, \(r_{c}=\sqrt{9\mu_{a}\lambda_{a}H/(2\rho_{d}g)}\) corresponding to \(\mathrm{St}_{g}=1\), tend to settle to the surfaces before being removed by ventilation. For a given droplet size \(r\), we write \(\mathrm{St}_{g}(r)=(r/r_{c})^{2}\). The droplets of interest in our model of airborne transmission are those with \(St_{g}<1\).
For submicron particles suspended in a well-mixed ambient, diffusion may influence the transfer of the particle through the lower viscous boundary layer, either by Brownian motion or eddy diffusion for the case of a turbulent boundary layer. The importance of such particle diffusion is prescribed by the diffusional Stokes number, \(St_{d}=D/(\delta v_{a})\), where \(D\) is the particle diffusivity and \(\delta\) is the viscous boundary layer thickness near the depositing surface, which sets the diffusional mass-transfer coefficient, \(h_{d}=D/\delta\). We may alternatively write \(St_{d}=\overline{\mathrm{Sh}}(\mathrm{Re},\mathrm{Sc})/\mathrm{Pe}\), where the Pelet number, \(\mathrm{Pe}=v_{a}H/D\), prescribes the relative magnitudes of convection and diffusion, and the Sherwood number, \(\overline{\mathrm{Sh}}=h_{d}H/D\), is the dimensionless diffusion mass-transfer coefficient, averaged over the surface.
We first consider Brownian droplet diffusion through a laminar boundary layer, as is typical of natural ventilation over horizontal surfaces. For a given flow field, kinematic viscosity \(\nu_{a}=\mu/\rho_{a}\) and Brownian diffusivity \(D=k_{B}T/6\pi\mu_{a}\tau_{d}\) (as follows from the Stokes-Einstein relation), the Sherwood number depends on the Schmidt number \(\mathrm{Sc}=\nu_{a}/D\) and Reynolds number \(\mathrm{Re}=\mathrm{Pe}/\mathrm{Sc}\). Using the relation, \(\overline{\mathrm{Sh}}=0.664\,\mathrm{Re}^{1/2}\mathrm{Sc}^{1/3}\), relevant for a laminar boundary layer on a flat plate, we estimate, for the case of bioaerosols with radius (\(r=0.5\mu\)m) with poor ventilation (0.35 ACH), that \(\mathrm{St}_{d}=7\times 10^{-6}\ll 1\) (\(\mathrm{Sc}=5\times 10^{5},\ \mathrm{Re}=47,\ \mathrm{Sh}=180,\ \mathrm{Pe}=2.5\times 10^{7}\)), which indicates that particle diffusion can be safely neglected. Indeed, the removal of droplets by Brownian diffusion becomes comparable to that by gravitational settling, \(\mathrm{St}_{d}>\mathrm{St}_{g}\), only for \(r<13\) nm at 0.35 ACH, a critical radius much smaller than that of a single SARS-CoV-2 virion (\(r_{c}=60\)nm).
Next, we consider droplet diffusion through a turbulent boundary layer, as might arise for high ventilation rates. In their seminar work on aerosol mass transfer, Corner and Pendleton augmented the Brownian diffusivity, \(D\), with the turbulent eddy diffusivity, \(D_{e}=K_{e}y^{2}\), where \(K_{e}\) is a turbulence intensity parameter, proportional to the local mean velocity gradient, and \(y\) is the distance from the surface. A better fit to experimental data was achieved by expressing the eddy diffusion as \(D_{e}=K_{e}\delta^{2}(y/\delta)^{n}\), where \(\delta\) is the boundary layer thickness \(\delta\) and \(n=2.6-2.8\) is an empirical scaling exponent. Using this approach, Lai & Nazaroff developed a comprehensive, experimentally validated model of aerosol mass transfer to surfaces and showed that, even for the highest building ventilation rates, turbulent diffusion competes with gravitational settling only for particles with \(r<0.2\mu\)m. This critical size is much smaller than that of stable respiratory droplets, and only a few times larger than a single virion. We thus conclude that gravitational settling dominates diffusion, both Brownian and turbulent, in respiratory aerosol removal from indoor air.
Finally, the role of droplet deposition is determined by \(\mathrm{St}_{dep}=v_{dep}/v_{a}=\mathrm{St}_{g}v_{dep}/v_{s}\), where \(v_{dep}\) is the net liquid deposition velocity, specifically the surface adsorption flux per bulk liquid concentration, as accounts for the probability of droplets sticking to the surface rather than bouncing off. Experiments have shown that \(v_{dep}/v_{s}\) is approximately constant for water droplets with characteristic diameter of 1-10 \(\mu\)m in a variety of settings, including droplets settling from clouds onto the forest canopy and from humid air onto acrylic pipes). For droplets of radius \(r=5\mu\)m settling at \(v_{s}=0.306\) cm/s, the deposition velocity \(v_{dep}\approx 5\) cm/s. We thus conclude that deposition kinetics are fast compared to droplet transport, since \(\mathrm{St}_{dep}\approx 20\,\mathrm{St}_{g}\), and can be safely neglected as a small mass-transfer resistance in series.
In summary, for the respiratory droplets of interest, the dominant contribution to droplet mass transfer to surfaces for the relevant range of respiratory aerosols, \(r=0.1-10\mu m\) comes from gravitational settling, \(h\approx v_{s}\).
\[\eta\approx\mathrm{St}_{g}=\left(\frac{r}{r_{c}}\right)^{2} \tag{3}\]
This deduction allows us to conveniently express the droplet mass transfer from complex indoor airflows in terms of the Stokes settling velocity. The effects of boundary-layer or surface mass-transfer resistance are negligible, and the timescale of settling of respiratory droplets from a well-mixed ambient is prescribed by the Stokes settling time.
## 2 Deduction of the indoor safety guideline from epidemiological models
We here demonstrate that our indoor safety guideline (Eq.) may be deduced from standard epidemiological models.
While our theoretical model of the well-mixed room was developed to describe airborne transmission from a single individual to a fixed number of others in a well-mixed room, it bears noting that this scenario is but one of a broader class of transmission events. First, there are many situations where air conditioning or forced ventilation mixes air between rooms, in which case the compound room is effectively a well-mixed space. Second, there are incidents when several individuals are initially infected. Third, the population may be together for a period long with respect to the incubation time (approximately 5.5 days), in which case the number of infectious individuals necessarily increases with time. Examples of this broader class of transmission events might include cruise ships [], meat and poultry processing facilities [] and prisons []. We proceed by detailing the epidemiological models describing this more general class of events.
Following Noakes et al.[], we adopt the standard SEIR model from epidemiology [], an extension of the original SIR model of Kermack and McKendrick[] of susceptible (\(S\)), infected (\(I\)) and recovered (\(R\)) populations to include an exposed population (\(E\)) that has acquired the pathogen and so become infected but not yet infectious:
\[\frac{dS}{dt}=-\beta SI,\;\frac{dE}{dt}=\beta SI-\alpha E,\;\frac{dI}{dt}= \alpha E-\gamma I,\;\frac{dR}{dt}=\gamma I \tag{4}\]
To describe a spreading event in a closed environment, we consider \(I_{0}\) infected people entering, at time \(t=0\), a room full of \(S_{0}=N-I_{0}\) susceptible individuals, none of which were previously exposed, \(E_{0}=0\). In the case where the population is being tested and infected individuals removed from the population via isolation, \(\gamma\) may alternatively be considered as a proxy for testing frequency. Noting that the combined incubation time and time to recovery for COVID-19 is thought to exceed 2 weeks [], we here consider spreading events of duration \(\tau\) that are short relative to the recovery time, \(\tau\ll\gamma^{-1}\), and so eliminate \(R\) from consideration.
The Wells-Riley model is effectively a reduction of the SIR model based on the assumption of slow incubation over the timescale of the event, \(\tau\ll\alpha^{-1}\), in which case the number of infected persons in the room remains fixed, \(I(t)=I_{0}\). One expects such to be the case for events of relatively short duration, such as the Skagit Choir incident. However, such an approximation is not likely to be valid in the case of indoor super-spreading events of longer duration, \(\tau>\alpha^{-1}\). To adequately model such events, we consider the possibility that the number of infectors increases with time, which requires a description of the nonlinear dynamics of disease transmission.
The resulting SEI model to be considered here is a system of three nonlinear ordinary differential equations. While the system may be solved numerically, deduction of a safety guideline requires analytical results. Our goal is thus to solve this SEI model for the infection (or "secondary attack") rate, \(i_{S}(\tau)=(E(\tau)+I(\tau)-I_{0})/S_{0}\). Since exact solutions may be cumbersome (as for the SIR model []), we simplify the analysis by considering two limits, where the incubation time \(\alpha^{-1}\) is short or long relative to the event timescale, \(\tau\), and the transmission timescale \(\beta^{-1}\). While the incubation time of COVID-19 is not precisely known, it is bounded above by the time to develop symptoms, which spans 2-14 days with an average 5.5 days [].
For slow incubation (\(\alpha\ll\beta,\tau^{-1}\)) [], the number of infected persons remains nearly constant, \(I(t)\approx I_{0}\), and the resulting SE model is easily solved to derive the secondary attack rate [],
\[i_{S}(\tau)=1-e^{-I_{0}\int_{0}^{\tau}\beta(t)dt}, \tag{5}\]
In the opposite limit of fast incubation (\(\alpha\gg\beta,\tau^{-1}\)), exposed individuals are rapidly infected, so the exposed, non-infected population need not be considered, \(E(t)=0\).
\[i_{S}(\tau)=\left[1-i_{0}^{-1}\left(e^{N\int_{0}^{\tau}\beta(t)dt}-1\right)^{- 1}\right]^{-1}, \tag{6}\]
These simple solutions, and, cover the two limiting cases of fast and slow incubation relative to transmission.
The safety criterion \(\mathcal{R}_{in}<\epsilon\), which limits the probability of the first transmission to lie below a small tolerance, is universal, in that it does not depend the choice of model to describe the subsequent spreading dynamics.
\[\frac{\mathcal{R}_{in}}{N-1}=\int_{0}^{\tau}\beta(t)dt<\left\{\begin{array}{ ll}-\ln\left(1-\frac{\epsilon}{N-1}\right)&\mbox{(slow)}\\ \frac{1}{N}\ln\left[\frac{(N-1)+\epsilon}{N-1-\epsilon}\right]&\mbox{(fast)} \end{array}\right. \tag{7}\]
and for slow and fast incubation, respectively. In the small-tolerance limit, \(\epsilon\ll 1\), these bounds both reduce to, \(\mathcal{R}_{in}<\epsilon\), and are thus independent of the incubation rate. More generally, the linear response of any Markovian, mean-field theory (with neither memory nor many-body correlations) to any perturbation, such as the arrival of a new infector, must begin at the mean transmission rate. Indeed, the same universal bound may be simply derived from the infinitesimal cumulative probability of transmission \(\int_{0}^{\tau}\beta(t)\) from one infector to a set of \(N-1\) independent susceptibles.
## 3 Inference of infection quanta from disease spreading data
It is an important point that the concentration of "infection quanta" per exhaled air volume, \(C_{q}\), as may be inferred from spreading data, is necessarily model dependent. By definition, the time integral of the transmission rate, \(q(t)=\int_{0}^{\tau}\beta(t)dt\), is equal to the expected number of quanta transferred from one infector to one susceptible. In models of indoor airborne transmission [], infection quanta are further related to the evolving pathogen-laden droplet concentration by Eq. []. While the mathematical definition of infection quanta is unambiguous in terms of the instantaneous transmission rate, \(\beta(t)\), between two isolated individuals, the inference of quanta concentrations from field data for the spreading rate is inevitably model dependent because it involves interactions among an evolving population. Specifically, the long-time growth in the number of infections is influenced by nonlinearities in the transmission dynamics, as governed by the chosen epidemiological model, for example, the SEIR model, Eq. [S1].
In the original Wells-Riley model [], one infection quantum is defined as the amount of pathogen required to infect an average of \(1-1/e\approx 63.2\%\) of susceptible people in an enclosed space. This inference is based on fitting field data to Eq. [S2], which relates one net quantum transferred, \(I_{0}q(t)=1\), to the secondary infection rate, \(i_{S}(t)=1-(1/e)\). This approach is valid for times short relative to the incubation time and has been successfully applied to extract quanta emission rates for various viral diseases [], including SARS-CoV-2 []. However, the Wells-Riley model cannot be reliably used to infer infection quanta from super-spreading events evolving over time scales that exceed the incubation time.
For such situations, here we take an approach appropriate for the case of fast incubation that necessarily implies a different relation between released infection quanta and the observed secondary infection rate. If we adopt the SI model with fast incubation, then the long-term behavior of Eq. [S3] indicates that one quantum (\(I_{0}(t)=1\)) will infect a fraction \(i_{S}=[1+(N/I_{0})/(e^{N/I_{0}}-1)]^{-1}\) of \(N\) people in an enclosed space, \(I_{0}\) of which were initially infected, as a result of transmission amplification by the growing number of infecteds. In this model, a single quantum from one person reflects another with probability \(i_{S}=[1+2/(e^{2}-1)]^{-1}\approx 76.2\%\) for \(N=2\), but manages to infect everyone in a large group, \(i_{S}\to 1\) as \(N\rightarrow\infty\). This dependence of infection quanta on epidemiological model parameters, such as the incubation rate, reflects the fact that the fitted "infection quantum" is a measure of contagiousness at the scale of a group that is not necessarily proportional to the microscopic pathogen concentration. Notably, infection quanta are well defined in the limit of short times and slow transmission, where all models reduce to the Wells-Riley model with a constant number of infections. From the modeling perspective, the notion of infection quanta is thus unambiguous only in this limit. Finally, we recall that, regardless of the model used to infer it, the actual value of infection quanta may still vary considerably between spreading events, owing to its dependence on activity level of the population and other physiological factors [].
## 4 Fitting to super-spreading events
Table 1 shows the data used to infer the concentration of infection quanta \(C_{q}\) exhaled by an infected individual for four well-known indoor super-spreading events of COVID-19, for which physical parameters can be estimated with reasonable accuracy from published data: the Skagit Valley Chorale [], the Diamond Princess cruise ship [], the Ningbo tour bus [], and the initial Wuhan outbreak [], interpreted as mainly indoor spreading at home []. The best characterized case of the Skagit Valley Chorale is used in the main text to calibrate the safety guideline. Here we consider the other three spreading events, for which only relatively rough estimates of certain model parameters can be made. Despite the resulting uncertainty, these events provide additional support for the inferences made in the main text.
In all situations, we assume an effective particle radius \(\overline{r}=2.0\mu\)m at the upper limit of the infectious range of suspended droplets [], corresponding to an effective settling speed of \(v_{s}(\overline{r})=1.78\) m/h. Note that the effective radius would be somewhat larger, \(\overline{r}=3.0\mu\)m, if we were to neglect the size dependence of infectivity and set \(n_{q}=\)constant, and use our prediction of the steady-state airborne droplet distribution \(C_{s}(r)/C_{v}\) for singing in the choir room. We also assume no use of face masks, \(p_{m}=1\) and an airborne virus deactivation rate, \(\lambda_{v}=0.3\)/h [] that lies between the existing estimates of zero [] and \(0.63\)/h []
### The Diamond Princess
The data reported for the Diamond Princess is particularly useful in that it captures the time evolution of the infected persons among a fixed population over an extended period, corresponding to the 12-day quarantine [], after which passengers and crew began to disembark. The resulting data reported for \(I(t)\) is best described in terms of the fast-incubation limit. Fitting to the available data allows us to infer that the initial number of passengers infected on February 3, 2020 was approximately \(I_{0}=20\), and that the concentration of infection quanta characterizing this particular spreading event was \(C_{q}=30\) quanta/m\({}^{3}\). Furthermore, it suggests that the incubation time is significantly less than 12 days, as is consistent with current estimates for the average time between exposure and the onset of symptoms being 2-5 days [].
Our fitting of \(I_{0}\) and \(C_{q}\) for the Diamond Princess is based on the hypothesis of a "well-mixed ship".
\begin{table}
\begin{tabular}{l|c c c c c c c c c} \hline & \(N\) & \(\tau\) (h) & \(I_{0}\) & \(I(\tau)\) & \(\lambda_{v}\) (1/h) & \(A\) (m\({}^{2}\)) & \(H\) (m) & \(Q_{k}\) (m\({}^{3}\)/h) & \(C_{q}\) (q\({}^{3}\)/h) & \(\lambda_{q}\) (q\({}^{3}\)/h) \\ \hline Skagit Church Choir & 61 & 2.5 & 1 & 53 & 0.65 & 180 & 4.5 & 1.0 & 870 & 870 \\ Ningbo Tour Bus & 68 & 1.7 & 1 & 21 & 1.25 & 25 & 1.8 & 0.5 & 90 & 45 \\ Diamond Princess & 3711 & 288 & 20 & 354 & 8 & 139,00 & 2.1 & 0.5 & 30 & 15 \\ Wuhan City Outbreak & 3.03 & 132 & 1 & 1.63 & 0.34 & 90 & 2.4 & 0.5 & 29 & 14 \\ \hline \end{tabular}
\end{table}
Table 1: Data from four COVID-19 spreading events used to infer the concentration, \(C_{q}\), or emission rate, \(\lambda_{q}\), of exhaled infection quanta, on the basis of the assumption of indoor airborne transmission. The Skagit Valley Choir event []. We use existing estimates of relevant physical parameters [] and the Wells-Riley model [], Eq. [], appropriate for slow incubation. 2. A tour bus transported 68 people (including the driver) on a 100 minute round-trip journey to a Buddhist ceremony in Ningbo, China []. One index case infected 23 fellow passengers, three of which are assumed to have been infected at the ceremony, where the infection rate was \(7/172=4\%\) for other attendees. The interior bus dimensions are estimated from a Dongfeng 67-seat luxury tour bus made in Hubei, China, which has outer dimensions of 10.49m\(\times\)2.5m\(\times\)3.2m and matches the floor plan of the Ningbo tour bus []. The air change rate, \(\lambda_{v}=1.25\) ACh is estimated from previous studies of air quality in transit buses with closed windows []. 3. The Diamond Princess cruise ship during its 12-day port quarantine in Yokohama, Japan []. We infer \(I_{0}=20\) and \(N\beta=0.25/\)day by fitting the confirmed case history to our fast-incubation solution, Eq. [], as shown in We estimate relevant volume and area from floor plans of the Diamond Princess [], where passengers and crew mainly occupy 14 floors of living space of beam width 38 m, an average length equal to 90% of the ship’s length 290 m, and mean ceiling height 2.1 m. We also assume a standard cruise-ship ventilation rate (8 ACh) for partially recirculated air conditioning []. 4. Initial outbreak in Wuhan City, Hubei Province, China. We assume that the population-level spreading is dominated by indoor aerosol transmission with slow incubation [], the air-density apartments [] with a mean family size of 3.03, mean apartment area of 315 SF/person [] and mean ventilation rate of 0.34 ACh. We estimate a mean exposure time of \(\tau=5.5\) days until symptoms (and patient isolation), and use the average \(\mathcal{R}_{0}=3.3\) estimated for the population during the initial outbreak [] in place of \(\mathcal{R}_{in}(\tau)\).
Analysis of the ship's floor plans and ventilation system has indicated recirculation of heated interior air throughout the entirety of the ship during cold weather (-5\({}^{\circ}\) C), without adequate filtration for virus-containing aerosol droplets. Moreover, a detailed statistical analysis of the SARS-CoV-2 transmission history between passenger cabins revealed no significant correlation between new cases and the sharing of rooms with previously confirmed cases. Airborne transmission was further suggested by several examples of new cases emerging in single-occupancy cabins despite no known contact with other cases. Like many other indoor COVID-19 spreading events in which position in an enclosed space was uncorrelated with likelihood of transmission, the cruise line outbreaks present evidence that strongly supports the notion of airborne transmission of SARS-CoV-2 through well-mixed indoor spaces.
### Ningbo tour bus.
We proceed by considering another super-spreading event, involving a Buddhist blessing ceremony held at the Tiantong Temple in Ningbo, Zhejiang Province, China on January 19, 2020. The confirmed index case, Ms. S, was thought to have contracted the virus two days earlier from dinner guests who had traveled to Wuhan during the initial outbreak. Ms. S traveled to the ceremony on a tour bus (Bus 2) for 50 minutes with 68 people, including the driver, and returned on the same bus with the same seating arrangement. Since it was winter, the windows were likely closed. No outside air was supplied by mechanical ventilation, although the air was recirculated continuously. No masks were worn by the passengers, as there had not previously been any cases of COVID-19 in Zhejiang Province. Of the 68 passengers, 23 new cases of COVID-19 were confirmed, with their locations being evenly distributed across the bus, largely uncorrelated with proximity to Ms. S. Most had no close contact with the index case. However, some spatial patterns of transmission could be discerned on the bus, such as fewer cases among the window seats, possibly due to recirculation air flows. The epidemiological evidence for indoor airborne transmission is overwhelming.
Of the 172 others that attended the ceremony, only 7 individuals (4.1%) became infected at the 150-minute worship event, which was mostly held outside. Assuming that the bus passengers were infected at the temple at the same rate as the others, we may estimate that 3 of 23 transmissions occurred there, so only 20 on the round-trip bus ride. The published floorplan of the bus resembles that of a Dongfeng 67-seat luxury tour bus made in Hubel Province, China, whose specifications we use to estimate interior dimensions. The most uncertain model parameter is the air exchange rate, \(\lambda_{a}\), which we presume to be associated with natural ventilation. We further assume that windows were closed and that air filtration was limited. Although \(\lambda_{a}=1.8-3.7\)/h has been measured in passenger cars with closed windows and recirculating fans, transit buses tend to have lower values, such as \(\lambda_{a}=1.25\)/h, a value that we adopt here. We also assume a typical seated breathing flow rate, \(Q_{b}=0.5\) m\({}^{3}\)/h.
Using these approximations for the model parameters, we apply the slow-incubation model to infer \(C_{q}=90\) q/m\({}^{3}\) and \(\lambda_{q}=45\) q/h. This value of \(C_{q}\) falls in the range of intermediate speaking obtained from other inferences in the main text, which would be consistent with passengers speaking amongst themselves on the voyage. Given the uncertainty in the air exchange rate, the inferred value of \(C_{q}\) could also be consistent with normal breathing with only occasional speech. Finally, we note that the average age of the bus passengers was 59, which suggests a relatively vulnerable population, for which one expects to infer a relatively high \(C_{q}\).
### Wuhan outbreak.
Table 1 also shows how the theory can be used to interpret the population-level reproductive number in terms of indoor airborne transmission, assuming that the primary disease transmission arises in family apartments, as shown in a recent analysis of COVID-19 spreading in China. We consider the initial outbreak in Wuhan, Hubei Province and assume physical parameters appropriate for typical apartments and families. We then use the average population reproductive number to assert \(\mathcal{R}_{in}(\tau)=\langle\mathcal{R}_{0}\rangle=3.3\), where \(\tau=5.5\) days is the mean time for an newly infected family member to show symptoms and be isolated or removed.
As shown in the main text (Fig.2), the inferred values of \(C_{q}=29\) quanta/m\({}^{3}\) for family apartments in the Wuhan outbreak and \(C_{q}=30\) quanta/m\({}^{3}\) for the Diamond Princess cruise ship are consistent with the light respiratory activities expected to be most prevalent in those settings, such as sleeping and quiet speech. Both inferred \(C_{q}\) values are greatly exceeded by the inference of \(C_{q}=870\) (made here, using \(\bar{r}=2.0\mu\)m and \(\lambda_{a}=0.65\)/h; see Table 1) or 970 quanta/m\({}^{3}\) (made by Miller et al, averaging over simulations with variable \(\lambda_{a}=0.3-1.0\)/h and \(\lambda_{s}=0.3-1.5\)/h) for singing, but in a manner consistent with the increased pathogen output associated with more vigorous speaking or singing. These inferences (and others) build confidence in our estimates of exhaled quanta concentrations, \(C_{q}\), for various respiratory activities, as shown in of the main text.
Validation and calibration of the fast-incubation model for the super-spreading event on board the Diamond Princess cruise ship, during its twelve day quarantine at Yokohama, Japan in February 2020. Fitting the number of SARS-CoV-2 positive cases versus time (blue data points) during the quarantine period, to the fast-incubation solution of the SEI model, Eq., (red curve) yields estimates for the initial number infected (\(I_{0}=20\)) and the transmission rate (\(N=0.25\)/day), from which we infer the concentration of infection quanta from breathing (\(C_{q}=30\) quanta/m\({}^{3}\)). The relevant physical parameters are listed in Table 1.
## 5 The dependence of airborne disease transmission on respiratory activity
It is well established that aerosol droplet production varies strongly with the form of expiratory activity. For example, vocalization greatly increases aerosol emission relative to quiet breathing, roughly in proportion to the amplitude of the sound produced. In Table 2, the aerosol volume fraction produced by different activities, obtained by integrating the distributions in up to \(r_{c}=2.5\mu\)m, are used to rescale the inferred quanta concentration for singing in the Skagit Valley Choir room into those appropriate for other activities. The resulting values are consistent with the values of \(C_{q}\) inferred for the Diamond Princess quarantine and the initial Wuhan City outbreak (see Table 1 and Fig. 2).
## 6 Application of the Safety Guideline
In order to illustrate how to implement our safety guideline, we provide an Excel spreadsheet, COVID-19_Indoor Safety_Guideline.xlsx, as Supplementary Data, which has also been implemented for general use as an online app. We note that, following the submission of our manuscript, it has come to our attention that the groups of Jose-Luiz Jimenez and Lidia Morawska have produced spreadsheets with extensive documentation similar in spirit to ours, designed to provide quantitative risk assessments for safe management of indoor spaces during the COVID-19 pandemic. Since their analyses are based on the same physical picture of airborne transmission in a well-mixed space, their predictions are consistent with ours. However, their recommendations rely on calculations of pathogen concentration and risk in different settings, while ours are based entirely on our Safety Guideline, as succinctly expressed by the bound on cumulative exposure time in Eq..
Our spreadsheet and online app enable the calculation of the suggested maximum cumulative exposure times for specific indoor spaces. In this section, we offer guidance on how to use the spreadsheet for both safety assessment and contact tracing, specifically, how to select suitable parameters and properly interpret the results. The input parameters, colored in pink in the spreadsheet and in _italics_ below, are divided into the following four categories.
### Physical Parameters.
The geometry of the indoor space is specified by its _floor area_, \(A\), and _mean ceiling height_, \(H\), from which the volume \(V=AH\) is calculated using appropriate unit conversions. The _ventilation outflow rate_, \(Q=V\lambda_{a}\), is calculated from the air exchange rate, \(\lambda_{a}\), typically expressed in terms of air changes per hour (ACH). This critical input parameter is governed by national or local standards for different types of indoor spaces, such as the ASHRAE standards (62.1) in the United States. As noted in the main text, natural ventilation may be approximated as \(\lambda_{a}=0.34\)/h, which has been measured in bedrooms with closed windows and is considered to be the minimum standard, although this value will vary with both location and quality of construction. For residences, classrooms, businesses, and public spaces, \(\lambda_{a}\) usually falls in the range \(4-8/\)h. Crowded spaces, such as bars, nightclubs and restaurants, typically require more vigorous ventilation, \(\lambda_{a}=15-20/\)h. Minimum ventilation standards for American hospitals have increased from 12 to 18 ACH. Most chemical and biological laboratories have \(\lambda_{a}\) in the range of \(6-12/\)h, but those handling toxic or infectious materials may have \(\lambda_{a}\) as high as \(20-30/\)h. Revised ASHRAE standards, intended to mitigate the spread of airborne infectious diseases, recommend a minimum of \(\lambda_{a}=6/\)h for all indoor spaces.
Forced air filtration and droplet settling in ducts may also be included through the effective air filtration rate, \(\lambda_{f}(r)=p_{f}(r)\lambda_{r}\), where \(\lambda_{r}=Q_{r}/V\) is the _recirculation air exchange rate_ passing through the filter and \(p_{f}(r)\) is _droplet filtration probability_, taken to be a constant over the aerosol size range. The United States Environmental Protection Agency defines high-efficiency particulate air (HEPA) filtration as removing \(p_{f}=99.97\%\) of aerosol particles, while ordinary air filters are assigned Minimum Efficiency Reporting Value (MERV) ratings corresponding to \(p_{f}>20\%\)-\(90\%\) in specified aerosol size ranges. For ventilation systems with indoor air recirculation, the primary outdoor air fraction, \(Z_{p}=Q/(Q+Q_{r})\), is usually specified by indoor air quality (IAQ) standards. For example, \(Z_{d}=20\%\) for classrooms in the United States), where \(Q+Q_{r}\) is the total flow rate and \(v=(Q+Q_{r})/A\) is the mean air velocity. Alternatively, air filtration may be accomplished by indoor free-standing units with a specified recirculation flow rate of \(Q_{r}\).
The _relative humidity_\(RH\) of the indoor air is another physical input parameter, which affects both respiratory droplet evaporation and viral deactivation.
### Physiological Parameters.
The first physiological parameter is the _volumetric breathing flow rate_, \(Q_{b}\), which is approximately 0.5 m\({}^{3}\)/h for resting and light activity.
\begin{table}
\begin{tabular}{|l|l|l l|c c|} \hline Activity & Experiment & \(Q_{b}\) (m\({}^{3}\)/h) & \(\phi_{1}\) (\(10^{-16}\)) & \(C_{q}\) (q\(\)m\({}^{3}\)) & \(\lambda_{q}\) (qh) \\ \hline breathing at rest & nose in, nose out (b-m) & 0.5 & 0.35 & 8.8 & 4.2 \\ breathing heavily & nose in, mouth out (b-m) & 0.5 & 1.3 & 33 & 16 \\ \hline whispering & whisperged counting (\(\kappa\)-p) & 0.75 & 1.5 & 37 & 28 \\ speaking & voiced counting (\(\kappa\)-p) & 0.75 & 2.9 & 72 & 54 \\ \hline singing sctify & whisperged ‘aahs” (aah-w-p) & 1.0 & 4.1 & 103 & 103 \\ singing & voiced ‘aahs” (aah-w-p) & 1.0 & 39 & 970 & 970 \\ \hline \end{tabular}
\end{table}
Table 2: Activity dependence of airborne transmission of COVID-19. Expiratory droplet size distributions for different activities are taken from the experiments reported by Morawska et al., and reasonable estimates are made for the exhaled air volume per time \(Q_{b}\) from breathing (0.5 m\({}^{3}\)/h), speaking (0.75 m\({}^{3}\)/h) and singing (1.0 m\({}^{3}\)/h). Our model is then used to predict the steady-state aerosol volume fraction, \(\phi_{1}=\int_{0}^{r_{c}}\phi_{s}(r)\,dr\), that results from exhalation of a single infectious individual in a setting corresponding to the Skagit Valley Choir room (Table 1), by integrating the distributions shown in up to the critical radius \(r_{c}=2.5\mu\)m. The concentration of COVID-19 infection quanta in the breath of an infected individual is assumed to be \(C_{q}=970\) q/m\({}^{3}\) for the singing case, as estimated for the Skagit Valley Chorale incident by Miller et al., and values of \(C_{q}\) for other activities are calculated by rescaling with the appropriate ratio of aerosol volume fractions, \(\phi_{1}\). The quanta emission rate for each activity is then given by \(\lambda_{q}=Q_{b}C_{q}\).
The second physiological parameter is the mean respiratory aerosol droplet size \(\tilde{r}\) for the suspended infectious droplets responsible for airborne disease transmission. The precise definition of \(\tilde{r}\) is given in Eqs. and of the main text, in terms of the distribution of droplet sizes for different types of respiration [], the size-dependent infectivity of aerosol droplets [], and the settling and ventilation rates. As illustrated in the main text, a typical value for \(\tilde{r}\) is 2-3 \(\mu\)m. We note that these values are roughly consistent with the standard definition of aerosol droplets, as those having \(r<5\mu\)m []. The effect of relative humidity on the size of stable droplets after evaporation [] can be estimated by rescaling \(\tilde{r}\) by \(\sqrt{0.4/(1-RH)}\), since the droplet distributions used to calibrate the guideline were measured at \(RH=60\%\)[].
### Disease Parameters
The most important disease parameter is the _infectiousness of exhaled air_, \(C_{q}\), the infection quanta per volume. Using all of the limited information currently available, we estimate \(C_{q}=30\) q/m\({}^{3}\) for normal breathing and light activity and provide our best estimates of \(C_{q}\) for different respiratory activities in Our analysis indicates that \(C_{q}\) can be an order of magnitude larger for singing or other vigorous respiratory activities, or an order of magnitude smaller for sleeping and light nose breathing.
The second disease parameter is the _viral deactivation rate_, \(\lambda_{v}\), at which the aerosol-bound virus loses infectiousness, which for SARS-CoV-2 has been estimated to lie in the range of zero [] to 0.63/h []. Taking into account results for other aerosolized viruses [], the viral deactivation rate is approximated as linear in relative humidity, \(\lambda_{v}=\lambda_{v,50}RH\), where the value \(\lambda_{v,50}\) is specified. The effective viral deactivation rate may also be enhanced by ultraviolet radiation (UV-C) [] or airborne dispersal of chemical disinfectants (\(\it{e.g.}\) H\({}_{2}\)O\({}_{2}\), O\({}_{3}\)) [].
### Precautionary Parameters
The first precautionary parameter is the _mask filtration factor_, \(p_{m}\), defined as the fraction of infectious aerosol droplets that pass through the mask during exhalation or inhalation. Many studies are available to help assign this value for different types of face coverings, ranging from cloth coverings to surgical masks []. Although filtration efficiency depends on drop size, it is typically nearly constant in the aerosol range []. Typical values for disposable medical masks are in the range \(p_{m}=1-5\%\)[], while for simple cloth face masks, \(p_{m}=10-20\%\)[].
The second precautionary parameter is the _disease transmission tolerance_, \(\epsilon\). We note that \(\epsilon=1\) corresponds to the baseline of one expected transmission during the occupancy period. The choice of \(\epsilon\) should take into account the vulnerability of the population, which for COVID-19 is a strong function of age and pre-existing medical conditions []. Relative to the median age of 69 in the Skagit Valley Chorale spreading incident used to calibrate our model, the relative rate of hospitalization with COVID-19 [] can be calculated as 2.5% (ages 0-4), 0.8% (ages 5-17), 20% (ages 18-49), 61% (ages 50-64), 130% (ages 75-84), and 145% (ages \(>85\)). For the elderly, especially those with preexisting conditions or co-morbidity, \(\epsilon\ll 1\) should be chosen. For the young and healthy (in regions where hospitals are not overwhelmed and vulnerable groups are protected), larger values of \(\epsilon\) could be considered []. As noted in the main text, choosing a sufficiently small \(\epsilon\) will also serve to mitigate against prolonged exposure to respiratory jets, whose contribution to pathogen transport may dominate in the absence of face-mask use [].
### Results
The spreadsheet first computes properties of the infectious aerosol per infected individual in the room, which are primarily of technical interest: the effective droplet settling speed \(v_{s}(\tilde{r})\), the concentration relaxation rate \(\lambda_{c}(\tilde{r})\), the dilution factor, \(f_{d}\), and the infectiousness of the ambient air, \(f_{d}C_{q}\), in steady state per infected person in the room.
The spreadsheet computes the safety guideline in two ways with the key results highlighted in green. First, the occupancy limit \(N_{max}\) can be calculated for a given exposure time \(\tau\), as is set by the typical residence time of people in the indoor space. The corresponding minimum outdoor airflow per person, \(Q/N_{max}\), may be compared with local standards, such as 3.8 L/s/person for retail spaces and classrooms and 10 L/s/person for gyms and sports facilities in Europe [], or the ASHRAE Standards in the United States, typically 5-20 cfm/person depending on the type of space []. Second, the time limit \(\tau_{max}\) is calculated for a given occupancy \(N\). These bounds are plotted and may be compared to the Six-Foot Rule and 15-Minute Rule, both of which invariably violate our guideline. For the bounds on both \(N_{max}\) and \(\tau_{max}\), two results are reported: the transient bound, which accounts for the buildup of infectious aerosols in the air after the entrance of an infected person, and the more conservative steady-state bound, which is relevant after the relaxation time \(\lambda_{c}\tau\gg 1\).
### Contact Tracing
The spreadsheet can also be used as a tool for contract tracing. With a conservative tolerance, such as \(\epsilon=0.01\), the guideline defines whether or not the \(N\) occupants of a room visited by the index case for a time \(\tau\) should be considered as contacts for the purpose of tracing the infection network. If the guideline is violated, then _all_ occupants of the room must be considered contacts, regardless of their distance from the index case. Compared to the current CDC definition of contact [] - spending more than 15 minutes less than 6 feet apart from an infected person - this definition, based on our consideration of airborne transmission, may thus identify significantly more contacts to be traced and quarantined.
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182824_file03 | #### 1 The well-mixed room
Two flow types typically contribute to vigorous mixing of indoor air: buoyancy-driven and forced convection. Buoyancy-driven convection results from the action of gravity on differences in air density, typically due to temperature gradients. Forced-air heating (from below) or cooling (from above) of a room typically lead to localized flows that are subject to hydrodynamic instabilities that prompt mixing on a relatively larger scale. Air-conditioning units generate relatively cold, dense air that sinks as a turbulent plume and entrains ambient air as it sinks to the floor. Heating vents and radiators create buoyant counterparts, turbulent thermal plumes that rise to the ceiling. In relatively cool rooms, temperature gradients associated with body heat lead to turbulent thermal plumes rising from individuals. Respiratory jets, plumes and puffs also typically have some buoyancy, leading to updrafts from these turbulent respiratory flows. When masks are worn, the horizontal momentum of respiratory flows is greatly suppressed, but the exhaled air typically leads to a rising turbulent buoyant plume. Additional large-scale flows, either laminar or turbulent, are driven by horizontal temperature gradients in the vicinity of closed windows. The net effect of such buoyancy-driven flows is to promote mixing of the indoor air.
Room-scale forced convection may also be driven by the mechanical air circulation system or the respiration and movement of its occupants. The hydrodynamic stability of an air flow with a characteristic speed \(v\) and length scale \(L\) is prescribed by the Reynolds number, \(\mathrm{Re}=vL/\nu_{a}\), where \(\nu_{a}\) is the kinematic viscosity of air. For example, laminar flow around obstacles typically becomes unstable to vortex shedding for \(\mathrm{Re}>100\) and turbulence for \(\mathrm{Re}>2000\). For an indoor air flow forced by mechanical ventilation with a characteristic speed \(v=(Q+Q_{r})/A=(\lambda_{a}+\lambda_{r})H\) and length scale corresponding to that of a room, \(L=H=3\)m, the characteristic Reynolds number \(\mathrm{Re}\approx 110\) for \(\lambda_{a}=0.3/\mathrm{h}\) and \(\mathrm{Re}\approx 2000\) for \(\lambda_{a}=8/\mathrm{h}\), even in the absence of recirculation flow (\(\lambda_{r}=0\)). Thus, forced convection will typically lead to high-Reynolds-number flows that may be characterized by some combination of vortex shedding and turbulence. Use of fans, air-filtration units or open windows will further increase airflow and mixing. Human movement may also generate vigorous, high-Reynolds-number flows. Human respiration without masks leads to turbulent puff trains and jets, coughing and sneezing to turbulent, buoyant puff clouds.
In turbulent flows, the largest eddies are at the scale of the confining geometry and control the convective transport. Turbulent mixing by forced convection at the scale of the room is thus characterized by the eddy diffusivity, \(D_{e}\approx\frac{1}{2}vH\), as has been verified for the transport of tracer gas in instrumented homes. The characteristic mixing time, \(\tau_{mix}=H^{2}/2D_{e}=H/v=(\lambda_{a}^{-1}+\lambda_{r}^{-1})^{-1}\), is thus prescribed by the time scale of the faster of the two processes, outdoor air exchange and internal air recirculation. In either case, the room should be well mixed by the time the bioaerosol concentration reaches its steady state, since the concentration relaxation rate necessarily exceeds the air exchange rate due the influence of droplet settling, filtration and viral deactivation.
In summary, indoor air is typically well mixed by either laminar or turbulent flows driven by some combination of mechanical air circulation, buoyancy-driven flows and human activity. The success of turbulent deposition models in rationalizing measured aerosol mass transfer to indoor surfaces provides further support for the validity of the well-mixed-room approximation. While variations from well-mixedness may arise, for example through the development of stratification, the approximation of the well-mixed room has been widely applied in describing indoor settings, specifically in the context of long-range airborne disease transmission.
#### 2 Droplet transfer to surfaces
In the continuous stirred tank reactor (CSTR), a canonical system in chemical engineering, the relative rate of chemical reaction to convection is prescribed by the dimensionless Damkoller number. In the context of airborne disease transmission, we consider the'reaction' corresponding to aerosol-borne virion removal from a well-mixed room, and so define \(\mathrm{Da}=\lambda_{c}/\lambda_{a}\) in terms of the concentration relaxation rate \(\lambda_{c}(r)\) and the air change rate \(\lambda_{a}\).
\[\mathrm{Da}=\mathrm{Da}_{b}+\mathrm{Da}_{s}=\frac{(\lambda_{v}+\lambda_{f})V}{Q}+ \frac{hA}{Q}\.\] (S1)
Bulk disinfection of the air may arise through viral deactivation at a rate \(\lambda_{v}(r)\) or air filtration at a rate \(\lambda_{f}(r)=p_{f}(r)\lambda_{r}\). We denote by \(h\) the virion mass-transfer coefficient from the bulk to the surfaces, which necessarily has the units of velocity.
In the field of aerosol science, it is customary to refer to the dimensionless droplet mass-transfer coefficient as the 'deposition efficiency', \(\eta=hA/Q\), and to relate it to various particle transport resistances. Such resistances are expressed in dimensionless form in terms Stokes numbers, each of which represents the ratio of two particle speeds. There are three potentially relevant resistances to drop mass-transfer from the bulk air to surfaces: gravitational settling, diffusion and surface deposition. We thus express the efficiency of droplet deposition from the bulk in terms of three Stokes numbers:
\[\eta^{-1}=\left(\mathrm{St}_{g}+\mathrm{St}_{d}\right)^{-1}+\mathrm{St}_{dep}^ {-1}.\] (S2)
We note that the droplet deposition efficiency \(\eta\) is equivalent to the "particle loss-rate coefficient", \(\beta\), customarily defined for particulate aerosols in indoor air)
The gravitational Stokes number, \(St_{g}=v_{s}/v_{a}\), prescribes the relative magnitudes of the Stokes settling speed, \(v_{s}=2\rho_{d}gr^{2}/9\mu_{a}\) and the ambient air flow, \(v_{a}=Q/A=\lambda_{a}L\). We note that inertial corrections to Stokes law only become important for droplets with \(r>100\mu\)m, and so are not relevant for aerosols. For the largest respirable droplets (\(r=5\mu\)m) with poor, natural ventilation (0.35 ACH) in a typical room (\(H=2.7\)m), settling dominates convection since \(\mathrm{St}_{g}=12\gg 1\). Conversely, for smaller droplets (\(r=0.5\mu\)m) with hospitalized ventilation (25 ACH), settling can be neglected since \(\mathrm{St}_{g}=0.0017\ll 1\). Drops with radius exceeding a critical values, \(r_{c}=\sqrt{9\mu_{a}\lambda_{a}H/(2\rho_{d}g)}\) corresponding to \(\mathrm{St}_{g}=1\), tend to settle to the surfaces before being removed by ventilation. For a given droplet size \(r\), we write \(\mathrm{St}_{g}(r)=(r/r_{c})^{2}\). The droplets of interest in our model of airborne transmission are those with \(St_{g}<1\).
For submicron particles suspended in a well-mixed ambient, diffusion may influence the transfer of the particle through the lower viscous boundary layer, either by Brownian motion or eddy diffusion for the case of a turbulent boundary layer. The importance of such particle diffusion is prescribed by the diffusional Stokes number, \(St_{d}=D/(\delta v_{a})\), where \(D\) is the particle diffusivity and \(\delta\) is the viscous boundary layer thickness near the depositing surface, which sets the diffusional mass-transfer coefficient, \(h_{d}=D/\delta\). We may alternatively write \(St_{d}=\overline{\mathrm{Sh}}(\mathrm{Re},\mathrm{Sc})/\mathrm{Pe}\), where the Peclet number, \(\mathrm{Pe}=v_{a}H/D\), prescribes the relative magnitudes of convection and diffusion, and the Sherwood number, \(\overline{\mathrm{Sh}}=h_{d}H/D\), is the dimensionless diffusion mass-transfer coefficient, averaged over the surface.
We first consider Brownian droplet diffusion through a laminar boundary layer, as is typical of natural ventilation over horizontal surfaces. For a given flow field, kinematic viscosity \(\nu_{a}=\mu/\rho_{a}\) and Brownian diffusivity \(D=k_{B}T/6\pi\mu_{a}r_{d}\) (as follows from the Stokes-Einstein relation), the Sherwood number depends on the Schmidt number \(\mathrm{Sc}=\nu_{a}/D\) and Reynolds number \(\mathrm{Re}=\mathrm{Pe}/\mathrm{Sc}\). Using the relation, \(\overline{\mathrm{Sh}}=0.664\,\mathrm{Re}^{1/2}\mathrm{Sc}^{1/3}\), relevant for a laminar boundary layer on a flat plate, we estimate, for the case of bioaerosols with radius (\(r=0.5\mu\)m) with poor ventilation (0.35 ACH), that \(\mathrm{St}_{d}=7\times 10^{-6}\ll 1\) (\(\mathrm{Sc}=5\times 10^{5},\ \mathrm{Re}=47,\ \mathrm{Sh}=180,\ \mathrm{Pe}=2.5\times 10^{7}\)), which indicates that particle diffusion can be safely neglected. Indeed, the removal of droplets by Brownian diffusion becomes comparable to that by gravitational settling, \(\mathrm{St}_{d}>\mathrm{St}_{g}\), only for \(r<13\) nm at 0.35 ACH, a critical radius much smaller than that of a single SARS-CoV-2 virion (\(r_{v}=60\)nm).
Next, we consider droplet diffusion through a turbulent boundary layer, as might arise for high ventilation rates. In their seminar work on aerosol mass transfer, Corner and Pendleton augmented the Brownian diffusivity, \(D\), with the turbulent eddy diffusivity, \(D_{e}=K_{e}y^{2}\), where \(K_{e}\) is a turbulence intensity parameter, proportional to the local mean velocity gradient, and \(y\) is the distance from the surface. A better fit to experimental data was achieved by expressing the eddy diffusion as \(D_{e}=K_{e}\delta^{2}(y/\delta)^{n}\), where \(\delta\) is the boundary layer thickness \(\delta\) and \(n=2.6-2.8\) is an empirical scaling exponent. Using this approach, Lai and Nazaroff developed a comprehensive, experimentally validated model of aerosol mass transfer to surfaces and showed that, even for the highest building ventilation rates, turbulent diffusion competes with gravitational settling only for particles with \(r<0.2\mu\)m. This critical size is much smaller than that of stable respiratory droplets, and only a few times larger than a single virion. We thus conclude that gravitational settling dominates diffusion, both Brownian and turbulent, in respiratory aerosol removal from indoor air.
Finally, the role of droplet deposition is determined by \(\mathrm{St}_{dep}=v_{dep}/v_{a}=\mathrm{St}_{g}v_{dep}/v_{s}\), where \(v_{dep}\) is the net liquid deposition velocity, specifically the surface adsorption flux per bulk liquid concentration, as accounts for the probability of droplets sticking to the surface rather than bouncing off. Experiments have shown that \(v_{dep}/v_{s}\) is approximately constant for water droplets with characteristic diameter of 1-10 \(\mu\)m in a variety of settings, including droplets settling from clouds onto the forest canopy and from humid air onto acrylic pipes). For droplets of radius \(r=5\mu\)m settling at \(v_{s}=0.306\) cm/s, the deposition velocity \(v_{dep}\approx 5\) cm/s. We thus conclude that deposition kinetics are fast compared to droplet transport, since \(\mathrm{St}_{dep}\approx 20\,\mathrm{St}_{g}\), and can be safely neglected as a small mass-transfer resistance in series.
In summary, for the respiratory droplets of interest, the dominant contribution to droplet mass transfer to surfaces for the relevant range of respiratory aerosols, \(r=0.1-10\mu m\) comes from gravitational settling, \(h\approx v_{s}\).
\[\eta\approx\mathrm{St}_{g}=\left(\frac{r}{r_{c}}\right)^{2}\] (S3)
This deduction allows us to conveniently express the droplet mass transfer from complex indoor airflows in terms of the Stokes settling velocity. The effects of boundary-layer or surface mass-transfer resistance are negligible, and the timescale of settling of respiratory droplets from a well-mixed ambient is prescribed by the Stokes settling time.
## 2 Exact solution for the transient guideline
The general safety guideline, Eq., can be written as, \(\mathcal{R}_{in}(\tau)=N_{s}s_{r}\langle\beta_{a}\rangle\tau\), in terms of the time-averaged airborne transmission rate, which can be broken into steady-state and transient terms:
\[\langle\beta_{a}\rangle(\tau) = \frac{1}{\tau}\int_{0}^{\tau}\beta_{a}(t)dt=\overline{\beta}_{a}- \Delta\beta_{a}(\tau)\] (S4) \[\overline{\beta}_{a} = \frac{Q_{b}^{2}}{V}\int_{0}^{\infty}\frac{n_{q}(r)}{\lambda_{c}(r)}dr\] (S5) \[\Delta\beta_{a}(\tau) = \frac{Q_{b}^{2}}{V\tau}\int_{0}^{\infty}\frac{n_{q}(r)}{\lambda_{ c}(r)^{2}}\left(1-e^{-\lambda_{c}(r)\tau}\right)dr\] (S6)
The steady-state term \(\overline{\beta}_{a}\) can be expressed as Eq., where the mean sedimentation speed \(v_{s}(\overline{r})\) and mean suspended droplet size, \(\overline{r}\), are defined by
\[\frac{v_{s}(\overline{r})}{\nu(\overline{r})^{2}v}=\left(\frac{\overline{r}}{ \nu(\overline{r})rc_{c}}\right)^{2}=C_{q}\left(\int_{0}^{\infty}\frac{n_{q}(r )dr}{1+(r/(\nu(r)rc_{c}))^{2}}\right)^{-1}-1\] (S7)
For short exposures or poor ventilation, the transient correction can reduce the indoor reproductive number, resulting in a more permissive guideline. In the case of monodisperse droplets of size \(r=\bar{r}\), the transient term can be approximated as, \(\Delta\beta_{a}/\overline{\beta}_{a}=(1-e^{-\lambda_{c}\tau})/(\lambda_{c} \tau)\approx 1/(1+\lambda_{c}\tau)\).
\[N_{s}s_{r}\overline{\beta}\tau<\epsilon(1+(\lambda_{c}(r)\tau)^{-1})\] (SS)
In the limit of short exposures, \(\lambda_{c}(r)\tau\ll 1\), we obtain a refined safety guideline, \(N_{s}s_{r}(\overline{\beta}\tau)(\lambda_{c}(r)\tau)<\epsilon\), which is less strict because it reflects the leeway associated with the time taken for the build-up of the airborne pathogen following the arrival of an infected person. During this period, the safe exposure time scales as \(\tau_{max}\sim N_{s}^{-1/2}\), and the CET bound diverges as \(N_{s}\tau_{max}\sim\tau^{-1}\) in the \(\tau\to 0\) limit. This divergence simply reflects the fact that transmission will not occur if people do not spend sufficient time together.
## 3 Deduction of the indoor safety guideline from epidemiological models
We here demonstrate that our indoor safety guideline, Eq., may be deduced from standard epidemiological models.
While our theoretical model of the well-mixed room was developed to describe airborne transmission from a single individual to a fixed number of others in a well-mixed room, it bears noting that this scenario is but one of a broader class of transmission events. First, there are many situations where air conditioning or forced ventilation mixes air between rooms, in which case the compound room is effectively a well-mixed space. Second, there are incidents when several individuals are initially infected. Third, the population may be together for a period long with respect to the incubation time (approximately 5.5 days), in which case the number of infectious individuals necessarily increases with time. Examples of this broader class of transmission events might include cruise ships, meat and poultry processing facilities and prisons. We proceed by detailing the epidemiological models describing this more general class of events.
Following Noakes et al., we adopt the standard SEIR model from epidemiology, an extension of the original SIR model of Kermack and McKendrick of susceptible (\(S\)), infected (\(I\)) and recovered (\(R\)) populations to include an exposed population (\(E\)) that has acquired the pathogen and so become infected but not yet infectious:
\[\frac{dS}{dt}=-\beta SI,\ \frac{dE}{dt}=\beta SI-\alpha E,\ \frac{dI}{dt}= \alpha E-\gamma I,\ \frac{dR}{dt}=\gamma I\] (S9)
To describe a spreading event in a closed environment, we consider \(I_{0}\) infected people entering, at time \(t=0\), a room full of \(N_{s}=S_{0}=N-I_{0}\) susceptible individuals (setting \(p_{s}=1\)), none of which were previously exposed, \(E_{0}=0\). The reproductive number, \(\mathcal{R}_{0}=S_{0}\beta/\gamma\), describes the initial exponential rate of increase (\(\mathcal{R}_{0}>1\)) or decrease (\(\mathcal{R}_{0}<1\)) of the infected fraction of the population. In the case where the population is being tested and infected individuals removed from the population via isolation, \(\gamma\) may alternatively be considered as a proxy for testing frequency. Noting that the combined incubation time and time to recovery for COVID-19 is thought to exceed 2 weeks, we here consider spreading events of duration \(\tau\) that are short relative to the recovery time, \(\tau\ll\gamma^{-1}\), and so eliminate \(R\) from consideration.
The Wells-Riley model is effectively a reduction of the SIR model based on the assumption of slow incubation over the timescale of the event, \(\tau\ll\alpha^{-1}\), in which case the number of infected persons in the room remains fixed, \(I(t)=I_{0}\). One expects such to be the case for events of relatively short duration, such as the Skagit Choir incident. However, such an approximation is not likely to be valid in the case of indoor super-spreading events of longer duration, \(\tau>\alpha^{-1}\). To adequately model such events, we consider the possibility that the number of infectors increases with time, which requires a description of the nonlinear dynamics of disease transmission.
The resulting SEI model to be considered here is a system of three nonlinear ordinary differential equations. While the system may be solved numerically, deduction of a safety guideline requires analytical results. Our goal is thus to solve this SEI model for the infection (or "secondary attack") rate, \(i_{S}(\tau)=(E(\tau)+I(\tau)-I_{0})/S_{0}\). Since exact solutions may be cumbersome (as for the SIR model), we simplify the analysis by considering two limits, where the incubation time \(\alpha^{-1}\) is short or long relative to the event timescale, \(\tau\), and the transmission timescale \(\beta^{-1}\). While the incubation time of COVID-19 is not precisely known, it is bounded above by the time to develop symptoms, which spans 2-14 days with an average 5.5 days.
For slow incubation (\(\alpha\ll\beta,\tau^{-1}\)), the number of infected persons remains nearly constant, \(I(t)\approx I_{0}\), and the resulting SE model is easily solved to derive the secondary attack rate,
\[i_{S}(\tau)=1-e^{-I_{0}\int_{0}^{\tau}\beta(t)dt},\] (S10)
In the opposite limit of fast incubation (\(\alpha\gg\beta,\tau^{-1}\)), exposed individuals are rapidly infected, so the exposed, non-infected population need not be considered, \(E(t)=0\).
\[i_{S}(\tau)=\left[1-i_{0}^{-1}\left(e^{N\int_{0}^{\tau}\beta(t)dt}-1\right)^{-1} \right]^{-1},\] (S11)
These simple solutions, (S10) and (S11), cover the two limiting cases of fast and slow incubation relative to transmission.
The safety criterion \(\mathcal{R}_{in}<\epsilon\), which limits the probability of the first transmission to lie below a small tolerance, is universal, in that it does not depend on the choice of model to describe the subsequent spreading dynamics.
\[\frac{\mathcal{R}_{in}}{N-1}=\int_{0}^{\tau}\beta(t)dt<\left\{\begin{array}{ ll}-\ln\left(1-\frac{\epsilon}{N-1}\right)&\text{(slow)}\\ \frac{1}{N}\ln\left[\frac{(N-1)t+\epsilon)}{N-1-\epsilon}\right]&\text{(fast)} \end{array}\right.\] (S12)
(S10) and (S11) for slow and fast incubation, respectively. In the small-tolerance limit, \(\epsilon\ll 1\), these bounds both reduce to, \(\mathcal{R}_{in}<\epsilon\), and are thus independent of the incubation rate. More generally, the linear response of any Markovian, mean-field theory (with neither memory nor many-body correlations) to any perturbation, such as the arrival of a new infector, must begin at the mean transmission rate. Indeed, the same universal bound may be simply derived from the infinitesimal cumulative probability of transmission \(\int_{0}^{\tau}\beta(t)\) from one infector to a set of \(N-1\) independent susceptibles.
## 4 Inference of infection quanta from disease spreading data
It is an important point that the concentration of "infection quanta" per exhaled air volume, \(C_{q}\), as may be inferred from spreading data, is necessarily model dependent. By definition, the time integral of the transmission rate, \(p(\tau)=\int_{0}^{\tau}\beta(t)dt\), is equal to the expected number of quanta transferred from one infector to one susceptible. In models of indoor airborne transmission, infection quanta are further related to the evolving pathogen-laden droplet concentration by Eq.. While the mathematical definition of infection quanta is unambiguous in terms of the instantaneous transmission rate, \(\beta(t)\), between two isolated individuals, the inference of quanta concentrations from field data for the spreading rate is inevitably model dependent because it involves interactions among an evolving population. Specifically, the long-time growth in the number of infections is influenced by nonlinearities in the transmission dynamics, as governed by the chosen epidemiological model, for example, the SEIR model, Eq. [S1].
In the original Wells-Riley model, one infection quantum is defined as the amount of pathogen required to infect an average of \(1-1/e\approx 63.2\%\) of susceptible people in an enclosed space. This inference is based on fitting field data to Eq. [S2], which relates one net quantum transferred, \(I_{0}q(t)=1\), to the secondary infection rate, \(i_{S}(t)=1-(1/e)\). This approach is valid for times short relative to the incubation time and has been successfully applied to extract quanta emission rates for various viral diseases, including SARS-CoV-2. However, the Wells-Riley model cannot be reliably used to infer infection quanta from super-spreading events evolving over time scales that exceed the incubation time.
For such situations, here we take an approach appropriate for the case of fast incubation that necessarily implies a different relation between released infection quanta and the observed secondary infection rate. If we adopt the SI model with fast incubation, then the long-term behavior of Eq. [S3] indicates that one quantum (\(I_{0}q(t)=1\)) will infect a fraction \(i_{S}=[1+(N/I_{0})/(e^{N/I_{0}}-1)]^{-1}\) of \(N\) people in an enclosed space, \(I_{0}\) of which were initially infected, as a result of transmission amplification by the growing number of infectors. In this model, a single quantum from one person infects another with probability \(i_{S}=[1+2/(e^{2}-1)]^{-1}\approx 76.2\%\) for \(N=2\), but manages to infect everyone in a large group, \(i_{S}\to 1\) as \(N\rightarrow\infty\). This dependence of infection quanta on epidemiological model parameters, such as the incubation rate, reflects the fact that the fitted "infection quantum" is a measure of contagiousness at the scale of a group that is not necessarily proportional to the microscopic pathogen concentration. Notably, infection quanta are well defined in the limit of short times and slow transmission, where all models reduce to the Wells-Riley model with a constant number of infectors. From the modeling perspective, the notion of infection quanta is thus unambiguous only in this limit. Finally, we recall that, regardless of the model used to infer it, the actual value of infection quanta may still vary considerably between spreading events, owing to its dependence on activity level of the population and other physiological factors.
## 5 Fitting to super-spreading events
Table S1 shows the data used to infer the concentration of infection quanta \(C_{q}\) exhaled by an infected individual for four well-known indoor super-spreading events of COVID-19, for which physical parameters can be estimated with reasonable accuracy from published data: the Skagit Valley Chorale, the Diamond Princess cruise ship, the Ningbo tour bus, and the initial Wuhan outbreak, interpreted as mainly indoor spreading at home. The best characterized case of the Skagit Valley Chorale is used in the main text to calibrate the safety guideline. Here we consider the other three spreading events, for which only relatively rough estimates of certain model parameters can be made. Despite the resulting uncertainty, these events provide additional support for the inferences made in the main text.
In all situations, we assume an effective particle radius \(\overline{r}=2.0\mu\)m at the upper limit of the infectious range of suspended droplets, corresponding to an effective settling speed of \(v_{s}(\overline{r})=1.78\) m/h. Note that the effective radius would be somewhat larger, \(\overline{r}=3.0\mu\)m, if we were to neglect the size dependence of infectivity and set \(n_{q}=\)constant, and use our prediction of the steady-state airborne droplet distribution \(C_{s}(r)/c_{v}\) for singing in the choir room. We also assume no use of face masks, \(p_{m}=1\) and an airborne virus deactivation rate, \(\lambda_{v}=0.3\)/h that lies between the existing estimates of zero and \(0.63\)/h
### The Diamond Princess.
The data reported for the Diamond Princess is particularly useful in that it captures the time evolution of the infected persons among a fixed population over an extended period, corresponding to the 12-day quarantine, after which passengers and crew began to disembark. The resulting data reported for \(I(t)\) is best described in terms of the fast-incubation limit (Figure S1). Fitting to the available data allows us to infer that the initial number of passengers infected on February 3, 2020 was approximately \(I_{0}=20\), and that the concentration of infection quanta characterizing this particular spreading event was \(C_{q}=30\) quanta/m\({}^{3}\). Furthermore, it suggests that the incubation time is significantly less than 12 days, as is consistent with current estimates for the average time between exposure and the onset of symptoms being 2-5 days [].
Our fitting of \(I_{0}\) and \(C_{q}\) for the Diamond Princess is based on the hypothesis of a "well-mixed ship". While such an approach is not traditional, and would be contested by those who do not believe that airborne transmission was prevalent on the Diamond Princess [], it is consistent with a growing body of evidence []. Analysis of the ship's floor plans and ventilation system has indicated recirculation of heated interior air throughout the entirety of the ship during cold weather (-5\({}^{\circ}\) C), without adequate filtration for virus-containing aerosol droplets []. Moreover, a detailed statistical analysis of the SARS-CoV-2 transmission history between passenger cabins revealed no significant correlation between new cases and the sharing of rooms with previously confirmed cases. Airborne transmission was further suggested by several examples of new cases emerging in single-occupancy cabins despite no known contact with other cases []. Like many other indoor COVID-19 spreading events [] in which position in an enclosed space was uncorrelated with likelihood of transmission [], the cruise line outbreaks present evidence that strongly supports the notion of airborne transmission of SARS-CoV-2 through well-mixed indoor spaces [].
### Ningbo tour bus.
We proceed by considering another super-spreading event, involving a Buddhist blessing ceremony held at the Tiantong Temple in Ningbo, Zhejiang Province, China on January 19, 2020 []. The confirmed index case, Ms. S, was thought to have contracted the virus two days earlier from dinner guests who had traveled to Wuhan during the initial outbreak. Ms. S traveled to the ceremony on a tour bus [(Bus 2)] for 50 minutes with 68 people, including the driver, and returned on the same bus with the same seating arrangement. Since it was winter, the windows were likely closed.
Figure S1: Validation and calibration of the fast-incubation model for the super-spreading event on board the Diamond Princess cruise ship, during its twelve day quarantine at Yokohama, Japan in February 2020 []. Fitting the number of SARS-CoV-2 positive cases versus time (blue data points) during the quarantine period, to the fast-incubation solution of the SEI model, Eq. [], (red curve) yields estimates for the initial number infected (\(I_{0}=20\)) and the transmission rate (\(N\beta=0.25\)/day), from which we infer the concentration of infection quanta from breathing (\(C_{q}=30\) quanta/m\({}^{3}\)). The relevant physical parameters are listed in Table S1.
No masks were worn by the passengers, as there had not previously been any cases of COVID-19 in Zhejiang Province. Of the 68 passengers, 23 new cases of COVID-19 were confirmed, with their locations being evenly distributed across the bus, largely uncorrelated with proximity to Ms. S. Most had no close contact with the index case. However, some spatial patterns of transmission could be discerned on the bus, such as fewer cases among the window seats, possibly due to recirculation air flows. The epidemiological evidence for indoor airborne transmission is overwhelming.
Of the 172 others that attended the ceremony, only 7 individuals (4.1%) became infected at the 150-minute worship event, which was mostly held outside. Assuming that the bus passengers were infected at the temple at the same rate as the others, we may estimate that 3 of 23 transmissions occurred there, so only 20 on the round-trip bus ride. The published floorplan of the bus resembles that of a Dongfeng 67-seat luxury tour bus made in Hubei Province, China, whose specifications we use to estimate interior dimensions. The most uncertain model parameter is the air exchange rate, \(\lambda_{a}\), which we presume to be associated with natural ventilation. We further assume that windows were closed and that air filtration was limited. Although \(\lambda_{a}=1.8-3.7/\)h has been measured in passenger cars with closed windows and recirculating fans, transit buses tend to have lower values, such as \(\lambda_{a}=1.25/\)h, a value that we adopt here. We also assume a typical seated breathing flow rate, \(Q_{b}=0.5\) m\({}^{3}\)/h.
Using these approximations for the model parameters, we apply the slow-incubation model (S10) to infer \(C_{q}=90\) q/m\({}^{3}\) and \(\lambda_{q}=45\) q/h. This value of \(C_{q}\) falls in the range of intermediate speaking obtained from other inferences in the main text, which would be consistent with passengers speaking amongst themselves on the voyage. Given the uncertainty in the air exchange rate, the inferred value of \(C_{q}\) could also be consistent with normal breathing with only occasional speech. Finally, we note that the average age of the bus passengers was 59, which suggests a relatively vulnerable population, for which one expects to infer a relatively high \(C_{q}\).
### Wuhan outbreak
Table S1 also shows how the theory can be used to interpret the population-level reproductive number in terms of indoor airborne transmission, assuming that the primary disease transmission arises in family apartments, as shown in a recent analysis of COVID-19 spreading in China. We consider the initial outbreak in Wuhan, Hubei Province and assume physical parameters appropriate for typical apartments and families. We then use the average population reproductive number to assert \(\mathcal{R}_{in}(\tau)=\langle\mathcal{R}_{0}\rangle=3.3\), where \(\tau=5.5\) days is the mean time for an newly infected family member to show symptoms and be isolated or removed.
As shown in the main text (Fig.2), the inferred values of \(C_{q}=29\) quanta/m\({}^{3}\) for family apartments in the Wuhan outbreak and \(C_{q}=30\) quanta/m\({}^{3}\) for the Diamond Princess cruise ship are consistent with the light respiratory activities expected to be most prevalent in those settings, such as sleeping and quiet speech. Both inferred \(C_{q}\) values are greatly exceeded by the inference of \(C_{q}=870\) (made here, using \(\tilde{r}=2.0\mu\)m and \(\lambda_{a}=0.65/\)h; see Table S1) or 970 quanta/m\({}^{3}\) (made by Miller et al, averaging over simulations with variable \(\lambda_{a}=0.3-1.0/\)h and \(\lambda_{s}=0.3-1.5/\)h) for singing, but in a manner consistent with the increased pathogen output associated with more vigorous speaking or singing. These inferences build confidence in our estimates of exhaled quanta concentrations, \(C_{q}\), for various respiratory activities, as shown in of the main text.
## 6 The dependence of airborne disease transmission on respiratory activity
It is well established that aerosol droplet production varies strongly with the form of expiratory activity. For example, vocalization greatly increases aerosol emission relative to quiet breathing, roughly in proportion to the amplitude of the sound produced. In Table S2, the aerosol volume fraction produced by different activities, obtained by integrating the distributions in up to \(r_{c}=2.5\mu\)m, are used to rescale the inferred quanta concentration for singing in the Skagit Valley Choir room into those appropriate for other activities. The resulting values are consistent with the values of \(C_{q}\) inferred for the Diamond Princess quarantine and the initial Wuhan City outbreak (see Table S1 and Fig. 2).
## 7 Application of the Safety Guideline
In order to illustrate how to implement our safety guideline, we provide a spreadsheet as Supplementary Data, which has also been implemented for general use as an online app, translated into many languages. We note that, following the submission of our manuscript, it has come to our attention that the groups of Jose-Luiz Jimenez and LidiaMorawska [] have produced spreadsheets with extensive documentation [] similar in spirit to ours, designed to provide quantitative risk assessments for safe management of indoor spaces during the COVID-19 pandemic. Since their analyses and others [] are based on the same physical picture of airborne transmission in a well-mixed space, their predictions are consistent with ours. However, their recommendations rely on calculations of pathogen concentration and risk in different settings, while ours are based entirely on our Safety Guideline, as succinctly expressed by the bound on cumulative exposure time in Eq. [].
Our spreadsheet and online app enable the calculation of the suggested maximum cumulative exposure times for specific indoor spaces. In this section, we offer guidance on how to use the spreadsheet for both safety assessment and contact tracing, specifically, how to select suitable parameters and properly interpret the results. The input parameters, colored in pink in the spreadsheet and in _italics_ below, are divided into the following four categories.
### Physical Parameters
The geometry of the indoor space is specified by its _floor area_, \(A\), and _mean ceiling height_, \(H\), from which the volume \(V=AH\) is calculated using appropriate unit conversions. The _ventilation outflow rate_, \(Q=V\lambda_{a}\), is calculated from the air exchange rate, \(\lambda_{a}\), typically expressed in terms of air changes per hour (ACH). This critical input parameter is governed by national or local standards for different types of indoor spaces, such as the ASHRAE standards [(62.1)] in the United States []. As noted in the main text, natural ventilation may be approximated as \(\lambda_{a}=0.34\)/h, which has been measured in bedrooms with closed windows [] and is considered to be the minimum standard [], although this value will vary with both location and quality of construction. For residences, classrooms, businesses, and public spaces, \(\lambda_{a}\) usually falls in the range \(4-8\)/h. Crowded spaces, such as bars, nightclubs and restaurants, typically require more vigorous ventilation, \(\lambda_{a}=15-20\)/h. Minimum ventilation standards for American hospitals have increased from 12 to 18 ACH []. Most chemical and biological laboratories have \(\lambda_{a}\) in the range of \(6-12\)/h, but those handling toxic or infectious materials may have \(\lambda_{a}\) as high as \(20-30\)/h. Revised ASHRAE standards, intended to mitigate the spread of airborne infectious diseases, recommend a minimum of \(\lambda_{a}=6\)/h for all indoor spaces [].
Forced air filtration and droplet settling in ducts may also be included through the effective air filtration rate, \(\lambda_{f}(r)=p_{f}(r)\lambda_{r}\), where \(\lambda_{r}=Q_{r}/V\) is the _recirculation air exchange rate_ passing through the filter and \(p_{f}(r)\) is _droplet filtration probability_, taken to be a constant over the aerosol size range. The United States Environmental Protection Agency defines high-efficiency particulate air (HEPA) filtration [] as removing \(p_{f}=99.97\%\) of aerosol particles, while ordinary air filters are assigned Minimum Efficiency Reporting Value (MERV) ratings corresponding to \(p_{f}>20\%\)-\(90\%\) in specified aerosol size ranges []. For ventilation systems with indoor air recirculation, the primary outdoor air fraction, \(Z_{p}=Q/(Q+Q_{r})\), is usually specified by indoor air quality (IAQ) standards. For example, \(Z_{d}=20\%\) for classrooms in the United States [], where \(Q+Q_{r}\) is the total flow rate and \(v=(Q+Q_{r})/A\) is the mean air velocity. Alternatively, air filtration may be accomplished by indoor free-standing units with a specified recirculation flow rate of \(Q_{r}\).
The _relative humidity RH_ of the indoor air is another physical input parameter, which affects both respiratory droplet evaporation and viral deactivation [].
### Physiological Parameters
The first physiological parameter is the _volumetric breathing flow rate_, \(Q_{b}\), which is approximately 0.5 m\({}^{3}\)/h for resting and light activity. Average values for healthy males and females have been reported as 0.49, 0.54, 1.38, 2.35, and 3.30 m\({}^{3}\)/h for resting, standing, light exercise, moderate exercise and heavy exercise, respectively [], and used in simulations of airborne transmission of COVID-19 []. The second physiological parameter is the mean respiratory aerosol droplet size \(\bar{r}\) for the suspended infectious droplets responsible for airborne disease transmission. The precise definition of \(\bar{r}\) is given in Eq. (S7), in terms of the distribution of droplet sizes for different types of respiration [], the size-dependent infectivity of aerosol droplets [], and the settling and ventilation rates. As illustrated in the main text, a typical value for \(\bar{r}\) is 2-3 \(\mu\)m. We note that these values are roughly consistent with the standard definition of aerosol droplets, as those having \(r<5\mu\)m []. The effect of relative humidity on the size of stable droplets after evaporation [] can be estimated by rescaling \(\bar{r}\) by \(\sqrt{0.4/(1-RH)}\), since the droplet distributions used to calibrate the guideline were measured at \(RH=60\%\)[].
### Disease Parameters
The most important disease parameter is the _infectiousness of exhaled air_, \(C_{q}\), the infection quanta per volume. Using all of the limited information currently available, we estimate \(C_{q}=30\) q/m\({}^{3}\) for normal breathing and light activity and provide our best estimates of \(C_{q}\) for different respiratory activities in Our analysis indicates that \(C_{q}\) can be an order of magnitude larger for singing or other vigorous respiratory activities, or an order of magnitude smaller for sleeping and light nose breathing.
The second disease parameter, \(s_{r}\), is the _relative transmissibility_ (or susceptibility) of the virus. This transmissibility necessarily depends not only on the susceptibility of the population, which is known to be age-dependent [], but on the viral strain []. For example, a study of transmission in quarantined households during lockdowns in China reported \(s_{r}=0.23\) for children (aged 0-14) and \(s_{r}=0.68\) for adults (aged 15-64) relative to \(s_{r}=1\) for the elderly (over 65 years old) []. Initial estimates of \(\mathcal{R}_{0}\) from the United Kingdom for the new variant of concern (VOC 202012/01, lineage B.1.1.7) suggest that \(s_{r}\) is increased by 60% relative to the original strain of SARS-CoV-2 and show signs of elevated risk of infection among children [].
The third disease parameter is the _viral deactivation rate_, \(\lambda_{v}\), at which the aerosol-bound virus loses infectiousness, which for SARS-CoV-2 has been estimated to lie in the range of zero [] to 0.63/h []. Taking into account results for other aerosolized viruses [], the viral deactivation rate is approximated as linear in relative humidity, \(\lambda_{v}=\lambda_{v,50}RH\), where the value \(\lambda_{v,50}\) is specified. The effective viral deactivation rate may also be enhanced by ultraviolet radiation (UV-C) [] or airborne dispersal of chemical disinfectants (_e.g._ H\({}_{2}\)O\({}_{2}\), O\({}_{3}\)) [].
### Precautionary Parameters
The first precautionary parameter is the _mask penetration factor_, \(p_{m}\), defined as the fraction of infectious aerosol droplets that pass through the mask during exhalation or inhalation, averaging over any dependencies on respiratory activity or direction of airflow. Alternatively, the _filtration efficiency_ is defined as \(1-p_{m}\). Many studies are available to help assign this value for different types of face coverings, ranging from cloth coverings to surgical masks. Although filtration efficiency depends on drop size, it is typically nearly constant in the aerosol range, up to several microns in diameter. Typical values for disposable medical masks are in the range \(p_{m}=1-5\%\) and vary with fit and applied pressure, while for simple cloth face masks, values of \(p_{m}=10-40\%\) are typical for hybrid, multi-layer fabrics and \(p_{m}=40-80\%\) for single-layer or coarse fabrics.
The second precautionary parameter is the _disease transmission tolerance_, \(\epsilon\). We note that \(\epsilon=1\) corresponds to the baseline of one expected transmission during the occupancy period. The choice of \(\epsilon\) should take into account the vulnerability of the population, which for COVID-19 is a strong function of age and pre-existing medical conditions. Relative to the median age of 69 in the Skagit Valley Chorale spreading incident used to calibrate our model, the relative rate of hospitalization with COVID-19 can be calculated as 2.5% (ages 0-4), 0.8% (ages 5-17), 20% (ages 18-49), 61% (ages 50-64), 130% (ages 75-84), and 145% (ages \(>85\)). For the elderly, especially those with preexisting conditions or co-morbidity, \(\epsilon\ll 1\) should be chosen. For the young and healthy (in regions where hospitals are not overwhelmed and vulnerable groups are protected), larger values of \(\epsilon\) could be considered. As noted in the main text, choosing a sufficiently small \(\epsilon\) will also serve to mitigate against prolonged exposure to respiratory jets, whose contribution to pathogen transport may dominate in the absence of face-mask use.
### Results
The spreadsheet first computes properties of the infectious aerosol per infected individual in the room, which are primarily of technical interest: the effective droplet settling speed \(v_{s}(\bar{r})\), the concentration relaxation rate \(\lambda_{c}(\bar{r})\), the dilution factor, \(f_{d}\), and the infectiousness of the ambient air, \(f_{d}C_{q}\), in steady state per infected person in the room.
The spreadsheet computes the safety guideline in two ways with the key results highlighted in green. First, the occupancy limit \(N_{max}\) can be calculated for a given exposure time \(\tau\), as is set by the typical residence time of people in the indoor space. The corresponding minimum outdoor airflow per person, \(Q/N_{max}\), may be compared with local standards, such as 3.8 L/s/person for retail spaces and classrooms and 10 L/s/person for gyms and sports facilities in Europe, or the ASHRAE Standards in the United States, typically 5-20 cfm/person depending on the type of space. Second, the time limit \(\tau_{max}\) is calculated for a given occupancy \(N\). These bounds are plotted and may be compared to the Six-Foot Rule and 15-Minute Rule, both of which invariably violate our guideline. For the bounds on both \(N_{max}\) and \(\tau_{max}\), two results are reported: the transient bound, which accounts for the buildup of infectious aerosols in the air after the entrance of an infected person, and the more conservative steady-state bound, which is relevant after the relaxation time \(\lambda_{c}\tau\gg 1\).
### Contact Tracing
The spreadsheet can also be used as a tool for contract tracing. With a conservative tolerance, such as \(\epsilon=0.01\), the guideline defines whether or not the \(N\) occupants of a room visited by the index case for a time \(\tau\) should be considered as contacts for the purpose of tracing the infection network. If the guideline is violated, then _all_ occupants of the room must be considered contacts, regardless of their distance from the index case. Compared to the current CDC definition of contact - spending more than 15 minutes less than 6 feet apart from an infected person - this definition, based on our consideration of airborne transmission, may thus identify significantly more contacts to be traced and quarantined.
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185272_file03 | ## Principal components analysis
The NLPCA was performed on two random splits of the data to assess for stability in the underlying component dimensions and loading pattern. NLPCA aims to maximize the relations between the univariate outcomes and the underlying principal components through permitting nonlinear associations between the outcomes and component dimensions. In NLPCA, the principal components are identified through eigenvalue decomposition after a discretization step in which variables are scaled for the analysis. Next, the principal components with eigenvalues greater than one were selected for interpretation. The proportions of variance accounted for in the outcomes by each principal component, and the correlations between each outcome and component (i.e., the loadings) are estimated. Each principal component is standardized to a variance of 1 and a mean of 0. Given stability in the dimensions and loadings across separate splits, the NLPCA was re-run using the full sample to obtain final parameter estimates based on the full data. Components were interpreted if their eigenvalues exceeded a 1.00, and loadings onto each component were interpreted if they exceeded a value of 0.400. The variables selected for interpretation on each component were then used to inform the substantive labeling of each component.
## Confirmatory factor analysis
CFA was used to test the stability of the principal components over time. In CFA a hypothesized measurement model is specified through specifying latent factors onto which measures are expected to load (and to not load) as well as through the correlational structure among the measures and factors. This model is then tested against the observed covariance and mean structure of the data to assess the extent to which it fits or reproduces this structure. This is accomplished through iterative, maximum likelihood-based estimation that aims maximize the alignment between the model-estimated and the observed variances, covariances, and means among measures, given the constraints imposed by the latent measurement model. Based on the extent to which the measurement model fits the data, this model may be constrained or relaxed to improve the fit or test specific hypotheses about the configuration of the measures and latent factors. In the present analysis, we examined whether the loadings, intercepts, and residuals of the outcomes varied across time, based on a null hypothesis of measurement invariance across the eight measurement occasions. This analysis sought to replicate the findings of the NLPCA both in terms of the number of factors represented and in terms of the equality of model parameters over the eight assessment points.
The CFA's in the present analyses were parametrized as multi-group models and run at varying levels of model constraint. Each time-point was modeled as a distinct "group" of observations and constraints on the loadings, intercepts, and residuals associated with the measures were tested for equality across the time-point "groups." The likelihood of the observed data at each level of model constraint was comparedwith the likelihood of the data given the least constrained model to evaluate the extent to which constraints diminished the fit with the observed data. In addition, overall fit of the models at each level of constraint was assessed using the comparative fit index (CFI), root mean squared error of approximation (RMSEA), and squared root mean residual (SRMR) as relative fit indices. In simulation studies, approximate criteria of a CFI of.95 or greater, an RMSEA of 0.08 or below, and an SRMR of below 0.08 have been suggested for adequate model fit. These fit indices were interpreted together given that the CFI and RMSEA are least affected by model estimation technique, while the SRMR provides an absolute assessment of fit based on discrepancies between the model-estimated and observed variance-covariance matrices.
Four levels of equality constraint were tested across the study assessment points. For the least-constrained model, only the configuration of measures relative to the factors was constrained across time-points, such that measures were set to load onto the factors if their NLPCA loadings exceeded a value of 0.4 for that factor. Next, equality constraints were imposed on the factor loadings to assess whether variation in the relations between the measures and factors across time exceeded a probability greater than chance. Third, equality constraints were imposed on both the loadings and residuals to assess of whether equal portions of variance in the outcome measures were expected to be accounted for by the factors and measure-specific residuals across time-points. Finally, if equality was retained across all other levels of constraint, equality was imposed on the loadings, intercepts, and residuals to test for strict invariance in the latent structure of these measures over time.
## Growth mixture analyses
Growth mixture models (GMMs) were used to identify latent classes of participants characterized by common intercept and slope values across assessment-points on each outcome. GMM's assume an invariant within-group slope and intercept parameter in each latent growth class, and classes are estimated by maximizing between-class variance in the intercept and slope parameters. The GMMs in the present study were run across ascending a-priori numbers of classes and used iterative, maximum likelihood estimation procedures to estimate the slope and intercept parameters associated with each class and determine the subjects' posterior probabilities of belonging in each class. The models permitted the rate of change (the slope) and the intercepts of the growth trajectories to differ between classes for each outcome. The Bayesian information criterion (BIC), Lo-Mendell-Rubin likelihood ratio Test (LMRT), and bootstrap likelihood ratio test (BLRT) were used to compare the fit of models with sequentially increasing numbers of classes, and the optimal number of classes was selected through a combination of minimizing the BIC, improvement in fit versus fewer classes as indicated by the BLRT and LMRT, and avoiding overfitting with exceedingly small class sizes.
The stability of the optimal class solutions identified for each outcome was assessed by running the same analysis across 100 random ninety-percent splits of the data. Stability was determined by the proportion of times the original class number was selected as optimal and based on likelihood ratio comparisons between the original model and each of the randomly selected splits. Given stability in the solution for the GMM, participants were assigned to a growth trajectory class based on their posterior probability of belonging in that class. Participants' class assignments on the multivariate outcomes were used as the outcome in the random forest classification predictive analyses, while participants' probabilities of being assigned to the worst-faring univariate outcome classes were clustered via k-means and the resulting clusters were entered into the random forest classification analyses.
**K-means clustering**K-means clustering was applied to the results of the GMMs on the univariate outcomes to derive clusters for comparison against the multivariate growth classes. Specifically, k-means clustering was performed on participants' estimated probabilities of belonging to the worst-faring latent growth classes, which defined underlying clusters of participants whose probabilities shared proximity with \(k\) pre-defined centroids. The k-means algorithm aims to find the cluster solution that minimizes within-cluster variability (i.e., based on the squared Euclidean distances of points in a cluster around that cluster's centroid) and maximizes between-cluster variability (i.e., based on the squared Euclidean distances between cluster centroids) such that participants are optimally distinguished between clusters and maximally similar within clusters. This algorithm uses an iterative procedure to identify the best solution for the locations of centroids for a given number of \(k\) clusters, wherein centroids are initially randomly placed and the Euclidean distances between points and the centroids are computed, then the location of the centroids is updated across iterations such that minimizes the within-cluster sum of squares. In the present analysis, the optimal clustering solution for each value of \(k\) was determined through repeating this process 25 times with 100 iterations to minimize the within-cluster sum of squares for each repetition, and then selecting the optimal solution achieved across the 25 repetitions. The k-means clusters of univariate trajectory probabilities were then compared to the multivariate outcome scores and growth trajectory classes to corroborate which participants fell into the worst-faring group across outcomes.
## Random forest classification and feature selection analysis
Random forest classification analyses with feature selection (RFC-FS) was used to identify candidate predictors of which participants belonged to the worst-faring multivariate GMM trajectories as well as which participants belonged to the worst-faring k-means cluster. Each RFC-FS was run with a binary dependent variable indicating whether the participant was assigned to the worst-faring growth class or cluster compared with all other classes or clusters. RFC-FS involves growing multiple decision trees based on prediction of class membership through recursive partitioning of the sample, cross-validating that decision tree across subsets of the data, and selecting the variables that most strongly distinguish among participants assigned and not assigned to the class. The recursive partitioning algorithm entails selecting the variable at each node (i.e., branching point) of the decision tree that maximally distinguishes participants assigned to the class from those not assigned, and then repeating this process until no further partitions can be performed. These decision trees was cross validated through repeating 5-fold cross-validation across 10 iterations of folding the data (i.e., 10 x 5 fold cross-validation). Next, different subsets of features ranging from the top one to top 50 features were examined to identify the optimal number of predictors for distinguishing the worst-faring class or cluster of participants based on their sensitivity and specificity (i.e., using area under the curve). The best features were assessed sequentially at each measurement occasion by first including only measures assessed at baseline and then adding measures from each year of the study up to year 7. The top 20 features showing stability across time, or which emerged and remained salient following a given measurement occasion, were then interpreted as candidate prognostic predictors for the worst-faring group of veterans.
## Principal components analysis results
Three primary components were identified in each split of the data as well as when the analysis was applied to the full dataset. In the first split, the first, second, and third principal components explained 46.54%, 14.23%, and 12.00% of the variance across outcomes, respectively. In the second split, the first, second, and third principal components explained 41.90%, 14.84%, and 11.24% of the variance across outcomes. For the full dataset, the first, second, and third principal components explained 44.38%, 14.12%, and 11.28% of the variance across outcomes. Loadings estimated from the NLPCA are presented in the main text in Table 2.
### Confirmatory factor analysis results
Based on the results of the NLPCA, an initial CFA model was specified with two orthogonal factors and a unique dimension associated with the AUD-C. Figure S2 displays the hypothesized loading path diagram and residual structure across Distress/Impairment, Distress/Activity, and Alcohol Use Concerns dimensions for the CFA. In addition to what is displayed, the mean structure of the items was estimated freely, contributing an additional 25 degrees of freedom at each time-point across intercepts (for the continuously-scaled measures) and thresholds (for ordinally-scaled measures). The fit of this least-constrained CFA model was adequate according to global fit indices (CFI =.985, RMSEA =.074, and SRMR =.068). Given this, equality constraints were subsequently evaluated based on the chi-square likelihood ratio test statistic by comparing the more-constrained models to this least-constrained parametrization.
The results of the chi-square likelihood ratio tests comparing model constraints against the least constrained model are presented in Table S1. Significant chi-square test statistics indicate the null hypothesis of equality across time-points was rejected, such that there was a difference in fit between the unconstrained model and the model given a set of equality constraints. As this table shows, equality of loadings and equality of both loading and residuals was retained across time-points. However, equality of the intercepts across measurement occasions was rejected based on the chi-square likelihood ratio test, suggesting participants' average values on the individual measures likely differed.
Based on the results of the chi-square likelihood ratio tests, the global fit indices and parameters estimated from the model including equality of loadings and residuals across time-points were interpreted. This model implied equal variance-covariance matrices among the observed measures over time and equal variances of the latent variables across time-points, while allowing the mean structure of the measures to vary. Based on the global fit indices, this constrained model fit the data well (CFI =.979, RMSEA = 0.071, SRMR =.083). The results of the CFA's thus lend support for the stability of the factors across time-points. The present findings suggest the variance-covariance matrix among the measures can be adequately reproduced based on a measurement model including one Distress/Impairment factor with loadings from all outcome measures except the AUD-C; a Distress/Activity factor with loadings onto the PHQ, PCL, absolute activity, and relative activity variables; and a third orthogonal Alcohol Use dimension represented by the AUD-C. These results also suggest that the mean structure among the items varied over time, indicating that while the patterns of variance-covariance observed at each time-point may have been similar, there were differences in participants' relative levels of reporting on each of the outcomes over time. The standardized loadings from the final CFA model are presented in comparison to the NLPCA loadings based on full sample in Figure S2. As this figure illustrates, the loadings were largely similar across modeling approaches; slight variations in loadings may reflect differences in their meaning across models, where NLPCA loadings reflect variance explained in the component by the items and CFA loadings reflect variance explained in the items by the factors.
## Figure S2. Dimensions and associated loadings from the NLPCA and CFA analyses.
NLPCA = Nonlinear principal components analysis. CFA = Confirmatory factor analysis. AUD-C = Audit - Consumption scale. GH = SF-36 General Health. PCL = PTSD Checklist. Absolute = Absolute activity. Relative = Relative activity. PF = Sf-36 Physical Functioning. Quality = Diminished life quality. SR = SF-36 Social Role. PHQ = Patient Health Questionnaire.
## Growth mixture modeling (GMM) results
The slope and intercept values associated with each of the GMMs are presented in Table S2. of the main manuscript supplement shows the latent growth trajectories associated with each class estimated for the Distress/Impairment and Distress/Activity multivariate outcomes. The latent growth trajectory associated with the Alcohol Use dimension is presented in Figure S3 of this supplement. The worst-faring Distress/Impairment class was distinguished by a profile of rising severity, whereas the worst-faring Distress/Activity and Alcohol Use Concerns classes were distinguished by sustained elevations. The GMMs on each univariate outcome paralleled the pattern of results found across the multivariate outcome domains; there tended to be larger classes of participants with fewer symptom complaints or functional concerns and a smaller class representing a subgroup of veterans with a more persistent or deteriorating course on a given outcome measure.
## Table S2.
## Measure Class Size
## Slope
## Intercept Class
## Multivariate Outcome Measures
Distress/Impairment Class 1 - high & rising distress/impairment 76 0.22* 5.96 Class 2 - low & stable distress/impairment 159 0.02 -4.63 Class 3 - moderate & rising distress/impairment 236 0.14**
2.30 Class 4 - slight & stable distress/impairment 273 0.02 -1.11
## Figure S3. Growth trajectories on the Alcohol Use Concerns outcome.
Model-estimated growth trajectories in each class are shown by the blue lines, with individual trajectories of participants in the class shaded in grey. Assessment point 0 corresponds to the baseline assessment.
## K-means clustering analysis results
Several metrics were used to select the optimal number of clusters (i.e., the value of \(k\)) that reflected participants probabilities of belonging to the worst-faring univariate growth trajectories. Six clusters were identified as optimal across several metrics when the numbers of clusters between \(k=2\) and \(k=10\) were evaluated. The ratio of within-cluster sum of squares to the between cluster sum of squares plateaued at \(k\) = 6 clusters, such that reductions in this ratio were fairly consistent each additional cluster added to the solution beyond \(k=6\) clusters and were larger for each increase in clusters prior to \(k=6\). Internal cluster indices also tended to converge on a 6-cluster solution. The gap statistic compares the observed clustering solution across different values of \(k\) clusters against solutions obtained with 1000 repeated bootstrap draws of values from simulated data with equivalent variability to one's actual data but no underlying clustering8. The resulting gap statistics and associated standard errors are then plotted and the optimal number of clusters is identified based on (a) the extent to which the gap statistic continues to increase after a value of \(k\) clusters and (b) the overlap in the standard-error of the gap statistic between \(k\) clusters and \(k+1\) clusters. As displayed in Figure S4, the gap statistic did not show further sharp increases following 6 clusters, and the 95% confidence intervals around the gap statistics associated with 6 and 7 clusters overlapped, suggesting a 6 cluster solution was optimal.
Other internal clustering indices calculated included the average silhouette width, Calinski-Harabasz index, and the Davies-Bouldin index. The average silhouette width provides an assessment of the average similarity of participants in each cluster to their assigned cluster as compared with other clusters, with larger values indicating higher similarity. The Calinski-Harabasz index assesses the ratio of between-cluster to within-cluster sums of squares, adjusted by sample size and the number of k-means clusters, with larger values indicating a higher ratio of between-cluster variability relative to within-cluster variability. Finally, the Davies-Bouldin index is computed as a function of the centroid diameters of clusters relative to the distances between clusters, and as such penalizes for the inclusion of very wide clusters spanning a range of possible values. Lower values on the Davies-Bouldin index are indicative of tighter clustering.
The average silhouette width and Davies-Bouldin indexes both agreed with the ratio of within-cluster to between-cluster sums of squares and the gap statistic in identifying 6 clusters as the best solution, whereas the Calinski-Harabasz index indicated two clusters was optimal. In prior experimental comparisons among internal cluster validity indices, the Calinski-Harabasz index has shown a more steeply declining accuracy with larger values of \(k\) as compared with certain other indices (i.e., the Silhouette and sums of squares methods), and the average silhouette width and gap statistics have been identified as among the most accurate in comparisons of clustering indices. As such, a solution with \(k\) = 6 clusters was selected for interpretation based on consensus across clustering indices. The resulting average probabilities of belonging to the worst-faring latent growth classes across presented by each of the 6 clusters in Table S3.
Based on the average probabilities of being assigned to the worst-faring latent growth classes across univariate outcomes, Cluster 1 appeared to reflect participants with the poorest faring trajectories across domains. By contrast, the other clusters identified appeared to reflect groups of participants who fared poorly on one or a few outcomes. Cluster 2 reflected participants with a higher probability of being in the latent growth class characterized by elevated alcohol consumption, Cluster 3 reflected participants with a high probability of being in the worst-faring physical activity classes, Cluster 4 reflected participants with a high probability of being in the worst-faring PTSD latent growth class and moderate probabilities of being in the worst-faring depression and social functioning classes, and Cluster 6 was characterized by participants with a high probability of being in the worst-faring life quality latent growth class. Participants in Cluster 5 appeared to have a low probability of being in any of the worst-faring classes across univariate outcome domains.
### Random forest classifier with feature selection results
Figure S5 displays the areas under the curve (AUCs) of the top one, two, five, 10, 20, 50, and all features identified in the random forest classifier as predictive of membership in the worst-faring distress/impairment class and k-means cluster at each assessment point. Class and cluster membership were predicted as binary outcomes indicating belonging to the class or cluster. The predictive features included at each assessment point represented all measures taken at that year of the study combined with all measures taken at prior years. The top 20 features were selected for interpretation as they showed comparable AUC values relative to larger numbers of features across assessment points. Further, these features tended to represent a similar group of predictive domains with the inclusion of additional measures at each assessment point (see Table 2 of the main manuscript).
## Figure S5. Plot of areas under the curve for subsets of the top features from the random forest classifier analysis.** AUC = Area under the curve. BASE = Baseline. Y1 - Y7 = Year 1 - Year 7. Lines represent area under the curve computed based on the random forest classifier analysis for the top 1, 2, 5, 10, 20, and 50 features as well as all features. Each time-point includes possible predictors from that time point and all time-points prior. **A**. Areas under the curve predicting membership for the worst-faring distress/impairment class. **B
Areas under the curve predicting membership for the worst-faring k-means cluster.
|
186064_file02 | ### Sample processing and PBMC isolation
Peripheral blood was collected from hospitalized COVID-19 patients upon enrollment in the study at day 0 for isolation of serum, plasma and peripheral blood mononuclear cells (PBMCs). When possible, patients who remained in the hospital were also sampled consecutively at day 3 and day 7 post-enrollment. Blood processing was performed in BSL2+ laboratory conditions as approved following safety assessments. Blood was centrifuged at 400 x \(g\) for 5 min to separate cells from plasma. Cells were resuspended in RPMI, underlaid with Ficoll and centrifuged at 400 x \(g\) for 30 min without break at room temperature. The PBMC layer was then washed twice in RPMI and PBMCs were viably cryopreserved in FBS + 10% DMSO for future use.
### Immuno-metabolic ex vivo flow cytometry staining
All flow cytometry antibodies used for phenotypic and metabolic analysis can be found in table S1. PBMCs from hospitalized COVID-19 patients, hospitalized flu patients, COVID-19 convalescent plasma donors (recovered) and healthy controls were used for phenotypic and metabolic assessment. Cryopreserved PBMCs were thawed in RPMI (Gibco) + 50% FBS (Atlanta Biologicals). Cells were washed once in PBS and immediately stained for viability with Bilegend Live/Dead Zombie NIR Fixable Viability Dye and BD Fc Block(tm) for 10 min at room temperature. Cell surface staining was performed in 100uL of 20% BD Horizon(tm) Brilliant Stain Buffer + PBS with surface stain antibody cocktail for 20 min at room temperature. Cells were fixed and permeabilized with eBioscience(tm) FoxP3/Transcription Factor Staining kit 1x Fixation/Permeabilization reagent for 20 min at room temperature. Cells were washed with 1x Permeabilization/Wash buffer. Intracellular staining (ICS) was performed in 100uL 1x Permeabilization/Wash buffer with ICS antibody cocktail for 45 min at room temperature. Cells were washed once with Permeability/Wash buffer then resuspended in 1% Paraformaldehyde for acquisition by flow. Samples were run on a 3 laser Cytek Aurora spectralflow cytometer. FCS files were analyzed using Flowjo v10 (10.6.2.) software. Manual gating strategies for both the T cell and B cell/Myeloid panels can be found in Fig S1. High-dimensional unbiased analysis of cell phenotypes was performed using Flojo plugins Downsample v3 and UMAP.
### FACS cell sorting & TCRseq
PBMCs from three hospitalized COVID-19 patients were stained with the following antibodies to sort on the identified T cell population of interest: Live/Dead Fixable Aqua, CD3 BV786, CD4 BV605, CD8 BV650, H3K27Me3 PE, Tomm20 AF405. PBMCs were thawed as described and immediately filtered through cell strainer capped FACS tubes to avoid excessive cell clumping. Cells were stained for viability with Live/Dead Fixable Aqua and Fc Block for 10 min at room temperature followed by surface staining with CD3, CD4 and CD8 in 20% Brilliant Stain Buffer for 20 min at room temperature. Cells were washed once with PBS. Fixation/permeabilization was performed using ice cold 70% ethanol for 10 min at -20degC. Cells were washed with 2mL PBS + 0.5% BSA + 5mM EDTA and centrifuged at 2000 rpm for 5 min. ICS was performed for markers H2K27me3 and Tomm20 and cells were stained for 45 min at room temperature. Staining reactions were washed once with 2mL PBS + 0.5% BSA + 5mM EDTA and resuspended in 500uL PBS + 0.5% BSA + SmM EDTA for sorting. CD4\({}^{*}\) and CD8\({}^{+}\) cells with H3K27me3\({}^{+}\)/Tomm20\({}^{+}\) or H3K27me3\({}^{-}\)Tomm20\({}^{-}\) phenotype were sorted by FACS on a Beckman Coulter MyFlo XDP Cell Sorter. Sorted cells were further processed for TCR sequencing. DNA was isolated on sorted populations using QiaAMP micro DNA kit (Qiagen) per the manufacturer's protocol. DNA was incubated overnight in the final column step and eluted in 25uL buffer before quality was assessed via NanoDrop. TCR VbCDR3 sequencing was performed using the deep resolution Immunoseq platform (Adaptive Biotechnologies).
### Single-cell RNAseq
Single cell RNA-seq libraries were prepared from viably frozen PBMCs using the 10X Chromium platform, and 5' DGE library preparation reagents and kits according to the manufacturer's recommended protocols (10X Genomics, Pleasonton, CA). Briefly, viably frozen PBMCs were rapidly thawed at 37degC and were washed twice in DPBS to remove any dead cells and debris. Cells were counted manually with a hemocytometer and re-suspended in 0.04% BSA in DPBS to a final concentration of 1000 cells/uL. Cells and gel beads were loaded on a Chromium Next GEM Chip G to generate single cell emulsions using the 10x Chromium controller instrument with 5' Library Kit v1.1 reagents (PN1000202, PN1000127, PN1000167, PN1000020, PN1000213). Reverse transcription, cDNA amplification, library preparation, and sample index labelling were performed according to manufacturer's protocols. Libraries were sequenced on a NovaSeq 6000 instrument to achieve a target depth of ~50,000 reads per cell. Sequencing data were aligned and pre-processed to generate cell x gene counts matrix for each sample and also aggregate across samples using the cellranger software (v.3.1.0). These data were then imported into Seurat package (v3.1) for subsequent analysis. Data was clustered and visualized using the UMAP method. To analyze T cells, data was subsetted to include only CD3\({}^{+}\) cells. The newly subsetted data was then analyzed for differentially expressed genes between COVID-19 and healthy control samples. The gene list was then evaluated for functional enrichment of GO biological processes gene sets using PANTHER (v. 15.0) with Bonferroni correction for multiple hypothesis testing. GO terms were then condensed using ReviGO with a cutoff of 0.4. The fold enrichment determined by PANTHER was visualized. For myeloid cells, total PBMCs were first clustered using UMAP analysis. Clusters containing myeloid cells were subsetted and re-clustered. One cluster was derived predominantly from three COVID-19 patients that had high levels of CPT1a\({}^{*}\)VDAC\({}^{+}\) myeloid cells as determined by flow cytometry. To better understand the functionality of these cells specifically, the myeloid cells from these three donors were further analyzed, revealing 4 unique clusters. Clusters 1 and 3 were analyzed for differential gene expression compared to all other myeloid cells due to the high expression of VDAC and CPT1a, matching the flow cytometry data. The gene list was then evaluated for functional enrichment using the statistical over representation with Bonferroni correction using PANTHER (v. 15.0) and GO biological processes as gene sets. GO terms were then condensed using ReviGO with a cutoff of 0.4. The fold enrichment determined by PANTHER was visualized using JMP 14 Pro.
### Electron Microscopy
For transmission electron microscopy (TEM) PBMCs were thawed as described and washed once with PBS. Cells were chemically fixed as a cell pellet in 3% glutaraldehyde in 0.1M sodium phosphate buffer (pH 7.3) for 24 hours at 4\({}^{\circ}\)C, rinsed in 0.1M sodium phosphate buffer, and post-fixed in 1% osmium tetroxide in the same buffer for 1 hour at room temperature. The cells were dehydrated in a graded series of ethanol, transitioned with toluene, followed by infiltration and embedding in epoxy resin EPON 812 (Polysciences,Inc.). Following heat polymerization of the EPON blocks, semi-thin sections of 1000-2000nm thickness were cut and stained with 1% toluidine blue for visualization by light microscopy. Thin sections of selected areas were cut at a thickness of approximately 70-100nm (pale gold interference color) with a diamond knife (DIATOME), placed on 200 mesh copper grids, and dried at 60\({}^{\circ}\)C for 10 minutes. To impart electron contrast, the sections were stained with a saturated solution of uranyl acetate for 10 minutes followed by Reynold's lead citrate for 2 minutes. The sections were examined with a transmission electron microscope (JEOL JEM-1400 Plus TEM) using a lanthanum hexaboride cathode (DENKA) operating at an accelerating voltage of 60-80 keV. Images were acquired using an AMT NanoSprint12: 12 Megapixel CMOS TEM Camera (Advanced Microscopy Techniques).
### Immunofluorescence
For fluorescence detection of cytochrome \(c\) and CD3, cells were stained as described previously. Briefly, PBMCs were thawed and immediately placed on a glass microscope slide using a Cytospin 2 centrifuge (Shandon). After centrifugation, the cell monolayer was fixed with 10% formalin and air-dried. Cells were permeabilized with 0.3% Triton X-100 in PBS for 10 min and blocked with 3% BSA for 45 min. Cells were then incubated with primary antibodies against cytochrome \(c\) (BD Biosciences, cat.no. 556432) and CD3 (Dako, cat.no. A0452) at 4\({}^{\circ}\)C overnight. Fluorescent staining was performed for 30 min at room temperature using highly cross-adsorbed Alexa Fluor 488 and 594 secondary antibodies (Invitrogen). Cells were washed three times in PBS after each incubation step. Following, cells were covered with mounting medium containing DAPI nuclear stain (Sigma-Aldrich) and sealed with a coverslip. Imaging was performed with a DeltaVision Elite microscope system (GE Healthcare), equipped with a Scientific CMOS camera (Chip size: 2560 x 2160 pixels), an UltraFast solid-state illumination, a 60x (N.A. 1.42) oil immersion objective and the UltimateFocus module. Single image slices were acquired and deconvolved (Softwox, Applied Precision). Image preparation and analysis was performed using Fiji ([http://fiji.sc/Fiji](http://fiji.sc/Fiji)). Intensity profiles were measured using 'Analyze' and 'Plot Profile' on contrast adjusted images. Fluorescence intensities were normalized and plotted in colors corresponding to displayed images.
For fluorescence detection of MitoTracker Deep Red Dye (ThermoFisher, M22426) PBMCs were isolated fresh and labeled with MitoTracker Deep Red Dye for 20 minutes at 37\({}^{\circ}\)C in complete media. Cells were then washed with PBS and stained with CD3 FITC (Clone SK7, BD Biosciences). Slides were coated with 50ug/ml Poly-D Lysine (Sigma, P0899) and vigorously washed before addition of cells. Cells on slides were fixed with 4% paraformaldehyde (methanol free, Thermo Scientific, 28906) for 10 min before washing with PBS. Slides were then blocked in 10% goat serum (Gibco, 16210064) followed by staining with goat anti-mouse AF488 IgG(ThermoFisher, A-11017). Slides were mounted with Slow Fade Diamond anti-fade reagent with DAPI (Invitrogen, S36964). Cells were imaged with an LSM 880-Airyscan confocal microscope equipped with a PlanApochromat 63x/1.4 NA oil-immersion objective (Carl Zeiss). Images were processed with Zen Black software (Carl Zeiss).
_In vitro_ T cell stimulations
PBMCs were thawed as described above, cells counted, and resuspended to 1x10\({}^{6}\) cells/mL in complete media (R10; RPMI 1640/heat inactivated 10% FBS). Cells were plated in 96-well U bottom plates in the presence or absence of anti-CD3/28 stimulating antibodies (0.1mg/mL, Miltenyi), and in the presence or absence of Z-VAD-FMK (60nM, Cell Signaling Technology) or VBIT-4 (300nM, Fischer Scientific). The exact number of cells plated were stained directly _ex vivo_ to calculate percent survival (number of T cells at day 0/number of T cells at 48 hours). Plates were cultured at 37\({}^{\circ}\)C for 48 hours and cells were stained for flow cytometry. Flow staining was performed as described above using the limited panel consisting of CD3 BV786 (BD Biosciences, cat. no. 563800), CD8 BV480 (BD Biosciences, cat. no. 566121), CD4 PE Cy5 (Biological, 317412), H3K27me3 PE (CST, cat. no. 40724) and VDAC1 AF532 (Abcam, cat. no. ab14734).
### Feature importance and prediction analysis
Using the percentage of each cell population as features and the patients as samples, random forests (RF) were trained to classify patients into different groups using R package caret. The prediction performance was evaluated using the receiver operating characteristic (ROC) curve derived from leave-one-out cross-validation (LOOCV). Within each fold of LOOCV, the optimal model parameter was determined using a nested LOOCV within the training samples. Feature importance analysis was performed based on the RF models trained using all samples. A feature's importance was calculated using the decrease of accuracy after permuting the corresponding feature in out of bag samples in the RF. Features are ordered by their importance in predicting acute COVID-19 vs. Healthy controls, Severe COVID-19 vs. Flu, Severe COVID-19 vs. Recovered, and Severe vs. Mild COVID-19. For predicting COVID-19 severity, basic clinical variables including age, sex, and BMI were also added as features to RF and feature importance analysis was rerun for predicting Severe vs. Mild COVID-19. Based on the feature importance, two prediction models were rebuilt for predicting severity (Severe vs. Mild COVID-19) using the top-five-ranked features (i.e., percentage of VDAC\({}^{+}\)CPT1a\({}^{+}\) myeloid cells, PDC, and H3K27Me3\({}^{+}\)VDAC\({}^{+}\)CD4\({}^{+}\) cells, sex, and BMI) or the basic clinical information only (i.e., age, sex, and BMI). The two models' performances were compared based on ROC.
### Statistical analysis
Statistical calculations were performed in GraphPad Prism 8. Data are shown as mean\(\pm\)SEM unless otherwise noted. Comparison between conditions were performed using non-parametric tests as indicated in figure legends. A p value less than 0.05 was considered significant.
## Table S2. Characteristics of study subjects.
\begin{tabular}{l l l l l l} & COVID-A & Influenza & COVID-R & Acute HCV & Chronic HCV \\
## Demographics
& & & & & \\ Male N (\%) & 19 & 9 & 6 & 2 & 7 \\ Female N (\%) & 19 & 12 & 4 & 4 & 3 \\ Mean age (range) & 59.7 & 46.4 & 47.8 & 25.8 & 30.5 \\ \end{tabular}
## Fig. S1. Gating strategies for flow cytometry panels.
Representative flow plots from an acute COVID-19 subject show gating of all peripheral immune cells subsets assessed by one of two immuno-metabolic panels **(A)** T cell panel or **(B)** Myeloid and B cell panel.
Fig. S2. **Frequencies of T cell subsets and activation markers reveal few COVID19-specific differences. (A)** Frequency of indicated cell subset as percent of total live cells. Each dot represents one individual, significance tested using unpaired Kruskal-Wallis test compared to healthy control. (B) CD4:CD8 ratio. Each dot represents one individual, significance tested using unpaired Kruskal-Wallis test compared to healthy control. (C) Frequency of CD4+ and (D) CD8+ T cell subsets shown as percent of CD4 or CD8, respectively. Each dot represents one individual, significance tested using unpaired Kruskal-Wallis test compared to healthy control. (E) UMAP projection performed on a subset of COVID-A (blue) and HC subjects (grey). The two markers discovered to drive segregation of the COVID-A and HC cluster, H3K2ThrMe3 and VDAC, are depicted as histogram overlays and MFI heatmap overlays on UMAP projection. (F-H) UMAP projection of MFI heatmap overlays of indicated proteins. Significance is indicated as compared to healthy control, *p<0.05, **p<0.01, ***p<0.001, ***p<0.0001, if no significance is indicated the test is non-significant.
## Fig. S3. H3K27me3+VDAC+ T cell frequencies change over time and after cryopreservation. (A) Representative plots show increased H3K27me3+VDAC+ CD8+ T cells in a COVID-A subject at day 0 enrollment compared to day 90 in the same subject after recovery. (B) Frequency of H3K27me3+VDAC+ T cells from 8 total COVID-A subjects with samples available at day 0 enrollment and after recovery for CD8+ T cells (left) and CD4+ T cells (right). Significance tested using Wilcoxon matched-pairs signed rank test. (C) Representative plots show increased H3K27me3+VDAC+ CD4+ T cells in a COVID-A subject with cells stained fresh compared to after cryopreservation. (D) Frequency of H3K27me3+VDAC+ T cells from 4 total COVID-A subjects tested at day 0 enrollment stained fresh or after cryopreservation for CD8+ (left) and CD4+ (right) T cells. Significance tested using Wilcoxon matched-pairs signed rank test.
## Fig. S4. B cell frequencies and phenotypes differ in the memory compartment in COVID-19. (A-D) Frequency of indicated cell subset as percent of total live cells. Each dot represents one individual, significance tested using unpaired Kruskal-Wallis test compared to healthy control. (E-F) UMAP projection performed on a subset of COVID-A (blue), hospitalized Flu (red) and HC subjects (grey) (E) or COVID-A (blue) and COVID-R (light blue) (F). Manual gating overlays on UMAP projection color code total B cell (top) and memory B cell (bottom) subsets. UMAP projection MFI heat maps of indicated proteins. Significance is indicated as compared to healthy control, "p<0.05, "p<0.01, "**p<0.001, "***p<0.0001, if no significance is indicated the test is non-significant.
## Fig. S5. Unique NK cell population in COVID-A subjects identified by high dimensional phenotyping analysis.
## (A)** Frequency of indicated cell subset as percent of total live cells. Each dot represents one individual, significance tested using unpaired Kruskal-Wallis test compared to healthy control. **(B)** UMAP projection of total NK cells performed on a subset of COVID-A (blue), hospitalized Flu (red) and HC subjects (grey) (left). Arrow indicates unique COVID-A specific cluster identified. Manual gating overlays on UMAP projection (top) color code CD56+ (purple) and CD56 bright (pink) cells. UMAP projection MFI heat maps of indicated proteins are shown right. **(C)** Similar analysis as in **(B)
Significance is indicated as compared to healthy control, "p<0.05, "p<0.01, "***p<0.001, "***p<0.0001, if no significance is indicated the test is non-significant.
## Fig. S6. Myeloid subsets in viral infections.
## (A-C)** Frequency of indicated cell subset as percent of total live cells. Each dot represents one individual, significance tested using unpaired Kruskal-Wallis test compared to healthy control. **(D)** Frequency of indicated cell subset as percent of total live cells. To assess how dendritic cell frequencies changed in recovery, significance was tested using unpaired Kruskal-Wallis test comparing all possible combinations. **(E)** UMAP projection of total myeloid cells performed on a subset of hospitalized Flu (red) and HC subjects (grey). Manual gating overlays on UMAP projection color code myeloid and B cell subsets in the UMAP space. MFI histogram overlays of CD14+ myeloid populations of indicated proteins for hospitalized Flu (red) and HC (grey). Significance is indicated as compared to healthy control **(A-C)**, or between groups **(D)
*pC0.05, **p<0.01, ***pC0.001, ****p<0.0001, if no significance is indicated the test is non-significant.
## Fig. S7. Metabolic profile of immune cells predicts disease status. (A)
Receiver operating characteristic (ROC) curves for predicting different groups of patients (i.e., COVID-A vs. Healthy controls, Severe COVID-A vs. COVID-R, Severe COVID-A vs. Flu, and Severe vs. Mild COVID-A). The area under the curve (AUC) is indicated. (B) Feature importance analysis after adding basic clinical information (i.e., age, sex, and BMI) to the RF model for classifying severe vs. mild COVID-A. (C) ROC curves for comparing the performance of prediction models trained using the top-five-ranked features (i.e., top5) and basic clinical information (i.e., baseline) for classifying severe vs. mild COVID-A. AUC is indicated.
|
186221_file04 | ## Provide a description of the project with enough detail for the determination. Enter "N/A" where appropriate.
Describe the purpose, study question, study objectives or aims for this project:
The study question is whether diversity (age-gender-race-ethnicity) among matriculated residents in Internal Medicine Residency Program at Wayne State University/Ascension Providence Rochester Hospital over three years correlates with diversity (age-gender-race-ethnicity) among interviewed applicants and GME applicants for Internal Medicine Residency Program at Wayne State University/Ascension Providence Rochester Hospital for the same three years (via ERAS 2018-2020). The ERAS portal based database will be accessed for all the GME applicants as well as all the interviewed applicants for three years so as to non-identifiably tabulate their age group, gender, race and ethnicity and thereafter the matriculated residents for the same three years will also be non-identifiably tabulated per their age group, gender, race and ethnicity. Thereafter, the GME applicants' characteristics' proportions regarding their age group, gender, race and ethnicity will be correlated to the interviewed applicants' characteristics' proportions regarding their age group, gender, race and ethnicity which in turn will be correlated to the matriculated residents' characteristics' proportions regarding their age group, gender, race and ethnicity. These Pearson correlation coefficients (-1 to +1) for age group, gender, race and ethnicity will be able to inform how diversity among matriculated residents is correlating with diversity among interviewed applicants and thereto with diversity among GME applicants in Internal Medicine Residency Program at Wayne State University/Ascension Providence Rochester Hospital.
Describe how the results will be used including any plans for presentation or publication:
The results of this program evaluation/quality improvement/quality assurance project will be presented at local/regional/national conferences and/or published at peer-reviewed journals so as to share this local data's results with medical educators and clinical researchers globally.
State the location(s) where research activities will take place:
Internal Medicine Residency Program at Wayne State University/Ascension Providence Rochester HospitalDescribe the participants (if applicable) for the project:
The GME applicants' (along with interviewed applicants' and matriculated residents') characteristics accessible directly from ERAS portal based database for Internal Medicine Residency Program at Wayne State University/Ascension Providence Rochester Hospital
Describe the data/information that would be collected for the study and the source(s) of that data:
The GME applicants' (along with interviewed applicants' and matriculated residents') characteristics will be non-identifiably tabulated only for their age group, gender, race and ethnicity.
Describe how data will be obtained (e.g. survey, interview, observation, testing, review of existing records, etc.):
The GME applicants' (along with interviewed applicants' and matriculated residents') characteristics will be accessed directly from ERAS portal based database for Internal Medicine Residency Program at Wayne State University/Ascension Providence Rochester Hospital
Describe whether or not the data will include individually identifying information (e.g. name, DOB, MRN, email address, other codes; etc.):
Non-identifiable tabulations of age group, gender, race, ethnicity of GME applicants (along with interviewed applicants and matriculated residents) for three years 2018-2020
Could the identities of participants be known to, or be readily ascertained by the investigators?
Yes
No
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Decedents: Research limited to death records, autopsy materials or cadaver specimens.
|
186908_file02 | ### Statistical Analysis (additional details)
Due to convergence issues when using mixed effects models with a random effect of family, we controlled for family relatedness using a random subset of the sample that only included singletons. To ensure the stability of our findings we ran all models in 100 random subsamples of singletons and took the median of effect sizes across all iterations. We calculated effect sizes as \(R^{2}\) type III sum of squares using Nagelkerke's correction to Cox and Snell's formulation10,11. P-values were calculated using a log likelihood ratio test and significant associations determined using a falsediscovery rate (FDR) significance threshold calculated using the Benjamini-Hochberg method. This correction was made within each ancestry group and model type (univariate or multivariate) - i.e. correcting for 15 genetic/familial predictors and 41 behavioral assessments = 615 multiple tests. GLMs were implemented using the R stats package. Model output for all averaged models is downloadable as csv files (see Statistical Data Tables).
The distribution of each of the DVs fell into three categories a) normal, b) right skewed, zero inflated or c) binary, and we appropriately modelled each of these distributions differently. A) For normal distributions we further ensured normality by rank normalizing (as was performed for PRS), and fit GLMs using the default gaussian family. B) For the right skewed, zero inflated distributions we fit using a gamma distribution with a log link function, first ensuring that each distribution was non-negative to ensure correct bounds for the link function. C) For binary variables we performed logistic regression. KSADS symptom scores (except for the youth and caregiver reported total symptom score) were binarized using a median split, as they exhibited convergence issues when treated as continuous.
### Associations across ancestry strata
As PRS were trained on European individuals and ABCD has high ancestral admixture, the main analyses were performed in a European only sample (European Genetic Ancestry Factor (EUR-GAF)>0.9) and supplementary analyses were conducted in the full sample and a non-European sample (EUR-GAF<0.9) to check for consistency across ancestral groups. Allele frequency differences across ancestral groups can lead to spurious results when PRS trained on a single ancestral group are applied to samples of different or mixed genetic ancestry. Supplementary shows the same univariate and multivariable PRS and FH associations in the full sample (n=9,168 with complete genetic data) and a non-European sample (n=3,964). There was a similar pattern of associations for the full sample compared to the Europeans, but with far fewer significant associations for the non-European sample, despite very similar prevalence rates across KSADS diagnoses for the three samples (Supplementary Table 1 and 2). Supplementary shows broadly consistent analogous associations between European and non-European groups; however, there was moderate dispersion observed between estimated effect sizes between groups. These effects are difficult to interpret as the discovery sample only included European individuals. These inconsistencies once again demonstrate the issues of portability of GWAS between ancestry groups.
\begin{table}
\begin{tabular}{l l l l l} Questionnaire & Variables Analyzed & DEAP Variable Names & Informant & Domain \\ Child Behavior & CBCL Aggressive & cbl.scr.syn.aggressive\_r & Caregiver & Externalizing \\ Checklist (CBCL) & CBCL Anxious/Depressive & cbl.scr.syn.anordep.f & Internalizing \\ & CBCL Rule-breaking & cbl.scr.syn.athebreadx.r & Externalizing \\ & CBCL Inattention & cbl.scr.syn.attention\_r & Externalizing \\ & CBCL Social Problems & cbl.scr.syn.social.r & Developmental \\ & CBCL Thought Problems & cbl.scr.syn.thought.r & Psychosis-related \\ & CBCL Somatic Complaints & cbl.scr.syn.somatic\_r & Internalizing \\ & CBCL Withdrawn/Depressive & cbl.scr.syn.withdep.\_r & Internalizing \\ & CBCL Total Problems & cbl.scr.syn.lottopb.\_r (sum of all sub-scales) & NA \\ General Behavior & General Behavior Inventory - & pgbi\_ss\_score\_p & Caregiver & Psychosis-related \\ Inventory & Mania & & & \\ Prosocial Behavior & Prosociality & prosocial\_ss\_mean & Youth & Prosociality \\ Survey (youtt) & & & & \\ \hline \begin{tabular}{l} Prodromal \\ Questionnaire Brief \\ Version (PO-B) \\ \end{tabular} &
\begin{tabular}{l} Predromal Psychosis \\ Severity Score \\ \end{tabular} & prodrom\_psych\_ss\_severity\_score & Youth & Psychosis-related \\ \hline UPPS-P for Children & UPPS Lack of Perseverance & upps\_ss\_lack\_of\_perseverance & Youth & Externalizing \\ Short Scale & UPPS Lack of Planning & upps\_ss\_lack\_of\_planning & & Externalizing \\ UPPS Positive Urgency & upps\_ss\_positive\_urgency & & Externalizing \\ UPPS Negative Urgency & upps\_ss\_negative\_urgency & & Externalizing \\ UPPS Sensation Seeking & upps\_ss\_sensation\_seeking & & Externalizing \\ \hline Behavioral inhibition & BisBAS Drive & bisbas\_ss\_bs\_bs\_drive & Youth & Externalizing \\ and behavioral & BisBAS Fun Seeking & bisbas\_ss\_bs\_bs\_fs & & Externalizing \\ activation (BisBAS) & BisBAS Reward & bisbas\_ss\_bs\_nr & & Externalizing \\ scale & Responsiveness & bisbas\_ss\_bis\_sum & & Internalizing \\ & BisBAS Inhibition & & & \\ Kiddie Schedule for & KSADS Symptoms & Modules 1 (depressive disorder) \& 3 & Caregiver \& & Internalizing \\ Affective Disorders and & Depression & (distruptive mood dysregulation) & Youth & Psychosis-related \\ Schizophrenia (KSADS) & KSADS Symptoms Bipolar & Module 2 (all bipolar subtypes) & Caregiver \& & Internalizing \\ categorical diagnostic & KSADS Symptoms Anxiety & Module 8 (social anxiety) \& 10 (general & Youth & Internalizing \\ assessments & KSADS Symptoms OCD & Anxiety) & Caregiver \& & Internalizing \\ KSADS Symptoms Eating & Module 11 (OCD) & Youth & Externalizing \\ Disorder & Module 13 (eating disorders) & Caregiver & Externalizing \\ KSADS Symptoms & Module 14 (ADHD) & Caregiver & Developmental \\ ObsReginal/Control/Control & (control disorder) & Caregiver & Internalizing \\ KSADS Symptoms & Module 18 (other developmental disorder & Caregiver & Internalizing \\ Developmental Disorders & NOT autism) & Caregiver & NA \\ KSADS Symptoms PTSD & Module 21 (PTSD) & Caregiver \& & \\ KSADS Symptoms & Module 22 (sleep problems) & Youth & \\ KSADS Symptoms & Module 23 (suicidality) & Caregiver \& & \\ Suicidality & Summary score across all modules & Youth & \\ KSADS Total Symptoms & & & Caregiver \& \\ Youth & & & \\ \hline NIH Toolbox® & NIH Toolbox® Fluid & nihtbx\_cryst\_uncorrected & Youth & Cognition \\ Composite Score & nihtbx\_fluidcomp\_uncorrected & Youth & Cognition \\ NIH Toolbox® Crystallized & & & Youth & Cognition \\ Composite Score & & & Youth & Cognition \\ \hline \end{tabular}
\end{table}
Table 1: DEAP variable names for all behavioral variables analysed in this study. The KSADS symptom scores were calculated by summing all of the symptom items in each KSADS module indicated in the table. Symptom items were all binary (1 or 0). Both past and present symptoms were included in the summary scores, therefore summary scores represent a lifetime assessment of symptoms associated with a particular disorder. Symptom summary scores were calculated by summing the symptoms within each module (the exception was for ODD and CD which were summed together). All KSADS symptom scores were then coded as binary using a median split for statistical modeling. Behavioral domain represents broad categories of construct similarity used for data visualization. R code to extract and process the variables used for this analysis will be published on the ABCD study GitHub: [https://github.com/ABCD-STUDY/](https://github.com/ABCD-STUDY/).
\begin{tabular}{p{42.7pt}|p{341.4pt}|p{341.4pt}} Behavior & DEAP & Lead Question \\ & Variable & \\ & Name Lead Q & \\ \hline Alcohol use & **famk\_4\_p** & Has ANY blood relative of your child ever had any problems due to alcohol, such as: Marital separation or divorce; Laid off or fired from work; Arrests or DUIs; Alcohol harmed their health; in an alcohol treatment program; Suspended or expelled from school 2 or more times; Isolated self from family, caused arguments or were drunk a lot. \\ \hline Drug use & **famk\_history**, & Has ANY blood relative of your child ever had any problems due to drugs, such as: Marital separation or divorce; Laid off or fired from work; Arrests or DUIs; Drugs hammed their health; in a drug treatment program; Suspended or expelled from school 2 or more times; Isolated self from family, caused arguments or were high a lot. \\ \hline Depression & **famk\_history**, & Has ANY blood relative of your child ever suffered from depression, that is, have they felt so low for a period of at least two weeks that they hardly ate or slept or couldn't work or do whatever they usually do? \\ \hline Maria & **famk\_7\_yes** & Has ANY blood relative of your child ever had a period of time when others were concerned because they suddenly became more active day and night and seemed not to need any sleep and talked much more than usual for them? \\ \hline Psychosis (visions) & **famk\_8\_yes** & Has ANY blood relative of your child ever had a period lasting six months when they saw visions or heard voices or thought people were spying on them or plotting against them? \\ \hline Conduct problems (trouble) & **famk\_9\_yes** & Has ANY blood relative of your child been the kind of person who never holds a job for long, or gets into fights, or gets into trouble with the police from time to time, or had any trouble with the law as a child or an adult? \\ \hline Nerves & **famk\_10\_yes** & Has ANY blood relative of your child ever had any other problems with their nerves, or had a nervous breakdown? \\ \hline Seen a therapist (professional) & **famk\_11\_yes** & Has ANY blood relative of your child ever been to a doctor or a counselor about any emotional or mental problems, or problems with alcohol or drugs? \\ \hline Hospitalized & **famk\_12\_yes** & Has ANY blood relative of your child ever been hospitalized because of emotional or mental problems, or drug or alcohol problems? \\ \hline Suicide & **famk\_13\_yes** & Has ANY blood relative of your child ever attempted or committed suicide? \\ & **s\_no** & \\ \hline \end{tabular}
## Supplementary Table 2. Description of the family history variables used and the questions asked. If the participant had ANY blood relative who endorsed the described behavior the "DEAP variable name Lead Q" was endorsed with a 1 (if not = 0).
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|} \hline & \multicolumn{3}{c|}{**PRS Effect (beyond FH + covariates)**} & \multicolumn{3}{c|}{**FH Effect (beyond PRS + covariates)**} & \multicolumn{3}{c|}{**PRS + FH Effect (beyond covariates)**} \\ \hline DV & \(\Delta R^{2}\) & \(\chi^{2}\) & P(\(\chi^{2}\)) & \(\Delta R^{2}\) & \(\chi^{2}\) & P(\(\chi^{2}\)) & \(\Delta R^{2}\) & \(\chi^{2}\) & P(\(\chi^{2}\)) \\ \hline
## BISBAS Drive (Y)
& 0.14\% & 4.92 & 1.08E-01 & 0.20\% & 7.21 & 2.11E-01 & 0.35\% & 12.37 & 9.07E-02 \\ \hline
## BISBAS Fun Seeking (Y)
& 0.16\% & 7.64 & 2.22E-01 & 0.26\% & 12.25 & 3.42E-01 & 0.43\% & 20.63 & 2.20E-01 \\ \hline
## BISBAS Reward
& 0.37\% & 33.05 & 6.39E-03 & 0.12\% & 10.33 & 8.88E-01 & 0.49\% & 43.81 & 1.24E-01 \\ \hline
## BISBAS Inhibition (Y)
& 0.25\% & 10.37 & 5.57E-02 & 0.41\% & 17.08 & 5.87E-02 & 0.66\% & 28.04 & 1.52E-02 \\ \hline
## UPPS Lack of Perseverance
& 0.17\% & 6.07 & 3.05E-02 & 0.34\% & 12.18 & 5.86E-03 & 0.54\% & 19.33 & 5.85E-04 \\ \hline
## UPPS Lack of Planning (Y)
& 0.35\% & 13.74 & 9.14E-03 & 0.30\% & 11.78 & 2.17E-01 & 0.68\% & 26.66 & 1.31E-02 \\ \hline
## UPPS Positive Urgency (Y)
& 0.10\% & 4.31 & 1.61E-01 & 0.33\% & 14.73 & 2.55E-03 & 0.46\% & 20.35 & 1.11E-03 \\ \hline
## UPPS Negative Urgency (Y)
& 0.30\% & 11.98 & 2.35E-02 & 0.27\% & 10.91 & 2.96E-01 & 0.60\% & 24.25 & 3.50E-02 \\ \hline
## UPPS Sensation Seeking (Y)
& 0.24\% & 10.92 & 6.17E-02 & 0.26\% & 11.79 & 3.30E-01 & 0.49\% & 22.31 & 1.22E-01 \\ \hline
## CBCL Total Problems (C)
& 0.61\% & 21.00 & 6.50E-05 & 5.27\% & 190.82 & 1.86E-46 & 6.17\% & 225.69 & 2.73E-52 \\ \hline
## CBCL Aggressive (C)
& 0.32\% & 22.45 & 1.12E-02 & 2.34\% & 169.31 & 2.51E-19 & 2.81\% & 204.09 & 2.72E-21 \\ \hline
## CBCL Anxious/Depressive (C)
& 0.18\% & 11.42 & 9.41E-02 & 3.12\% & 197.88 & 8.37E-30 & 3.43\% & 218.15 & 2.96E-30 \\ \hline
## CBCL Rule Breaking (C)
& 0.69\% & 47.10 & 3.10E-04 & 2.66\% & 185.05 & 3.21E-15 & 3.73\% & 261.84 & 3.43E-20 \\ \hline
## CBCL Inattention (C)
& 0.65\% & 44.36 & 2.05E-06 & 2.03\% & 140.32 & 1.02E-18 & 2.85\% & 198.87 & 4.03E-25 \\ \hline
## CBCL Social Problems (C)
& 0.26\% & 18.12 & 9.82E-02 & 2.62\% & 189.85 & 1.90E-16 & 3.04\% & 220.84 & 3.97E-17 \\ \hline
## CBCL Thought Problems (C)
& 0.26\% & 15.50 & 3.54E-02 & 3.06\% & 188.48 & 3.28E-26 & 3.43\% & 212.51 & 3.99E-27 \\ \hline
## CBCL Somatic Complaints (C)
& 0.42\% & 26.50 & 1.25E-03 & 2.65\% & 171.39 & 6.51E-23 & 3.17\% & 205.64 & 2.30E-25 \\ \hline
## CBCL Withdrawn/Depressive** (C)
& 0.23\% & 16.31 & 1.84E-01 & 2.31\% & 168.37 & 1.43E-12 & 2.59\% & 189.32 & 3.09E-12 \\ \hline
## Psychosis Severity Score (Y)
& 0.59\% & 61.65 & 1.25E-03 & 1.00\% & 104.03 & 2.04E-04 & 1.72\% & 180.49 & 4.47E-07 \\ \hline
## Mania (C)
& 0.23\% & 18.83 & 4.06E-01 & 2.99\% & 250.72 & 1.24E-10 & 3.41\% & 286.29 & 2.19E-10 \\ \hline
## Prosociality (Y)
& 0.20\% & 6.24 & 1.33E-01 & 0.20\% & 6.42 & 5.60E-01 & 0.42\% & 13.10 & 2.75E-01 \\ \hline
## KSADS Symptoms Depression
& 0.09\% & 4.11 & 5.33E-01 & 1.99\% & 88.73 & 9.55E-15 & 2.15\% & 95.81 & 8.07E-14 \\ \hline
## KSADS Symptoms Bipolar (C)
& 0.36\% & 16.14 & 6.47E-03 & 1.39\% & 61.88 & 1.60E-09 & 1.86\% & 82.91 & 2.05E-11 \\ \hline
## KSADS Symptoms Anxiety (C)
& 0.30\% & 13.43 & 1.97E-02 & 2.35\% & 105.28 & 4.76E-18 & 2.64\% & 118.11 & 4.39E-18 \\ \hline
## KSADS Symptoms OCD (C)
& 0.06\% & 2.43 & 7.87E-01 & 1.47\% & 65.43 & 3.35E-10 & 1.52\% & 67.70 & 1.14E-08 \\ \hline
## KSADS Symptoms Eating
& 0.04\% & 1.87 & 8.66E-01 & 0.42\% & 18.51 & 4.69E-02 & 0.46\% & 20.33 & 1.60E-01 \\ \hline
## KSADS Symptoms ADHD (C)
& 0.28\% & 12.26 & 3.14E-02 & 1.92\% & 85.45 & 4.26E-14 & 2.29\% & 102.48 & 4.42E-15 \\ \hline \end{tabular}
**Supplementary Table 3.**_Unique and shared variance across behaviors predicted by PRS and FH. Change in R\({}^{2}\)% is calculated by comparing the R\({}^{2}\) from a reduced model with covariates of no interest and genetic predictors of no interest, and a full model including the nested reduced model plus the genetic predictors of interest. The \(\chi^{2}\) statistic and p-value from the likelihood ratio test comparing these models is also displayed.
Plot of SNP heritability (\(\hat{n}^{2}_{\textit{syn}}\)) and log(sample size) for each discovery GWAS sample, as reported in discovery papers, used to calculate PRS.
## Supplementary
Pairwise spearman correlations between all of the behavioral phenotypes in the European sample pre-residualized for covariates of no interest including socioeconomic status (SES). Caregiver reported measures were more strongly associated with each other than youth reported measures.
**Supplementary Figure 3.**_Pairwise spearman correlations between all of the genetic risk measures in the European sample pre-residualized for covariates of no interest including SES. FH measures were more strongly associated with each other than the PRS. The FH measures were moderately correlated with one another. There were limited associations between FH and PRS._
## Supplementary Behavioral associations in the European sample without controlling for SES.
Univariate (left) and multivariable (right) associations between the genetic predictors (PRS and Family History) and the behavioral phenotypes, controlling for covariates of no interest, but not controlling for SES. The main differences across the associations with and without controlling for SES were found with the cognitive performance measures. Many associations between genetic risk for psychopathology and cognitive function only reached threshold for statistical significance when SES was not taken into account due to the shared variance between sociodemographic factors and cognition.
## Supplementary
-_log(P-values) for all multivariable associations after controlling for SES (Y-axis) and before controlling for SES (X-axis) in the European sample. The pattern of associations was very similar with and without controlling for SES, however controlling for SES attenuated many of the associations._
## Supplementary Behavioral associations across ancestry strata.
Univariate and multivariable associations between the genetic predictors (PRS and Family History) and the behavioral phenotypes for the full ABCD sample and he non-European ancestry sample, controlling for covariates of no interest including SES. Models that did not converge after 10,000 iterations were left blank.
**Supplementary Figure 7.**_Signed Effect Sizes for all multivariable PRS associations for the European sample (X-axis) and non-European sample (Y-axis), controlling for covariates of no interest and SES. The estimated associations were broadly consistent between European and non-European groups, however, there was moderate dispersion observed between estimated effect sizes, which highlights difficulties in using PRS generated in certain ancestry groups to other ancestry groups._Statistical Data Tables
For completeness and transparency of reporting, we have generated additional data tables as.csv files with the results from all statistical models. Each table includes the beta estimate, t statistic, signed percentage variance explained (R\({}^{2}\)) and p-value for each predictor in each model. These results are the averaged statistics across 100 samples of singletons as outlined in the Supplementary Methods.
* Non EUR Ancestry Results
* Full Sample Results
Each file contains a separate sheet for:
1 Univariate SES covaried
2 Multivariable SES covaried multivariable
3 Univariate (not controlling for SES)
4 Multivariable (not controlling for SES)Supplementary Material References
|
186981_file03 | Table S2.
\begin{tabular}{|l|l|c|c|c|c|c|c|c|} \hline Variable 1 & Variable 2 & \(<\)- & \(\to\) & \(<\)o & \(\alpha\)-y & \(\alpha\)-y & \(<\)-y & No Edge \\ \hline Alcohol Use - BL & Alcohol Use - YR5 & 0.00 & 0.00 & 0.00 & 1.00 & 0.00 & 0.00 & 0.00 & 0.00 \\ \hline Alcohol Use - BL & Alcohol Use - YR3 & 0.00 & 0.00 & 0.00 & 1.00 & 0.00 & 0.00 & 0.00 \\ \hline Alcohol Use - BL & Alcohol Use - YR2 & 0.00 & 0.00 & 0.00 & 1.00 & 0.00 & 0.00 & 0.00 \\ \hline Alcohol Use - BL & Alcohol Use - YR4 & 0.00 & 0.00 & 0.00 & 1.00 & 0.00 & 0.00 & 0.00 \\ \hline Alcohol Use - BL & Alcohol Use - YR6 & 0.00 & 0.00 & 0.00 & 1.00 & 0.00 & 0.00 & 0.00 \\ \hline Alcohol Use - BL & Alcohol Use - YR7 & 0.00 & 0.00 & 0.00 & 1.00 & 0.00 & 0.00 & 0.00 \\ \hline PTSD Symptoms - YR1 & Depression - YR1 & 0.00 & 0.99 & 0.00 & 0.01 & 0.01 & 0.00 & 0.00 \\ \hline Physical Amount - YR1 & Physical Compared - YR4 & 0.00 & 0.88 & 0.00 & 0.13 & 0.00 & 0.00 & 0.00 \\ \hline PTSD Symptoms - YR2 & Depression - YR2 & 0.00 & 0.93 & 0.00 & 0.06 & 0.01 & 0.00 & 0.00 \\ \hline PTSD Symptoms - YR3 & Depression - YR3 & 0.00 & 0.98 & 0.00 & 0.01 & 0.01 & 0.00 & 0.00 \\ \hline PTSD Symptoms - YR5 & Depression - YR5 & 0.00 & 1.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 \\ \hline Overall Health - BL & Quality of Life - BL & 0.00 & 0.00 & 0.01 & 0.00 & 0.99 & 0.00 & 0.00 \\ \hline PTSD Symptoms - YR7 & Depression - YR7 & 0.01 & 0.99 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 \\ \hline Physical Amount - YR2 & Physical Compared - YR2 & 0.00 & 0.89 & 0.00 & 0.11 & 0.00 & 0.00 & 0.00 \\ \hline Overall Health - YR2 & Quality of Life - YR2 & 0.03 & 0.96 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 \\ \hline Physical Limit - YR6 & Physical Limit - YR7 & 0.00 & 0.96 & 0.00 & 0.04 & 0.00 & 0.00 & 0.01 \\ \hline Physical Amount - YR4 & Physical Compared - YR4 & 0.00 & 0.69 & 0.00 & 0.31 & 0.00 & 0.00 & 0.01 \\ \hline Quality of Life - YR3 & Quality of Life - YR4 & 0.00 & 0.96 & 0.00 & 0.04 & 0.00 & 0.00 & 0.01 \\ \hline Physical Limit - YR1 & Physical Limit - YR2 & 0.00 & 0.85 & 0.00 & 0.13 & 0.00 & 0.00 & 0.02 \\ \hline PTSD Symptoms - BL & Depression - BL & 0.04 & 0.00 & 0.00 & 0.00 & 0.94 & 0.00 & 0.02 \\ \hline PTSD Symptoms - YR1 & PTSD Symptoms - BL & 0.05 & 0.00 & 0.93 & 0.00 & 0.00 & 0.00 & 0.02 \\ \hline PTSD Symptoms - YR6 & Depression - YR6 & 0.04 & 0.88 & 0.00 & 0.05 & 0.00 & 0.00 & 0.02 \\ \hline Physical Compared - YR5 & Physical Compared - YR6 & 0.00 & 0.98 & 0.00 & 0.00 & 0.00 & 0.00 & 0.02 \\ \hline Overall Health - YR5 & Quality of Life - YR5 & 0.24 & 0.70 & 0.00 & 0.03 & 0.00 & 0.00 & 0.03 \\ \hline PTSD Symptoms - YR3 & PTSD Symptoms - YR4 & 0.00 & 0.92 & 0.00 & 0.02 & 0.00 & 0.00 & 0.06 \\ \hline Physical Limit - YR1 & Physical Limit - YR3 & 0.00 & 0.80 & 0.00 & 0.13 & 0.00 & 0.00 & 0.07 \\ \hline Overall Health - YR6 & Quality of Life - YR6 & 0.18 & 0.75 & 0.00 & 0.00 & 0.00 & 0.00 & 0.07 \\ \hline Physical Limit - YR5 & Physical Limit - YR6 & 0.00 & 0.90 & 0.00 & 0.03 & 0.00 & 0.00 & 0.07 \\ \hline PTSD Symptoms - YR6 & PTSD Symptoms - YR7 & 0.00 & 0.87 & 0.00 & 0.06 & 0.00 & 0.00 & 0.07 \\ \hline Overall Health - YR3 & Physical Compared - YR3 & 0.00 & 0.90 & 0.00 & 0.03 & 0.00 & 0.00 & 0.07 \\ \hline Physical Limit - YR5 & Physical Limit - YR4 & 0.70 & 0.00 & 0.21 & 0.00 & 0.00 & 0.00 & 0.09 \\ \hline Overall Health - YR4 & Physical Compared - YR4 & 0.00 & 0.90 & 0.00 & 0.01 & 0.00 & 0.00 & 0.10 \\ \hline Quality of Life - YR1 & Quality of Life - BL & 0.00 & 0.00 & 0.90 & 0.00 & 0.00 & 0.00 & 0.10 \\ \hline Quality of Life - YR7 & Quality of Life - YR7 & 0.00 & 0.90 & 0.00 & 0.00 & 0.00 & 0.00 & 0.10 \\ \hline PTSD Symptoms - BL & Social Function - YR4 & 0.00 & 0.05 & 0.00 & 0.85 & 0.00 & 0.00 & 0.10 \\ \hline Physical Amount - YR3 & Physical Compared - YR3 & 0.00 & 0.58 & 0.00 & 0.31 & 0.00 & 0.00 & 0.10 \\ \hline Overall Health - YR5 & Overall Health - YR6 & 0.00 & 0.86 & 0.00 & 0.04 & 0.00 & 0.00 & 0.11 \\ \hline PTSD Symptoms - YR4 & PTSD Symptoms - YR5 & 0.00 & 0.66 & 0.00 & 0.22 & 0.00 & 0.00 & 0.12 \\ \hline Overall Health - BL & Physical Limit - BL & 0.00 & 0.00 & 0.01 & 0.01 & 0.85 & 0.00 & 0.14 \\ \hline Quality of Life - YR2 & Quality of Life - YR3 & 0.00 & 0.83 & 0.00 & 0.00 & 0.00 & 0.00 & 0.17 \\ \hline Social Function - YR5 & PTSD Symptoms - BL & 0.04 & 0.00 & 0.78 & 0.00 & 0.00 & 0.00 & 0.18 \\ \hline Physical Limit - YR1 & Physical Limit - BL & 0.01 & 0.00 & 0.81 & 0.00 & 0.00 & 0.00 & 0.18 \\ \hline Social Function - YR3 & PTSD Symptoms - BL & 0.04 & 0.00 & 0.78 & 0.00 & 0.00 & 0.00 & 0.18 \\ \hline Social Function - BL & Depression - BL & 0.04 & 0.00 & 0.00 & 0.00 & 0.78 & 0.00 & 0.18 \\ \hline Overall Health - YR4 & Overall Health - YR3 & 0.78 & 0.00 & 0.03 & 0.00 & 0.00 & 0.00 & 0.19 \\ \hline Overall Health - YR1 & Overall Health - BL & 0.01 & 0.00 & 0.80 & 0.00 & 0.00 & 0.00 & 0.19 \\ \hline \end{tabular}
Table S2.
\begin{tabular}{|l|l|l|l|l|l|l|l|l|} \hline Variable 1 & Variable 2 & \(<\)- & \(\rightarrow\) & \(<\)o & o-\(>\) & o-o & \(<\)-\(>\) & No Edge \\ \hline Physical Limit - YR1 & Physical Amount - YR7 & 0.00 & 0.33 & 0.00 & 0.04 & 0.00 & 0.00 & 0.63 \\ \hline Physical Amount - YR1 & Physical Amount - YR6 & 0.00 & 0.32 & 0.00 & 0.05 & 0.00 & 0.00 & 0.63 \\ \hline Social Function - YR2 & PTSD Symptoms - BL & 0.02 & 0.00 & 0.35 & 0.00 & 0.00 & 0.00 & 0.63 \\ \hline PTSD Symptoms - YR1 & Social Function - YR1 & 0.13 & 0.00 & 0.23 & 0.00 & 0.00 & 0.00 & 0.64 \\ \hline Overall Health - YR4 & Overall Health - YR2 & 0.36 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.64 \\ \hline Quality of Life - YR5 & Quality of Life - YR6 & 0.00 & 0.35 & 0.00 & 0.00 & 0.00 & 0.00 & 0.65 \\ \hline PTSD Symptoms - YR3 & PTSD Symptoms - YR6 & 0.00 & 0.33 & 0.00 & 0.01 & 0.00 & 0.00 & 0.66 \\ \hline Depression - YR1 & Quality of Life - YR1 & 0.04 & 0.28 & 0.00 & 0.00 & 0.00 & 0.00 & 0.68 \\ \hline Quality of Life - YR5 & Quality of Life - YR7 & 0.00 & 0.32 & 0.00 & 0.00 & 0.00 & 0.00 & 0.68 \\ \hline Physical Limit - YR1 & Social Function - YR1 & 0.15 & 0.00 & 0.17 & 0.00 & 0.00 & 0.00 & 0.69 \\ \hline Overall Health - YR1 & Physical Amount - YR5 & 0.00 & 0.27 & 0.00 & 0.05 & 0.00 & 0.00 & 0.69 \\ \hline Physical Limit - YR6 & Physical Limit - YR4 & 0.29 & 0.00 & 0.02 & 0.00 & 0.00 & 0.00 & 0.70 \\ \hline Overall Health - YR7 & Physical Compared - YR7 & 0.30 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.70 \\ \hline Social Function - YR1 & PTSD Symptoms - BL & 0.01 & 0.00 & 0.28 & 0.00 & 0.00 & 0.00 & 0.71 \\ \hline Physical Compared - YR3 & Physical Compared - YR7 & 0.00 & 0.29 & 0.00 & 0.00 & 0.00 & 0.00 & 0.71 \\ \hline Quality of Life - YR3 & Quality of Life - YR7 & 0.00 & 0.28 & 0.00 & 0.01 & 0.00 & 0.00 & 0.71 \\ \hline Depression - YR1 & Depression - BL & 0.02 & 0.00 & 0.27 & 0.00 & 0.00 & 0.00 & 0.72 \\ \hline Quality of Life - YR3 & Quality of Life - BL & 0.00 & 0.00 & 0.28 & 0.00 & 0.00 & 0.00 & 0.72 \\ \hline Physical Compared - YR7 & Physical Compared - YR4 & 0.28 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.72 \\ \hline Social Function - YR2 & Social Function - BL & 0.02 & 0.00 & 0.26 & 0.00 & 0.00 & 0.00 & 0.73 \\ \hline PTSD Symptoms - YR5 & Social Function - YR5 & 0.27 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.74 \\ \hline Physical Compared - YR2 & Quality of Life - YR2 & 0.26 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.74 \\ \hline Quality of Life - YR5 & Quality of Life - YR4 & 0.25 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.74 \\ \hline Overall Health - YR4 & Overall Health - YR5 & 0.00 & 0.25 & 0.00 & 0.01 & 0.00 & 0.00 & 0.75 \\ \hline Depression - YR2 & Depression - BL & 0.01 & 0.00 & 0.24 & 0.00 & 0.00 & 0.00 & 0.75 \\ \hline Overall Health - YR2 & Overall Health - YR3 & 0.00 & 0.24 & 0.00 & 0.00 & 0.00 & 0.00 & 0.76 \\ \hline Physical Compared - YR5 & Physical Compared - YR4 & 0.24 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.76 \\ \hline PTSD Symptoms - BL & Social Function - BL & 0.00 & 0.01 & 0.00 & 0.00 & 0.23 & 0.00 & 0.76 \\ \hline Physical Amount - YR3 & Overall Health - BL & 0.01 & 0.00 & 0.22 & 0.00 & 0.00 & 0.00 & 0.77 \\ \hline Physical Limit - YR5 & Physical Limit - YR7 & 0.00 & 0.21 & 0.00 & 0.00 & 0.00 & 0.00 & 0.79 \\ \hline Depression - YR7 & Social Function - YR7 & 0.20 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.80 \\ \hline Physical Limit - YR3 & Physical Limit - BL & 0.01 & 0.00 & 0.19 & 0.00 & 0.00 & 0.00 & 0.80 \\ \hline Overall Health - YR2 & Social Function - YR2 & 0.16 & 0.00 & 0.03 & 0.00 & 0.00 & 0.00 & 0.80 \\ \hline Overall Health - YR1 & Overall Health - YR3 & 0.00 & 0.17 & 0.00 & 0.02 & 0.00 & 0.00 & 0.81 \\ \hline PTSD Symptoms - YR2 & Social Function - YR2 & 0.18 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.81 \\ \hline Physical Compared - YR3 & Physical Compared - YR6 & 0.00 & 0.19 & 0.00 & 0.00 & 0.00 & 0.00 & 0.81 \\ \hline Social Function - YR7 & Depression - BL & 0.01 & 0.00 & 0.18 & 0.00 & 0.00 & 0.00 & 0.81 \\ \hline PTSD Symptoms - YR1 & PTSD Symptoms - YR4 & 0.00 & 0.19 & 0.00 & 0.00 & 0.00 & 0.00 & 0.81 \\ \hline Overall Health - YR3 & Physical Limit - YR3 & 0.06 & 0.13 & 0.00 & 0.00 & 0.00 & 0.00 & 0.81 \\ \hline Depression - YR4 & Depression - YR5 & 0.00 & 0.19 & 0.00 & 0.00 & 0.00 & 0.00 & 0.81 \\ \hline Physical Limit - YR6 & Social Function - YR6 & 0.19 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.81 \\ \hline Overall Health - YR7 & Overall Health - YR7 & 0.00 & 0.18 & 0.00 & 0.01 & 0.00 & 0.00 & 0.81 \\ \hline Depression - YR5 & Depression - YR6 & 0.00 & 0.18 & 0.00 & 0.00 & 0.00 & 0.00 & 0.82 \\ \hline Depression - YR2 & Quality of Life - YR2 & 0.13 & 0.05 & 0.00 & 0.00 & 0.00 & 0.00 & 0.82 \\ \hline Overall Health - YR3 & Overall Health - YR7 & 0.00 & 0.17 & 0.00 & 0.01 & 0.00 & 0.00 & 0.82 \\ \hline Overall Health - YR2 & Depression - YR2 & 0.18 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.82 \\ \hline Quality of Life - YR7 & Quality of Life - YR4 & 0.17 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.83 \\ \hline \end{tabular}
Table S2.
\begin{tabular}{|l|l|c|c|c|c|c|c|c|} \hline Variable 1 & Variable 2 & \(<\)- & \(\to\) & \(<\)o & \(\alpha\)-y & \(\alpha\)-y & \(<\)-y & No Edge \\ \hline Quality of Life - YR2 & Depression - YR3 & 0.00 & 0.17 & 0.00 & 0.00 & 0.00 & 0.00 & 0.83 \\ \hline Social Function - YR5 & Depression - BL & 0.01 & 0.00 & 0.17 & 0.00 & 0.00 & 0.00 & 0.83 \\ \hline Depression - YR5 & Quality of Life - YR5 & 0.16 & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 0.83 \\ \hline Overall Health - YR5 & Overall Health - BL & 0.00 & 0.00 & 0.17 & 0.00 & 0.00 & 0.00 & 0.83 \\ \hline Depression - YR3 & Depression - YR5 & 0.00 & 0.16 & 0.00 & 0.00 & 0.00 & 0.00 & 0.83 \\ \hline Quality of Life - YR6 & Quality of Life - YR4 & 0.16 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.84 \\ \hline Physical Amount - YR1 & Physical Amount - YR3 & 0.00 & 0.15 & 0.00 & 0.01 & 0.00 & 0.00 & 0.84 \\ \hline Physical Limit - YR1 & Physical Amount - YR5 & 0.00 & 0.14 & 0.00 & 0.02 & 0.00 & 0.00 & 0.84 \\ \hline Physical Limit - YR2 & Depression - YR2 & 0.11 & 0.04 & 0.00 & 0.00 & 0.00 & 0.00 & 0.84 \\ \hline Social Function - YR6 & Depression - BL & 0.01 & 0.00 & 0.15 & 0.00 & 0.00 & 0.00 & 0.84 \\ \hline Overall Health - YR4 & Overall Health - YR7 & 0.00 & 0.15 & 0.00 & 0.00 & 0.00 & 0.00 & 0.85 \\ \hline Physical Limit - YR2 & Physical Limit - YR4 & 0.00 & 0.16 & 0.00 & 0.00 & 0.00 & 0.00 & 0.85 \\ \hline Physical Limit - BL & Depression - BL & 0.00 & 0.00 & 0.00 & 0.05 & 0.11 & 0.00 & 0.85 \\ \hline Physical Amount - YR5 & Physical Limit - BL & 0.00 & 0.00 & 0.15 & 0.00 & 0.00 & 0.00 & 0.85 \\ \hline Quality of Life - YR1 & Quality of Life - YR3 & 0.00 & 0.14 & 0.00 & 0.00 & 0.00 & 0.00 & 0.85 \\ \hline Quality of Life - YR2 & Social Function - YR2 & 0.11 & 0.00 & 0.03 & 0.00 & 0.00 & 0.00 & 0.85 \\ \hline Physical Limit - YR2 & Social Function - YR2 & 0.11 & 0.00 & 0.04 & 0.00 & 0.00 & 0.00 & 0.86 \\ \hline Depression - YR3 & Depression - BL & 0.00 & 0.00 & 0.14 & 0.00 & 0.00 & 0.00 & 0.86 \\ \hline Physical Limit - YR4 & Social Function - YR4 & 0.14 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.86 \\ \hline Depression - YR3 & Depression - YR6 & 0.00 & 0.14 & 0.00 & 0.00 & 0.00 & 0.00 & 0.86 \\ \hline Social Function - YR1 & Physical Amount - YR7 & 0.00 & 0.06 & 0.00 & 0.08 & 0.00 & 0.00 & 0.86 \\ \hline PTSD Symptoms - YR5 & PTSD Symptoms - YR7 & 0.00 & 0.14 & 0.00 & 0.00 & 0.00 & 0.00 & 0.86 \\ \hline Physical Limit - YR2 & Physical Limit - BL & 0.01 & 0.00 & 0.12 & 0.00 & 0.00 & 0.00 & 0.87 \\ \hline Quality of Life - YR2 & Quality of Life - YR7 & 0.00 & 0.13 & 0.00 & 0.00 & 0.00 & 0.00 & 0.87 \\ \hline Depression - YR3 & Social Function - YR3 & 0.12 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.87 \\ \hline PTSD Symptoms - YR4 & PTSD Symptoms - YR6 & 0.00 & 0.12 & 0.00 & 0.00 & 0.00 & 0.00 & 0.88 \\ \hline Physical Limit - YR1 & Physical Amount - YR2 & 0.00 & 0.10 & 0.00 & 0.02 & 0.00 & 0.00 & 0.88 \\ \hline Physical Compared - YR3 & Physical Limit - YR7 & 0.00 & 0.12 & 0.00 & 0.00 & 0.00 & 0.00 & 0.88 \\ \hline Physical Compared - YR5 & Depression - YR5 & 0.00 & 0.11 & 0.00 & 0.00 & 0.00 & 0.00 & 0.89 \\ \hline Overall Health - YR3 & Physical Compared - YR7 & 0.00 & 0.11 & 0.00 & 0.00 & 0.00 & 0.00 & 0.89 \\ \hline Social Function - YR2 & Physical Limit - BL & 0.00 & 0.00 & 0.11 & 0.00 & 0.00 & 0.00 & 0.89 \\ \hline Social Function - YR1 & Physical Limit - BL & 0.00 & 0.00 & 0.11 & 0.00 & 0.00 & 0.00 & 0.89 \\ \hline Physical Amount - YR2 & Physical Limit - YR2 & 0.00 & 0.08 & 0.00 & 0.02 & 0.00 & 0.00 & 0.89 \\ \hline Overall Health - YR1 & Physical Amount - YR3 & 0.00 & 0.09 & 0.00 & 0.02 & 0.00 & 0.00 & 0.90 \\ \hline Physical Compared - YR4 & Physical Compact - YR4 & 0.10 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.90 \\ \hline Physical Amount - YR1 & Physical Amount - YR7 & 0.00 & 0.09 & 0.00 & 0.01 & 0.00 & 0.00 & 0.90 \\ \hline Physical Limit - YR7 & Social Function - YR7 & 0.10 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.90 \\ \hline Physical Amount - YR3 & Quality of Life - BL & 0.00 & 0.00 & 0.10 & 0.00 & 0.00 & 0.00 & 0.90 \\ \hline PTSD Symptoms - YR1 & Physical Limit - YR4 & 0.00 & 0.10 & 0.00 & 0.01 & 0.00 & 0.00 & 0.90 \\ \hline PTSD Symptoms - YR3 & PTSD Symptoms - BL & 0.01 & 0.00 & 0.09 & 0.00 & 0.00 & 0.00 & 0.90 \\ \hline Quality of Life - YR1 & Physical Amount - YR7 & 0.00 & 0.10 & 0.00 & 0.00 & 0.00 & 0.00 & 0.90 \\ \hline PTSD Symptoms - YR2 & PTSD Symptoms - YR4 & 0.00 & 0.09 & 0.00 & 0.01 & 0.00 & 0.00 & 0.90 \\ \hline Depression - YR6 & Quality of Life - YR6 & 0.00 & 0.10 & 0.00 & 0.00 & 0.00 & 0.00 & 0.90 \\ \hline PTSD Symptoms - BL & Quality of Life - BL & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.90 \\ \hline Depression - YR5 & Social Function - YR5 & 0.10 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.90 \\ \hline PTSD Symptoms - YR3 & Depression - YR4 & 0.00 & 0.09 & 0.00 & 0.00 & 0.00 & 0.00 & 0.90 \\ \hline Social Function - YR1 & Depression - BL & 0.01 & 0.00 & 0.09 & 0.00 & 0.00 & 0.00 & 0.91 \\ \hline \end{tabular}
Table S2.
\begin{tabular}{|l|l|l|l|l|l|l|l|l|} \hline Variable 1 & Variable 2 & \(<\)- & \(\to\) & \(<\)o & \(\alpha\)-y & \(\alpha\)-y & \(<\)-y & No Edge \\ \hline Physical Limit - YR1 & Physical Amount - YR4 & 0.00 & 0.08 & 0.00 & 0.01 & 0.00 & 0.00 & 0.91 \\ \hline Overall Health - YR6 & Physical Compared - YR6 & 0.09 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.91 \\ \hline Overall Health - BL & PTSD Symptoms - BL & 0.00 & 0.00 & 0.00 & 0.00 & 0.09 & 0.00 & 0.91 \\ \hline Overall Health - YR2 & Physical Limit - YR3 & 0.00 & 0.08 & 0.00 & 0.00 & 0.00 & 0.00 & 0.92 \\ \hline Social Function - YR1 & Physical Amount - YR5 & 0.00 & 0.04 & 0.00 & 0.04 & 0.00 & 0.00 & 0.92 \\ \hline PTSD Symptoms - YR6 & Quality of Life - YR6 & 0.04 & 0.04 & 0.00 & 0.00 & 0.00 & 0.00 & 0.92 \\ \hline Physical Limit - YR3 & Physical Limit - YR6 & 0.00 & 0.08 & 0.00 & 0.00 & 0.00 & 0.00 & 0.92 \\ \hline Overall Health - BL & Social Function - BL & 0.00 & 0.00 & 0.00 & 0.00 & 0.08 & 0.00 & 0.92 \\ \hline PTSD Symptoms - YR6 & Physical Limit - YR6 & 0.01 & 0.06 & 0.00 & 0.01 & 0.00 & 0.00 & 0.93 \\ \hline Physical Amount - YR5 & Quality of Life - BL & 0.00 & 0.00 & 0.07 & 0.00 & 0.00 & 0.00 & 0.93 \\ \hline Physical Limit - YR6 & Depression - YR6 & 0.07 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.93 \\ \hline Depression - BL & Social Function - YR4 & 0.00 & 0.00 & 0.00 & 0.07 & 0.00 & 0.00 & 0.93 \\ \hline Physical Limit - YR1 & Physical Limit - YR4 & 0.00 & 0.06 & 0.00 & 0.01 & 0.00 & 0.00 & 0.93 \\ \hline Depression - YR2 & Depression - YR4 & 0.00 & 0.07 & 0.00 & 0.00 & 0.00 & 0.00 & 0.93 \\ \hline Depression - YR2 & PTSD Symptoms - YR7 & 0.00 & 0.07 & 0.00 & 0.00 & 0.00 & 0.00 & 0.93 \\ \hline PTSD Symptoms - BL & Physical Limit - BL & 0.00 & 0.00 & 0.00 & 0.00 & 0.06 & 0.00 & 0.93 \\ \hline Physical Limit - YR2 & Physical Limit - YR3 & 0.00 & 0.06 & 0.00 & 0.01 & 0.00 & 0.00 & 0.93 \\ \hline Quality of Life - YR2 & Quality of Life - YR5 & 0.00 & 0.07 & 0.00 & 0.00 & 0.00 & 0.00 & 0.93 \\ \hline Overall Health - YR3 & Overall Health - YR6 & 0.00 & 0.06 & 0.00 & 0.00 & 0.00 & 0.00 & 0.94 \\ \hline Quality of Life - YR2 & Quality of Life - BL & 0.00 & 0.00 & 0.06 & 0.00 & 0.00 & 0.00 & 0.94 \\ \hline Social Function - YR2 & Physical Limit - YR4 & 0.00 & 0.06 & 0.00 & 0.01 & 0.00 & 0.00 & 0.94 \\ \hline Social Function - YR3 & Physical Limit - YR4 & 0.00 & 0.06 & 0.00 & 0.01 & 0.00 & 0.00 & 0.94 \\ \hline PTSD Symptoms - YR1 & PTSD Symptoms - YR7 & 0.00 & 0.06 & 0.00 & 0.00 & 0.00 & 0.00 & 0.94 \\ \hline Quality of Life - YR2 & Depression - YR5 & 0.00 & 0.06 & 0.00 & 0.00 & 0.00 & 0.00 & 0.94 \\ \hline Social Function - YR3 & Social Function - BL & 0.00 & 0.00 & 0.06 & 0.00 & 0.00 & 0.00 & 0.94 \\ \hline Overall Health - YR4 & Overall Health - YR1 & 0.04 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.94 \\ \hline Overall Health - YR6 & Social Function - YR6 & 0.05 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.95 \\ \hline Overall Health - YR2 & Physical Compared - YR3 & 0.00 & 0.05 & 0.00 & 0.00 & 0.00 & 0.00 & 0.95 \\ \hline Physical Compared - YR5 & 0.00 & 0.05 & 0.00 & 0.00 & 0.00 & 0.00 & 0.95 \\ \hline PTSD Symptoms - YR7 & PTSD Symptoms - BL & 0.00 & 0.00 & 0.05 & 0.00 & 0.00 & 0.00 & 0.95 \\ \hline Physical Limit - YR5 & Physical Limit - BL & 0.00 & 0.00 & 0.05 & 0.00 & 0.00 & 0.00 & 0.95 \\ \hline Quality of Life - YR2 & Quality of Life - YR4 & 0.00 & 0.05 & 0.00 & 0.00 & 0.00 & 0.00 & 0.95 \\ \hline Depression - YR1 & Physical Amount - YR4 & 0.00 & 0.05 & 0.00 & 0.00 & 0.00 & 0.00 & 0.95 \\ \hline Overall Health - YR3 & Physical Compared - YR4 & 0.00 & 0.05 & 0.00 & 0.00 & 0.00 & 0.00 & 0.95 \\ \hline PTSD Symptoms - YR5 & PTSD Symptoms - BL & 0.00 & 0.00 & 0.05 & 0.00 & 0.00 & 0.00 & 0.95 \\ \hline Overall Health - YR6 & Physical Limit - YR4 & 0.04 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.95 \\ \hline Overall Health - YR7 & Physical Amount - YR2 & 0.00 & 0.04 & 0.00 & 0.00 & 0.00 & 0.00 & 0.96 \\ \hline Quality of Life - YR1 & Physical Amount - YR6 & 0.00 & 0.04 & 0.00 & 0.00 & 0.00 & 0.00 & 0.96 \\ \hline Social Function - YR3 & Depression - BL & 0.00 & 0.00 & 0.04 & 0.00 & 0.00 & 0.00 & 0.96 \\ \hline Physical Amount - YR6 & Physical Limit - YR6 & 0.00 & 0.02 & 0.00 & 0.02 & 0.00 & 0.00 & 0.96 \\ \hline Social Function - YR2 & Depression - BL & 0.00 & 0.00 & 0.04 & 0.00 & 0.00 & 0.00 & 0.96 \\ \hline Overall Health - YR3 & Depression - YR3 & 0.03 & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 0.96 \\ \hline Overall Health - BL & Depression - BL & 0.00 & 0.00 & 0.00 & 0.00 & 0.04 & 0.00 & 0.96 \\ \hline Physical Limit - YR3 & Depression - YR3 & 0.04 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.96 \\ \hline Depression - YR5 & Depression - YR7 & 0.00 & 0.04 & 0.00 & 0.00 & 0.00 & 0.00 & 0.96 \\ \hline Depression - YR5 & Depression - BL & 0.00 & 0.00 & 0.04 & 0.00 & 0.00 & 0.00 & 0.96 \\ \hline Physical Amount - YR5 & 0.00 & 0.04 & 0.00 & 0.00 & 0.00 & 0.00 & 0.96 \\ \hline \end{tabular}
Table S2.
\begin{tabular}{|l|l|l|l|l|l|l|l|l|} \hline Variable 1 & Variable 2 & \(<\)- & \(\rightarrow\) & \(<\)o & o-\(>\) & o-o & \(<\)-\(>\) & No Edge \\ \hline Overall Health - YR2 & Overall Health - YR6 & 0.00 & 0.04 & 0.00 & 0.00 & 0.00 & 0.00 & 0.96 \\ \hline Overall Health - YR5 & Physical Compared - YR6 & 0.00 & 0.04 & 0.00 & 0.00 & 0.00 & 0.00 & 0.96 \\ \hline Depression - YR3 & Quality of Life - YR3 & 0.04 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.96 \\ \hline Physical Amount - YR7 & Overall Health - BL & 0.00 & 0.00 & 0.04 & 0.00 & 0.00 & 0.00 & 0.96 \\ \hline Depression - YR1 & Physical Amount - YR7 & 0.00 & 0.04 & 0.00 & 0.00 & 0.00 & 0.00 & 0.96 \\ \hline Physical Compared - YR3 & Physical Limit - YR3 & 0.04 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.96 \\ \hline Physical Compared - YR6 & Quality of Life - YR6 & 0.00 & 0.04 & 0.00 & 0.00 & 0.00 & 0.00 & 0.96 \\ \hline PTSD Symptoms - YR1 & Physical Amount - YR4 & 0.00 & 0.04 & 0.00 & 0.00 & 0.00 & 0.00 & 0.96 \\ \hline Physical Amount - YR7 & Quality of Life - BL & 0.00 & 0.00 & 0.04 & 0.00 & 0.00 & 0.00 & 0.96 \\ \hline Physical Limit - YR1 & Quality of Life - YR1 & 0.04 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.96 \\ \hline Physical Limit - YR2 & Physical Limit - YR6 & 0.00 & 0.04 & 0.00 & 0.00 & 0.00 & 0.00 & 0.96 \\ \hline Overall Health - YR2 & Depression - YR3 & 0.00 & 0.04 & 0.00 & 0.00 & 0.00 & 0.00 & 0.96 \\ \hline Quality of Life - YR5 & Social Function - YR5 & 0.04 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.96 \\ \hline Overall Health - YR1 & Physical Limit - YR1 & 0.01 & 0.02 & 0.00 & 0.01 & 0.00 & 0.00 & 0.97 \\ \hline Overall Health - YR2 & Overall Health - YR5 & 0.00 & 0.03 & 0.00 & 0.00 & 0.00 & 0.00 & 0.97 \\ \hline Physical Limit - YR5 & Physical Limit - YR7 & 0.00 & 0.03 & 0.00 & 0.00 & 0.00 & 0.00 & 0.97 \\ \hline Physical Amount - YR4 & Physical Limit - YR4 & 0.00 & 0.02 & 0.00 & 0.01 & 0.00 & 0.00 & 0.97 \\ \hline Physical Amount - YR5 & Overall Health - BL & 0.00 & 0.00 & 0.03 & 0.00 & 0.00 & 0.00 & 0.97 \\ \hline Quality of Life - YR1 & Social Function - YR1 & 0.01 & 0.00 & 0.02 & 0.00 & 0.00 & 0.00 & 0.97 \\ \hline Overall Health - YR6 & PTSD Symptoms - YR6 & 0.02 & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 0.97 \\ \hline Physical Amount - YR6 & Physical Limit - BL & 0.00 & 0.00 & 0.03 & 0.00 & 0.00 & 0.00 & 0.97 \\ \hline Physical Compared - YR1 & Physical Limit - YR1 & 0.02 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.97 \\ \hline Physical Amount - YR2 & Physical Compared - YR3 & 0.00 & 0.03 & 0.00 & 0.01 & 0.00 & 0.00 & 0.97 \\ \hline Physical Amount - YR3 & Physical Limit - BL & 0.00 & 0.00 & 0.03 & 0.00 & 0.00 & 0.00 & 0.97 \\ \hline Physical Compared - YR7 & Physical Compared - YR7 & 0.00 & 0.03 & 0.00 & 0.00 & 0.00 & 0.00 & 0.97 \\ \hline Overall Health - YR5 & Physical Compared - YR5 & 0.01 & 0.02 & 0.00 & 0.00 & 0.00 & 0.00 & 0.97 \\ \hline Physical Limit - YR3 & Physical Limit - YR7 & 0.00 & 0.03 & 0.00 & 0.00 & 0.00 & 0.00 & 0.97 \\ \hline Overall Health - YR7 & Overall Health - BL & 0.00 & 0.00 & 0.03 & 0.00 & 0.00 & 0.00 & 0.97 \\ \hline Social Function - BL & Social Function - YR4 & 0.00 & 0.00 & 0.00 & 0.03 & 0.00 & 0.00 & 0.97 \\ \hline Physical Limit - YR7 & Depression - YR7 & 0.03 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.97 \\ \hline Overall Health - YR1 & Overall Health - YR7 & 0.00 & 0.03 & 0.00 & 0.00 & 0.00 & 0.00 & 0.97 \\ \hline Physical Compared - YR5 & Quality of Life - YR5 & 0.01 & 0.02 & 0.00 & 0.00 & 0.00 & 0.00 & 0.97 \\ \hline Overall Health - YR7 & Physical Limit - YR7 & 0.01 & 0.02 & 0.00 & 0.00 & 0.00 & 0.00 & 0.97 \\ \hline Overall Health - YR3 & Social Function - YR3 & 0.03 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.98 \\ \hline PTSD Symptoms - YR4 & PTSD Symptoms - BL & 0.00 & 0.00 & 0.02 & 0.00 & 0.00 & 0.00 & 0.98 \\ \hline Alcohol Use - YR1 & Social Function - BL & 0.00 & 0.00 & 0.02 & 0.00 & 0.00 & 0.00 & 0.98 \\ \hline Overall Health - YR2 & Depression - YR5 & 0.00 & 0.02 & 0.00 & 0.00 & 0.00 & 0.00 & 0.98 \\ \hline Overall Health - YR4 & Physical Limit - YR4 & 0.01 & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 0.98 \\ \hline Quality of Life - YR7 & Quality of Life - BL & 0.00 & 0.00 & 0.02 & 0.00 & 0.00 & 0.00 & 0.98 \\ \hline Quality of Life - BL & Social Function - BL & 0.00 & 0.00 & 0.00 & 0.00 & 0.02 & 0.00 & 0.98 \\ \hline Quality of Life - YR7 & Quality of Life - YR7 & 0.00 & 0.02 & 0.00 & 0.00 & 0.00 & 0.00 & 0.98 \\ \hline PTSD Symptoms - YR6 & PTSD Symptoms - BL & 0.00 & 0.00 & 0.02 & 0.00 & 0.00 & 0.00 & 0.98 \\ \hline PTSD Symptoms - YR7 & Physical Limit - YR7 & 0.02 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.98 \\ \hline Overall Health - YR4 & Quality of Life - YR5 & 0.00 & 0.02 & 0.00 & 0.00 & 0.00 & 0.00 & 0.98 \\ \hline Overall Health - YR4 & Overall Health - BL & 0.00 & 0.00 & 0.02 & 0.00 & 0.00 & 0.00 & 0.98 \\ \hline Physical Compared - YR1 & Overall Health - BL & 0.00 & 0.00 & 0.02 & 0.00 & 0.00 & 0.00 & 0.98 \\ \hline \end{tabular}
Table S2.
\begin{tabular}{|l|l|l|l|l|l|l|l|l|} \hline Variable 1 & Variable 2 & \(<\)- & \(\rightarrow\) & \(<\)o & o-\(>\) & o-o & \(<\)-\(>\) & No Edge \\ \hline Social Function - YR6 & Quality of Life - BL & 0.00 & 0.00 & 0.02 & 0.00 & 0.00 & 0.00 & 0.98 \\ \hline Physical Limit - YR1 & Depression - YR1 & 0.02 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.98 \\ \hline Physical Limit - YR1 & Physical Limit - YR5 & 0.00 & 0.02 & 0.00 & 0.00 & 0.00 & 0.00 & 0.98 \\ \hline Quality of Life - YR1 & Physical Compared - YR4 & 0.00 & 0.02 & 0.00 & 0.00 & 0.00 & 0.00 & 0.98 \\ \hline Physical Amount - YR2 & Depression - BL & 0.00 & 0.00 & 0.02 & 0.00 & 0.00 & 0.00 & 0.98 \\ \hline Depression - YR2 & Depression - YR3 & 0.00 & 0.02 & 0.00 & 0.00 & 0.00 & 0.00 & 0.98 \\ \hline Overall Health - YR3 & Depression - YR5 & 0.00 & 0.02 & 0.00 & 0.00 & 0.00 & 0.00 & 0.98 \\ \hline PTSD Symptoms - YR3 & PTSD Symptoms - YR7 & 0.00 & 0.02 & 0.00 & 0.00 & 0.00 & 0.00 & 0.98 \\ \hline PTSD Symptoms - YR5 & Physical Limit - YR5 & 0.02 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.98 \\ \hline Physical Limit - YR5 & Social Function - YR5 & 0.02 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.98 \\ \hline Physical Limit - YR2 & Quality of Life - YR2 & 0.02 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.98 \\ \hline Physical Limit - YR1 & Physical Amount - YR6 & 0.00 & 0.02 & 0.00 & 0.00 & 0.00 & 0.00 & 0.98 \\ \hline Quality of Life - YR4 & Quality of Life - YR4 & 0.00 & 0.02 & 0.00 & 0.00 & 0.00 & 0.00 & 0.98 \\ \hline Social Function - YR1 & Social Function - BL & 0.00 & 0.00 & 0.02 & 0.00 & 0.00 & 0.00 & 0.98 \\ \hline PTSD Symptoms - YR2 & PTSD Symptoms - YR7 & 0.00 & 0.02 & 0.00 & 0.00 & 0.00 & 0.00 & 0.98 \\ \hline Depression - YR6 & Physical Limit - YR7 & 0.00 & 0.02 & 0.00 & 0.00 & 0.00 & 0.00 & 0.98 \\ \hline Social Function - YR6 & Social Function - BL & 0.00 & 0.00 & 0.02 & 0.00 & 0.00 & 0.00 & 0.98 \\ \hline Overall Health - YR1 & Quality of Life - BL & 0.00 & 0.00 & 0.02 & 0.00 & 0.00 & 0.00 & 0.98 \\ \hline Physical Amount - YR1 & Depression - YR1 & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.98 \\ \hline Social Function - YR1 & Physical Amount - YR6 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 0.98 \\ \hline Social Function - YR3 & Physical Limit - BL & 0.00 & 0.00 & 0.02 & 0.00 & 0.00 & 0.00 & 0.98 \\ \hline Physical Compared - YR1 & Quality of Life - YR1 & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.99 \\ \hline Social Function - YR3 & Quality of Life - YR4 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 0.99 \\ \hline Physical Amount - YR5 & Physical Limit - YR5 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 0.99 \\ \hline Depression - YR5 & Quality of Life - YR7 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 0.99 \\ \hline Social Function - YR6 & Overall Health - BL & 0.00 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.99 \\ \hline Physical Amount - YR7 & Depression - BL & 0.00 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.99 \\ \hline Physical Limit - BL & Social Function - BL & 0.00 & 0.00 & 0.00 & 0.00 & 0.01 & 0.00 & 0.99 \\ \hline Overall Health - YR1 & Physical Compared - YR4 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 0.99 \\ \hline Physical Amount - YR1 & Physical Limit - BL & 0.00 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.99 \\ \hline Social Function - YR1 & PTSD Symptoms - YR2 & 0.00 & 0.00 & 0.00 & 0.01 & 0.00 & 0.00 & 0.99 \\ \hline Physical Compared - YR3 & Depression - YR5 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 0.99 \\ \hline Overall Health - YR1 & Quality of Life - YR7 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 0.99 \\ \hline Physical Limit - YR3 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 0.99 \\ \hline Depression - YR1 & PTSD Symptoms - YR4 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 0.99 \\ \hline Physical Amount - YR2 & Overall Health - BL & 0.00 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.99 \\ \hline Physical Amount - YR5 & PTSD Symptoms - BL & 0.00 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.99 \\ \hline Physical Amount - YR5 & Depression - BL & 0.00 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.99 \\ \hline Overall Health - YR6 & Physical Limit - YR6 & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.99 \\ \hline Overall Health - YR4 & Physical Limit - YR7 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 0.99 \\ \hline Physical Limit - YR7 & Physical Limit - YR6 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 0.99 \\ \hline Social Function - YR1 & Quality of Life - BL & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 0.99 \\ \hline Overall Health - YR3 & Quality of Life - YR6 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 0.99 \\ \hline Physical Amount - YR5 & Physical Compared - YR6 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 0.99 \\ \hline PTSD Symptoms - YR7 & Social Function - YR7 & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.99 \\ \hline Social Function - BL & Physical Limit - YR4 & 0.00 & 0.00 & 0.00 & 0.01 & 0.00 & 0.00 & 0.99 \\ \hline Physical Limit - YR2 & Depression - BL & 0.00 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.99 \\ \hline \end{tabular}
Table S3.
\begin{tabular}{|l|l|c|c|c|c|c|c|c|} \hline Variable 1 & Variable 2 & \(<\)- & \(\to\) & \(<\)o & \(\alpha\)-y & \(\alpha\)-y & \(<\)-y & No Edge \\ \hline Physical Amount - YR3 & Physical Limit - YR3 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 0.99 \\ \hline PTSD Symptoms - YR4 & Physical Limit - YR4 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 0.99 \\ \hline PTSD Symptoms - YR5 & Social Function - BL & 0.00 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.99 \\ \hline Physical Amount - YR5 & Physical Compared - YR7 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 0.99 \\ \hline Physical Amount - YR5 & Quality of Life - YR5 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 0.99 \\ \hline Quality of Life - YR6 & Social Function - YR6 & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.99 \\ \hline Alcohol Use - BL & PTSD Symptoms - BL & 0.00 & 0.00 & 0.00 & 0.00 & 0.01 & 0.00 & 0.99 \\ \hline PTSD Symptoms - YR1 & PTSD Symptoms - YR6 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 0.99 \\ \hline Social Function - YR1 & Physical Limit - YR4 & 0.00 & 0.00 & 0.00 & 0.01 & 0.00 & 0.00 & 0.99 \\ \hline Overall Health - YR2 & PTSD Symptoms - YR2 & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.99 \\ \hline PTSD Symptoms - YR2 & PTSD Symptoms - YR6 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 0.99 \\ \hline Physical Limit - YR2 & Physical Limit - YR7 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 0.99 \\ \hline PTSD Symptoms - YR4 & Quality of Life - YR4 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 0.99 \\ \hline Physical Limit - YR6 & PTSD Symptoms - YR7 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 0.99 \\ \hline Social Function - BL & Physical Amount - YR4 & 0.00 & 0.00 & 0.00 & 0.01 & 0.00 & 0.00 & 0.99 \\ \hline PTSD Symptoms - YR1 & Physical Limit - YR1 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 0.99 \\ \hline Social Function - YR2 & Overall Health - BL & 0.00 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.99 \\ \hline Overall Health - YR3 & Physical Limit - YR4 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 0.99 \\ \hline Depression - YR3 & Quality of Life - YR4 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 0.99 \\ \hline PTSD Symptoms - YR5 & Depression - BL & 0.00 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.99 \\ \hline Physical Limit - YR5 & Depression - YR5 & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.99 \\ \hline Overall Health - YR6 & Overall Health - BL & 0.00 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.99 \\ \hline Depression - YR7 & Quality of Life - YR7 & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.99 \\ \hline Social Function - YR7 & Quality of Life - BL & 0.00 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.99 \\ \hline Overall Health - YR4 & Depression - YR4 & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.99 \\ \hline Overall Health - YR1 & Physical Amount - YR6 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 0.99 \\ \hline Physical Compared - YR1 & Physical Compared - YR5 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 0.99 \\ \hline Physical Amount - YR2 & Social Function - BL & 0.00 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.99 \\ \hline Physical Compared - YR2 & Physical Limit - YR2 & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.99 \\ \hline Overall Health - YR5 & Depression - YR5 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 0.99 \\ \hline Depression - YR6 & Depression - BL & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 0.99 \\ \hline Physical Amount - YR7 & Physical Limit - BL & 0.00 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.99 \\ \hline Quality of Life - BL & Quality of Life - YR4 & 0.00 & 0.00 & 0.00 & 0.01 & 0.00 & 0.00 & 0.99 \\ \hline Overall Health - YR1 & Social Function - YR1 & 0.00 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.99 \\ \hline PTSD Symptoms - YR1 & Physical Amount - YR7 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 0.99 \\ \hline Depression - YR1 & PTSD Symptoms - YR5 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 0.99 \\ \hline Depression - YR1 & Depression - YR6 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 0.99 \\ \hline Social Function - YR1 & Physical Amount - YR4 & 0.00 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.99 \\ \hline PTSD Symptoms - YR2 & PTSD Symptoms - YR5 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 0.99 \\ \hline PTSD Symptoms - YR2 & Physical Limit - YR2 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 0.99 \\ \hline Physical Amount - YR3 & Depression - BL & 0.00 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.99 \\ \hline Social Function - YR3 & Overall Health - BL & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 0.99 \\ \hline PTSD Symptoms - YR6 & Depression - BL & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 0.99 \\ \hline PTSD Symptoms - YR7 & Depression - BL & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 0.99 \\ \hline Physical Limit - BL & Physical Limit - YR4 & 0.00 & 0.00 & 0.00 & 0.01 & 0.00 & 0.00 & 0.99 \\ \hline Alcohol Use - BL & Quality of Life - BL & 0.00 & 0.00 & 0.00 & 0.00 & 0.01 & 0.00 & 1.00 \\ \hline Overall Health - YR4 & Depression - YR5 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline \end{tabular}
Table S3.
\begin{tabular}{|l|l|l|l|l|l|l|l|l|} \hline Variable 1 & Variable 2 & \(<\)- & \(\to\) & \(<\)o & \(\circ\)- & \(\circ\)-o & \(<\)- & No Edge \\ \hline Physical Amount - YR2 & Physical Limit - BL & 0.00 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Depression - YR2 & PTSD Symptoms - YR3 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Quality of Life - YR2 & Quality of Life - YR6 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Quality of Life - YR2 & Depression - YR6 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline PTSD Symptoms - YR3 & Social Function - BL & 0.00 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Physical Amount - YR3 & Social Function - BL & 0.00 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Social Function - YR3 & PTSD Symptoms - YR5 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Depression - YR4 & Depression - BL & 0.00 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Physical Compared - YR6 & Overall Health - BL & 0.00 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Quality of Life - YR6 & Overall Health - YR7 & 0.00 & 0.01 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Overall Health - YR4 & Social Function - YR3 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Overall Health - YR4 & Physical Limit - YR3 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Overall Health - YR4 & Physical Compared - YR7 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Overall Health - YR1 & Physical Amount - YR1 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Physical Amount - YR1 & Social Function - YR1 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Depression - YR1 & Physical Amount - YR2 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Depression - YR1 & Social Function - YR1 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Quality of Life - YR1 & Physical Amount - YR5 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Overall Health - YR2 & Physical Limit - YR7 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Depression - YR2 & Depression - YR5 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Depression - YR2 & PTSD Symptoms - YR5 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Quality of Life - YR2 & Depression - YR4 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Depression - YR3 & PTSD Symptoms - YR5 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Quality of Life - YR3 & Overall Health - YR6 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Social Function - YR3 & Quality of Life - BL & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Depression - YR4 & Depression - YR6 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Physical Limit - YR5 & Quality of Life - YR5 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Social Function - YR5 & Depression - YR6 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Social Function - YR5 & Social Function - BL & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Physical Amount - YR6 & Overall Health - BL & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Physical Compared - YR6 & Physical Limit - YR6 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Physical Limit - YR6 & Physical Limit - BL & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Physical Amount - YR7 & Social Function - BL & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Physical Compared - YR7 & Depression - YR7 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Overall Health - YR1 & Physical Compared - YR5 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline PTSD Symptoms - YR1 & Quality of Life - YR1 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Physical Compared - YR1 & Quality of Life - BL & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Physical Limit - YR1 & Overall Health - YR2 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Depression - YR1 & Depression - YR3 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Depression - YR3 & Physical Limit - YR4 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Physical Compared - YR3 & Overall Health - YR6 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Physical Limit - YR3 & Depression - YR4 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline \end{tabular}
Table S3.
\begin{tabular}{|l|l|c|c|c|c|c|c|c|} \hline Variable 1 & Variable 2 & \(<\)- & \(\to\) & \(<\)o & \(\alpha\)-y & \(\alpha\)-o & \(<\)-y & No Edge \\ \hline Depression - YR3 & Physical Limit - YR7 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Overall Health - YR5 & Physical Compared - YR7 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline PTSD Symptoms - YR5 & Physical Limit - YR6 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Physical Amount - YR5 & Social Function - BL & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Depression - YR5 & Overall Health - YR6 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Quality of Life - YR5 & Quality of Life - BL & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Social Function - YR5 & Overall Health - YR7 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Social Function - YR5 & Physical Limit - YR6 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Physical Amount - YR6 & PTSD Symptoms - BL & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Physical Compared - YR6 & Quality of Life - BL & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Physical Compared - YR7 & Physical Limit - YR4 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Alcohol Use - YR1 & Depression - YR1 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Overall Health - YR1 & PTSD Symptoms - YR3 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Overall Health - YR1 & Quality of Life - YR2 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Overall Health - YR1 & Overall Health - YR6 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Overall Health - YR1 & Physical Amount - YR7 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline PTSD Symptoms - YR1 & Overall Health - YR3 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline PTSD Symptoms - YR1 & Physical Amount - YR5 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Physical Amount - YR1 & Physical Compared - YR2 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Physical Amount - YR1 & Overall Health - BL & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Physical Limit - YR1 & Physical Compared - YR4 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Depression - YR1 & Depression - YR2 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Depression - YR1 & PTSD Symptoms - YR2 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Depression - YR1 & Physical Amount - YR6 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Social Function - YR1 & Physical Amount - YR2 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Alcohol Use - YR2 & Physical Limit - BL & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Overall Health - YR2 & PTSD Symptoms - YR3 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Overall Health - YR3 & Physical Limited - YR5 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Physical Compared - YR3 & Quality of Life - YR3 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Physical Compared - YR3 & Depression - YR6 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Physical Limit - YR3 & Social Function - BL & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Quality of Life - YR3 & Overall Health - YR7 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Depression - YR4 & Depression - YR7 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline PTSD Symptoms - YR5 & Quality of Life - YR5 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline PTSD Symptoms - YR5 & Physical Compared - YR5 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Physical Amount - YR5 & Physical Limit - YR6 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Physical Limit - YR5 & Overall Health - YR6 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline \end{tabular}
Table S4.
Table S3.
\begin{tabular}{|l|l|c|c|c|c|c|c|c|} \hline Variable 1 & Variable 2 & \(<\)- & \(\to\) & \(<\)o & \(\alpha\)-y & \(\alpha\)-o & \(<\)-y & No Edge \\ \hline Quality of Life - YR1 & Depression - BL & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Social Function - YR1 & Overall Health - YR3 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Social Function - YR1 & Depression - YR2 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Alcohol Use - YR2 & Social Function - BL & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Overall Health - YR2 & Physical Amount - YR2 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Overall Health - YR2 & Quality of Life - YR5 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Overall Health - YR2 & Physical Compared - YR6 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Overall Health - YR2 & PTSD Symptoms - BL & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline PTSD Symptoms - YR2 & Quality of Life - YR2 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline PTSD Symptoms - YR2 & Depression - YR7 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline PTSD Symptoms - YR2 & Depression - BL & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Physical Amount - YR2 & Overall Health - YR6 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Depression - YR2 & Physical Limit - YR3 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Depression - YR2 & Social Function - BL & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Quality of Life - YR2 & Physical Compared - YR3 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Quality of Life - YR2 & Overall Health - YR7 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Social Function - YR2 & Physical Compared - YR3 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Social Function - YR2 & Overall Health - YR3 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Social Function - YR2 & Quality of Life - BL & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline PTSD Symptoms - YR3 & Physical Limit - YR3 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Physical Compared - YR3 & Overall Health - YR5 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Physical Limited - YR3 & Overall Health - YR6 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Physical Limit - YR3 & Physical Compared - YR7 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Physical Limit - YR3 & Overall Health - BL & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Quality of Life - YR3 & Depression - YR4 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Quality of Life - YR3 & Physical Compared - YR6 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Quality of Life - YR3 & Physical Limited - YR4 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Social Function - YR3 & Overall Health - YR6 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline PTSD Symptoms - YR4 & Overall Health - YR7 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline PTSD Symptoms - YR4 & Social Function - BL & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Depression - YR4 & PTSD Symptoms - YR5 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Alcohol Use - YR5 & Social Function - BL & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Overall Health - YR5 & Physical Limit - YR5 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Overall Health - YR7 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline PTSD Symptoms - YR5 & Overall Health - YR6 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline PTSD Symptoms - YR5 & Quality of Life - YR7 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Physical Compared - YR5 & Physical Limit - YR6 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Physical Compared - YR5 & Physical Amount - YR4 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Physical Limit - YR5 & PTSD Symptoms - YR7 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Physical Limit - YR5 & Social Function - BL & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Depression - YR5 & Physical Limit - YR7 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Depression - YR5 & PTSD Symptoms - YR6 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Depression - YR5 & PTSD Symptoms - YR6 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Depression - YR5 & Overall Health - BL & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Depression - YR5 & Social Function - BL & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline \end{tabular}
Table S3.
\begin{tabular}{|l|l|c|c|c|c|c|c|c|} \hline Variable 1 & Variable 2 & \(\prec\) & \(\neg\) & \(\prec\)o & \(\circ\)-o & \(\prec\)-s & No Edge \\ \hline Depression - YR5 & Social Function - YR4 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Depression - YR5 & Quality of Life - YR4 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Quality of Life - YR5 & Depression - YR6 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Social Function - YR5 & PTSD Symptoms - YR7 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Overall Health - YR6 & Physical Limit - YR7 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Overall Health - YR6 & Physical Limit - BL & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Overall Health - YR6 & Social Function - BL & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Overall Health - YR6 & Social Function - YR4 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline PTSD Symptoms - YR6 & Physical Limit - BL & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Physical Amount - YR6 & Social Function - BL & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Physical Compared - YR6 & Quality of Life - YR4 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Quality of Life - YR6 & Depression - YR7 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Quality of Life - YR6 & Quality of Life - BL & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Social Function - YR6 & Physical Limit - BL & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Alcohol Use - YR7 & PTSD Symptoms - YR7 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Overall Health - YR7 & Quality of Life - YR4 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline PTSD Symptoms - YR7 & Physical Limit - YR4 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Physical Amount - YR7 & Physical Limit - YR7 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Physical Limit - YR7 & Physical Limit - YR4 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Quality of Life - YR7 & Depression - BL & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Social Function - YR7 & Physical Limit - BL & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Social Function - YR7 & Overall Health - BL & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Social Function - YR7 & Social Function - BL & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Overall Health - BL & Physical Limit - YR4 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Physical Limit - BL & Quality of Life - BL & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Physical Limit - BL & Social Function - YR4 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline Physical Compared - YR4 & Quality of Life - YR4 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 0.00 & 1.00 \\ \hline \end{tabular}
_Note_. Numbers represent probability (0=low, 1=high) of edge type in GFC1 network.
BL = Baseline, YR = follow up years
Edge types:
-> 1) V1 is a driver of V2; AND 2) V1 and V2 are not confounded; AND 3) V2 is not a driver of V1.
- 1) V2 is a driver of V1; AND 2) V1 and V2 are not confounded; AND 3) V1 is not a driver of V2.
-o 1) V2 drives V1; OR 2) V1 and V2 are confounded; OR 3) both are true.
o-o 1) V1 drives V2; OR 2) V2 drives V1; OR 3) V1 and V2 are confounded;
OR 4) Both 1) and 3) are true; OR 5) Both 2) and 3) are true. \(\(\prec\)\(\prec\)\)1) A latent variable drives
V1 and V2; AND 2) V1 and V2 are not direct drivers of each other. |
187054_file03 | ## Supplementary Results of transcriptome-wide association study of bipolar disorder performed using FUSION and eQTL data from the PsychENCODE Consortium
Genes which are labeled passed the Bonferroni corrected significance threshold of P < 3.72E-06, adjusting for 13,435 genes tested. Association results are based on two-sided tests conducted using least absolute shrinkage and selection operator (lasso), bayesian sparse linear mixed model (bslmm), elastic net or best linear unbiased prediction (blup) models. TWAS Z-score - direction of effect of bipolar disorder risk alleles on predicted gene expression level.
## Supplementary Regional plot of bipolar disorder association statistics in the extended major histocompatibility complex (MHC)
The \(x\) axis shows genomic position and the \(y\) axis shows statistical significance as -log\({}_{10}\)(_P_ value). P values are based on an inverse variance weighted fixed effects meta-analysis of 41,917 bipolar disorder cases and 371,549 controls. P values are uncorrected and two-sided. SNPs are colored by linkage disequilibrium (r\({}^{2}\)) to the top lead SNP rs13195402, which is shown as a purple diamond.
## Supplementary Odds ratio for bipolar disorder for the five most common _C4_ locus structures, in a joint analysis that includes lead SNP rs13195402
_C4_ alleles were imputed for 32,749 bipolar disorder cases and 53,370 controls. Odds ratios are calculated relative to the BS haplotype. Error bars represent the 95% confidence interval around the effect size estimate for each allele. Because many _C4_ alleles have arisen on multiple SNP haplotype backgrounds, results are shown for each specific haplogroup (small circles) as well as their combined association (large circles). There is no clear difference in bipolar disorder risk levels across these _C4_ haplotypes.
## Supplementary Association of bipolar disorder to chromosome 6 variation around and within the major histocompatibility complex (MHC) locus, including genetically predicted expression of _C4A_
The height of each point represents the statistical strength (-log10(_P_ value)) of association with bipolar disorder (BD). Genetically predicted _C4A_ expression is represented by the orange diamond.
## Supplementary Increase of phenotypic variance in bipolar disorder explained by polygenic risk scores in independent non-European datasets, as European discovery sample size increases
Variance explained is presented on the liability scale, assuming a BD population prevalence of 2%. The numbers of cases and controls are shown under the name of each test dataset from left to right. For each test dataset, we plot prediction performance as the PGC BD sample size has increased across freezes of the data. Top panel: Optimization of P value threshold in each dataset while setting the linkage disequilibrium (LD)-clumping threshold to 0.1. The color of the bars represents the P value threshold used to select SNPs from the discovery GWAS. Bottom panel: Optimization of LD-clumping threshold in each dataset while setting the P value threshold to the optimal for each dataset, selected in the top panel. The color of the bars represents the LD threshold used to clump SNPs from the discovery GWAS. P values for association of BD PRS with case-control status are shown for the best setting above each set of results. P values are based on logistic regression, are uncorrected and two-sided.
## Supplementary Bivariate MiXeR results comparing bipolar disorder (BD) to other traits of interest
Venn diagrams depict the estimated number of influencing variants shared (grey) between BD and each trait of interest and unique (colors) to either of them. The number of causal variants and standard error in thousands is shown. The size of the circles reflects the polygenicity of each trait, with larger circles corresponding to greater polygenicity and vice versa. The estimated genetic correlation (\(r_{g}\)) for each pair of traits is also shown below the corresponding Venn diagram, with an accompanying scale (negative; blue shades, positive; red shades). Conditional quantile-quantile (Q-Q) plots are shown of observed versus expected -log10 P-values in the primary trait (e.g.BD) as a function of significance of association with a secondary trait (e.g. ADHD) at the level of P <= 0.1 (orange lines), P <= 0.01 (green lines), P <= 0.001 (red lines). P values are two-sided and based on logistic or linear regressions. Blue line indicates all SNPs. Dotted lines in blue, orange, green, and red indicate model predictions for each stratum. Black dotted line is the expected Q-Q plot under null (no SNPs associated with the phenotype). Log-likelihood curves highlight the goodness of model fit, by plotting the negative log-likelihood function (lower values correspond to better model fit) against the \(\pi_{12}\) parameter (number of influencing variants shared between two traits). The remaining parameters of the model were constrained to their fitted values. The \(\pi_{12}\) range on the log-likelihood plots goes from the smallest possible value \(\pi_{12}\)=\(r_{g}\)*sqrt(\(\pi_{1}^{u}\), \(\pi_{2}^{u}\)) that is still compatible with the estimated genetic correlation, up to the largest possible value \(\pi_{12}\)=min(\(\pi_{1}^{u}\), \(\pi_{2}^{u}\)) that corresponds to the minimum total polygenicity among the two traits. The minimum point indicates the best-fitting model estimate of the number of influencing variants shared between two traits. ASD, autism spectrum disorder. EDU, educational attainment. AUD, alcohol use disorder. PAU, problematic alcohol use. DRINK, drinks per week. CPD, cigarettes per day,. MOOD, mood instability. SLEEP, sleep duration. SMOKE, smoking initiation.
|
187641_file02 | ## Figure S2 - Incidence of reported COVID-19 cases and population density in the Netherlands.
(A) The number of reported COVID-19 cases per municipality in the Netherlands over time in the period of the first outbreak, shown per 100,000 inhabitants. Data are based on SARS-CoV-2RT-PCR positive swaps obtained predominantly from hospitalized individuals or symptomatic individuals with a recent travel history to high risk areas. (B) The province of North Brabant and the municipalities of Peel en Maas and Amsterdam are highlighted by blue outlines. (C) Population density in the different municipalities of the Netherlands in 2015. All data are derived from websites by the Dutch Institute for Public Health and Environment ([https://www.rivm.nl/coronavirus-covid-19/actueel](https://www.rivm.nl/coronavirus-covid-19/actueel) and [https://www.volksgezondheidenzorg.info](https://www.volksgezondheidenzorg.info)).
## Figure S3 - SARS-CoV-2 LFA and NCP IgG ELISA results depending on month of symptom onset.
LFA and NCP ELISA results are shown for n=7144 individuals that were tested by either Boson or BIOSYNEX LFA and completed follow-up by EUROIMMUN NCP ELISA if tested positive by LFA. n=97 individuals did not provide a follow-up serum sample for ELISA in time and are not included into this analysis. Data are shown as the number (A) or proportion (B) of individuals negative or positive by LFA that had a negative, borderline or positive result in the NCP IgG ELISA, stratified by month of reported symptom onset. Out of the n=7144 individuals, a number of individual reported symptoms without a specific date of onset (n=144), no symptoms (n=827) or made no report about whether or not they had symptoms (n=470)._- SARS-CoV-2 S1 or NCP specific and neutralizing antibodies in BIOSYNEX LFA positive and negative individuals. A selection of n=266 serum samples from individuals tested in the mobile lab was assessed side-by-side by BIOSYNEX LFA, EUROIMMUN S1 and NCP IgG ELISA and sVNT. ELISA and sVNT results are shown for (A) n=60 LFA negative and (B) n=206 LFA positive serum samples.
- Correlation of SARS-CoV-2 S1 or NCP specific and neutralizing antibodies. A selection of n=266 serum samples from individuals tested in the mobile lab was assessed side-by-side by EUROIMMUN S1 and NCP IgG ELISA and sVNT. Spearman correlation analysis is shown for (A) anti-S1 vs anti-NCP IgG levels, (B) anti-NCP IgG levels versus inhibition by sVNT and (C) anti-S1 IgG levels versus inhibition by sVNT.
## Tables
## Table S1 - Claimed and verified characteristics of serological tests
\begin{tabular}{|l|l|l|l|l|} \hline & \multicolumn{2}{|c|}{**Claimed by manufacturer**} & \multicolumn{2}{|c|}{**Verified**} \\ \hline & Sensitivity & Specificity & Sensitivity\({}^{1}\) & Specificity\({}^{2}\) \\ \hline LFA & & & & \\ \hline Xiamen Boson & IgG and/or & IgM: 99.7\% & IgG and/or & IgM: 99\% \\ & IgM: 87.8\% & (304/305) & IgM: 90.5\% & (99/100) \\ & (65/74) & IgG: 99.3\% & (19/21) & IgG: 98\% \\ & & (303/305) & & (98/100) \\ \hline BIOSYNEX & IgM: 91.8\% & IgM: 99.2\% & IgG and/or & IgM: 100\% \\ & (74/81) & (372/375) & IgM: 90.0\% & (223/224) \\ & IgG:100\% & IgG: 99.5\% & (18/20) & IgG: 100\% \\ & (77/77) & (367/369) & & (224/224) \\ \hline ELISA & & & & \\ \hline EUROIMMUN IgA - S1 & 100\% (5/5)\({}^{1}\) & 92.5\% & 83\% (5/6) & 89\% (76/85) \\ & & (185/200) & & \\ \hline EUROIMMUN IgG - S1 & 90.0\% (27/30) & 100\% (80/80) & 100\% (11/11) & 98\% (87/89) \\ \hline EUROIMMUN IgG - NCP & 86.7\% (26/30) & 99.8\% & 100\% (11/11) & 100\% \\ & & (1036/1038) & & (115/115) \\ \hline Mikrogen recomWell IgG - & 100\% (28/28) & 98.7\% & 100\% (11/11) & 97\% (179/185) \\ NCP & & (296/300) & & \\ \hline
## Immunoblot
& & & & \\ \hline Mikrogen recomLine IgG & 96.3\% (52/54) & 98.8\% & 100\% (2/2) & 100\% for \\ & & (564/571) & & SARS-CoV-2 \\ & & & & \\ & & & & \\ & & & & (26/26). 92\% \\ & & & & \\ & & & & \\ & & & & \\ \hline \end{tabular}
## Surrogate Virus Neutralization Test
\begin{tabular}{|l|l|l|l|} \hline Genscript SARS-CoV-2 SVNT & 93.3\% (56/60) & 100\% (97/97) & 100\% (11/11) & 100\% (84/84) \\ (cPass(tm)) & & & & \\ \hline \end{tabular}
## 1.
These percentages have a large confidence interval due to the small number of samples available. The focus in this study was to prevent false positive results, which made sensitivity of lesser importance.
2. In all ELISA results for specificity calculations, a borderline outcome was interpreted as a positive outcome.
\begin{table}
\begin{tabular}{c|c c c c c|c c c c|c c c} & \multicolumn{2}{c|}{**The Netherlands**} & \multicolumn{2}{c|}{**North Brabant\({}^{\$}\)**} & \multicolumn{2}{c|}{**Kessel\({}^{\$}\)**} & \multicolumn{2}{c}{**Amsterdam\({}^{\$}\)**} \\ \hline & BIOSYNEX & Xiamen & **Total** & BIOSYNEX & Xiamen & **Total** & BIOSYNEX & Xiamen & **Total** & BIOSYNEX & Xiamen & **Total** \\ & & Boson & & & Boson & & & Boson & & & Boson \\ Total tested & 5630 & 1611 & **7241** & 2895 & 1405 & **4300** & 84 & 210 & **294** & 323 & 59 & **382** \\
## Symptoms\({}^{\$}\)** & & & & & & & & & & & \\ Total & 4654 & 1267 & **5921** & 2394 & 1154 & **3548** & 70 & **164** & **234** & 268 & **31** & **299** \\ LFA positive & 907 & **426** & **1333** & 482 & 396 & **878** & 16 & 79 & **95** & 46 & 12 & **58
\\
[no follow-up\({}^{\$}\)] & & & & & & & & & & & & **** \\ ELISA positive & 771 & 297 & **1068** & 417 & 274 & **691** & 15 & 69 & **84** & 37 & 9 & 46 \\
[borderline\({}^{\$}\)] & & & **** & & & **** & & & & & & **** \\ \hline
## No symptoms** & & & & & & & & & & & & \\ Total & 526 & 308 & **834** & 273 & 222 & **495** & 13 & 43 & 56 & 41 & 28 & 69 \\ LFA positive & 32 & 43 & **75** & 15 & 35 & **50** & 3 & 7 & **10** & **1** & **1** & **2
\\
[no follow-up\({}^{\$}\)] & & & & & & & & & & & \\
[class positive & 22 & 20 & **42** & 10 & 18 & 28 & 2 & 3 & 5 & 1 & 0 & **1** \\
[borderline\({}^{\$}\)] & & & **** & & & & & & & & & **** \\ \hline
## Unknown\({}^{\$}\)** & & & & & & & & & & & & \\ Total & 450 & 36 & **486** & 228 & 29 & **257** & 1 & 3 & 4 & 14 & 0 & **14** \\ LFA positive & 386 & 9 & **395** & 31 & 8 & **39** & 0 & 0 & 0 & 2 & 0 & **2
\\
[no follow-up\({}^{\$}\)] & & & **** & & & **** & & & & & & & **** \\ ELISA positive & 37 & 6 & **43** & 17 & 5 & **22** & 0 & 0 & 0 & 1 & 0 & **1** \\
[borderline\({}^{\$}\)] & & & **** & & & **** & & & & & & **** \\ \end{tabular}
\end{table}
Table 2: SARS-CoV-2 LFA and NCP IgG ELISA results by area |
188045_file02 | #missed definite** & **\#missed** & **\#missed** & **\#missed** \\ & **(CI)** & **(CI)** & & & & & **requiring** & & & **TB (\%)** & **asymptomatic** & **asymptomatic** & **TB** \\ & & & & & & **sputum testing** & & & & & **(\%)** & **(\%)** \\ \hline
## Radiolog
& 80.8 (71.7-88.0) & 66.9 (65.6-68.2) & 4.7 (3.8-5.8) & 99.4 (99.1-99.7) & 2,002 (20.2) & 25 & 19 (19.2) & 15 (15.2) \\
## ist:
Any & & & & & & & & & & & & \\ CXR & & & & & & & & & & & & \\ abnormal & & & & & & & & & & & & \\ \hline CXR & 30.3 (21.5-40.4) & 97.0 (96.5-97.4) & 16.9 (11.7-23.3) & 98.6 (98.2-98.9) & 202 (2.0) & 6.7 & 69 (69.7) & 55 (55.6) \\ & & & & & & & & & & & & \\ active TB & & & & & & & & & & & & \\ \hline
## CAD4TB** & **v5** & **v6** & **v5** & **v6** & **v5** & **v6** & **v5** & **v6** & **v5** & **v6** & **v5** & **v6** & **v5** & **v6
\\ \hline
20 & 99.0 & 92.9 & 1.4 & 11.7 & 2.0 & 2.1 & 98.5 & 98.8 & 9,047 & 6,990 & 92 & 76 & 1 (1.0) & 7 (7.0) & 0 & 5 \\ & (94.5- & 100) & 97.1 & 1.7) & (10.8- & (11.6- & (1.7- & (92.1- & (97.5- & (91.3) & (70.5) & & & (0.0) & (5.1) \\ & & 100) & 97.1) & 1.7) & 12.6) & 2.4) & 2.6) & 100) & 99.5) & & & & & \\ \hline
25 & 96.0 & 90.9 & 8.0 & 16.9 & 2.1 & 2.2 & 99 & 98.9 & 5,906 & 6,276 & 62 & 70 & 4 (4.0) & 9 (9.1) & 1 & 6 \\ & (90.0- & (83.4- & (7.3- & (15.9- & (1.7- & (1.8- & (97.4- & (98.7- & (97.4- & (98.7- & (99.5- & (59.6- & (63.3)- & & (1.0) & (6.1) \\ & 98.9- & 95.8 & 8.8- & 18) & 2.5) & 2.7) & 99.7) & 99.5) & & & & & \\ \hline
30 & 91.9 & 89.9 & 28.7 & 22.4 & 2.6 & 2.3 & 99.4 & 99.1 & 4,532 & 5,635 & 50 & 63 & 8 (8.1) & 10 (10.1) & 5 & 7 \\ & (84.7- & (82.2- & (27.5- & (21.2- & (2.1- & (1.8- & (98.9- & (98.3- & (45.7) & (56.84) & & & (5.1) & (7.1) \\ & & 96.4) & 95) & 30.0) & 23.6) & 3.1) & 2.8) & 99.8) & 99.6) & & & & \\ \hline \end{tabular}
\end{table}
Table 2: Performance of the radiologist and CAD4TRv5 and v6 to identify definite TB. Performance among participants with microbiological sputum test results (n=4,976). Definite TB was defines as either positive XpertUltra or liquid culture test result (n=99). Performance is given as sensitivity, specificity, positive predictive value (PPV) and negative predictive value (NPV) in % with 95% confidence intervals (CI), number of participants need to test and missed definite TB cases. Further listed are the percentage of participants who required sputum testing due to lung field abnormality, deemed by the radiologist and CAD4TB and the number of needed tests (NNT) to find one participant with definite TB. Numbers of missed definite TB cases (all and asymptomatic) are listed as absolute numbers and relative to all definite TB cases (n=99).
\begin{tabular}{|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|r|} \hline
48 & 72.7 & 76.8 & 71.8 & 68.0 & 5.0 & 4.6 & 99.2 & 99.3 & 1,762 & 1,997 & 25 & 26 & 27 & 23 (23.2) & 20 & 18 \\ & (62.9- & (67.2- & (70.5- & (66.7- & (3.9- & (3.7- & (98.8- & (99.5)- & (17.8) & (20.1) & & & (27.3) & & (20.2) & (18.2) & \\ & 81.2) & 84.7) & 73.1 & 69.3 & 6.2 & 5.8 & 99.5 & 99.6 & & & & & & & & \\ \hline
49 & 71.7 & 74.7 & 73.2 & 72.6 & 5.2 (4- & 5.3 & 99.2 & 99.3 & 1,684 & 1,701 & 24 & 23 & 28 & 25 (25.3) & 21 & 19 \\ & (61.8- & (65- & (72- & (71.4- & 6.5) & (4.1- & (98.8- & (99- & (17.0) & (17.2) & & & (28.3) & & (21.2) & (19.2) & \\ & 80.3) & 82.9) & 74.5 & 73.9 & & 6.6 & 99.5 & 99.6 & & & & & & & & \\ \hline
50 & 69.7 & 70.7 & 74.5 & 76.4 & 5.3 & 5.7 & 99.2 & 99.2 & 1,598 & 1,474 & 23 & 21 & 30 & 29 (29.3) & 23 & 22 \\ & (59.6- & (60.7- & (73.3- & (75.1- & (4.1- & (4.5- & (98.8- & (98.9- & (16.1)- & (14.9) & & (30.3) & & (23.2) & (22.2) & (22.2) \\ & 78.5) & 79.4) & 75.8 & 77.5 & 6.6 & 7.2 & 99.4 & 9.5 & & & & & & & \\ \hline
60 & 55.6 & 55.6 & 87.9 & 89.9 & 8.6 & 10.1 & 99.0 & 99.0 & 751 & 623 & 14 & 11 & 44 & 44 (44.4) & 35 & 34 \\ & (45.2- & (45.2- & (87.0- & (87.0- & (6.5- & (7.7- & (98.6- & (98.7- & (7.6) & (6.3) & & & (44.4) & & (35.4) & (34.3) \\ & 65.5) & 65.5) & 88.8 & 90.7 & 11 & 12.9 & 99.3 & 99.3 & & & & & & & \\ \hline
70 & 40.4 & 36.4 & 93.5 & 94.6 & 11.3 & 12.0 & 98.7 & 98.7 & 98.7 & 401 & 342 & 10 & 10 & 59 & 63 (63.6) & 45 & 49 \\ & (30.7- & (26.9- & (92.8- & (93.9- & (8.2- & (8.5- & (8.4- & (98.3- & (4.0) & (3.4) & & (59.6) & & (45.5) & (49.5) \\ & 50.7) & 46.6) & 94.2) & 95.2) & 15.0) & 16.2) & 99.0) & 99.0) & & & & & & & \\ \hline
80 & 24.2 & 19.2 & 96.2 & 97.4 & 11.5 & 13.2 & 98.4 & 98.3 & 234 & 165 & 10 & 9 & 75 & 80 (80.8) & 60 & 64 \\ & (16.2- & (12.0- & (95.6- & (97.0- & (7.5- & (8.1- & (8.1- & (98.0- & (97.9- & (2.4) & (1.7) & & & (75.8) & & (60.6) & (64.6) \\ & 33.9) & 28.3) & 96.7) & 97.9) & 16.6) & 19.8) & 98.8) & & & & & & & \\ \hline
90 & 19.2 & 4.0 & 97.9 & 99.1 & 16.0 & 8.3 & 98.4 & 98.1 & 133 & 54 & 7 & 14 & 80 & 95 (96.0) & 65 & 75 \\ & (12.0- & (1.1- & (97.5- & (98.8- & (9.9- & (2.3- & (98.0- & (97.6- & (1.3) & (0.5) & & & (80.8) & & (65.7) & (75.8) \\ & 28.3) & 10) & 98.3) & 99.3) & 23.8) & 20.0) & 98.7) & 98.4) & & & & & & \\ \hline \end{tabular}
\begin{table}
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|} \hline & **Sensitivity \% (CI)** & **Specificity \% (CI)** & **PPV \% (CI)** & **NPV \% (CI)** & **Participants** & **NNT** & **\#missed definite** & **\#missed** & **\#missed** \\ & & & & & & & & **requiring** & & **TB, trace** & **asymptomatic, trace** & **asymptomatic, trace** \\ & & & & & & & & **spunting (\%)** & & & & **excluded (\%)** & **excluded (\%)** \\ \hline
## Radiologist:
& 85.3 (75.3-92.4) & 66.9 (65.6-68.2) & 3.8 (3.0-4.8) & 99.7 (99.4-99.8) & 2,002 (20.2) & 31 & 11 (14.7) & 9 (12.0) \\
## A**y
& & & & & & & & & & & & & & & \\
**abnormality & & & & & & & & & & & & & & & & \\
## C
& 33.8 (23.0-46.0) & 97.0 (96.5-97.4) & 14.0 (9.2-20.2) & 99.0 (98.7-99.3) & 202 (2.0) & 8 & 50 (50.5) & 41 (41.4) \\
## active TB
& & & & & & & & & & & & & & & \\ \hline
## CAD4TB score** & **v5** & **v6** & **v5** & **v6** & **v5** & **v6** & **v5** & **v6** & **v5** & **v6** & **v5** & **v6** & **v5** & **v6** & **v5** & **v6** & **v5** & **v6
\\ \hline
20 & 100 & 96 (88.8-9.2) & 1.4 (1.1-1) & 11.7 (10.8-1) & 1.5 (1.2-1) & 1.6 (1.2-1) & 99.5 (1.3-1) & 99.46 (98.5-91.3) & 9,047 (70.5) & 6,990 (0.0) & 3 (4.0) & 0 (0.0) & 2 (2.7) \\ & & 100 & & 12.6 (1.9) & 1.9 (2.1-1) & 100 & 99.9 (9.1-9) & 99.9 (9.1-9) & & & & & & & \\ \hline
25 & 97.3 & 96.0 & 8.0 (7.3-16.9) & 1.6 (1.7-1) & 99.5 (1.3-2) & 99.6 (1.4-1) & 98.2-99.1 (99.1-9) & 5,906 (6.3) & 81 & 87 & 2 (2.7) & 3 (4.0) & 1 (1.3) & 2 (2.7) \\ & & 99.7 (9.2) & 18 (1.8) & 2.2 (2.2) & 99.9 (9.9-9) & 99.9 (9.1-9) & & & & & & & & \\ \hline
30 & 94.7 & 94.7 & 28.7 & 22.4 & 2.0 & 1.8 (99.7-99.6) & 4,532 (45.7) & 5,635 (56.8) & 64 & 79 & 4 (5.3) & 3 (4.0) & 3 (4.0) \\ & & (86.9-9.6) & (86.9-9.7) & (27.5-21.2-1) & (1.6-1) & (1.4-99.3-99.1-9) & (99.9-9) & & & & & & & \\
98.5 & 98.5 & 98.5 & 30.0 (23.6) & 2.5 (2.3) & 99.9 (9.9-9) & & & & & & & & \\ \hline
35 & 92.0 & 94.7 & 45.6 & 28.0 & 2.5 (2.0 & 99.7-99.7) & 3,459 (34.8) & 5,042 (50.9) & 50 & 71 & 6 (8.0) & 4 (5.3) & 5 (6.7) & 3 (4.0) \\ & & (83.4- & 68.9-4.2) & (64.2-6.7-3) & 3.2 (1.6-99.4-99.2-9) & (1.6-99.9-9) & & & & & & & & \\ \hline
40 & 85.3 & 94.7 & 57.4 & 33.3 & 2.0 & 21.9 (99.6-99.4) & 99.8 (2.67-99.4) & 4,550 (45.9) & 42 & 64 & 11 (14.7) & 4 (5.3) & 8 (10.7) & 3 (4.0) \\ & & (75.3- & 86.9- & (56- & (31.9-1).9-9.3-99.4-99.4-99.4-99.4-99.4-99.4-99.4-99.4-9.4-99.4-9.4-99.4-9.4-9.99.4-9.4-9.4-9.9-9.4-9.4-99.4-9.4-9.9.4-9.9.4-9.4-9.9-9.4-9.9.4-99.4-9.4-9.9-9.4-9.4-9.4-9.9-9.4-9.4-9.9-9.4-9.9-9.4-9.9.4-9.4-9.9-9.4-9.9-9.4-9.9-9.4-9.4-9.9-9.4-9.9-9.4-9.
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|} \hline
60 & 62.7 & 62.7 & 62.7 & 87.9 & 89.9 & 74.4 & 8.7 & 99.4 & 99.4 & 751 & 623 & 14 & 11 & 28 & 28 & 28 & 23 (30.7) & 22 (29.3) \\ & (50.7- & (50.7- & (87.6) & (87.8 & (89. & (5.5- & (6.5- & (99.1- & (99.1- & (7.6) & (6.3) & (6.3) & & (37.3) & (37.3) & & 22 (29.3) \\ & 73.6) & 73.6) & 88.8 & 90.7 & 9.7 & 11.4 & 99.6 & 99.6 & 99.6 & & & & & & & \\ \hline
70 & 44.0 & 40.0 & 93.5 & 94.6 & 9.5 & 10.2 & 99.1 & 99.0 & 401 & 342 & 10 & 10 & 42 & 45 & (56.0) & 32 (42.7) & 35 (46.7) \\ & (32.5- & (28.9- & (92.8- & (93.9- & (66.6- & (70.8- & (98.8- & (98.7- & (4.0) & (3.4) & (3.4) & & (56.0) & (60.0) & 32 (42.7) & 35 (46.7) \\ & 55.9) & 52.0 & 94.2) & 95.2 & 13.1 & 14.2 & 99.3 & 99.3 & & & & & & & \\ \hline
80 & 26.7 & 18.7 & 96.2 & 97.4 & 9.8 & 10.1 & 98.8 & 98.7 & 234 & 165 & 10 & 9 & 55 & 61 & 44 (58.7) & 49 (65.3) \\ & (17.1- & (10.6- & (95.6- & (97. & (6.1- & (5.6- & (98.4- & (2.4) & (1.7) & & & (73.3) & (81.3) & & 44 (58.7) \\ & 38.1) & 29.3) & 96.7) & 97.9 & 14.7 & 16.3 & 99.1 & 99.1 & 99.9 & & & & & & \\ \hline
90 & 20.0 & 5.3 (1.5- & 97.9 & 99.1 & 13.0 & 8.3 & 98.8 & 98.6 & 133 & 54 & 7 & 14 & 60 & 71 & 49 (65.3) & 56 (74.7) \\ & (11.6- & (13.1) & (97.5- & (98.8- & (7.5- & (2.3- & (98.4- & (98.2- & (1.3) & (0.5) & & & (80.0) & (94.7) & & \\ & 30.8) & & & 98.3) & 20.6 & 20.0 & 99.1 & 98.9 & & & & & & & & \\ \hline \end{tabular}
## Table S3: Performance of CAD4TBv5 to identify probable TB.
Performance among participants who underwent chest radiography (n=9,914). Probable TB was defined as radiological evidence indicated by the radiologist by 'CXR diagnostic of active TB' but no microbiological evidence (n=172). Performance is given as sensitivity, specificity, positive predictive value (PPV) and negative predictive value (NPV) in % with 95% confidence intervals (CI). The numbers of missed probable TB cases (all and asymptomatic) are listed as absolute numbers absolute and relative to all probable TB cases (n=172).
\begin{tabular}{|r|l|l|l|l|l|l|l|l|l|l|l|l|l|l|} \hline
80 & 62.8 & 44.8 & 98.7 & 99.1 & 46.2 & 46.7 & 99.3 & 99.0 & 64 & 95 & 46 & 68 \\ & (55.1- & (37.2- & (98.5- & (98.9- & (39.6- & (39.6- & (38.9- & (99.2- & (98.8- & (37.2) & (55.2) & (26.7) & (39.5) \\ & 70) & 52.5) & 98.9) & 99.3) & 52.8) & 54.6) & 99.5) & 99.2) & & & \\ \hline
90 & 41.9 & 18.6 & 99.4 & 99.8 & 54.1 & 59.3 (45- & 99.0 & 98.6 & 100 & 140 & 74 & 104 \\ & (34.4- & (13.1- & (99.2- & (99.7- & (45.3- & 72.4) & (98.8- & (98.8- & (58.1) & (81.4) & (43.0) & (60.5) \\ & 49.6) & 25.2) & 99.5) & 99.9) & 62.8) & & 99.2) & 98.8) & & & \\ \hline \end{tabular}
\begin{tabular}{|r|l|l|l|l|l|l|l|l|l|l|l|l|l|l|} \hline
80 & 62.8 & 44.8 & 98.7 & 99.1 & 46.2 & 46.7 & 99.3 & 99.0 & 64 & 95 & 46 & 68 \\ & (55.1- & (37.2- & (98.5- & (98.9- & (39.6- & (39.6- & (38.9- & (99.2- & (98.8- & (37.2) & (55.2) & (26.7) & (39.5) \\ & 70) & 52.5) & 98.9) & 99.3) & 52.8) & 54.6) & 99.5) & 99.2) & & & \\ \hline
90 & 41.9 & 18.6 & 99.4 & 99.8 & 54.1 & 59.3 (45- & 99.0 & 98.6 & 100 & 140 & 74 & 104 \\ & (34.4- & (13.1- & (99.2- & (99.7- & (45.3- & 72.4) & (98.8- & (98.8- & (58.1) & (81.4) & (43.0) & (60.5) \\ & 49.6) & 25.2) & 99.5) & 99.9) & 62.8) & & 99.2) & 98.8) & & & \\ \hline \end{tabular}
\begin{table}
\begin{tabular}{|l|l|l|} \hline & CAD4TBv5 & CAD4TBv6 \\ \hline Define TB vs. Definite TB, trace excluded & 0.28 & 0.18 \\ \hline Define TB vs. Probable TB & 5.25x10-11 & 9.05x10-10 \\ \hline Define TB, trace excluded vs. Probable TB & 4.51x10-7 & 2.5x10-6 \\ \hline \end{tabular}
\end{table}
Table 6: P-values of comparing the diagnostic performance of CAD4TB to gold standards measured in area under the curve (AUC) between HIV-positive and negative individuals.** Gold standards were defined as either definite TB with microbiological evidence (M+), definite TB excluding M+ samples that only had a XpertUltra trace result, or probable TB with no microbiological evidence but radiological signs of TB (M-/0 R+). CAD4TB scores from version 5 (v5) and 6 (v6) were compared against these gold standards.
\begin{table}
\begin{tabular}{|l|l|l|l|} \hline & **Definite TB** & **Definite TB trace excl.** & **Probable TB** \\ \hline v5 AUC (CI) & 0.78 (0.73-0.83) & 0.82 (0.77-0.87) & 0.96 (0.95-0.98) \\ \hline v5 AUC (CI) HIV-negative & 0.75 (0.68-0.83) & 0.81 (0.74-0.89) & 0.96 (0.93-0.98) \\ \hline v5 AUC (CI) HIV-positive & 0.80 (0.72-0.87) & 0.82 (0.74-0.89) & 0.97 (0.96-0.99) \\ \hline v6 AUC (CI) & 0.79 (0.73-0.84) & 0.84 (0.79-0.89) & 0.96 (0.95-0.98) \\ \hline v6 AUC (CI) HIV-negative & 0.76 (0.68-0.84) & 0.83 (0.76-0.91) & 0.95 (0.93-0.98) \\ \hline v6 AUC (CI) HIV-positive & 0.81 (0.74-0.88) & 0.82 (0.76-0.89) & 0.97 (0.97-0.98) \\ \hline \end{tabular}
\end{table}
Table 4: Area under the receiver operating curves (AUC) from CAD4TBv5 and v6 compared to diagnostic microbiological and/or radiological evidence. Positive TB was defined as either definite TB with microbiological evidence, definite TB excluding samples that only had a XpertUltra trace result, or probable TB with radiological signs of TB but no microbiological evidence.
\begin{table}
\begin{tabular}{|l|l|l|} \hline & **Definite TB** & **Definite TB trace excl.** & **Probable TB** \\ \hline v5 AUC (CI) & 0.78 (0.73-0.83) & 0.82 (0.77-0.87) & 0.96 (0.95-0.98) \\ \hline v5 AUC (CI) HIV-negative & 0.75 (0.68-0.83) & 0.81 (0.74-0.89) & 0.96 (0.93-0.98) \\ \hline v5 AUC (CI) HIV-positive & 0.80 (0.72-0.87) & 0.82 (0.74-0.89) & 0.97 (0.96-0.99) \\ \hline v6 AUC (CI) & 0.79 (0.73-0.84) & 0.84 (0.79-0.89) & 0.96 (0.95-0.98) \\ \hline v6 AUC (CI) HIV-negative & 0.76 (0.68-0.84) & 0.83 (0.76-0.91) & 0.95 (0.93-0.98) \\ \hline v6 AUC (CI) HIV-positive & 0.81 (0.74-0.88) & 0.82 (0.76-0.89) & 0.97 (0.97-0.98) \\ \hline \end{tabular}
\end{table}
Table 5: P-values of comparing the diagnostic performance of CAD4TB to gold standards measured in area under the curve (AUC) between diagnostic groups.
*Vukuzazi Team: Staff who significantly contributed to the implementation and conduct of Vukuzazi.
* Denotes team members who were closely involved with the design, implementation and oversight of Vukuzazi.
\begin{tabular}{|l|l|} \hline
## Name** & **Role
\\ \hline *Alison Grant\({}^{2,4,6,10}\) & Co-investigator \\ \hline Anand Ramananan\({}^{2}\) & Procurement \\ \hline Anele Mkhwanazi\({}^{2}\) & Clinical Research Assistant Supervisor \\ \hline Antony Rapulana\({}^{2}\) & Laboratory Technologist \\ \hline Anupa Singh\({}^{2}\) & Laboratory Technician \\ \hline Ashentha Govender\({}^{2}\) & Laboratory Technician \\ \hline *Ashmika Surujdeen\({}^{2}\) & Study Coordinator \\ \hline Ayanda Zungu\({}^{2}\) & Clinical Research Assistant \\ \hline Boitsholo Mfolo\({}^{14}\) & Radiographer \\ \hline Bongani Magwaza\({}^{2}\) & General Worker \\ \hline Bongumenzi Ndlovu\({}^{2}\) & Enrolled Nurse \\ \hline Clive Mavimbela\({}^{2}\) & Operational Oversight \\ \hline Costa Criticos\({}^{2}\) & Operational Oversight \\ \hline *Day Munatsi\({}^{2}\) & Head: Research Data Systems \\ \hline *Deenan Pillay\({}^{2,5}\) & Principal Investigator \\ \hline *Dickman Gareta\({}^{2}\) & Head: Research Data Management \\ \hline Dilip Kalyan\({}^{2}\) & Operational Oversight \\ \hline Doctar Mlambo\({}^{2}\) & Enrolled Nurse \\ \hline *Emily Wong\({}^{2,11,12,13}\) & Co-Principal Investigator \\ \hline Fezeka Mfeka\({}^{2}\) & Clinical Research Assistant \\ \hline Freddy Mabetlela\({}^{2}\) & Laboratory Technologist \\ \hline *Gregory Ording-Jespersen\({}^{2}\) & Laboratory Data Supervisor \\ \hline Hannah Keal\({}^{2}\) & Communications \\ \hline Hlengiwe Dlamini\({}^{2}\) & Enrolled Nurse \\ \hline \end{tabular}
Hlengiwe Khathi\({}^{2}\) & Biorepository Research Assistant
Hlobisile Chonco\({}^{2}\) & Enrolled Nurse
Hlobisile Gumede\({}^{2}\) & Clinical Research Assistant
Hlobisile Gumede\({}^{2}\) & Clinical Research Assistant
Hlolisile Khumalo\({}^{2}\) & Nursing Manager
Hloniphile Ngubane\({}^{2}\) & Professional Nurse
*Hollis Shen\({}^{2}\) & Head: Exploratory Research Division
Hosea Kambonde\({}^{15}\) & IT Systems Developer
*Innocentia Mpofana\({}^{2}\) & Diagnostic Laboratory Manager
Jabu Kwinda\({}^{14}\) & Driver
*Jaco Dreyer\({}^{2}\) & Senior Research Data Manager
Jade Cousins\({}^{2}\) & Laboratory Technologist
Jaikrishna Kalideen\({}^{16}\) & Radiologist
*Janet Seeley\({}^{6}\) & Co-investigator
Kandaseelan Chetty\({}^{2}\) & Laboratory Technician
*Kathy Baisley\({}^{2,6}\) & Co-investigator
Kayleen Brien\({}^{2}\) & Laboratory Technologist
Kennedy Nyamande\({}^{17}\) & Pulmonary Consultant
Kgaugelo Moropane\({}^{14}\) & Radiographer
Khabonina Malomane\({}^{14}\) & Radiographer
*Khadija Khan\({}^{2}\) & Biorepository Manager
Khanyisani Buthelezi\({}^{2}\) & Professional Nurse
Kimeshree Perumal\({}^{2}\) & Laboratory Intern
*Kobus Herbst\({}^{2}\) & Co-investigator
Lindani Mthembu\({}^{2}\) & Information Technology Assistant
Logan Pillay\({}^{2}\) & Laboratory Technician
Mandisi Dlamini\({}^{2}\) & Enrolled Nurse
Mandlakayise Zikhali\({}^{2}\) & Clinical Research Assistant Supervisor
*Mark Siedner\({}^{2,10,11,12}\) & Co-Principal InvestigatorMbali Mbuyisa\({}^{2}\) & Enrolled Nurse \\ \hline Mbuti Mofokeng\({}^{2}\) & Clinical Specimen Driver/Laboratory Assistant \\ \hline Melusi Sibiya\({}^{2}\) & Enrolled Nurse \\ \hline Mlungisi Dube\({}^{2}\) & Clinical Research Assistant \\ \hline Mosa Suleman\({}^{17}\) & Pulmonology Consultant \\ \hline Mpumelelo Steto\({}^{2}\) & Driver \\ \hline Mzamo Buthelezi\({}^{2}\) & Clinical Research Assistant \\ \hline Nagavelli Padayachi\({}^{2}\) & Laboratory Technologist \\ \hline Nceba Gqaleni\({}^{2,18}\) & Public Engagement \\ \hline *Ngcebo Mhlongo\({}^{2}\) & Study Physician \\ \hline Nokukhanya Ntshakala\({}^{2}\) & Laboratory Technician \\ \hline Nomathamsanqa Majozi\({}^{2}\) & Public Engagement \\ \hline Nombuyiselo Zondi\({}^{2}\) & Professional Nurse \\ \hline Nomfundo Luthuli\({}^{2}\) & Laboratory Technician \\ \hline Nomfundo Ngema\({}^{2}\) & Laboratory Technician \\ \hline Nompilo Buthelezi\({}^{2}\) & Training Coordinator \\ \hline Nonceba Mfeka\({}^{2}\) & Clinical Research Assistant \\ \hline Nondumiso Khulusue\({}^{2}\) & Biorepository Laboratory Technician \\ \hline Nondumiso Mabaso\({}^{2}\) & Laboratory Intern \\ \hline Nondumiso Zitha\({}^{2}\) & Biorepository Research Assistant \\ \hline Nonhlanhla Mfekayi\({}^{2}\) & Clinical Research Assistant \\ \hline Nonhlanhla Mzimela\({}^{2}\) & Enrolled Nurse \\ \hline Nozipho Mbonambi\({}^{2}\) & Professional Nurse \\ \hline Ntombiyenhlanhla Mkhwanazi\({}^{2}\) & Clinical Research Assistant \\ \hline Ntombiyenkosi Ntombela\({}^{2}\) & Enrolled Nurse \\ \hline *Olivier Koole\({}^{2,6}\) & Co-Principal Investigator \\ \hline Pamela Ramkalawon\({}^{2}\) & Laboratory Research Technician \\ \hline Pfarelo Tshivase\({}^{17}\) & Driver \\ \hline Phakamani Mkhwanazi\({}^{2}\) & Clinical Research Assistant \\ \hline \end{tabular}
Philippa Mathews\({}^{2}\) & Clinical Governance
\begin{tabular}{|l|l|} \hline Phumelele Mthethwa\({}^{2}\) & Enrolled Nurse \\ \hline Phumla Ngcobo\({}^{2}\) & Communications \\ \hline Ramesh Jackpersad\({}^{19}\) & Radiologist \\ \hline Raynold Zondo\({}^{2}\) & Operational Oversight \\ \hline *Resign Gunda\({}^{2,4,5}\) & Programme Manager \\ \hline Rochelle Singh\({}^{2}\) & Laboratory Technician \\ \hline Rose Myeni\({}^{2}\) & Clinical Research Assistant \\ \hline *Sanah Bucibo\({}^{2}\) & Lead Nurse \\ \hline Sandile Mthembu\({}^{2}\) & Enrolled Nurse \\ \hline *Sashen Moodley\({}^{2}\) & Microbiology Laboratory Supervisor \\ \hline Sashin Harilall\({}^{2}\) & Grants Office \\ \hline Senamile Makhari\({}^{2}\) & Biorepository Laboratory Technician \\ \hline Seneme Mchunu\({}^{2}\) & Information Technology Assistant \\ \hline Senzeni Mkhwanazi\({}^{2}\) & Clinical Research Assistant \\ \hline Sibahle Gumbi\({}^{2}\) & Research Admin Assistant \\ \hline Siboniso Nene\({}^{2}\) & Professional Nurse \\ \hline Sibusios Mhlongo\({}^{2}\) & Driver \\ \hline Sibusios Mkhwanazi\({}^{2}\) & Driver \\ \hline Sibusios Nsibande\({}^{2}\) & Driver \\ \hline Simphiwe Ntshangase\({}^{2}\) & Laboratory Technician/LIMS Administrator \\ \hline Siphephelo Dlamini\({}^{2}\) & AHRI Nursing Manager \\ \hline Sitemobile Ngcobo\({}^{2}\) & Laboratory Technologist \\ \hline Siyabonga Nsibande\({}^{2}\) & General Worker \\ \hline *Siyabonga Nxumalo\({}^{2}\) & Research Data Manager \\ \hline Sizwe Ndlela\({}^{2}\) & Laboratory Technician \\ \hline Skhumbuzo Mthombeni\({}^{2}\) & General Worker \\ \hline Smangaliso Zulu\({}^{2}\) & Clinical Research Assistant \\ \hline Sphiive Clement Mthembu\({}^{2}\) & General Worker \\ \hline \end{tabular}
\begin{tabular}{|l|l|} \hline Sphiwe Ntuli\({}^{2}\) & Professional Nurse \\ \hline \multicolumn{2}{|l|}{*Stephen Olivier\({}^{2}\)} & Statistician \\ \hline Talente Ntimbane\({}^{2}\) & Enrolled Nurse \\ \hline Thabile Zondi\({}^{2}\) & Laboratory Technologist \\ \hline \multicolumn{2}{|l|}{*Thandeka Khoza\({}^{2}\)} & Co-investigator (2019-present) \\ \hline Thengokwakhe Nkosi\({}^{2}\) & Driver \\ \hline \multicolumn{2}{|l|}{*Theresa Smit\({}^{2}\)} & Head: Diagnostic Research \\ \hline Thokozani Bhengu\({}^{2}\) & Enrolled Nurse \\ \hline Thokozani Simelane\({}^{2}\) & Professional Nurse \\ \hline \multicolumn{2}{|l|}{*Thumbi Ndung'u\({}^{2,5,7,8,9}\)} & Co-investigator \\ \hline \multicolumn{2}{|l|}{*Tshwaraganang Modise\({}^{2}\)} & Research Data Manager \\ \hline Tumi Madolo\({}^{2}\) & Research Data Manager \\ \hline Velile Vellem\({}^{14}\) & Driver \\ \hline Welcome Petros Mthembu\({}^{2}\) & Enrolled Nurse \\ \hline \multicolumn{2}{|l|}{*Willem Hanekom\({}^{2}\)} & Principal Investigator (2019-present) \\ \hline Xolani Mkhize\({}^{2}\) & Enrolled Nurse \\ \hline Zamashandu Mbatha\({}^{2}\) & Enrolled Nurse \\ \hline Zinhle Buthelezi\({}^{2}\) & Enrolled Nurse \\ \hline Zinhle Mthembu\({}^{2}\) & Enrolled Nurse \\ \hline \multicolumn{2}{|l|}{*Zizile Sikhosana\({}^{2}\)} & Somkhele Laboratory Supervisor \\ \hline \end{tabular} |
19010082 | ## Methods
### TCGA datasets
We obtained the 32 cancer multi-omic datasets from NCBI using TCGA portal ([https://tcga-data.nci.nih.gov/tcga/](https://tcga-data.nci.nih.gov/tcga/)). We used the package TCGA-Assembler (versions 2.0.5) and wrote custom scripts to download RNA-Seq (UNC IlluminaHiSeq RNASeqV2), miRNA Sequencing (BCGSC IlluminaHiSeq, Level 3), and DNA methylation (JHU-USC HumanMethylation450) data from the TCGA website on November 4-14\({}^{\text{th}}\), 2017. We also obtained the survival information from the portal: [https://portal.gdc.cancer.gov/](https://portal.gdc.cancer.gov/). We used the same preprocessing steps as detailed in our previous study. We first downloaded RNA-Seq, miRNA-Seq and methylation data using the functions _DownloadRNASeqData_, _DownloadmiRNASeqData_, and _DownloadMethylationData_ from TCGA-Assembler, respectively. Then, we processed the data with the functions _ProcessRNASeqData_,_ProcessmiRNASeqData_, and _ProcessMethylation450Data_. In addition, we processed the methylation data with the function _CalculateSingleValueMethylationData_. Finally, for each omic data type, we created a gene-by-sample data matrix in the Tabular Separated Value (TSV) format using a custom script.
### Validation datasets
For breast cancer data, we use four public breast cancer gene expression microarray datasets and one Metabric RNA-Seq dataset as the validation datasets. Four public datasets (all on Affymetrix HG-U133A microarray platform) were downloaded from Gene Expression Omnibus (GEO). Their accession IDs are GSE4922, GSE1456, GSE3494 and GSE7390. Their pre-processing was described in a previous study. For the Metabric dataset, we obtained approval from the Synapse repository: [https://www.synapse.org/#](https://www.synapse.org/#)!Synapse:syn1688369, and used the provided normalized data described in the Breast Cancer Challenge. The metabric dataset consists of 1981 breast cancer samples, from which we extracted RNA-Seq data. For hepatocarcinoma datasets, we used two larger datasets: LIRI and GSE datasets, as described in the previous study.
### DeepProg framework
DeepProg is a semi-supervised flexible hybrid machine-learning framework that takes multiple omics data matrices and survival information as the input. For each sample \(s\), the survival data have two features: the observation time \(t\) and the observed event (death) \(e\). The pipeline is composed of the following unsupervised and supervised learning modules (the detail of each step is described in the subsequent paragraphs). Module 1: unsupervised subtype inference: each input matrix is processed with: a) normalization, b) transformation using an autoencoder for each omics data type, and c) selection of the survival-associated latent-space features from the bottle neck layer of autoencoders. The selected survival-associated latent-space features from all the omics are then combined for clustering analysis. Module 2: supervised prediction of a new sample, this module is composed of the following steps: a) construction of a classifier using the training set, b) selection and normalization of the common featureswith the new sample, c) prediction. For both unsupervised and supervised inferences, we use an ensemble of DeepProg models through boosting approach: each model is constructed with a random subset (80%) of the training dataset. The clustering and the prediction results are combined according to the relevance of each model.
### Normalization
As default, DeepProg first selects the top 100 features from the training set that have the highest variance. Then for each sample, we inversely rank the features and divide them by 100, so that the score is normalized between 0 and 1. Next we compute the sample-sample Pearson correlation matrix of size \(n\), the number of samples. For each sample, we use the sample-sample distances as new features and normalize them using the rank as well. As a result, each sample has \(n\) features with the score of the first feature equal to 1.0 and the last feature equal to 0.
To normalize a new sample (in the model prediction stage), we first select the set of common features between the new sample and the training set. We then perform the same steps as described above: a) selection of top 100 features, b) rank-based normalization, c) distance computation with the samples from the training set, and d) rank normalization.
### Autoencoder transformation
An autoencoder is a function _f_(_v_) = _v'_ that reconstructs the original input vector \(v\) composed of \(m\) features through multiple nonlinear transformations (_size_(_v_) = _size_(_v'_) = _m_). For each omic data type, we create one autoencoder with one hidden layer of size \(h\) (default 100) that corresponds to the following equation:
\[f(v) = tanh\ \left( {W^{\prime}.s(W.v + b)\ +\ b^{\prime}} \right)\]
_W'_, \(W\) are two weight matrices of size _h by m_ and _m by h_, and b, b' are two bias vectors of size \(h\) and _h'_. _tanh_ is a nonlinear, element-wise activation function defined as
\[f(x)\ =\ \left( {exp(x)\ -\ exp(-x)} \right)/\left( {exp(x)\ +\ exp(-x)} \right).\]To train our autoencoders, we search the optimal _W*, W*, b*_ and b'* that minimizes the log-loss function.
We use python (2.7) Keras package (1.2.2) with theano as tensor library, to build our autoencoders. We use the Adam optimization algorithm to identify _W*, W*, b*_ and b'*. We train our autoencoder on 10 epochs and introduce 50% of dropout (i.e. 50% of the coefficients from W and W' will be randomly set to 0) at each training iteration.
#### Hyperparameter tuning
To help selecting the best set of hyperparameters (i.e. number of epochs, network shape, dropout rate...), DeepProg has an optional hyperparameter tuning module based on Gaussian optimization and it relies on the _scikit-optimize_ ([https://scikit-optimize.github.io/stable/](https://scikit-optimize.github.io/stable/)) and the _tune_ ([https://docs.ray.io/en/latest/tune.html](https://docs.ray.io/en/latest/tune.html)) python libraries. The computation of the ensemble of models and/or the hyperparameters grid-search can optionally be distributed on multiple nodes and external supercomputers using the python ray framework ([https://docs.ray.io/en/latest/](https://docs.ray.io/en/latest/)).
#### Selection of new hidden-layer features linked to survival
For each of the transformed feature in the hidden layer, we build a univariate Cox-PH model using the python package _lifelines_ ([https://github.com/CamDavidsonPilon/lifelines](https://github.com/CamDavidsonPilon/lifelines)) and identify those with log-rank p-values (Wilcoxon test) \(<\) 0.01. We then extract all the significant new latent features from all autoencoders and combine them as a new matrix Z.
#### Cancer subtype detection
The default clustering method to identify subtypes is the gaussian mixture model-based clustering. We use the _GaussianMixture_ function from the scikit-learn package with 1000 iterations, 100 initiations and a diagonal covariance matrix. The resulting clusters are sorted according to their median survival levels: the cluster labelled as "0" has the overall lowest median survival, while the last cluster "N" has the highest survival overall. Other clustering methods, K-means and dichotomized Lasso Cox-PH model, can replace the default gaussian mixture method.
#### Construction of supervised classifiers to predict the cancer subtype in new samples
We use the cluster labels obtained from the above Gaussian mixture model to build several supervised machine learning models that can classify any new sample, under the condition that they have at least a subset of features in common with those input features from the training set. First, we compute a Kruskal-Wallis test for each omic type and each feature, in order to detect the most discriminative features with respect to the cluster labels. Then we select the 50 most discriminative features for each omic type and combine them to form a new training matrix M. We apply Support Vector Machine (SVM) algorithm to construct a predictive model using M as the input and the cluster labels as classes. To find the best hyperparameters of the classifier, we perform a grid-search using a 5-fold cross-validation on M, with the objective to minimize the errors of the test fold. The algorithm constructs at first a classifier using all the omic types from the training samples. If a new sample shares only a subset of omics data types and a subset of the features with the training samples (eg. a sample has only RNA-Seq measurement), then DeepProg constructs a classifier using only this subset of omics data type and features, before applying it to the new sample. We use the python _sklearn_ package to construct SVM models and infer the class probability with the _predict_proba_ function, by fitting a logistic regression model on the SVM scores.
#### Boosting procedure to enhance the robustness of DeepProg
To obtain a more robust model, we aggregate multiple DeepProg models constructed on a random subset of the training samples. As the default, we use 10 models with 80% of original training samples to construct all the cancer models, except for LUSC and PRAD which we use 20 models since they are more difficult to train. The aggregation of these models (per cancer) works as the following: after fitting, we eliminate those models without any new features linked to survival or having no cluster labels significantly associated with survival (log-rank p-value > 0.05). For a given sample, the probability of belonging to a particular cancer subtype is the average of the probabilities given by all the remaining models. We use the class probability of the worst survival subtype to assign the final label.
### Choosing the correct input number of clusters and performance metrics
When fitting a model, DeepProg computes several quality metrics: the log-rank p-value for a Cox-PH model using the cluster labels from all or only the hold-out samples as described above, the concordance index (C-index), and the Silhouette score measuring the clusters homogeneity. In addition, DeepProg measures the clustering stability, that is, the consistency of class labeling among the different models during boosting. We compute the clustering as the following: _a)_ For each pair of models, we compute the adjusted Rand Index between the two set of cluster labels (ARI), _b)_ we then calculate the mean of all the pair-wise rand indexes. For each cancer model we test different initial number of clusters (K=2,3,4,5). We then select the K presenting the best overall results based on silhouette score. Furthermore, we also select carefully the K that minimizes the crossovers on the Kaplan-Meier (KM) plots, when plotting the stratified patient survival groups according to the cluster labels.
To identify the input omics features differentially expressed between the worst survival subtype and other(s), we perform two-group (worst survival subgroup and the other remaining samples) Wilcoxon rank-sum test for each feature, using the Scipy.stats package. We then select features significantly over- or under-expressed with p-values\(<\)0.001. Next, we rank the differentially expressed features among the 32 cancers. For this purpose, we construct a Cox-PH model for each cancer and each significant feature and rank the features according to their -log10 (log-rank p-value). We then normalize the ranks among these significant features between 0 and 1, where 1 is attributed to the feature with the lowest Cox-PH log-rank p-value and 0 is assigned to the feature with the highest Cox-PH log-rank p-value in the set. We then sum the ranks of each feature among the 32 cancers to obtain its final score.
We use xCell web interface to infer the tumor composition amongst 67 reference cell types. We construct 11-penalized logistic regression using the _statsmodels_ python library model, _fit_regularized_ function from the _logit_ class with alpha=1.0 for each gene with and without the tissue composition as cofounders and using the cluster labels as outcome. Prior to the regression, we scale the features to have mean=0 and std=1 for each features using the _RobustScaler_ from scikit-learn. We rank the significant (the two-tailed t-stats p-values <0.05) coefficient for the two types of models and compared their overall similarities using the Kendall-Tau correlation measurement similar to before.
#### Comparison with other data integration methods
To infer clusters from SNF, we use rpy2 to call SNF from python with the '_ExecuteSNF_' function from the _CancerSubtypes_ R library (v1.16) with the default parameters and use the same number of clusters (\(k\)) for DeepProg. We also substitute the autoencoder step of the DeepProg configuration with two other matrix factorization methods: MOFA+ and MAUI, using TCGA HCC and BRCA datasets. In each alternative approach, we transform the multi-omic matrices into 100 new components, followed by the same remaining steps in DeepProg (eg. survival associated feature filtering, clustering). For MOFA+ method (package _MOFA_), we obtain 100 features using the following parameters _iterations\(=\)500, convergence_mode\(=\)'slow', startELBO=1, freqELBO=1_. For MAUI (package _maui_ for python3, Released: Sep 17, 2020), we obtain 100 latent features using the following parameters _learning rate \(=\) 0.0001, epochs\(=\)500, one hidden layer of 1100 nodes_. However, none of the 100 features is significantly (P\(<\)0.05) associated with survival in Cox-PH regression step of DeepProg workflow. Finally, we also substitute the autoencoder step by standard PCA using the _scikit-learn_ python library.
#### Construction of the co-expression network
For each cancer, we first identify (at most) the top 1000 RNA-Seq genes enriched in the worst subtype according to their Wilcoxon rank test p-value. We then use these genes to construct a Gene RegulatoryNetwork. For each pair of genes (nodes), we obtain an interaction score based on their correlations, and assign it to the edge between them. For each network, we normalize the scores by dividing them with the maximal value. We then score each gene with the sum of its edge scores. We combine the network obtained for the 32 cancers into a global pan-cancer co-expression network, using the GRNBoost2 algorithm from the python package \(arboreto\). Specifically, we use the following steps: _a)_ aggregating the nodes, node weights, edges, and edge weights of each cancer network into a consensus graph, _b)_ selecting the top 200 genes and construct its corresponding subgraph, _c)_ performing edge pruning on each gene by removing all but the top 10 edges, according to their weights, and _d)_applying a community detection algorithm on the graph using the random-walk algorithm from the python library igraph, and visualizing the graph using Gephi.
|
19013136 | ## MATERIALS AND METHODS
### Data collection and pre-processing
We obtained in total 175 records by searching public metagenomic databasesincluding NCBI PubMed and GMrepo using key words such as metagenomics and relevant disease names (see Fig. S1 for details). We aimed to collect metagenomics sequencing data with high-resolution for better understanding the functions of microbes. After filtering out the duplicates, 16s rRNA sequencing data and the metagenomics data without detailed metadata or not meeting minimum samples requirements, we selected in total thirteen metagenomics datasets, including three, three, and seven datasets for CD, UC and CRC respectively. Please consult Fig. S1 for the selection procedure and results, and Table S1 for the thirteen datasets.
* Raw sequencing reads were retrieved from European Nucleotide Archive (ENA) under the following identifiers: PRJEB6070, PRJEB27928.
* PRJEB12449, PRJEB10878, PRJEB7774, PRJDB4176, cohort 1 of PRJNA447983, SRP057027, PRJEB1220.
* PRJNA400072 and PRJNA389280; sample metadata were also downloaded from ENA. For projects containing samples resulting from longitudinal surveys, i.e., participants were sampled multiple times over extended periods of time and/or during treatment/intervention, including SRP057027, PRJEB1220 and PRJNA389280, we selected the first time-point from each participant to avoid false positive in following analysis. In total, we obtained in total 632 non-disease controls and 763 patients for the following meta-analysis, including 354, 177 and 232 samples of CRC, UC and CD (Table S1).
Taxonomic and functional profiling of metagenomics data
* 2 To keep only the high quality data, low quality reads and adapters were firstly removed via Trimmomatic (version 0.35) using the Truseq3 adapter files (TruSeq3-PE.fa for paired-end data and TruSeq3-SE.fa for single-end data) and a MINLEN cutoff of 50. The remaining "clean" reads were then mapped to the human reference genome (hg19) using bowtie2 (version 2.3.4.3) with default settings to identify and remove human reads. The identified human reads were also used to compute HDC for each sample as the percentage of mapped reads out of total clean reads, which have been shown to be a marker for intestinal barrier dysfunction and correlate with the marker species of several intestinal diseases. For samples that were sequenced multiple times (e.g., for the purpose of increasing sequencing depths), the resulting multiple sequencing files were merged before further analysis. The merged and clean non-human reads were then quantified in taxonomic and functional levels using MetaPhilAn2 mapping to mpa_v20_m200 database and HUMAnN2 mapping to ChocoPhilAn database and full UniRef90 database.
* 18 To avoid the noise of low-abundance, pathways with zero value in over 15% samples of a dataset were excluded. Species and pathways that did not meet a maximum relative abundance cutoff of 1x10-3 and 1x10-6 separately in at least 50% datasets for a specified disease were removed. The abundance data were then loaded into R (ver 3.6.3 mainly; [https://www.r-project.org](https://www.r-project.org)) and analyzed.
* 2 Controlling for confounding factors and identification of marker species and pathways
* 3 Within-project confounding factors, i.e., those showed significant differences between phenotype groups in a dataset were firstly identified using Wilcoxon rank sum test or chi-squared test on per-dataset basis. Then, the identified confounding factors (see Table S1 for the results) in differential analysis were controlled for using MaAsLin2 package in R ver 4.0.0, a multivariable analysis tool to adjust the covariates and identify association effects of the species and pathways to disease in each dataset. Accounting for the heterogeneity between datasets, we performed meta-analysis to aggregate the association effects via MMUPHin package in R ver 4.0.0, and identify the final "maker" species and pathways. Here an adjusted p-value < 0.05 from meta-analysis was used as the cutoff for the makers.
* 4 Clustering of disease-enriched species and their prevalence in the three diseases
* 5 Consistently disease-enriched marker species (i.e., those were marker species in at least two datasets of the same disease) were grouped into disease-specific or common to multiple diseases according to their association with the diseases. To observe the prevalence of the clusters in the overall patients and a unique disease (i.e., CRC, CD and UC), their prevalence in the diseased samples were first calculated: for each selected marker species, its 95% percentile abundance in all controls was used as a cutoff to defined its presence ("1", i.e., its relative abundance in the sample was higher than the 95% quantile relative abundance of all control samples) or absence ("0"). By doing so, we obtained a binarized matrix with each row representing a disease-enriched marker microbe, and each column representing a patient. The prevalence matrix from all patients was used to calculate the Jaccard distances among the species using the diversity function of vegan package. We compared the inner Jaccard similarities among the clusters of disease-enriched marker species using Wilcoxon rank sum test (for pairwise comparisons) and Kruskal-Wallis rank sum test (for multi-group comparisons). The prevalence of each cluster between patients and controls in each disease were also compared using the Cochran-Mantel-Haenszel test with "dataset" as the blocked object by cmh_test function of coin package. Phylogenetic relationship of disease-enriched marker species To show the phylogenetic relationships among the disease-enriched marker species, a phylogenetic tree was generated based on their NCBI taxonomy using an online tool, phyloT ([https://phylot.biobyte.de/](https://phylot.biobyte.de/)), setting internal nodes collapsed and polytomy as no. The tree file then was visualized using Evolview ver3, a webserver for annotation and management phylogenetic trees. The nodes were colored depending on their corresponding clusters identified in previous section. The last common ancestors (LCAs) were determined according to the NCBI taxonomy of the species in corresponding branch.
Identification of HDC-correlated features
* 2 For each dataset, Spearman's rank correlation was used to identify HDC-related microbial features (e.g., species and functions) using a p-value cutoff of 0.05. Features that maintained a significant positive or negative relationship with HDC in at least two datasets of a disease were identified as HDC-related features.
* 3 Functional profile of metabolic modules
* 4 According to the category of MetaCyc database, we concluded the microbial functions into their corresponding superclasses as metabolic modules. The expression of each metabolic module was summarized as the average logarithm relative abundance of its contained functions. Setting the quantiles from 0.1 to 0.9 and the increment as 0.1, we calculated the generalized fold changes of modules between the controls and cases, and performed the Wilcoxon rank sum test with the "datasets" as the blocked object to evaluate the differences.
* 5 Microbial ecosystem analyses using species-species correlations
* 6 To characterize the relationships among the marker species and the resulting interaction networks, SparCC, a sparse correlation method for compositional data was used to identify correlations among marker species. SparCC was previously shown to be able to reduce the high false positive by Spearman's rank correlation in metagenomics data. The tool requires read counts as input, therefore we multiplied the relative abundances of the species to the number of reads mapping to mpa_v20_m200 database, and got the microbial counts of each sample. For each dataset, species-species correlations were calculated for control and case samples separately. By setting both the iteration number and simulation as 100 and threshold of correlation strength as \(0.05\), SparCC generated the correlation matrices of the real data and 100 simulated datasets. The pseudo P-values were assessed as the proportion of simulated datasets with a correlation value at least as extreme as that calculated from the real data. After filtering correlations with P-value < 0.05, we performed meta-analysis to aggregate correlation coefficients for each disease type via random-effects model, which summarizes overall correlation based on Fisher's z transformation with metacor function []. The summarized correlations with adjusted p-values <0.05 in meta-analysis were used to construct networks. The networks were analyzed in Cytoscape [] to identify modules using mode with default parameters. We then evaluated eigenvector centrality and betweenness centrality of networks using correlation strength as weight, and visualized networks with igraph package in R. The size of node indicated prevalence of the bacteria in counterpart samples. Positive and negative correlation coefficients as strength of edges were painted gray and red separately.
### Correlating functional profiles with species
To identify species underlying functional changes in the metagenomic data, correlations between relative abundance values of marker species and marker
[https://github.com/whchenlab/2019-puzi-multi-g-ut-disease-classifier](https://github.com/whchenlab/2019-puzi-multi-g-ut-disease-classifier).
* Correspondence and requests for materials should be addressed to W.H.C. and X.M.Z...
*
*
*
* We thank Na L Gao, Lei Liu and Xinming Li for valuable discussion.
*
* This work was partly supported by National Key Research and Development Program of China [2019YFA0905600 to W.H.C.], National Natural Science Foundation of China [61932008, 61772368, 61572363 to X.M.Z], National Key R&D Program of China [2018YFC0910500 to X.M.Z], Natural Science Foundation of Shanghai [17ZR1445600 to X.M.Z], Shanghai Municipal Science and Technology Major Project [2018SHZDZX01 to X.M.Z] and ZJLab. The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.
* W.H.C. and X.M.Z. designed the study. P.J. and S.W. collected and analyzed the data, Q.L. coordinated the data downloads and analysis. W.H.C., and P.J. wrote the manuscript with all authors contributing to the writing and providing feedbacks. All authors read and approved the final version of the manuscript.
* We declare no competing interests.
# 10 Supplemental Material
Table S1. A list of CRC and IBD datasets used in the study and statistical results of confounding factors, HDCs and Shannon diversity. The project "SRP057027" lacks detailed information about age, BMI and gender, but the original literature gave a statistical table which shows that there were no significant differences in age and gender between controls and CD patients. Numerical variables were reported as the median values in the corresponding group. The P-values were calculated using Wilcoxon rank sum test or chi-squared test to compare cases to controls.
Fig. S1. The pipeline for metagenomics data collection. We collected records about IBD and CRC in public databases until Sep, 2019. The requirements for samples were that the number of each group in each dataset was not below 20, and there were no overlapping samples across datasets.
* Fig. S2. The associated effects of identified marker species in each dataset of each disease. The marker species which were also significantly differential species in corresponding dataset (P-value < 0.05) were plot. Each block indicates a marker species of corresponding disease. Red means that the case-enriched species and blue means the control-enriched one. A, CRC; B, CD; C, UC.
* Fig. S3. Phylogenetic relationships of disease-specific and shared marker species. Phylogenetic relationships of the marker species were based on the NCBI common tree, generated using the online phyloT tool ([https://phylot.biobye.de](https://phylot.biobye.de)), and visualized using Evolview ver3.0 (with manual annotations). The LCAs were determined according to the NCBI taxonomy information of the species in corresponding branch.
* Fig. S4. Identified marker pathways that showed consistent changes in the respective diseases. The relative abundances of pathways were identified using HuManN2 on the metagenomics data. Pathways significantly enriched in cases (or controls) of corresponding disease in meta-analysis are shown (fdr < 0.05, Benjamini-Hochberg FDR correction, see Materials and Methods). Red block indicates case-enriched pathway, and blue block indicatescontrol-enriched one.
* 2 Fig. S5. Marker microbes showed distinct biosynthesis and other metabolic pathways preferences. Similar to Fig. 3, however, shown here are the correlations of meta-analysis in relative abundances between the non-degradation pathways and the marker species (see Materials and Methods). The pathways were clustered using'mcapuity' algorithm, while the species were sorted by their related diseases and changing trends. The blocks in the heatmap show the overall coefficients from the meta-analysis. The red block indicates positive correlation and blue indicates negative one. The asterisk indicates adjusted P-value of the coefficient in meta-analysis is below 0.05.
* 3 Fig. S6. Some marker species and pathways correlated significantly with HDCs. Each block indicates the marker species (A) and marker species (B) identified in meta-analysis. Red means that the species/pathways was HDC-related evidently in at least two datasets of corresponding disease type. Blue means the species/pathways was not HDC-related.
* 4 Fig. S7. Correlation networks among disease-altered species in CRC datasets (A-B). CD datasets (C-D) and UC datasets (E-F). Color of nodes means the alteration trends of species in its corresponding datasets. The sizes mean the prevalence of the bacteria in the overall controls (or cases) of corresponding datasets. Gray edges indicate positive relationship and red edges indicate negative. Thickness of edges indicates correlation strength.
Fig. S8. Evaluation for ECSs and BCSs of networks showed in Fig. S7. Blue bars indicate the centralies of control network from datasets, and red bars indicate centralities in case network. A-B, CRC; C-D, CD; E-F, UC.
* Fig. S9. Cross-validation models (A-B) and LODO models (C) based on various types of features for different purposes. A: The heatmap despicts the cross-validation results of multi-class models built on corresponding features. Rownames indicate the classification tasks (Four-class: CTR/UC/CD/CRC; Three-class: CTR/IBD/CRC; Cases: UC/CD/CRC). Column names indicate the type of features. Each block indicates the accuarcy of each model. B: Confusion matrix evaluation of four-class model built on combined profile in taxonomic and functional level for distinguishing different disease and controls. The number in row i and column j in the matrix on the left part indicates how many samples with state i actually were categorized to state j in model. Color filling the cell means the relative size of the number in the corresponding row. The right part is the TPR for per physical condition. Total accuracy indicates the fraction of all correct predictions, and 95% CI is the confidence interval of accuracy. C. The heatmap despicts the training results and validation result of each LODO model. Each row indicates the result of the LODO models training in the remaining data except the appointed dataset (see Materials and Methods). Column names were the combination of the classification task and type of features. For example, the 'Four-class All' means the LODO models based on combined profile were used to distinguish four classes (CTR/UC/CD/CRC), when the 'Four-class Dif' means means the LODO models based on combined markers to distinguish four classes. In this plot we only showed the models based on either combined profile (All) or combined markers (Dif). For the multi-class models, including the models starting with 'Four-class', 'Three-class' and 'Cases', we used the accuracy as the evaluation of classification. For the binary models, including 'Binary All' and 'Binary Dif', were displayed as AUROCs. The model average were the mean values of each column. The LODO validation were the integrated validation results of the LODO models in the same column.
_A. vsignalis_ |
19013243 | ## 1 Introduction
Visual perception, screening, stroke, assessment, clinical needs, facilitators, barriers
## Introduction
Visual perception is the dynamic process of perceiving the environment through sensory inputs and translating the sensory input into meaningful concepts associated with visual knowledge of the environment. Visual perception problems are therefore distinct from sensory visual impairments such as reduced visual acuity, visual field and eye movements. Where sensory visual impairments result from damage to the eye or early visual pathways from the eye to the primary visual cortex, visual perception deficits are attributed to impaired function in later visual processing areas in the occipital, parietal and temporal cortex. Examples of visual perceptual deficits include apperceptive and associative agnosia (object recognition difficulties), prosopagnosia (face recognition difficulties), akinetopsia (difficulties in perceiving motion), achromatopsisia (difficulties in perceiving motion), problems in visual memory (remembering what you have seen before), and in visuospatial abilities (e.g. judging distances or spatial relations between objects). Visual inattention or hemispatial neglect is sometimes considered to be part of visual perception, though neuropsychology research attributes this to an attentional deficit. In particular, the presence of preserved perception when attention is stretched to focus on the stimuli, the existence of cross-modal neglect and manipulations of stimulus density on the extent of neglect support the classification of hemispatial neglect as a disorder of attention. Rowe and colleagues reported that 20.5% of stroke survivors with a suspected visual difficulty have visual perception deficits such as visual inattention (14%), visual hallucinations (2.5%), and object agnosia (2.2.%) This study made use of reports by stroke survivors and carers rather than formal assessment (except for visual inattention). With systematic screening with the Rivermead Perceptual Assessment Battery, Edmans and Lincoln identified visual perception problems in 76% of hemiplegic stroke survivors. The discrepancy between prevalence with self-reports compare to neuropsychological assessmentsuggests that not all visual perceptual problems are picked up based on self-report. This means many stroke survivors are discharged without the appropriate rehabilitation or adjustments in their home environment or care packages.
* Under-diagnosis of visual perception problems can severely impact stroke survivors' quality of life, functional outcome, participation in the community, independence and pose substantial risk. For instance, participation in traffic with visual perception problems can be dangerous and even life-threatening. Risks are also heightened indoors when preparing a meal or in perceiving trip hazards. Better diagnosis of visual perception difficulties after stroke will allow better care planning and substantially impact stroke survivors' life.
* The first step toward better diagnosis is an in-depth understanding of the clinical reality and the reasons behind under-diagnosis. We need to understand what the challenges are in screening for visual perceptual difficulties after stroke. This can then inform the development of solutions in the future.
* In the current study, we aimed to conduct an in-depth exploration of current clinical practice, challenges and facilitators of screening for visual perception problems after stroke. To achieve a rich understanding of these issues, we performed semi-structured interviews with orthoptists and occupational therapists. These professionals are most commonly involved in visual perception screening after stroke in the United Kingdom's National Health Service.
Materials and methods
* 89 _Participants_
* 90 All participants were recruited via opportunistic and snowball sampling. Invitations for the interviews were sent out through (i) email to the British and Irish Orthoptic Society Stroke and Neuro Rehab Clinical Advisory Group, (ii) Twitter, (iii) a sign-up sheet at a conference poster and (iv) informal face-to-face conversations at the United Kingdom Stroke Forum 2018. Participants met inclusion criteria if they were working in the National Health Service as an occupational therapist or an orthoptist, and were involved in the assessment of visual perceptual problems after stroke. The participants were informed about the aims of the study, the organisations running the study (University of Oxford and North Bristol NHS Trust), and the planned outcomes and dissemination. The project was reviewed and approved by the Patient Safety Assurance & Audit Service at NHS North Bristol Trust as a Clinical Effectiveness study (CE45999). All participants gave verbal consent.
* 101 _Interviewer's training_
* 102 All interviews were conducted over the phone by the first author, KV, who holds an MSc in Clinical Psychology and a PhD in Experimental Psychology. At the time of the research study KV was working as a postdoctoral research fellow at the University of Oxford. KV had nine years' experience as a researcher, including one year as a qualitative researcher. Her formal training in qualitative research included an undergraduate course in qualitative research methods at the University of Leuven which included a research project. In preparation for the current project, she was trained and supervised by senior author, OH. OH is a clinical psychologist who has worked predominantly as a qualitative researcher and health care professional within the field of intellectual disabilities. OH has numerous publications within this field, teaches qualitative research methods at the University of Oxford, and has supervised a number of doctoral projects using various qualitative methodologies. KV's training included reading and reflecting on reference works in qualitative research, a question and answer session with an experienced moderator, and guidance during coding and analyses via regular meetings with OH.
#### Model
The interview process and qualitative analysis was guided by the Value Proposition Canvas. This model was originally designed to guide product development, but can be applied to different contexts. Central to this model is the principle that development of products or services are best informed by the users. A good product or service takes into account the goals of the user, it reduces the pains a user experiences while trying to achieve their goals, and it provides gains in achieving their goals. For instance a good electric car helps a person to get to work (goal to achieve) without having to fear that the battery will run out (reduce pains) while at the same time provides an attractive design to impress colleagues and family (increase gains). We can apply this model in trying to understand current clinical practice in visual perception screening after stroke (goal), the challenges (pains) it brings, and what facilitates the process (gains).
#### Data collection
A semi-structured interview guide was developed by KV in collaboration with an occupational therapist and an orthoptist (table 1). The interview guide was reviewed by an experienced moderator and piloted with one orthoptist and three occupational therapists. The interviews consisted of open-ended questions about current practice in visual perception screening after stroke, and the challenges and facilitators of practice. The interviewer conducted interviews at the participant's workplace or over the phone in a quiet office with no other people present. The participants took the call in a location of their choice. The location and presence of others at the participant's side was not recorded. After obtaining participant consent, the interview was audio recorded. All participants were interviewed once.
#### 14.2.1 Qualitative Analyses
As a method of data analysis we used thematic analysis. Interviews were transcribed verbatim by a professional typist. The transcripts were not returned to the participants for feedback. Two researchers (KV and MC) were involved in data analysis. KV was familiar with the data from conducting the interviews (Phase 1 in thematic analysis). The first 15 interviews were checked and coded by KV in NVivo Software (Version 12.0). She developed an initial coding tree (Phase 2 in thematic analysis). Overall themes were set in advance in alignment with the Value Proposition Model: Jobs, Challenges, and Facilitators. The coding tree was reviewed and substantially adapted after coding of five interviews. MC familiarised himself with the data by checking transcripts and reading through interviews coded by KV. Two of these interview transcripts were checked, coded and discussed by both KV and MC to align their coding. MC checked and coded the remaining 10 interview transcripts. The frequency of text extracts coded under each node was visualised with a hierarchical chart of nodes in NVivo to explore overall patterns in the data describing current practice. The use of frequencies in qualitative analysis can be a valuable strategy when used as a complement to an overall process orientation to the research. They can provide evidence for generalizability of the findings between participants, highlight diversity, reveal larger patterns beyond a participant's immediate experience, minimise cherry picking of the data. This chart shows the frequency of references for each node when participants were talking about current practice in routine visual and visual perception screening. If a participant referred to a node multiple times during one interview, each reference was counted. Only nodes with at least ten references were included in the hierarchical chart of nodes. Overall themes and subthemes were derived from all data by KV (Phase 3 of thematic analysis). This was done in two stages: we performed search queries of coded text for challenges and facilitators of visual perception screening in current practice and read through the resulting text.
* Challenges and Facilitators (see table 1). The information was then synthesised by KV (Phase 4 of thematic analysis). Lastly, themes and subthemes were reviewed, refined and defined by KV (Phase 5 of thematic analysis) and a report was prepared (Phase 6 of thematic analysis).
* This report was sent out to the participants for validation. Ten out of 25 participants replied and nine agreed with the thematic analysis. One participant pointed out that participants' understanding of visual perception was underexplored. We added a results section on this topic posthoc.
* Results
* 12 occupational therapists and 13 orthoptists from 16 health care organisations in England took part in the study. Characteristics such as gender, years of experience and main clinical setting of each participant are reported in table 2. All participants worked in England, and were based across the East Midlands (n=1), East of England (n=1), Greater London (n=2), North East (n=3), North West (n=4), South East (n=6), South West (n=4), and Yorkshire and the Humber (n=4). The interviewer had no personal relationship with any of the participants. Two orthoptists received referrals from the same acute stroke unit where the first author recruits stroke survivors as participants for other studies (pseudonyms cannot be disclosed to ensure anonymity). One of the participants was also involved in the development of the interview guide. All but one participant (Jessica) agreed to be audio recorded. For Jessica, notes were made during and immediately after the interview. Interviews lasted between 16 and 46 minutes with an average of 27 minutes. For Christopher, the interview was split over two consecutive days.
* 192 could offer inpatient appointments on the stroke unit, inpatient appointments in the eye clinic and outpatient appointments in the eye clinic.
* 193
* 194
* 195 _Lack of clarity around visual perception_
* 196 The interviews highlighted that participants' understanding of visual perception differed from textbook definitions of visual perception. Visual perception is defined as a dynamic process of translating sensory visual information into meaning percepts. These percepts can subsequently be linked to higher cognitive functions like visual memory for recognition (ventral or what stream) and praxis for visually guided actions (dorsal or where stream).
* 197 Visual perception must be differentiated from low level sensory visual functions like acuity,
* 198
\begin{table}
\begin{tabular}{c c c c c} \hline \hline Pseudonym & Gender & Profession & Clinical setting\({}^{\dagger}\) & Years of experience in stroke care \\ \hline Amanda & Female & Orthoptist & Eye clinic & 10\(+\) years \\ Amber & Female & Occupational therapist & Rehabilitation service & 10\(+\) years \\ Amy & Female & Orthoptist & Eye clinic & unknown \\ Brittany & Female & Occupational therapist & Rehabilitation service & 10\(+\) years \\ Christopher & Male & Occupational therapist & Acute stroke service & unknown \\ Crystal\({}^{\text{a}}\) & Female & Occupational therapist & Rehabilitation service & 5-10 years \\ Danielle & Female & Occupational therapist & Acute stroke service & unknown \\ Elizabeth & Female & Orthoptist & Eye clinic & 10\(+\) years \\ Emily\({}^{\text{a}}\) & Female & Occupational therapist & Rehabilitation service & unknown \\ Erin & Female & Occupational therapist & Acute stroke service & 5-10 years \\ Heather\({}^{\text{b}}\) & Female & Orthoptist & Eye clinic & 10\(+\) years \\ Jamie\({}^{\text{b}}\) & Female & Orthoptist & Eye clinic & 2-5 years \\ Jessica\({}^{\text{c}}\) & Female & Orthoptist & Eye clinic & 10\(+\) years \\ Joshua & Male & Orthoptist & Eye clinic & 2-5 years \\ Kimberley & Female & Occupational therapist & Acute stroke service & 2-5 years \\ Matthew & Male & Orthoptist & Eye clinic & 5-10 years \\ Megan & Female & Occupational therapist & Rehabilitation service & 10\(+\) years \\ Melissa & Female & Occupational therapist & Acute stroke service & 10\(+\) years \\ Michelle & Female & Occupational therapist & Rehabilitation service & 2-5 years \\ Nicole & Female & Orthoptist & Eye clinic & unknown \\ Rachel & Female & Orthoptist & Eye clinic & unknown \\ Rebecca & Female & Occupational therapist & Acute stroke service & 5-10 years \\ Sarah\({}^{\text{c}}\) & Female & Orthoptist & Eye clinic & 10\(+\) years \\ Stephanie & Female & Orthoptist & Eye clinic & unknown \\ Tiffany & Female & Orthoptist & Eye clinic & 2-5 years \\ \hline \hline \end{tabular}
\end{table}
Table 2: Participant characteristicsvisual fields, and ocular movements, and from higher cognitive processes like (visual)
* 203 memory or (visual) inattention, although some authors consider visual inattention to be part of visual perception. Our participants seemed to have a broader understanding of visual perception and often did not differentiate between sensory and higher cognitive functions.
* 206 Participants typically mentioned the following examples when asked about what they consider visual perceptual problems (in descending order of frequency): visual inattention, agnosia's for objects, faces, letters, or shapes, hallucinations or Charles Bonnet syndrome, difficulties in depth perception, visual field deficits like hemanopia, and spatial vision (e.g. navigating and perceiving space around them).
* 211 Participants' understanding seemed to vary widely but we observed general trends in the different professions. Orthoptists seemed to differentiate visual perception difficulties from low level sensory visual impairments, but considered visual inattention the prime (and only) example of visual perception difficulties after stroke.
* 215 "[_Interviewer: What comes to your mind, when I say visual perception problems in stroke patients?_] So I would probably say visual neglect, ignoring one side of their world when the other side is presented to them as well, is the main definition of it. That it's decreased awareness of that side of their vision and their external world as well as themselves as well, on that side. _[Interviewer: Anything else, that falls under that term for you?]_ No, not that I can think of, off the top of my head, no." (Tiffany, Orthoptist in an eye clinic)
* 212 In addition to visual inattention, occupational therapists mentioned impairments that are typically (but not exclusively) related to low level sensory vision like contrast sensitivity, hemianopia, and depth perception. They seemed to interpret visual perception more broadly.
"A range really. So we would look at visual perception as things like depth perception,... recognition of objects,... and any kind of visual inattention or neglect, that sort of thing... But yes, that's it basically." (Danielle, Occupation Therapist in an acute stroke service)
227 These observations are relevant in interpreting the subsequent results. Although the interview questions asked for experiences with visual perception assessment after stroke, the results below should be interpreted as potentially referring to all or any of the following: sensory visual impairments (for occupational therapist participants), visual perception impairments (for all participants), and visual inattention (for all participants).
232 _Current Practice_
233 A hierarchical chart of nodes is presented in The figure illustrates that participants most often mentioned occupational therapists working in acute stroke or rehabilitation services when discussing screening for visual neglect, visual field deficits, and ocular movements. For screening they referred to in-house developed screening tools, standardised tests or observations in functional tasks like dressing and making a cup of tea.
238 "In terms of the visual field, we do the standard, you know, wiggle your fingers test to see how people respond. We do the tracking tests. Otherwise it's mainly through observing people in functional tasks what they're doing.... Through that you can often realise... if they're having problems with their visual perception because they're missing things or not seeing things." (Crystal, occupational therapist in a stroke rehabilitation service)
244 "I'd rather do it in function. It's more meaningful especially with stroke patients because it makes more sense. Rather than getting them to balance cubes on each other or, you know, I can say 'Can you find the toothpaste?' " (Megan, occupational therapist in an acute stroke service)250 reflects the frequency of references for each node with larger boxes demonstrating more frequency mentioned nodes. Parent nodes are shown in lightly shaded boxes, child nodes are shown in darker shaded boxes within 252 their parent's box. The colours are added for easy distinction between different parent boxes but have no further meaning. Text is filtered for extracts where participants were talking about current practice in routine visual and visual perceptions screening. Only nodes with at least ten references are shown.
255
256 Most participants mentioned that the service they work within has a referral pathway in place: if problems are suspected following screening by the occupational therapist, a referral is made to orthoptics. A stroke orthoptist will then see the stroke survivor as an inpatient on the unit or as an outpatient after discharge from the hospital.
260 "It's really as and how other health professionals have identified them, then an orthoptist will go up to try and assert a diagnosis and then give them the rehabilitation options." (Amy, orthoptist in an eye clinic)
Hierarchical chart of nodes showing the frequency of references for each node. The size of a box reflects the frequency of references for each node with larger boxes demonstrating more frequency mentioned nodes. Parent nodes are shown in lightly shaded boxes, child nodes are shown in darker shaded boxes within 252 their parent’s box. The colours are added for easy distinction between different parent boxes but have no further meaning. Text is filtered for extracts where participants were talking about current practice in routine visual and visual perceptions screening. Only nodes with at least ten references are shown.
Challenges
* 264 Themes around challenges in visual perception screening are presented in table 3. We identified five major themes and 13 subthemes.
* 266 _Lack of Time_
* 267 Occupational therapists and orthoptists both reported that time pressure makes visual perception screening difficult. They mentioned that because of understaffing they spend little time with stroke survivors or experience delays in seeing them following referral. In addition, occupational therapists report that stroke survivors are discharged from an acute stroke unit as soon as medically safe and a suitable discharge location has been organised. For survivors with milder strokes, discharge is reported to happen within 1-2 days, giving very little time for therapists to complete their assessments.
* 274 "Well one _[challenge]_ is just logistically and organisationally, just in terms of caseload and time to hand. We are having to prioritise more direct functional assessments in terms of establishing readiness for discharge." (Christopher, occupational therapist in an acute stroke service)
* 278 "There's not a lot of OTs who are actually for _[delivering]_ the therapy, so time-wise we haven't got a lot of capacity at times." (Danielle, occupational therapist in an acute stroke service)
* 281 "Lack of time is always going to be frustrating knowing that you've got a clinic here and you can't get up to the ward and there's an urgent stroke survivor."
* 283 (Heather, orthoptist in an eye clinic)
* 284 "Erm... it sounds awful doesn't it when you're constantly having to slim down what you do." (Melissa, occupational therapist in an acute stroke service)Training is another theme that frequently emerged across both professions. Visual perception difficulties following stroke appear to be only briefly covered in the undergraduate education of orthoptists and occupational therapists, and is mostly learned about post-qualification through on-the-job-training. Many occupational therapists mentioned that they rotate between services, leaving little time for them to be trained in many aspects of stroke care. In particular, they said that this lack of experience made them feel uncertain when it comes to vision and visual perception deficits following stroke. Inexperience and limited training seemed to be an important hurdle for occupational therapists in visual perception screening. Because vision and visual perception was not well understood by the staff (see section 'Lack of clarity around visual perception'), participants reported that mistakes in assessments are commonly made, leading to a potential under-diagnosis of visual perception deficits.
"[It] can be a bit frustrating... lots of the occupational therapists are on a rotational job. So getting them _[occupational therapists]_ trained up _[is difficult]_, I think they _[occupational therapists]_ do find vision scary.... Vision, it's the scariest thing about stroke." (Stephanie, orthoptists in an eye clinic, using 'vision' as a general term to cover a wide range of sensory and perceptual visual functions)
"[Visual perception is ]_ one of those things that is perhaps not widely understood.... think unless you've got a unit with a special interest in stroke and you've taken the time to look into that... then it's perhaps under-diagnosed as well, so yeah I think it's recognition that it's a potential problem." (Amanda, orthoptist in an eye clinic)
"The key is really, somebody in the hospital to be able to deliver the training and the therapy staff to actually take on board the training and to actually deliver it." (Sarah, orthoptist in an eye clinic)* 311 "I think it probably is underreported; the amount of incidents of perceptual problems post stroke." (Rachel, orthoptist in an eye clinic)
* 313 _Environmental and Stroke Survivor Factors_
* 314 Participants reported that visual perception screening is limited by the environment in which they take place. They said that in acute stroke care, most assessments are done in a hospital bay with several beds. Even if curtains can be drawn around the stroke survivor's bed, distractions were reported to be numerous: sounds from neighbouring beds, interruptions for timed caring needs, distractions from medical equipment around the bed and presence of personal objects on a small table in front of the stroke survivor (spectacles, drinks, food, tissues, personal care items, newspaper, get well cards, crossword book, pen, etc.) can be visually distracting and interfere with visual perceptual assessment.
* 312 "Frustrating for us is... that we.. depending on which unit we are _[on]_ or where we are, it can be quite difficult to do _[our assessment at]_ the bedside if there is a lot _[of]_ distractions going on; if there is no quiet space to take the patient.
* 313 "It's _[the]_ environment. Often _[it]_ doesn't lend itself to a nice quiet space where patients can attend." (Danielle, occupational therapist in an acute stroke service)
* 314 "I think it probably is underreported; the amount of incidents of perceptual problems post stroke." (Rachel, orthoptist in an eye clinic)
* 315 _Environmental and Stroke Survivor Factors_
* 316 "Participants reported that visual perception screening is limited by the environment in which they take place. They said that in acute stroke care, most assessments are done in a hospital bay with several beds. Even if curtains can be drawn around the stroke survivor's bed, distractions were reported to be numerous: sounds from neighbouring beds, interruptions for timed caring needs, distractions from medical equipment around the bed and presence of personal objects on a small table in front of the stroke survivor (spectacles, drinks, food, tissues, personal care items, newspaper, get well cards, crossword book, pen, etc.) can be visually distracting and interfere with visual perceptual assessment.
* 317 "Frustrating for us is... that we.. depending on which unit we are _[on]_ or where we are, it can be quite difficult to do _[our assessment at]_ the bedside if there is a lot _[of]_ distractions going on; if there is no quiet space to take the patient.
* 318 "It's _[the]_ environment. Often _[it]_ doesn't lend itself to a nice quiet space where patients can attend." (Danielle, occupational therapist in an acute stroke service)
* 319 "Participants also mentioned the condition of the stroke survivors as a limiting factor to visual perception screening. Both professions reported that tests and tools are often not suitable for stroke survivors with poor alertness, poor cognition, aphasia or severe weakness in their upper limbs. For instance, stroke survivors may not able to answer a question on whether their vision has changed because they developed aphasia following stroke.
336 survivor who can no longer hold a pen.
337
338
339 "Another component would be around the client or the patient themselves in terms of factors that might work against screening: so attention, concentration, fatigue, the ability to deliver a verbal response in terms of aphasia or dysarthria difficulties.... That has significant impact on our ability to undertake formal testing of whatever nature." (Christopher, occupational therapist in an acute stroke service)
340
341 "Our patients who either are fatigued quite quickly, or are... medically not well enough to do a lot of taking down to the therapy department..., or their attention span is quite limited, or they've got a weakness in their upper limb that makes it more difficult to complete the tests." (Danielle, occupational therapist in an acute stroke service)
342
343 _Continuation of Care_
344
A further concern of the participants was the follow-up process after screening for visual perception deficits. They highlighted that quite often the information from screening is not passed on to the next care team. Therefore, even if visual perception problems are picked up in an acute setting, no follow-up assessments are carried out or no rehabilitation is provided in their experience. With respect to rehabilitation, occupational therapists found it frustrating that few treatment options are available. They reported that little information and few guidelines are available on how visual perception problems can be treated or managed. Some noted that the lack of options for rehabilitation reduced their motivation to screen for visual perception problems.
345 "Yes, and it [_the discharge summary_] is very medical because the occupational therapists or myself don't like the discharge summaries.... We do all this information and then it gets lost...Yeah, it's not part of our discharge summary in enough detail, so when they go somewhere new which could be two or three weeks later... they don't have that information." (Matthew, orthoptist in an eye clinic)
* "It might be because it [_visual perception deficits_] is limited in treatment... that's why it's not the focus. So... it would be more useful to spend time during my assessment speaking to them about adapting to their field loss and giving them a prism or occlusion for their double vision." (Rachel, orthoptist in an eye clinic)
* _Test Characteristics_
* Both professions highlighted limitations in the characteristics of the available tests for visual perception. Occupational therapists more frequently reported to be hindered by practical limitations and the unknown impact on daily life. With respect to the practical limitations, they referred to a large number of test materials like stimulus booklets, stopwatch, cubes, etc. needed for assessment or too many loose pages. With respect to the unknown impact on daily life, they referred to stimuli and tests that were thought to be limited in ecological validity.
* They considered the tests too abstract with no clear link to the implications for everyday tasks.
* "We have our little screening tool. It's a few pages, just to prompt us.... That's all right but then... everything else you are... searching together from different kits.... That's a little bit frustrating." (Amber, occupational therapist in a stroke rehabilitation service)
* "There's an awful lot of bits of paper and a bit of raffing about and preparing to get it all ready before we actually go out to see the patients." (Melissa, occupational therapist in an acute stroke service)* 384 "We use Rivermead Perceptual Battery. But to be fair, I don't tend to use it as often because I'd rather do it in function....It's more meaningful, especially with stroke patients because it makes more sense. Rather than getting them to balance cubes on each other or, you know I can say "Can you find the toothpaste? Can you take the lid off? Can you brush your own teeth?" and then it just makes more sense. And then... it's easier for them to identify _[a]_ goal." (Megan, occupational therapist in a stroke rehabilitation service)
* 391 Orthoptists, on the other hand, seemed to emphasize more the lack of evidence and consequently the lack of specific clinical guidelines on how to assess visual perception.
* 393 "If you see the national guidelines for visual problems after stroke, they have a really small section on vision with orthoptics but we don't really have anything in it that's specific to what we should be screening them with and what we should be treating them with. So even though we're using evidence-based practice, the evidence sometimes isn't great and I think that's probably why it's not in the guidelines because there's not really good evidence to support it. But sometimes you're seeing a patient and you're not entirely sure if you're doing the right thing because you're maybe giving them information based on clinical experience, what other people have been doing but you're not really sure if that is the best thing to be doing or could you be doing something else with them." (Amy, orthoptist in an eye clinic)* 406 _Facilitators_
* 408 The facilitators to practice that participants reported, largely mirrored the challenges reported above (table 4). We identified three major themes and 12 subthemes.
* 410 _Practical Tool_
* 411 On a practical level, participants preferred a tool that can be administered in approximately 412 10-20 minutes, so it can fit in with busy every-day practice and current staff levels. They also favoured a tool that consists of few test materials and pages to prevent test materials getting 414 lost or mixed up during testing. According to participating orthoptists, the tool should have a 415 1 to 2 page proforma. They reported that it should include questions to ask the stroke survivor and simple quick tests for a range of functions. They suggested that the proforma could subsequently be used in a referral for orthotopic input. To allow bedside testing or testing in the community, participants preferred portable tools. Lastly, many participants highlighted that a tool should ideally be suitable for all stroke survivors, such as those with aphasia, poor concentration, poor cognition or severe fatigue.
\begin{table}
\begin{tabular}{l l l l} \hline Major themes & Subthemes & Endorsed by occupational therapists & Endorsed by orthoptists \\ \hline Lack of time & Limited time with stroke survivor due to discharge pressure & x & x \\ & Limited time with stroke survivor due to staff shortage & x & x \\ Lack of training & Inexperienced staff with limited training & x & x \\ & Vision and visual perception is not well understood & x & x \\ & Mistakes made in assessment & x & x \\ & Vision and visual perception deficits are underdiagnosed & x & x \\ Environmental and & Condition of stroke survivor (e.g. low alertness, poor cognition, aphasia, not mobile) & x & x \\ & Distractions in test environment (often in hospital bay) & x & x \\ Continuation of care & Information on vision and visual perception problems gets lost after discharge & x & x \\ & No information on treatment or management of vision or visual perception problems & x & \\ Test characteristics & Test materials not readily available or making use clumsy & x & \\ & Lack of evidence-based screening instruments & x & x \\ & No specific recommendations in clinical guidelines & x & x \\ & Tests are not meaningful for everyday life & x & \\ \hline \end{tabular}
\end{table}
Table 3: Challenges in visual perception screening * 421 "It needs to be something that's fairly quick and easy to administer." (Danielle, occupational therapist in an acute stroke service)
* 423 "Just pen and paper, quite simple or a few things to hand that will fit in something that's quite portable and mobile, I think [_that_] would be handy, yes." (Brittany, occupational therapist in a stroke rehabilitation service)
* 426 "Reasonably short... for logistical [_reasons_]:...
* 427 "concentration time, fatigue in the more acute stages. I think really half an hour is the maximum time." (Christopher, occupational therapist in an acute stroke service)
* 429 "It would have to be a list of standardised questions: Are they able to look
* 431 "between two points specifically?...
* 432 "be if they're following a moving object?...
* 433 "their friends or their family? Can they recognise themselves in a photo?" (Rachel, orthoptist in an eye clinic)
* 435 _Training and Experience_
* 436 "Orthoptists and occupational therapists agreed on the importance of training and experience
* 437 "for robust visual perception screening.
* 438 "other staff members was seen as very advantageous.
* 439 "perception highlighted above, a tool that is easy to administer and score was preferred by our
* 440 "participants.
* 441 "provide clear guidance for management of the deficit (if present).
* 442 "If it was something that was quite self-explanatory then anybody could do it and
* 443 "therefore anybody can interpret it, then that would be much clearer." (Amy, orthoptist in an eye clinic)* "Just easy to administer and easy to score.... So making instructions clear and easy to understand would be good." (Emily, occupational therapist in a stroke rehabilitation service)
* _Staff Roles and Interactions_
* Occupational therapists reported that their preferred practice is to screen stroke survivors for vision and visual perception problems during their functional assessments (e.g. washing, making a cup of tea) or via a screening tool. Both professions mention that if a problem is flagged, more in-depth assessment can then take place.
* "Whereas since we've set up a proper vision screening it just means that things have been a lot more efficient and that's made a much better service because they're not having to see a lot of people that don't need to be seen." (Nicole, orthoptists in an eye clinic)
* "So, I'm happy with the main basic screen to begin with, and if it digs something up then we'll dig it in some more detail. I think that works quite well." (Matthew, orthoptists in an eye clinic)
* "I think the key is having the staff, the occupational therapist and the physio staff actually take that on board." (Sarah, orthoptist in an eye clinic)
* "I think the key is having the staff, the occupational therapist and the physio staff actually take that on board." (Sarah, orthoptist in an eye clinic)
* "I think the key is having the staff, the occupational therapist and the physio staff actually take that on board." (Sarah, orthoptist in an eye clinic)
## 4.7 Discussion
The aim of this qualitative research was to gain a deeper understanding of current practice in visual perception screening after stroke, the challenges faced by health care professionals. In our participants' stroke care services, occupational therapists most often screened for visual and visual perceptual difficulties.
\begin{table}
\begin{tabular}{l l l l} \hline Major themes & Subthemes & Endorsed by & Endorsed by \\ & & occupational & orthoptists \\ & & therapists & \\ \hline Practical tool & Quick to administer (10-20 min) & x & x \\ & Paper and pen based without too many test materials or pages & x & x \\ & Proforma with questions and simple tests to be used in referral & & x \\ & Portable & x & \\ & Suitable for stroke survivors with poor concentration, & x & \\ & communication and fatigue & x & \\ Training and & Easy to administer and score & x & x \\ experience & Easy to interpret with management advice included & x & x \\ & Trained and experienced staff & x & x \\ Staff roles and & Screening for visual and visual perception problems by & x & x \\ interactions & occupational therapists during functional assessment or with & & \\ & screening tool & In depth assessment with range of complimentary tests & x & x \\ & Specialised staff for visual (orthoptists) and visual perceptual & & x \\ & (occupational therapists) problems & & \\ & Good relationship between stroke and eye departments & & x \\ \hline \end{tabular}
\end{table}
Table 4. Facilitators to visual perception screening The qualitative approach of our study allowed us to gather views directly and in depth.
* 483 Instead of reporting frequency of views (e.g. how many health care professionals report staff shortage), we focus on how central certain views are to a person's experience. Our sample covers the two main professions involved in visual perception screening after stroke.
* 486 National Clinical Guidelines recommend that every stroke survivor who appears to have perceptual difficulties should have an assessment with standardised measures. As is evident from our interviews, only a small proportion of stroke survivors receive an assessment with standardised measures for visual perceptions difficulties, and screening is not routinely done. The means of assessment of visual perception deficits varied widely between participants. Orthoptists will often use standardised tools in their assessments, though these are not necessarily validated with stroke survivors. Overall, standardised assessments were rarely mentioned by our participants. Occupational therapists expressed preferring assessment during functional tasks like washing and dressing and assessment with in-house developed screening checklists. This may be due to a lack of a validated screening tool for a wide range of visual and visual perceptual deficits that can be used by any health care professional. The diversity in tools that we observed in our group of English participants contrasts with the reported use of standardised tools in an Australian population where the Occupational Therapy Adult Perceptual Screening Test and the Loewenstein Occupational Therapy Cognitive Assessment are most commonly used to evaluate visual perceptual difficulties.
* 490 McCluskey and colleagues investigated the barriers and enablers for following recommended practice in stroke care. In line with our findings the occupational therapists they interviewed reported the condition of the stroke survivors as a barrier for standardised assessments. Many tests are not designed and not suitable for stroke survivors with aphasia and/or dysarthria. Occupational therapists in their study also mentioned the lack of training and knowledge, specifically for visual neglect rehabilitation. Time pressure and fluctuating staff levels meant occupational therapists in their study prioritised assessments and interventions which would produce the best clinical outcome. A lack of time to see stroke survivors was also mentioned by their orthoptists. However, in our study this referred to the lack of time to see all referred stroke survivors before they were discharged, while in the study by McCluskey, the orthoptists referred to the lack of time to treat stroke survivors. The standardised assessments used by Australian occupational therapists, Occupational Therapy Adult Perceptual Screening Test and the Loewenstein Occupational Therapy Cognitive Assessment, require training and take 20-45 minutes to complete. Given the frequently reported lack of training and time, it may appear that the standardised tools recommended by clinical guidelines are not adapted to the clinical reality of the National Health Service in England. Although McCluskey's study was limited to one Australian hospital and only involved 5 occupational therapists and 2 orthoptists, all working in the same service and circumstances, the barriers are remarkably similar to what our 12 occupation therapists and 13 orthoptists reported experiencing in 16 English healthcare services. The stroke survivor's condition, lack of time and staff seem to be universal barriers for providing evidence-based stroke care across domains, not just visual perception screening. Also, the lack of information on treatment or management of vision or visual perception problems that occupational therapists mention as a barrier is not surprising given the very limited evidence for treatment and management options. The first challenge exposed by our study is the variation between participants in their understanding of constitute visual perception problems after stroke. This led to participants answering interview questions with different reference frameworks. When sharing the challenges of visual perception screening in their clinical practice, some might have been considering challenges in just screening for visual inattention difficulties while othersconsidered a broad range of sensory and cognitive visual impairments. To maintain an equal relationship between participant and interviewer, and an open non-judgemental environment to freely share their experiences, participants' definition of visual perception was not challenged during the interview. A disadvantage of this approach is that it is unclear whether certain themes apply specifically to one aspect of visual and visual perception screening or to the whole range of vision related difficulties after stroke.
* The second challenge lies in our sample size. Our sample, though the largest for a qualitative study in this topic, is not representative for the whole population of health care professionals involved in visual perception screening after stroke. We limited ourselves to occupational therapists and orthoptists as they are most commonly involved in visual perception screening in England. Experiences might be very different in clinical settings without an orthotopic department or with more involvement of neuropsychologists in stroke care. In addition, voluntary participation and asking our participants to commit 30 minutes of their time might have induced a bias for allied health professionals with a keen interest in the topic. We have possibly missed opinions from people with a more negative or neutral attitude towards visual perception screening. In addition, newly qualified health care professionals with limited experience in stroke care might not have felt confident enough to share their opinions on the topic. Lack of confidence on this topic with junior staff was brought up by several of our participants. However, the aim of this qualitative research was not to generalise findings to the population, but rather to provide an in-depth exploration of the topic to generate hypotheses. We are following this research up with a large scale survey for all health care professionals involved in visual perception screening in the United Kingdom and Republic of Ireland. In the recruitment to this survey study, we are emphasizing that we welcome the opinions of heath care professionals with all levels of experience.
A third potential limitation is that the interviewer was the principal investigator of the study and was therefore not independent. Unconscious bias of the interviewer might have guided the participants' answers. We have tried to minimize this by using a detailed interview guide that included a list of cues that could be given. In addition, all interviews were recorded and a second coder was involved.
* Our study limits itself to health care professionals' perceptive on visual perception screening after stroke. We have not explored experiences by stroke survivors, although they can be substantially different. Also, we have not investigated the management of visual perceptual problems after stroke of their impact in daily life as is previously reported for sensory visual problems.
* The current research highlighted that a clear and consistent definition of visual perception should be provided to orthoptists and occupational therapists. More training is needed on the assessment (and management) of visual perceptual screening. This is preferably provided via professional organisations to ensure consistency and in line with national guidelines.
* This will raise awareness and reduce insecurity experienced by junior staff members.
* Establishing good relationships between staff at stroke and eye departments is strongly recommended. We suggest this could be achieved in the form of knowledge exchanges or via a re-evaluation of the existing referral system. Lastly, a quick and portable visual perception screening tool that is easy to administer, score and interpret would highly benefit both staff and stroke survivors if it is inclusive for stroke survivors with aphasia, motor impairments and cognitive problems. The tool should be evidence-based and self-explanatory to use. Such a tool is currently not available. Our research provides test developers with the requirements of occupational therapists and orthoptists for such a screening tool to be clinically useful and thereby increase the likelihood of adoption.
|
19014159 | ###### Abstract
Prefrontal synthesis (PFS) is defined as the ability to juxtapose mental objects at will. Paradysis of PFS may be responsible for the lack of comprehension of spatial prepositions, semantically-reversible sentences, and recursive sentences observed in 30 to 40% of individuals with ASD. In this report we present data from a three-year-long clinical trial of 6,454 ASD children aged 2-12 years, which were administered a PFS-targeting intervention. Tablet-based verbal and nonverbal exercises emphasizing mental-juxtaposition-of-objects were organized into an application called _Mental Imagery Therapy for Autism_ (MITA). The test group included participants who completed more than one thousand exercises and made no more than one error per exercise. The control group included the rest of participants. The test group participants were matched to the control group by age, gender, expressive language, receptive language, sociability, cognitive awareness, and health at the 1st evaluation. The test group showed 1.7-fold improvement in receptive language score vs. control group (p=0.0002) and 1.4-fold improvement in expressive language (p=0.0144). No statistically significant change was detected in other subscales not targeted by the exercises. These findings show that language acquisition improves by training PFS and warrants further investigation of the PFS-targeting intervention in a randomized controlled study.
*Corresponding author: Andrey Vyshedskiy, Ph.D., Boston University, Boston, USA, Tel: +1 433-7724; E-mail:
_Keywords_: autism; ASD; language delay; language therapy; imagination; theory of mind
## Introduction
Full command of complex language depends on understanding of vocabulary as well as on the mechanism of juxtaposition of mental objects into novel combinations, called Prefrontal Synthesis (PFS). Without developed PFS it is impossible to understand the difference between sentences with identical words and grammar, such as "the cat on the mat" and "the mat on the cat." Most people anthropomorphically assume innate PFS abilities in all individuals. Scientific evidence, however, suggests a more intricate story. While propensity toward PFS is innate in humans, acquisition of PFS seems to be the function of using recursive language in early childhood. The myelination of frontoposterior fiber tracts mediating PFS depends on early childhood conversations. In the absence of normal recursive conversations, children do not fine-tune these neurological connections and, as a result, do not acquire PFS. The autism community refers to the phenomenon whereby individuals cannot combine disparate objects into a novel mental image as _stimulus overselectivity_, or _tunnel vision_, or _the lack of multi-cue responsivity_. Failure to juxtapose mental objects, called _PFS paralysis_, results in life-long inability to understand spatial prepositions, semantically-reversible sentences (e.g., "the cat on the mat"), and recursion. Among individuals diagnosed with ASD, the prevalence of PFS paralysis is 30 to 40% and may be as high as 60% among children enrolled into special ASD schools.
We hypothesized that early PFS-targeting intervention can improve language ability in children with ASD. Accordingly, we designed various developmental activities, all of which follow a systematic approach to train PFS verbally as well as outside of the verbal domain. To make these activities dynamic and attractive to children, we organized them into an application called _Mental Imagery Therapy for Autism_ (MITA). The MTA app was released in 2015 and quickly rose to the top of the "antism apps" charts.
MITA verbal activities start with simple vocabulary-building exercises and progress toward exercises aimed at higher forms of language, such as noun-adjective combinations, spatial prepositions, recursion, and syntax. E.g., a child can be instructed to _select the [small/large] [red/blue/green/orange] ball_, or to _put the cup [on/under/behind/in front of] the table_. All exercises are deliberately limited to as few nouns as possible since the aim is not to expand a child's one-word vocabulary, but rather to teach him/her to integrate mental objects in novel ways by utilizing PFS.
MITA activities outside of the verbal domain aim to provide the same PFS training visually through implicit instructions as has been described in Ref.. E.g., a child can be presented with two separate images of a train and a window pattern, and a choice of complete trains. The task is to find the correct complete train and to place it into the empty square. This exercise requires not only attending to a variety of different features in both the train and its windows, but also combining two separate pieces into a single image (in other words, mentally _integrating_ separate train parts into a single unified gestalt). As levels progress, the exercises increase in difficulty, requiring attention to more and more features and details. Upon attaining the most difficult levels, the child must attend to as many as eight features simultaneously. Previous results from our studies have demonstrated that children who cannot follow the explicit verbal instruction can often follow an equivalent command implicit in the visual set-up of the puzzle.
PFS is an internal, subjective function that does not easily manifest itself to evaluators. Most receptive language tests are based on vocabulary assessment and may miss the profound deficit in PFS. Furthermore, unlike vocabulary acquisition, PFS takes many years to develop in an ASD child. With long intervention time and in the absence of accepted PFS tests, randomized controlled trial (RCT) of a PFS-targeting intervention is an arduous proposition. We were not able to generate support for a long RCT and therefore resolved to conduct a simpler observational trial.
We have previously described a framework for investigating targeted interventions for ASD children epidemiologically, whereby caregivers submit multiple assessments longitudinally. When a single parent completes the same evaluation over multiple years, changes in the score become a meaningful measure of child's progress despite a possible bias in the absolute score. Using the comprehensive 77-question Autism Treatment Evaluation Checklist (ATEC) over the period of several years we have demonstrated significant differences in outcomes along several parameters. Younger children improved more than the older children in all four ATEC subscales - Language, Sociability, Cognitive awareness, and Health. Children with milder ASD demonstrated higher improvement in the Language subscale than children with more severe ASD. No difference between females vs. males was registered in all cohorts studied.
In this report we apply the same framework to study the PFS intervention called MITA in children aged 2 to 12 years. The data collected over five years shows greater language improvement in MITA-engaged children compared to controls matched by age, gender, expressive language, receptive language, sociability, cognitive awareness, and health at the 1st evaluation.
## Methods
### MITA exercises
MITA includes both verbal and nonverbal exercises aiming to develop voluntary imagination ability in general and Prefrontal Synthesis (PFS) ability in particular. The fidelity, validity and reliability of the MITA was discussed in detail in Refs.. MITA verbal activities use higher forms of language, such as noun-adjective combinations, spatial prepositions, recursion, and syntax to train PFS: e. g., a child can be instructed to put the _large red dog behind the orange chair_, Figure 1A; or _identify the wet animal_ after _the lion was showered by the monkey_; or _take animals home_ following an explanation that _the lion lives above the monkey and under the cow_, In every activity a child listens to a short story and then works within immersive interface to generate an answer. Correct answers are rewarded with pre-recorded encouragement and flying stars. To avoid routinization, all instructions are generated dynamically from individual words. Collectively, verbal activities have over 10 million different instructions, therefore a child will almost never hear the same instruction once again.
MITA nonverbal activities aim to provide the same PFS training visually through implicit instructions. E.g., a child can be presented with two separate images of a train and a window pattern, and a choice of complete trains. The task is to find the correct complete train. The child is encouraged to avoid trial-and-error and integrate separate train parts mentally, thus training PFS, Different games use various tasks and visual patterns to keep the child engaged, Most puzzles are assembled dynamically from multiple pieces in such a way that they never repeat themselves.
Examples of MITA verbal exercises. (A) A child is instructed to put the _large red dog behind the orange chair._ (B) A child is instructed: _Imagine. The lion lives above the monkey and under the cow. Take animals home._ Note that animals cannot be dragged to their apartments during instructions, encouraging a child to imagine animals’ correct positions in the mind.**
Examples of MITA nonverbal exercises. (A) Implicit instruction: _Find the correct train._ (B) Implicit instruction: _Find the correct patch._
MITA also includes a number of hybrid activities that start children on easier nonverbal exercises and then gradually increase in difficulty, first to a combination of a verbal instruction and a visual clue and later to a verbal instruction alone, Collectively, MITA activities are designed to last for approximately 10 years.
### Participants
The MITA app was made available gratis at all major app stores in September 2015. Once the app was downloaded, the caregiver was asked to register and to provide demographic details, including the child's diagnosis and age. Caregivers consented to anonymized data analysis and completed Autism Treatment Evaluation Checklist (ATEC) as well as an evaluation of the receptive language using MSEC checklist. The first evaluation was administered approximately one month after the first use of MITA and once 100 puzzles had been completed. The subsequent evaluations were administered at approximately three-month intervals. To enforce regular evaluations, MITA app became unusable at the end of each three-month interval and parents needed to complete an evaluation to regain its functionality.
From this pool of potential study participants, we selected participants based on the following criteria:
## 1) Consistency:
Participants must have filled out at least three ATEC evaluations and the
Examples of a MITA game that teach spatial prepositions _above_ and _under_. (A) The game starts with the implicit instruction to combine an animal and a vehicle. (B) At more difficult levels a child must notice the correct positioning of the animal (_above_ or _under_), which is announced verbally and also indicated by a visual clue in the top left corner of the matrix. At the most difficult levels (not shown) the visual clue is hidden and a child must rely on the verbal instruction alone.
## 2) Diagnosis:
The subjects must have self-reported their diagnosis as ASD. The ASD diagnosis was not verified directly, as we cannot ask participants to submit documentation. However, ATEC scores support ASD diagnosis. Average initial ATEC total score in the test group was 68.71 \(\pm\) 24.26, and 67.95 \(\pm\) 23.68 in the control group, Table 1, which corresponds to medium-to-severe ASD as delineated in Ref. and Table 2.
## 3) Maximum age:
Participants older than twelve years of age were excluded from this study.
## 4) Minimum age:
Participants who completed their first evaluation before the age of two years were excluded from this study.
After excluding participants that did not meet these criteria, there were 6,454 total participants, from whom we have selected the test and control groups, Table 1.
### Test and control groups
Since our application was available for free to the general public, there was a large volume of downloads by people of widely ranging commitment. To assess the effect of MITA intervention we had to identify participants who have not just downloaded MITA and used trial-and-error to arrive at solutions, but actively engaged with MITA. Thus, we have selected participants who completed at least one thousand exercises and made no more than one error per exercise (N=1,009). The test group participants were matched to the control group by age, gender, expressive language, receptive language, sociability, cognitive awareness, and health at 1st evaluation (baseline) using propensity score analysis.
## Outcome measures
A caregiver-completed Autism Treatment Evaluation Checklist (ATEC) and Mental Synthesis Evaluation Checklist (MSEC) were used to track the efficacy of the treatment. The complete ATEC questionnaire (can be accessed freely at www.autism.org) is comprised of four subscales: 1) Speech/Language/Communication, 2) Sociability, 3) Sensory/Cognitive Awareness, and 4) Physical/Health/Behavior. The first subscale, Speech/Language/Communication, contains 14 items and its score ranges from 0 to 28 points. The Sociability subscale contains 20 items within a score range from 0 to 40 points. The third subscale, referred here as the Cognitive Awareness subscale, has 18 items and scores range from 0 to 36 points. The fourth subscale, referred here as the Health subscale contains 25 items and scores range from 0 to 75 points. The scores from each subscale are combined in order to calculate a Total Score, which ranges from 0 to 179 points. A lower score indicates lower severity of ASD symptoms and a higher score indicates more severe symptoms of ASD. ATEC is not a diagnostic checklist.
\begin{table}
\begin{tabular}{|p{113.8pt}|p{113.8pt}|p{113.8pt}|p{113.8pt}|} \hline & **Test** & **Control** & **P-value** \\ \hline
## Participants in each age group (total)
& 1009 & 1009 & n/a \\ \hline
## Age at baseline (mean ± SD)
& 5.3 ± 2.1 & 5.3 ± 2.4 & 0.87 \\ \hline
## Male Gender
& 74\% & 75\% & 0.90 \\ \hline
## Receptive Language (mean ± SD)
& 14.4 ± 6.2 & 14.5 ± 6.4 & 0.26 \\ \hline
## Expressive Language (mean ± SD)
& 14.4 ± 6.2 & 14.5 ± 6.4 & 0.21 \\ \hline
## Sociability (mean ± SD)
& 14.6 ± 7.0 & 14.7 ± 7.1 & 0.67 \\ \hline
## Cognitive Awareness (mean ± SD)
& 16.4 ± 6.3 & 16.2 ± 6.7 & 0.91 \\ \hline
## Health (mean ± SD)
& 21.5 ± 11.4 & 22.0 ± 12.3 & 0.07 \\ \hline
## ATEC Total (mean ± SD)
& 68.71 ± 24.26 & 67.95 ± 23.68 & 0.89 \\ \hline \end{tabular}
\end{table}
Table 1: **Test and control group characteristics at the 1st evaluation. A lower score indicates a lower severity of ASD symptoms.**approximately. Table 2 lists approximate ATEC total score as related to ASD severity and age as described elsewhere.
ATEC was selected because it is one of the few measures validated to evaluate treatment effectiveness. In contrast, another popular ASD assessment tool, ADOS, has been only validated as a diagnostic tool. Various studies confirmed validity and reliability of ATEC and several trials confirmed ATEC's ability to longitudinally measure changes in participant performance. Whitehouse et al. used ATEC as a primary outcome measure for a randomized controlled trial of their iPad-based intervention for ASD named TOBY and noted ATEC's "internal consistency and adequate predictive validity". These studies support the effectiveness of ATEC as a tool for longitudinal tracking of symptoms and assessing changes in ASD severity.
### Expressive language assessment
ATEC Speech/Language/Communication subscale starts by assessing the simplest linguistic abilities, such as 1) Knows own name, 2) Responds to 'No' or 'Stop', 3) Can follow some commands, 4) Can use one word at a time (No!, Eat, Water, etc.), 5) Can use 2 words at a time (Don't want, Go home), 6) Can use 3 words at a time (Want more milk) and progress to interrogate complex language abilities, such as 7) Knows 10 or more words, 8) Can use sentences with 4 or more words, 9) Explains what he/she wants, 10) Asks meaningful questions, 11) Speech tends to be meaningful/relevant, 12) Often uses several successive sentences, 13) Carries on fairly good conversation, and 14) Has normal ability to communicate for his/her age. With the exception of the first three items, all the Language subscale items primarily depend on expressive language. Accordingly, the ATEC subscale 1 is referred in this manuscript as Expressive Language subscale to distinguish it from the Receptive Language subscale tested by the MSEC evaluation.
### Receptive language assessment
MSEC evaluation was designed to be complementary to ATEC in measuring receptive language and PFS. Out of 20 MSEC items those that directly assess receptive language are the following: 1) Understands simple stories that are read aloud; 2) Understands elaborate fairy tales that are read aloud (i.e. stories describing FANTASY creatures); 6) Understands some simple modifiers (i.e. green apple vs. red apple or big apple vs. small apple); 7) Understands several modifiers in a sentence (i.e. small green apple); 8) Understands size (can select the largest/smallest object out of a collection of objects); 9) Understands possessive pronouns (i.e. your apple vs. her apple); 10) Understands spatial prepositions (i.e. put the apple ON TOP of the box vs. INSIDE the box vs. BEHIND the box); 11) Understands verb tenses (i.e. I will eat an apple vs. I ate an apple); 12) Understands the change in meaning when the order of words is changed (i.e. understands the difference between 'a cat ate a mouse' vs. 'a mouse ate a cat'); 20) Understands explanations about people, objects or situations beyond the immediate surroundings (e.g., "Mom is walking the dog," "The snow has turned to water"). MSEC consists of 20 questions and is scored similarly to ATEC: a lower score indicates better receptive language and PFS ability. To simplify interpretation of figure labels, the subscale 1 of the ATEC evaluation is referred to as the Expressive Language subscale and the MSEC scale is referred as the Receptive Languagesubscale.
### Statistical analysis
The framework for evaluation of ATEC score changes over time was explained in detail earlier. In short, the concept of a "Visit" was developed by dividing the three-year-long observation interval into 3-month periods. All evaluations were mapped into 3-month-long bins with the first evaluation placed in the first bin. When more than one evaluation was completed within a bin, their results were averaged to calculate a single number representing this 3-month interval. It was then hypothesized that there was a two-way interaction between Visit and treatment. Statistically, this hypothesis was modeled by applying the Linear Mixed Effect Model with Repeated Measures (MMRM), where a two-way interaction term was introduced to test the hypothesis. The model (Endpoint \(\sim\) Baseline + Gender + Severity + Treatment * Visit) was fit using R Bioconductor library of statistical packages, in particular "nlme" package. The subscale score at baseline, gender, and severity were used as covariates. Conceptually, the model fits a plane into n-dimensional space. This plane takes into account a complex variability structure across multiple visits, including baseline differences. Once such plane is fit, the model calculates Least Squares Means (LS Means) for each subscale and treatment group at each visit. The model also calculates LS Mean differences between the treatment and control groups at each visit.
Participants in the test group were matched to those in the control group using propensity score analysis based on age, gender, expressive language, receptive language, sociability, cognitive awareness, and health at the 1st evaluation (baseline).
|
19014571 | ## Conclusion:
19 out of 30 studies on BCI-robotic systems for hand rehabilitation report systems at prototype or pre-clinical stages of development. We identified large heterogeneity in reporting and emphasise the need to develop a standard protocol for assessing technical and clinical outcomes so that the necessary evidence base on efficiency and efficacy can be developed.
Background
There is growing interest in the use of robotics within the field of rehabilitation. This interest is driven by the increasing number of people requiring rehabilitation following problems such as stroke (with an ageing population), and the global phenomenon of insufficient numbers of therapists able to deliver rehabilitation exercises to patients. Robotic systems allow a therapist to prescribe exercises that can then be guided by the robot rather than the therapist. An important principle within the use of such systems is that the robots assist the patient to actively undertake a prescribed movement rather than the patient's limb being moved passively. This means that it is necessary for the system to sense when the patient is trying to generate the required movement (given that, by definition, the patient normally struggles with the action). One potential solution to this issue is to use force sensors that can detect when the patient is starting to generate the movement (at which point the robot's motors can provide assistive forces). It is also possible to use measures of muscle activation (EMGs) to detect the intent to move. In the last two decades there has been a concerted effort by groups of clinicians, neuroscientists and engineers to integrate robotic systems with brain signals correlated with a patient trying to actively generate a movement, or imagine a motor action, to enhance the efficacy and effectiveness of stroke rehabilitation- these systems fall under the definition of Brain Computer Interfaces, or BCIs. BCIs allow brain state-dependent control of robotic devices to aid stroke patients during upper limb therapy. While BCIs in their general form have been in development for almost 50 years and were theoretically made possible since the discovery of the scalp-recorded human electroencephalogram (EEG) in the 1920s, their application to rehabilitation is more recent. Graimann et al. defined a BCI as an artificial system that provides direct communication between the brain and a device based on the user's intent; bypassingthe normal different pathways of the body's peripheral nervous system. A BCI recognises user intent by measuring brain activity and translating it into executable commands usually performed by a computer, hence the term "brain-computer interface".
Most robotic devices used in upper limb rehabilitation exist in the form of exoskeletons or end-effectors. Robotic exoskeletons (i.e., powered orthoses, braces) are wearable devices where the actuators are biomechanically aligned with the wearer's joints and linkages; allowing the additional torque to provide assistance, augmentation and even resistance during training. In comparison, end-effector systems generate movement through applying forces to the most distal segment of the extremity via handles and attachments.
Rehabilitation robots are classified as Class II-B medical devices (i.e., a therapeutic device that administers the exchange of energy, mechanically, to a patient) and safety considerations are important during development. Most commercial robots are focused on arms and legs, each offering a unique therapy methodology. There is also a category of device that target the hand and finger. While often less studied than the proximal areas of the upper limb, hand and finger rehabilitation are core component in regaining activities of daily living (ADL). Many ADLs require dexterous and fine motor movements (e.g. grasping and pinching) and there is evidence that even patients with minimal proximal shoulder and elbow control can regain some hand capacity long-term following stroke.
The strategy of BCI-robot systems (i.e. systems that integrate BCI and robots into one unified system) in rehabilitation is to recognise the patient's intention to move or perform a task via a neural or physiological signal, and then use a robotic device to provide assistive forces in a manner that mimics the actions of a therapist during standard therapy sessions. The resulting feedback is patient-driven and is designed to aid in closing the neural loop from intention to execution. This process is said to promote use-dependent neuroplasticity within intact brain regions and relies on the repeated experience of initiating and achieving a specified target; making the active participation of the patient in performing the therapy exercises an integral part of the motor re-learning process.
The aforementioned scalp-recorded EEG signal is a commonly used instrument for data acquisition in BCI systems because it is non-invasive, easy to use and can detect relevant brain activity with high temporal resolution. In principle, the recognition of motor imagery (MI), the imagination of movement without execution, via EEG can allow the control of a device independent of muscle activity. It has been shown that MI-based BCI can discriminate motor intent by detecting event-related spectral perturbations (ERSP) and/or event-related desynchronisation/synchronisation (ERD/ERS) patterns in the \(\upmu\) (9-11 Hz) and \(\upbeta\) (14-30 Hz) sensorimotor rhythm of EEG signals. However, EEG also brings with it some challenges. These neural markers are often concealed by various artifacts and may be difficult to recognise through the raw EEG signal alone. Thus, signal processing (including feature extraction and classification) is a vital part of obtaining a good MI signal for robotic control. A general pipeline for EEG data processing involves several steps. First, the data undergo a series of pre-processing routines (e.g., filtering and artifact removal) before feature extraction and classification for use as a control signal for the robotic hand. There are variety of methods to remove artifact from EEG and these choices depend on the overall scope of the work. For instance, Independent Component Analysis (ICA) and Canonical Correlation Analysis (CCA) can support real-time applications but are dependent on manual input. In contrast, regression and wavelet methods are automated but support offline applications. There also exist automated and real-time applications such as adaptive filtering or using blind source separation (BSS) based methods. Recently, the research community has been pushing real-time artifact rejection by reducing computational complexity e.g. Enhanced Automatic Wavelet-ICA (EAWICA), hybrid ICA - Wavelet transform technique (ICA-W) or by developing new approaches such as adaptive denoising frameworks and Artifact Subspace Reconstruction (ASR). Feature extraction involves recognising useful information (e.g., spectral power, time epochs, spatial filtering) for better discriminability among mental states. For example, the common spatial patterns (CSP) algorithm is a type of spatial filter that maximises the variance of band pass-filtered EEG from one class to discriminate it from another. Finally, classification (which can range from linear and simple algorithms such as Linear Discriminant Analysis (LDA), Linear Support Vector Machine (L-SVM) up to more complex techniques in deep learning such as Convolutional Neural Networks (CNN) and Recurrent Neural Networks (RNN) involves the translation of these signals of intent to an action that provides the user feedback and closes the loop of the motor intent-to-action circuit.
The potential of MI-based BCIs has gained considerable attraction because the neural activity involved in the control of the robotic device may be a key component in the rehabilitation itself. For example, MI of movement is thought to activate some of the neural networks involved in movement execution (ME). The resulting rationale is that encouraging the use of MI could increase the capacity of the motor cortex to control major muscle movements and decrease the necessity to use neural circuits damaged post-stroke. The scientific justification for this approach was first provided by Jeannerod who suggested that the neural substrates of MI are part of a shared network that is also activated during the simulation of action by the observation of action (AO). These'mirror neuron' systems are thought to be an important component of motor control and learning - hence the belief that activating these systems could aid rehabilitation. The use of a MI-BCI to control a robot in comparison to traditional MI and physical practice provides a number of benefits to its user and the practitioner. These advantages include the fact that the former can provide a more streamlined approach such as sensing physiological states, automating visual and/or kinaesthetic feedback and enriching the task and increasing user motivation through gamification. There are also general concerns around the utility of motor imagery without physical movement (and the corresponding muscle development that comes from these) and it is possible that these issues could be overcome through a control strategy that progressively reduces the amount of support provided by the MI-BCI system and encourages active motor control.
* A recent meta-analysis of the neural correlates of action (MI, AO and ME) quantified 'conjunct' and 'contrast' networks in the cortical and subcortical regions. This analysis, which took advantage of open-source historical data from fMRI studies, reported consistent activation in the premotor, parietal and somatosensory areas for MI, AO and ME. Predicated on such data, researchers have reasoned that performing MI should cause activation of the neural substrates that are also involved in controlling movement and there have been a number of research projects that have used AO in combination with MI in neurorehabilitation and motor learning studies over the last decade.
* One implication of using MI and AO to justify the use of BCI approaches is that great care must be taken with regard to the quality of the environment in which the rehabilitation takes place. While people can learn to modulate their brain rhythms without using motor imagery and there is variability across individuals in their ability to imagine motor actions, MI-driven BCI systems require (by design at least) for patient to imagine a movement. Likewise, AO requires the patients to clearly see the action. This suggests that the richness and vividness of the visual cues provided is an essential part of an effective BCI system. It is also reasonable to assume that feedback is important within these processes and thus the quality of feedback should be considered as essential. Afterall, MI and AO are just tools to modulate brain states and the effectiveness of these tools vary from one stroke patient to another. Finally, motivation is known to play an important role in promoting active participation during therapy. Thus, a good BCI system should incorporate an approach (such as gaming and positive reward) that increases motivation. Recent advances in technology make it far easier to create a rehabilitation environment that provides rich vivid cues, gives salient feedback and is motivating. For example, the rise of immersive technologies, including virtual reality (VR) and augmented reality (AR) platforms, allows for the creation of engaging visual experiences that have the potential to improve a patient's self-efficacy and thereby encourage the patient to maintain the rehabilitation regime. One specific example of this is visually amplifying the movement made by a patient when the movement is of limited extent so that the patient can see their efforts are producing results.
In this review we set out to examine the literature to achieve a better understanding of the current value and potential of BCI-based robotic therapy with three specific objectives:
1. Identify how BCI technologies are being utilised in controlling robotic devices for hand rehabilitation. Our focus was on the study design and the tasks that are employed in setting up a BCI-hand robot therapy protocol.
2. Document the readiness of BCI systems. Because BCI for rehabilitation is still an emerging field of research, we expected that most studies would be in their proof-of-concept or clinical testing stages of development. Our purpose was to determine the limits of this technology in terms of: (a) resolution of hand MI detection and (b) the degree of robotic control.
* Evaluate the clinical significance of BCI-hand robot systems by looking at the outcome measures in motor recovery and determine if a standard protocol exists for these interventions.
* It is important to note that there have been several recent reviews exploring BCI for stroke rehabilitation. For example, Monge-Pereira et al. compiled EEG-based BCI studies for upper limb stroke rehabilitation. Their systematic review (involving 13 clinical studies on stroke and hemiplegic patients) reported on research methodological quality and improvements in the motor abilities of stroke patients. Cervera et al. performed a meta-analysis on the clinical effectiveness of BCI-based stroke therapy among 9 randomised clinical trials (RCT). McConnell et al. undertook a narrative review of 110 robotic devices with brain-machine interfaces for hand rehabilitation post-stroke. These reviews, in general, have reported that such systems provide improvements in both functional and clinical outcomes in pilot studies or trials involving small sample sizes. Thus, the literature indicates that EEG-based BCI are a promising general approach for rehabilitation post-stroke.
* The current work complements these previous reports by providing the first systematic examination on the use of BCI-robot systems for the rehabilitation of fine motor skills associated with hand movement and profiling these systems from a technical and clinical perspective.
Methods
* 208 Protocol Registration
* 209 Details of the protocol for this systematic review were registered on the International Prospective Register of Systematic Reviews (PROSPERO) and can be accessed at www.crd.york.ac.uk/PROSPERO (ID: CRD42018112107).
* 211
* 212
* 213 Search Strategy and Eligibility
* 214 An in-depth search of articles from January 2010 to October 2019 was performed on Ovid MEDLINE, Embase, PEDro, PsycINFO, IEEE Xplore and Cochrane Library. Only full-text articles published in English were selected for this review. Table 1 shows the combination of keywords used in the literature searching.
* 215
* 216
* 217
* 218
* 219 The inclusion criteria for the articles were: publications that reported the development of an EEG-based BCI; studies targeted towards the rehabilitation of the hand after stroke; studies that involved the use of BCI and a robotic device (e.g., exoskeleton, end-effector type, platform-types, etc.); studies that performed a pilot test on healthy participants or a clinical trial with people who have had a stroke.
\begin{table}
\begin{tabular}{l l l} \hline \hline
## Set 1 (OR)** & **Set 2 (OR)** & **Set 3 (OR)
\\ \hline Brain-computer interface/BCI & Stroke (rehabilitation/ & Robotic (exoskeleton/ \\ Electroencephalography/EEG & therapy/treatment/recovery) & orthosis) \\ Brain-machine interface/BMI & Motor (rehabilitation, & Powered (exoskeleton/ \\ Neural control interface & AND & therapy/treatment/recovery) \\ Mind-machine interface & Neurorehabilitation & Robot \\ & Neurotherapy & Device \\ & Hand (rehabilitation/therapy/ & \\ & recovery/exercises/movement) & \\ \hline \hline \end{tabular}
\end{table}
Table 1: **Keyword Combinations**following exclusion criteria: studies that targeted neurological diseases other than stroke; studies that used other intention sensing mechanisms (electromyography/EMG,
* electroencephalography/EOG, non-paretic hand, other body parts, etc.).
* Two authors performed independent screenings of titles and abstracts based on the inclusion and exclusion criteria. The use of a third reviewer was planned a priori in cases where a lack of consensus existed around eligibility. However, consensus was achieved from the first two authors during this stage. Full-text articles were then obtained, and a second screening was performed until a final list of studies was agreed to be included for data extraction.
* Data Extraction
* The general characteristics of the study and their corresponding results were extracted from the full-text articles by the reviewers following the Preferred Reporting Items for Systematic Reviews and Meta-Analysis (PRISMA) checklist.
* Study design: general description of study design, experimental and control groups
* Task design: description of the task instructed, and stimuli presentation (cue and feedback modalities, i.e.: visual, kinaesthetic, auditory, etc.)
* Technical specifications of the system: EEG system used (including number of channels), robot device used (e.g. hand exoskeleton, end-effector, etc.), actuation mode, and control strategy Main outcomes of the study: clinical outcomes (for studies involving stroke patients), classification accuracies (participant, group and study-levels), other significant findings
* This data extraction strategy allowed us to further evaluate the technology and clinical use of the BCI-robot systems used in this study.
* **Technology Evaluation**
* _EEG Acquisition_
* The signal acquisition element of an EEG-based BCI is critical to its success in recognising task-related intent. To better understand current practice, we gathered the type of electrode used (i.e., standard saline-soaked, gel or dry electrodes), the number of channels and its corresponding placement in the EEG cap. To illustrate where signals are recorded from, we plotted the frequency with which electrodes were used across studies on a topographical map using the 10-20 international electrode placement system.
* _Signal Processing_
* We evaluated the signal processing strategies used by each study looking specifically at the feature extraction and classification techniques within the data pipeline. For the studies that reported classification accuracies (i.e., comparing the predicted class against the ground truth), we were able to compare their results among the current state-of-the-art classification accuracies published in literature.
* _Robot-Assisted Rehabilitation_
* As the receiving end of the BCI pipeline and the provider of kinaesthetic feedback to the user, the robot-assisted device for hand rehabilitation plays a key role in providing the intervention in this therapy regimen. The robot components were evaluated based on their actuation type, targeted body-part (i.e., single-finger, multi-finger, whole hand), and control strategy. We also reported on commercially available systems, which having passed a series of regulatory processes making them fit for commercial use, were classified as gold standard devices.
#### Technological Readiness
We assessed the development stages of the system as a whole by performing a Technological Readiness Assessment (TRA). Using this strategy, we were able to determine the maturity of the systems through a Technology Readiness Level (TRL) scale of 1-9 and quantify its implementation in a research or clinical setting. Since a BCI-robot for rehabilitation can be categorised as a Class II-B medical device we have adapted a customised TRL scale to account for these requirements. The customised TRL accounts for prototype development and pilot testing in human participants (TRL 3), safety testing (TRL 4-5), and small scale (TRL 6) to large scale (TRL 7-8) clinical trials. Performing a TRA on each device should allow us to map out where the technology is in terms of adoption and perceived usefulness. For example, if most of the studies have used devices that have TRL below the clinical trials stage (TRL 6-8), then we can have some confidence that said BCI-robot system is not yet widely accepted in the clinical community. In this way we can focus on questions that improve our understanding on the factors that impede its use as a viable therapy option for stroke survivors.
#### Clinical Use
For studies involving stroke patients, clinical outcomes were obtained based on muscle improvement measures such as Fugl-Meyer Motor Assessment Upper Extremity (FMA-UE) scores, Action Research Arm Test (ARAT) scores, United Kingdom Medical Research Council (UK-MRC) muscle grade, Grip Strength (GS) Test and Pinch Strength (PS) Test scores (i.e., kilogram force collected using an electronic hand dynamometer) among others.
* _Physiotherapy Evidence Database (PEDro) Scale for Methodological Quality_
* A methodological quality assessment was also performed for clinical studies based on the PEDro Scale. This scale evaluates studies with a checklist of 11 items based on experts' consensus criteria in physiotherapy practice. The complete details of the criteria can be found online. A higher score in the PEDro scale (6 and above) implied better methodological quality but are not used as a measure of validity in terms of clinical outcomes. Pre-defined scores from this scale were already present in studies appearing in the PEDro search. However, studies without PEDro scores or are not present in the PEDro database at all had to be manually evaluated by the authors against the 11-item checklist (five of seven studies).
Results
* 315 Search Results
* 316 shows the study selection process and the number of articles obtained at each stage.
A total of 590 studies were initially identified. After deduplication, 330 studies underwent title and abstract screening. Forty six studies passed this stage and among these, 16 were removed after full-text screening due to the following reasons: insufficient EEG and robotic data, the study was out of scope, the study design was not for hand/finger movement, no robot or mechatronic device was involved in the study. A final sample of 30 studies were included in the qualitative review.
Study Selection Flowchart
* Table 2 shows a summary of the relevant data fields extracted from these studies.
* Table 2 Around Here
* _Studies with Healthy Participants (Prototype Group)_
* The studies which involved pilot testing on healthy human participants had a combined total of 207 individuals (sample size ranging from 1-32) who had no history of stroke or other neurological diseases. Right-handed individuals made up 44.24% of the combined population while the other 55.76% were unreported. These studies aimed to report the successful implementation of a BCI-robot system for hand rehabilitation and were more heterogeneous in terms of study and task designs than those studies that involved clinical testing. The most common approach was to design and implement a hand orthosis controlled by MI which accounted for 9 out of the 19 studies and were measured based on classification accuracy during the calibration/training period and online testing. Li et al. and Stan et al. also aimed to trigger a hand orthosis but instead of MI, the triggers used by Li et al. is based on an attention threshold while Stan et al. used a vision-based P300 speller BCI. Bauer et al. compared MI against ME using a BCI-device while Ono et al. studied the implementation of an action observation strategy with a combined visual and kinaesthetic feedback or auditory feedback. Five more studies focused on varying the feedback while two more assessed the performance and safety of a hybrid BCI with EMG, EOG or both.
* _Studies with Stroke Patients (Clinical Group)_A total of 208 stroke patients (with sample size varying 3-74) were involved in the 11 clinical studies. One study reported a 3-armed RCT with control groups as device-only and SAT while another study was a multi-centre RCT with sham as the control group. Five studies were uncontrolled - where the aims were either to study classification accuracies during sessions, to monitor clinical outcomes improvement from Day 0 until the end of the programme or both. Two studies compared effects of the intervention against SHAM feedback. Another study compared the classification accuracies of healthy and hemiplegic stroke patients against two BCI classifiers while the remaining study compared classification accuracies from stroke patients who receive congruent or incongruent visual and kinaesthetic feedback.
## Technology Evaluation
### EEG Acquisition
The EEG acquisition systems involved in the studies ranged from low-cost devices having few electrode channels (2-15 gel or saline-soaked silver/silver chloride [Ag/AgCl] electrodes) to standard EEG caps that had higher spatial resolution (16-256 gel or saline-soaked Ag/AgCl electrodes). The placement of EEG channels was accounted for by studies involving MI (N=21). This allowed us to determine the usage frequency among electrodes and is presented in as a heat map generated in R Studio (using the packages: "akima", "ggplot2" and "reshape2") against the 10-20 international electrode placement system.
It can be seen that the EEG channels used for MI studies are concentrated towards electrodes along the central sulcus (C) region and the frontal lobe (F) region of the placement system where the motor cortex strip lies. Among these, C3 (N=17) and F3 (N=14) were mostly used, presumably because a majority of the participants were right-handed. The next most frequent were C4 (N=13) and the electrodes F4, Cz and CP3 (N=10).
#### Signal Processing: Feature Extraction and Classification
In the EEG-based BCI studies examined, it was found that the feature extraction and classification techniques were variable between systems. Table 3 provides a summary of pre-processing, feature extraction and classification techniques across the studies.
EEG Channel Usage across Motor Imagery Studies (N=21)
## 3.1.
\begin{table}
\begin{tabular}{l l l l l} \hline \hline
## Study** & **Pre-Processing** & **Feature Extraction** & **Classification** & **Hand Task
\\ \hline Ang et al. & Band-pass & Filter Bank Common & Calibration model & MI vs rest \\ & (0.05-40 Hz) & Spatial Pattern & (unspecified) & \\ & & (FBCSP) algorithm & & \\ & & & & \\ Barsotti et al. & Band-pass (8-24 & ERD (β and μ- & SVM with linear kernel & MI vs rest \\ & Hz) & decrease), CSP & & \\ Bauer et al. & Band-pass (6-16 & ERD (β-decrease) & Linear autoregressive model & MI vs rest \\ & Hz using zero- & & based on Burg Algorithm & \\ & phase lag FIR & & & \\ Bundy et al. & Unspecified & ERD (β and μ- & Linear autoregressive model & MI (affected, unaffected) vs \\ & & decrease) & & rest \\ Chowdhury et al. & Band-pass (0.1 & CSP Covariance- & SVM with linear kernel, & left vs right MI \\ & Hz-100 Hz), & based, ERD/ERS (β & Covariate Shift Detection & \\ & Notch (50 Hz) & and μ-change) & (CSD)-based Adaptive & \\ & & Classifier & & \\ Coffey et al. & Band-pass (0.5 & CSP Covariance- & Linear Discriminant & MI vs rest \\ & Hz-30 Hz), & based & Analysis (LDA) classifier & \\ & Notch (50 Hz) & & & \\ Diab et al. & Unspecified & Time epochs & Artificial Neural Network & Non-MI open vs \\ & & (unspecified) & (ANN)-based Feed Forward & closed \\ & & & Back Propagation & \\ Frolov al. & Band-pass (5-30 & Time epochs & Bayesian-based EEG & MI (affected, \\ & Hz), FIR (order & (10 s) & covariance classifier & unaffected) vs \\ & & & & rest \\ & Chebyshev type & & & \\ & I filter (50 Hz) & & & \\ Ono et al. & Band-pass (0.5- & Time epochs (700 & Linear Discriminant & MI vs rest \\ & 30 Hz), notch & ms), ERD (μ- & Analysis (LDA) classifier & \\ & & & & \\ & (50 or 60 Hz) & decrease) & & \\ \hline \hline \end{tabular}
\end{table}
Table 3.: BCI Feature Extraction and ClassificationRamso-Murguialday Unspecified Time epochs (5 s), et al. Spatial filter, ERD/ERS (b and m-change) \[\text{Vukelic and}\] High-pass (unspecified) \[\text{Gharabaghi}\] ( \[\text{Windowsit}\] ) \[\text{Band-pass (0.4-}\] \[\text{ERD/ERS (b and m-change)}\] \[\text{Linear autoregressive model}\] \[\text{MI vs rest}\] \[\text{Witkowski et al.}\] \[\text{70 Hz}\] \[\text{Laplacian filter}\] \[\text{SAV} = \text{Support Vector Machines, FIR = Finite Impulse Response, IIR Infinite Impulse Response}\]
While classification accuracy is contingent on the number of mental state classes the system is trying to discriminate, classification accuracies do provide a comparable metric among BCI systems. In our review, we found high variation in the reported mean classification accuracies among the BCI systems in this study (i.e., 2-class left-hand and right-hand classification)-ranging from 40% (below chance-level) up to 95%. For reference, two recent reviews on the state-of-the-art in classification accuracies for motor imagery BCI find ranges between 63-97% and 68-90%.
#### Robot-Assisted Rehabilitation
Robotic hand rehabilitation systems provide kinaesthetic feedback to the user during BCI trials. Most of these devices are powered by either DC motors, servomotors or pneumatic actuators that transmit energy via rigid links or Bowden cables in a tendon-like fashion. The studies in this review included single-finger, multi-finger (including EMOHEX), full hand gloves (including mano: Hand Exoskeleton and Gloreha) and full arm exoskeletons with isolated finger actuation (BRAVO-Hand). Nine of the studies presented their novel design of a hand rehabilitation device within the article while some reported on devices reported elsewhere (i.e., in a previous study of the group or a research collaborator). Two commercially-available devices were also used: AMADEO (Tyromotion, Austria) is an end-effector device used in 3 studies, and Gloreha (Idrogenet, Italy) is a full robotic hand glove used by Tacchino et al.. AMADEO and Gloreha are both rehabilitation devices that have passed regulatory standards in their respective regions. AMADEO remains the gold standard for hand rehabilitation devices as it has passed safety and risk assessments and provided favourable rehabilitation outcomes. The International Classification of Functioning, Disability and Health (ICF) provides three specific domains that can be used to assess an intervention of this kind: improving impairments, supporting performance of activities and promoting participation. In this case, a gold standard device not only prioritises user safety (established early in the development process) but also delivers favourable outcomes in scales against these domains. shows the main types of robotic hand rehabilitation devices.
## Technology Readiness Assessment
A Technology Readiness Assessment (TRA) was performed for each study and the Technology Readiness Levels (TRL) are presented in Table 4.
9+), we performed a TRA on the whole system (the interaction between BCI and robotics) to provide an evaluation of its maturity and state-of-the-art development with regard to rehabilitation medicine. We further assessed the TRL of each system at the time of the publication and its subsequent development.
\begin{table}
\begin{tabular}{l c c} \hline \hline
## Levels** & **Description** & **Studies
\\ \hline TRL 1 & • Lowest level of technological readiness & • Literature reviews and initial market surveys & • Scientific application to defined problems \\ TRL 2 & • Generation of hypotheses & • Development of research plans and/or protocols & \\ TRL 3 & • Testing of hypotheses – basic research, data collection and analysis & Most studies from the prototype group (N=18) \\ • & • Testing of design/prototype – verification and critical component specifications & & \\ TRL 4 & • Proof-of-concept of device/system in defined laboratory/animal models & Witkowski et al., 2014 & \\ TRL 5 & • Comparison of device/system to other existing modalities or equivalent devices/systems & & \\ • & Further development – testing through simulation (tissue or organ models), animal testing &, Tsuchimoto et al., 2019 & \\ \hline \hline \end{tabular}
\end{table}
Table 4: Technology Readiness Assessment of the BCI-Hand Robot Systems- under carefully controlled and intensely monitored clinical conditions
* safety and effectiveness integration in operational environment
* evaluation of overall risk-benefit of device/system use
* Confirmation of QSR compliance
* Awarding of PMA for device/system by CDRH or equivalent agency
* The device/system may be distributed/marketed
* QSR = Quality System Requirements, PMA = Premarket Approval, CDRH = Center for Devices and Radiological Health
* Clinical Use
* Clinical Outcomes Measures
* Most of the studies adopted FMA-UE, ARAT and GS measurements to assess clinical outcomes. Six studies reported patient improvement in these measures when subjected to BCI-hand robot interventions; in contrast with their respective controls or as recorded through time in the programme. For Ang et al., FMA-UE Distal scores were reported in weeks 3, 6, 12 and 24 and the BCI-device group (N=6) yielded the highest improvement in scores across all time points as compared to the device only (N=8) and SAT (N=7) groups. Bundy et al. reported an average of 6.20\(\pm\)3.81 improvement in the ARAT scores of its participants (N=10) in the span of 12 weeks while Chowdhury et al. reported a group mean difference of +6.38 kg (p=0.06) and +5.66 (p<0.05) in GS and ARAT scores, respectively (N=4). Frolov et al.'s multi-centre RCT reported a higher improvement in the FMA-UE Distal, ARAT Grasp and ARAT Pinch scores of the BCI-device group (N=55) when compared to the control/SHAM group (N=19), but not in the ARAT Grip scores where the values are both equal to 1.0 with p<0.01 for the BCI-device group and p=0.045 for the control.
* _Physiotherapy Evidence Database (PEDro) Scale for Methodological Quality_ For the studies that had a clinical testing component, a methodological quality assessment by the PEDro Scale was performed. Two studies which appeared on the PEDro search had predetermined scores in the scale and were extracted for this part while the rest were manually evaluated by the authors. Table 5 shows the results of the methodological quality assessment against the scale. Note that in the PEDro Scale, the presence of an eligibility criteria is not included in the final score.
* **Table 5.
To the best of our knowledge, this is the first systematic examination of BCI-driven robotic systems specific for hand rehabilitation. Through undertaking this review we found several limitations present from the studies identified and we examine these in more detail here and provide recommendations for future work in this area.
To provide clarity on the state of the current development of BCI-hand robot systems, we looked into the maturity of technology used in each study as determined by its readiness level (TRL). All but one in the prototype group was rated as having TRL 3 while the clinical group was more varied in their TRL (ranging from 5-7). The system used by Witkowski et al., a prototype study, was rated TRL 4 due to the study being performed on the basis of improving and assessing its safety features. It is also worth noting that while a formal safety assessment was not performed for the TRL 3 prototypes of Stan et al., Randazzo et al. and Tacchino et al., safety considerations and/or implementations were made; a criterion to be satisfied before proceeding to TRL 4. The system used by Chowdhury et al. is a good example of improving a TRL from 5 to 6 with a pilot clinical study published within the same year. The two systems used in the RCT studies by Ang et al. and Frolov et al. achieved the highest score (TRL 7) among all of the studies which also meant that no BCI-hand robot system for stroke rehabilitation has ever been registered and commercially-released to date. This suggests that such systems lack the strong evidence that would propel commercialisation and technology adoption.
Heterogeneity in the study designs was apparent in both the clinical and prototype groups. The lack of control groups and random allocation in clinical studies (e.g., only 2 out of 7 studies are in the huge sample size RCT stage) made us unable to perform a meta-analysis of effects and continue the study by Cervera et al with a focus on BCI-hand robot interventions. Results from the methodological quality assessment showed that only two studies had a score of 7 in the PEDro scale. Although non-conclusive, these results support the notion that most of the studies are not aligned with the criteria of high-quality evidence-based interventions.
Almost all the clinical studies (except for Carino-Escobar et al. and Frolov et al.) limited their recruitment to chronic stroke patients. The reason may be due to the highly variable rates of recovery in patients at different stages in their disease. Baseline treatments were also not reported among the clinical studies. Instead, the BCI-robot interventions were compared to control groups using standard arm therapy; an example of this was done by Ang et al.. The heterogeneity of experimental designs reported in this review raises the need to develop clearly defined protocols when conducting BCI-hand robot studies on stroke patients. Until new systems have been assessed on this standard, it will be difficult to generate strong evidence supporting the effectiveness of BCI-robotic devices for hand rehabilitation.
In the development of any BCI-robotic device there are several design and feature considerations that need to be made to ensure that the systems are both fit for purpose and acceptable to the end-user. These design considerations must go beyond the scope of understanding the anatomy of the hand and the physiology of motor recovery in response to therapy. Feedback from stroke patients should also be an essential part of this design process. Among the extracted studies, we surveyed the extent of end-user involvement in the initial stages of development (i.e., through consultations, interviews and therapy observations) and we found that there were no explicit statements about these in the reports. We recommend, as good practice, for future work in this area to report the type and degree of patient and/or physician involvement in device development to allow reviewers and readers to more readily gauge the potential usability of the system.
* We were able to profile the BCI-hand robot systems regarding their technical specifications and design features. In hardware terms, a BCI-hand robot system involves three major components: An EEG data acquisition system with several electrodes connected to a signal amplifier; A computer where raw EEG data is received then processed by filters and classifiers and where most of the cues and feedback during training is presented via a visual display; a robotic hand rehabilitation system for providing the physical therapy back to the user.
* The majority of the studies (N=19) used a BCI solely based on EEG while the rest were combined with other sensors: EEG with EMG, EEG with force sensors and an EEG-EMG-EOG hybrid system. The purpose of this integration is mainly to improve signal quality by accounting for artifact or to provide added modalities. Action potentials such as those caused by ocular, muscular and facial movements interfere with nearby electrodes and the presence of an added electrophysiological sensor accounting for these would enable the technician to perform noise cancellation techniques as a first step in signal processing.
* The choice of EEG system as well as the type of electrodes provides a technical trade-off and affects the session both in terms of subjective experiences (i.e., ease-of-use, preparation time, cleaning, comfortability) and data performance. Due to the presence of a conducting gel/solution, standard "wet" electrodes provide a degree of confidence in preventing signal disruption within a short duration usually enough for a standard stroke therapy session. However, this also makes the setup, use and cleaning in the experiment more challenging, non-ambulatory and reliant on a specialised laboratory setup. Conversely, dry electrodes offer an accessible, user-friendly and portable alternative by using dry metal pins or coatings that comb through hair and come in contact directly with the scalp. The signal fidelity of dry electrodes is still a matter of debate in the BCI community. A systematic comparison between dry passively-amplified and wet actively-amplified electrodes reported similar performance in the detection of event-related potentials (ERP). However, for a study involving dry active electrodes, high inter-electrode impedance resulted in increased single-trial and average noise levels as compared to both active and passive wet electrodes. In classifying MI, movement-related artifacts adversely affect active dry electrodes, but these can be addressed through a hybrid system of other physiological sensors to separate sources.
Almost all of the studies included used a standard EEG system with "wet" electrodes (e.g., g.USBamp by g.tec and BrainAmp by Brain Products) while three used Emotiv EPOC+, a semi-dry EEG system that uses sponge conductors infused with saline solution. While the use of dry electrodes has been observed in pilot and prototype studies of BCI-hand robot systems and other motor imagery experiments, no dry EEG system was used in the final 30 studies that tested healthy or stroke participants. It is expected that as dry EEG systems continue to improve, their use in clinical studies of BCI will also become increasingly prominent.
The degree of BCI-robotic control for the majority of the studies (N=26) was limited to triggering the device to perform grasping (opening and closing of hand) and pinching (a thumb-index finger pinch or a 3-point thumb-index-middle finger pinch) movements usingMI and other techniques. A triggered assistance strategy provides the minimum amount of active participation from the patient in a BCI-robot setup. The main advantages of this is that it is easy to implement; requiring less computational complexity in signal processing. However, a higher spatial or temporal volitional control over the therapeutic device increases its functionality and can be used to develop more engaging tasks for the stroke therapy. Among the studies, no robotic control setup was able to perform digit-specific MI which corresponds to the spatial aspects of volitional control. This is a limitation caused by the non-invasive setup of EEG and is due to the low spatial resolution brought by the distances between electrodes. The homunculus model, a representation of the human body in the motor strip, maps the areas of the brain where activations have been reported to occur for motor processes. The challenge of decoding each finger digit MI in one hand is that they only tend to occupy a small area in this strip. Hence even the highest resolution electrode placement system (i.e., the five percent or 10-5 system - up to 345 electrodes) would have difficulties accounting for digit-specific MI for BCI. In contrast to EEG, electrocorticography (ECoG) have been used to detect digit-specific MI. The electrodes of ECoG come in contact directly with the motor cortex and is an invasive procedure; making it non-ideal for use in BCI therapy. It is worth noting however that some studies were successful in implementing continuous control based on ERD/ERS patterns. A continuous control strategy increases the temporal volitional control over the robot as opposed to triggered assistance where a threshold is applied, and the robot finishes the movement for the participant. Bundy et al. and Norman et al. were both able to apply continuous control of a 3-DOF pinch-grip exoskeleton based on spectral power while Bauer et al. provided ERD-dependent control of finger extension for an end-effector robot. These continuous control strategies have been shown to be very useful in BCI-hand robots for assistive applications (i.e., partial or full device dependence for performing ADL tasks). Whether this type of control can significantly improve stroke recovery is still in question as the strategy of robots for stroke rehabilitation can be more classified as a therapeutic "exercise" device.
* Signal processing and machine learning play a vital role in the development of any EEG-based BCI. The pre-processing techniques (e.g., filtering, artifact removal), types of features computed from EEG, and the classifier used in machine learning can significantly affect the performance of the robotic system in classifying the user's intent via MI. False classification, especially during feedback, could be detrimental to the therapy regime as it relates to the reward and punishment mechanisms that are important in motor relearning. For example, false negatives hinder the reward strategy that is essential to motivate the patient while false positives would also reward the action with the wrong intent. In this review, a critical appraisal of the signal processing techniques was done on each system to recognise the best practices involved. The current list of studies has revealed that approaches to develop MI-based EEG signal processing are highly diverse in nature, which makes it difficult to compare across the systems and hinders the development of new BCI systems informed by the strengths and weaknesses of existing state-of-the-art systems. The diversity in the design process can be beneficial to develop complex MI EEG-based BCI systems to achieve high efficiency and efficacy. However, such newly developed systems should be open sourced and easily reproducible by the research community to provide valid performance comparisons and drive forward the domain of robotic-assisted rehabilitation.
* In addition to MI, other strategies for robotic control were reported. Diab et al. and King et al. both facilitated the movements of their respective orthoses by physical practice while Stan et al. utilised a P-300 evoked potential speller BCI, where the user visually focused on a single alphanumerical character situated in a grid. The chosen character then corresponded to a command for the hand orthosis thereby producing the desired stimulus for the patient. While the latter study reported 100% accuracy rate in terms of intention and execution, the EEG channels were situated in the visual cortex rather than the motor strip which deviates from the goal of activating the desired brain region for plasticity. This highlights a broader issue on the intent behind a BCI-robotic system. Given that any potential signal that can be reliably modulated by a patient can be used to trigger a robot, and that such an approach would be antithetical to the goal of many MI-based systems, engineers may consider how they can tailor their systems to ensure that the appropriate control strategy (and corresponding neural networks) are implemented by a user (e.g. by taking a hybrid approach that includes EMG and force sensors).
In order to facilitate hand MI and account for significant time-points in the EEG data, all the studies employed a cue-feedback strategy during their trials. 19 of the studies presented a form of visual cue while the rest, except for two unspecified, involved cues in auditory ("bleep"), textual or verbal forms. As for the provision of a matching sensory feedback, 16 studies presented a combination of kinaesthetic and visual feedback with some also providing auditory feedback during successful movement attempts. All the studies provided kinaesthetic feedback through their robotic devices. Some systems with visual feedback, such as Wang et al., Li et al., Chowdhury et al. in both of their clinical studies and Ono et al. in their clinical and pilot testing experiments, used a video of an actual hand performing the desired action. Ang et al. and Stan et al., in a different strategy, provided visual feedback through photo manipulation and textual display, respectively.
Future Directions
* There is clearly great potential for the use of BCI-hand robots in the rehabilitation of an affected hand following stroke. Nevertheless, it is important to emphasise that there is currently insufficient evidence to support the use of such systems within clinical settings.
* Moreover, the purported benefits of these systems rest on conjectures that require empirical evidence. In other words, there are grounds for supposing that MI could be useful within these rehabilitation settings but no supporting evidence. This systematic review has also revealed that there are a number of technological limitations to existing BCI-hand robotic systems. We stress an urgent need to address these limitations to ensure that the systems meet the minimum required levels of product specification (in measuring brain activity, processing signals, delivering forces to the hand and providing rich feedback and motivating settings).
* We question the ethics or usefulness of conducting clinical trials with such systems until they can demonstrate minimum levels of technological capability. We consider below what standards these systems should obtain before subjecting them to a clinical trial and discuss might constitute an acceptable standard for a clinical trial.
* **Ideal Setup for a BCI-hand Robot**
* We summarise the information revealed via the systematic review about what constitutes an acceptable setup for a BCI-hand robot for stroke rehabilitation. We focus on improving individual components in data acquisition, data processing, the hand rehabilitation robot, and the visual cue and feedback environment. Table 6 presents the features and specifications of a fully integrated acceptable system.
Nevertheless, end-user involvement in the design with the prioritisation of safety while allowing the most natural hand movement and ROM as possible is the recommended goal.
#### Ideal Setup for Clinical Trials
We also propose a set of specialised criteria for BCI-hand robot systems in addition to the standard motor improvement scores (e.g. ARAT, FMA-UE) evaluated during clinical trials. Firstly, classification accuracies between intended and interpreted actions from the data acquisition and software component should always be accounted to track the effectiveness of BCI in executing the clinical task. In addition to this, system calibration and training procedures, especially its duration, should be detailed in the protocol to document the reliability of the classification algorithm. There is not much to consider in the use of robotic devices as they are most likely to be mature (if not yet commercially available) before being used as the hardware component in the study. However, the devices' functionality (i.e., task to be performed, degree of control and motion, actuation and power transmission etc.) should always be stated as they contribute to the evaluation of interactions between other components in the system. Lastly, controls for the clinical study must always be included, even with small-scale patient studies. As discussed in this article, these controls may be in the form of sham, standard arm therapy (SAT), standard robotic therapy, congruency feedback and quality of stimuli among others. Having regarded and implemented these criteria would help homogenise the clinical data for future meta-analyses, strengthen evidence-based results and provide a reliable way of documentation for individual and/or interacting components.
Proposed roadmap
* We suggest that the immediate focus for BCI-controlled robotic device research should be around the engineering challenges. It is only when these challenges have been met that it is useful and ethical to subject the systems to clinical trials. We recommend that the challenges be broken down into the following elements: data acquisition; signal processing and classification; robotic device; priming and feedback environment; integration of these four elements. The nature of these challenges means that a multidisciplinary approach is required (e.g. the inclusion of psychologists, cognitive neuroscientists and physiologists to drive the adoption of reliable neural data acquisition). It seems probable that progress will be made by different laboratories tackling some or all of these elements and coordinating information sharing and technology improvements. Once the challenges have been met (i.e. there is a system that is able to take neural signals and use these to help drive a robotic system capable of providing appropriate forces to the hand within a motivating environment) then robust clinical trials can be conducted to ensure that the promise of this approach does translate into solid empirical evidence supporting the use of these systems within clinical settings.
Declarations
* Funding This work was supported by a Newton Fund PhD grant, ID 331486777, under the Newton-Agham partnership. The grant is funded by the UK Department for Business, Energy and Industrial Strategy and the Philippine Commission on Higher Education and delivered by the British Council. For further information, please visit www.newtonfund.ac.uk. Authors F.M and M.M-W were supported by Fellowships from the Alan Turing Institute and a Research Grant from the EPSRC (EP/R031193/1).
Availability of Data and Materials
* A full database of selected studies including those extracted during the search and selection process is available from the corresponding author on reasonable request.
*
* **Authors' Contributions**
* PDEB and ECS performed the initial search and screening of the studies. MA performed the analysis of signal processing techniques. AA, AEJ and RJH made contribution to the robotics, design and other engineering aspects of the current work. FM provided analysis related to EEG and BCI. MMW contributed to the clinical and overall direction of the review. PDEB, FM and MMW were the major contributors to the writing of the manuscript. All authors read and approved the final manuscript.
*
* **Competing Interests**
* The authors declare that they have no competing interests.
*
* **Ethics Approval and Consent to Participate**
* Not applicable.
* **Consent for Publication**
* Not applicable.
* **Acknowledgements**
* Not applicable.
|
19015503 | ## 1 Abstract
* INTRODUCTION: Hearing aid usage has been linked to improvements in cognition, communication, and socialization, but the extent to which it can affect the incidence and progression of dementia is unknown. Such research is vital given the high prevalence of dementia and hearing impairment in older adults, and the fact that both conditions often coexist. In this study, we examined for the first time the effect of the use of hearing aids on the conversion from mild cognitive impairment (MCI) to dementia and progression of dementia.
* METHODS: We used a large referral-based cohort of 2114 hearing-impaired patients obtained from the National Alzheimer's Coordinating Center. Survival analyses using multivariable Cox proportional hazards regression model and weighted Cox regression model with censored data were performed to assess the effect of hearing aid use on the risk of conversion from MCI to dementia and risk of death in hearing-impaired participants. Disease progression was assessed with CDR(r) Dementia Staging Instrument Sum of Boxes (CDRSB) scores. Three types of sensitivity analyses were performed to validate the robustness of the results.
* RESULTS: MCI participants that used hearing aids were at significantly lower risk of developing all-cause dementia compared to those not using hearing aids (hazard ratio [HR] 0.73, 95%CI, 0.61-0.89; false discovery rate [FDR] _P_=0.004). The mean annual rate of change (standard deviation) in CDRSB scores for hearing aid users with MCI was 1.3 (1.45) points and significantly lower than for individuals not wearing hearing aids with a 1.7 (1.95) point increase in CDRSB per year (_P_=0.02). No association between hearing aid use and risk of death was observed. Our findings were robust subject to sensitivity analyses.
DISCUSSION: Among hearing-impaired adults, hearing aid use was independently associated with reduced dementia risk. The causality between hearing aid use and incident dementia should be further tested.
Keywords: dementia; Alzheimer's disease; mild cognitive impairment; MCI; dementia onset; dementia incidence; hearing impairment; hearing loss; hearing aid; risk factor; disease progression; cognitive decline; survival analysis; National Alzheimer's Coordinating Center* 35 High prevalence of dementia and hearing impairment in older adults
* 36 Hearing aid (HA) use associated with a lower risk of incident dementia
* 37 Slower cognitive decline in users than non-users of HA with mild cognitive impairment
* 39 The relationship between hearing impairment and dementia should be further tested Background
The escalating costs and devastating psychological and emotional impact of dementia on affected individuals, their families and caregivers makes the prevention, diagnosis, and treatment of dementia a national public health priority worldwide. While the process of drug development to delay the onset of dementia has been slower than initially hoped, there is evidence that behavioural and lifestyle interventions might reduce dementia risk. Numerous studies have investigated the effects of physical exercise, healthy diet, and management of medical conditions, such as diabetes and heart disease, on cognitive decline and risk of developing dementia. However, there is a paucity of research on hearing impairment and dementia. Such research is vital, given the high prevalence of dementia and hearing impairment in older adults, and the fact that both conditions often coexist.
The prevalence of hearing loss is higher among older than younger individuals, with over 70% of adults aged 70 and older having hearing loss in at least 1 ear. In the United States (U.S), mild hearing loss affects 23% of the population over the age of 12, with moderate hearing loss more prevalent in those over 80 years. More importantly, approximately 23 million adults with hearing loss in the U.S. do not use hearing aids even though the negative impact of untreated hearing loss has been widely documented. The low level of hearing aid adoption is associated with stigma and affordability of hearing aids. Adults with impaired hearing, who do not wear hearing aids demonstrate significantly higher rates of depression, anxiety, and other psychosocial disorders. Hearing loss was also associated with increased risk of incident dementia.
Despite the observed relationship between hearing loss and cognition, surprisingly few studies have investigated the association between the use of hearing aids, cognitive decline, and risk for developing dementia. One study found little evidence that hearing aids promoted cognitive function but acknowledged that they may be effective in reducing hearing handicap. Other work showed that hearing aid use was associated with better cognition while controlling for confounding by age, sex, general health, and socioeconomic status. A recent randomized pilot study examined the changes in cognition due to treatment of hearing loss, with some promising results for proximal outcomes (perceived hearing handicap, loneliness) that may mediate a relationship between hearing and cognition. Better understanding of the relationship between use of hearing aids cognitive function, and risk of dementia is of utmost importance since it has the potential to significantly impact public health, as hearing aids represent a minimally invasive, cost effective treatment to mitigate the impact of hearing loss on dementia. In fact, it is postulated that up to 9% of dementia cases could be prevented with proper hearing loss management. Slower conversion from MCI to dementia and progression of dementia following hearing aid use could potentially lead to the reduced incidence of dementia and extended preservation of functional independence in people with dementia.
In this study, we used data from a large referral-based cohort to examine for the first time the effect of the use of hearing aids on the conversion from Mild Cognitive Impairment (MCI) to dementia and risk of death. We tested if the use of hearing aids is independently associated with a decreased risk of incident all-cause dementia diagnosis for MCI patients and reduced risk of death in individuals with dementia. We also examined if the rate of cognitive decline is slower for hearing aid userswhen compared to those not using hearing aids in participants with both MCI and dementia at baseline.
## 2 Methods
### Participants
We conducted a retrospective analysis of the demographic and clinical data obtained from the National Alzheimer's Coordinating Center (NACC). The NACC database consists of data from Alzheimer's Disease Research Centers (ADRCs) supported by the National Institute on Aging (NIA) (grant U01AG016976). Details about the NACC consortium, data collection process, and design and implementation of the NACC database have been reported previously. The data set used in our longitudinal investigation was the NACC Uniform Data Set (UDS).
The analytic sample for this study included 2114 participants (age >50) with hearing impairment who had UDS data in the NACC database available between 2005 and 2018. All subjects were classified into two groups according to the disease stage. Group 1 included 939 individuals that were diagnosed with MCI at baseline, namely, 497 MCI converters (MCI-c) and 442 MCI non-converters (MCI-nc). Group 2 consisted of 1175 participants that were diagnosed with dementia at baseline: 349 of those died during the follow-up. The 829 dementia participants who did not die during the study follow-up were censored at their last clinical evaluation. Note that only patients that clearly progressed from one stage to another were included in the study. In addition, only active participants who continued to return for annual follow-up visits were taken into account and hence, any subject that missed a scheduled appointment (7%) was discarded from the analysis.
* The incidence of MCI and all-cause dementia was determined based on the clinical diagnosis made by a single clinician or a consensus panel. The clinical diagnosis took into account patient's medical history, medication use, neuropsychological test performance, and other modifying factors, such as educational and cultural background, and behavioural assessments. In NACC-UDS Version 1 and 2, the procedure of clinical diagnosis of all-cause dementia depended on the diagnostic protocol of the ADRC, but each Center generally adhered to standardized clinical criteria as outlined by the DSM-IV or NINDS-ADRDA guidelines. In NACC-UDS Version 3, the coding guidebook criteria for all-cause dementia were modified from the McKhann all-cause dementia criteria. Diagnoses of MCI were made using the modified Petersen criteria.
* In addition, we used the CDR(r) Dementia Staging Instrument Sum of Box (CDRSB) scores to assess a decline due to cognitive changes in six functional domains, namely, memory, orientation, judgment and problem solving, community affairs, home and hobbies, and personal care. CDRSB has a total score range from 0 to 18 points, with higher scores indicating greater cognitive impairment. CDRSB has been commonly used as a reliable tool for assessing dementia severity.
* _2.3 Hearing assessment_
* The information on presence of hearing loss and use of hearing aids were extracted from the NACC UDS Physical Evaluation form. Information on hearing loss was collected via self-report using a single hearing screening question: "Without a hearing aid(s), is the subject's hearing functionally normal?", which provided possible responses of 'yes' or 'no'. Participants that responded 'yes' were defined as individuals with hearing loss and those that responded 'no' were excluded from the analysis. The determination of severity of hearing loss was not a part of a standardized clinical evaluation given to NACC participants. Although participants were allowed to wear hearing aids during the cognitive assessments, it was not reported to NACC whether a participant was wearing a hearing aid during cognitive testing. Missing codes were however entered when ADRCs had a reason to believe that the test was invalid, including if they were aware that the participant was unable to hear properly. All participants with missing codes were excluded from the analysis.
* Information on hearing aid use was collected via self-report using a single question: "Does the subject usually wear a hearing aid(s)?", which provided possible responses of 'yes' or 'no'. Participants that responded 'yes' were classified as hearing aid users and those that responded 'no' were classified as non-users of hearing aids. The consistent use (or non-use) of hearing aids was established if the participant answered "yes" or "no" to the above question at every consecutive visit. There was no additional information in the NACC-UDS on the number of hours of daily use of hearing aids, the type of hearing aids used, or the history of hearing aid use before the enrolment in the NACC-UDS.
* Accordingly, data from individuals identified with impaired hearing at every annual clinical evaluation, that consistently reported non-use or use of hearing aids as well as functionally normal hearing when wearing hearing aids served as the sample for our study. The subject's hearing was characterised as functionally normal with a hearing aid if there was no evidence of reduced ability to do everyday activities such as listening to the radio/television or talking with family/friends. This information was based on self-report. On the other hand, the group of participants excluded from the analysis consisted of subjects without hearing impairment or with inconsistent hearing impairment labelling as indicated by the records from each follow-up visit. Participants with inconsistent records relating to the use or non-use of hearing aids or without functionally normal hearing when wearing a hearing aid were also excluded. The baseline characteristics of participants included and excluded from the study are shown in Table 1. Among 2114 patients with hearing impairment included in the study, 636 subjects in Group 1 and 710 in Group 2 were classified as using hearing aids.
### Statistical analysis
Baseline summary statistics are presented as proportions for categorical data and means with standard deviations (SD) for continuous variables. Unadjusted analyses for comparison of demographic and clinical features between individuals with hearing impairment that used and did not use hearing aids were performed with the Fisher's exact test and unpaired t test. The average annual rate of change in CDRSB score in individuals using and not using hearing aids was compared by applying Mann Whitney U method. The assumption of normality of CDRSB data was tested using Shapiro-Wilk test.
A Cox model with censored data was used to study time to incident dementia diagnosis for MCI patients (Group 1) and death for individuals diagnosed with dementia (Group 2). Censoring was accounted for in the analysis to allow for valid inferences. Ignoring censoring and equating the observed follow-up time of censored subjects with the unobserved total survival time would likely lead to an overestimate of the overall survival probability. The proportional hazards assumption for the Cox regression model fit was tested with the Schoenfeld residuals method and satisfied for Group 1 (_P_ = 0.7). The presence of non-proportional hazards was observed in Group 2 (_P_ = 0.001), with the proportional hazard assumption violated for age (_P_ < 0.001) and CDRSB (_P_ = 0.007) variables. Accordingly, we used the Cox proportional hazards regression model to model time to incident dementia for MCI patients (Group 1) and implemented weighted Cox regression accounting for time-varying effects to determine the survival rate of individuals diagnosed with dementia (Group 2). Weighted Cox regression allowed for providing unbiased estimates of hazard ratios irrespective of proportionality of hazards. Hazard ratios (HR) with 95% confidence intervals (95% CI) were calculated for each group by comparing the hazard rates for individuals with hearing impairment who used and did not use hearing aids. All comparisons were adjusted by age, gender, years of education (measured as the number of years of education completed) and CDRSB score to remove their possible confounding effect. The linearity assumption of the relationship between continuous confounding variables (i.e. age, education, CDRSB) and the log-hazard of the time-to-event outcome was tested using the Box-Tidwell approach and satisfied in both groups (p > 0.05).
201 For each MCI individual in Group 1 and dementia participant in Group 2, time 'zero' was defined as the date of the baseline evaluation. The diagnosis of MCI in Group 1 and dementia in Group 2 referred to the initial event while the endpoint event was considered the conversion to all-cause dementia in Group 1 and the occurrence of death in Group 2 (0 - censored, 1 - uncensored). Survival time was determined by the year. MCI-nc subjects and dementia participants who did not die during the study follow-up were censored at the last clinical assessment.
To avoid the inflation of false-positive findings, the Benjamini-Hochberg false discovery rate (FDR) procedure was used to adjust for multiple hypothesis-testing. False discovery-adjusted \(P\) values (FDR _P_) less than 0.05 were considered as statistically significant.
### 2.5 Sensitivity analysis
To validate the robustness of the main findings, we performed three different sensitivity analyses: a) propensity score matching to control for measured confounding, b) the analysis for unmeasured confounding to assess the sensitivity of our main conclusions with respect to confounders not included in our study, and c) the inverse probability of treatment weighting method to reduce selection bias within our study population.
Propensity scores were generated for hearing aid status using multivariable logistic regression model and adjusting for baseline covariates, including age, gender, education, and CDRSB. The standardized mean difference between two patient groups i.e., patients with and without hearing aids, was then calculated for each covariate and compared before and after the matching process to determine covariate balance between the two groups. A standardized difference of less than 0.1 was considered negligible in the prevalence of a covariate.
Sensitivity analysis for unmeasured confounding was conducted to measure the potential influence an unmeasured covariate might have on the HR estimates of the association between hearing aid use and a) incident dementia in Group 1 and b) death in Group 2. We considered prevalence rates for the confounder of 5%, 10%, and 20% in the group of hearing aid users and three different values of HR (0.5,2.0,4.0) for the association between the confounder and exposure. We then varied the prevalence of the unmeasured confounder in the group of subjects without hearing aids, from 10% to 30% to determine the extent to which its distribution under these conditions would need to be imbalanced to influence the statistical significance of our findings, i.e., when the upper limit of the 95% CI of HR crosses 1.0.
The inverse probability of treatment weighting method was used to attenuate potential selection bias in the sampling and recruitment of NACC participants. Weights were derived from propensity score modelling of the probability of hearing aid use as a function of measured covariates using the Generalized Boosted Model. A multivariable Cox proportional hazards regression model and weighted Cox regression model were then fitted using derived weights to examine the risk of incident dementia and death for hearing aid users and non-users in Group 1 and 24 respectively.
## 3 Results
### Participant Characteristics
Baseline demographic and clinical characteristics of participants by the hearing aid status are presented in Table 1. Statistically significant differences in the use of hearing aids were found between men and women both in Group 1 (_P_ = 0.01) and Group 2 (_P_ = 0.02), with higher rates of hearing aid use in males. Hearing aid users with baseline MCI were significantly older than MCI individuals not using hearing aids (\(P\square\textless\square 0.001\)). Age was comparable for users/non-users of hearing aids in Group 2 (_P_ = 0.32). Hearing aid users with dementia had more years of education completed (_P_ < 0.001). The CDRSB score was significantly lower in both individuals with baseline MCI and dementia who used hearing aids (_P_ = 0.01 and \(P\) < 0.001 respectively).
* 257 During the study follow-up, 497 MCI subjects in Group 1 developed dementia. The median time to incident dementia was 2 years for non-hearing aid users and 4 years for hearing aid users. The 5-year overall survival rate, which is the percentage of participants that did not convert to dementia 5 year after the baseline MCI diagnosis, was 19% for non-hearing aid users and 33% for individuals using hearing aids.
* 262 In the multivariable Cox proportional hazards regression model, the major risk factor for MCI-to-dementia conversion was the CDRSB score (HR 1.39, 95%CI, 1.30-1.48, FDR \(P\) < 0.001; Table 2), while a significantly reduced risk of dementia was associated with the use of hearing aids (HR 0.73, 95%CI, 0.61-0.89, FDR \(P\) = 266 0.004).
* 267 The observed mean annual (SD) rate of change in CDRSB for non-hearing aid users with MCI was 1.7 (1.95) points per year and significantly higher than the average rate of change for hearing aid users of 1.3 (1.45) CDRSB points per year (_P_ = 0.02).
* 270 _3.3 Hearing aid status and mortality risk in participants with dementia_
* 271 Group 2 consisted of 1175 individuals diagnosed with dementia at baseline: 349 of those died during the follow-up. The median survival time for dementia participants who did not use hearing aids was 6 years and the 5-year overall survival rate was 58%. For hearing aid users, the median survival time was 7 years and the 5-year overall survival rate was 67%.
* 276 In the weighted Cox regression model accounting for time-varying effects, the relationship between the use of hearing aids and mortality risk was not statistically significant (HR, 0.98; 95% CI, 0.78-1.24; FDR \(P\) = 0.89; Table 3). Higher CDRSBscores were associated with the increased risk of death (HR,\(\square\)1.08; 95% CI, 1.05-280 1.11; FDR \(P\square\)<\(\square\)0.001).
281 The average (SD) annual rate of change in CDRSB score of 0.96 (1.02) for hearing aid users with dementia was not significantly different from the 0.94 (1.19) point increase in CDRSB score per year for individuals with dementia not using hearing aids (\(P\) = 0.75).
285 3.4 Sensitivity analysis
286 The distributions of potential confounders were similar between the hearing aid and non-hearing aid user groups after propensity score matching (standardized difference < 0.1). Again, we found that MCI individuals using hearing aids were at lower risk of developing dementia when compared to non-users of hearing aids (HR 290 0.67, 95%CI, 0.50-0.80, FDR \(P\) = 0.01) (Table 4). No link between hearing aid use and risk of death was found for individuals with dementia (Table 4).
292 Sensitivity analysis for unmeasured confounding performed for each of two studied groups produced virtually unchanged findings (Table 5). Within Group 1, we observed a lower risk of incident dementia for hearing aid users with the estimated HR for incident dementia in the group of participants with hearing aids below 1 for all considered values of the strength of the confounder-outcome association (HR 0.5, 297 1.5, 2.0, 4.0), and the prevalence of potential confounder in the group of hearing aid users (5%, 10%, 20%) and non-users (10%, 20%, 30%). No association between hearing aid use and risk of death was found in Group 2.
300 The results of the inverse weighted propensity showed the increased risk of dementia for MCI subjects in Group 1 (HR 0.72, 95%CI, 0.60-0.88, FDR \(P\) = 0.003)and no statistically significant association between hearing aid use and risk of death for dementia participants in Group 2.
* 304 A lack of improvement in hearing, when a hearing aid is used, may be an indicator of central auditory processing issues rather than a faulty device. As such, we performed additional analysis on a group of hearing aid users that included subjects who still experienced auditory difficulties when wearing a hearing aid (Table A.3). In total, 129 participants in Group 1 and 174 participants in Group 2 were identified as those without functionally normal hearing when wearing a hearing aid. A majority of them, 63% in Group 1 and 68% in Group 2, were males. We observed a lower risk of developing dementia in subjects using hearing aids in Group 1 (HR,\(\square\)0.74; 95% Cl, 312 0.61-0.89; FDR \(P\square\)=\(\square\)0.003) and no statistically significant relationship between the use of hearing aids and mortality risk in Group 2 (HR,\(\square\)0.99; 95% Cl, 0.80-1.23; FDR \(P\square\)=\(\square\)0.92).
## 4 Discussion
Despite the prevalence of auditory impairment in dementia, hearing loss is often not diagnosed and not treated even though hearing loss has been shown to be an independent risk factor for poorer cognitive function, depression and loneliness, and diminished functional status. Several longitudinal studies indicated that individuals with hearing impairment experience substantially higher risk of incident all-cause dementia. For instance, the study of Lin et al observed a strong relationship between hearing loss and risk of developing dementia. While the authors observed no association between use of hearing aids and reduced risk of dementia, they found a strong link between degree of hearing loss and dementia incidence. In Ray et al, the association between cognitive impairment and degree of hearing loss was also observed but only in individuals who did not use hearing aids.
* 328 Hypothesized mechanisms explaining the association between hearing impairment and cognitive function included the reallocation of cognitive resources to auditory perceptual processing, cognitive deterioration due to long-term deprivation of auditory input, a common neurodegenerative process in the aging brain, and social isolation caused by both sensory and cognitive loss. In addition, recent findings have suggested that hearing impairment manifested as central auditory dysfunction may be an early marker for dementia. Previous studies concluded that intervention in the form of hearing aids may have a positive effect on cognition and reduce the impact of behavioural and psychological symptoms of dementia.
* 329 In this study, we investigated the relationship between the use of hearing aids with incidence and progression of dementia. Our results clearly suggest that the use of hearing aids is independently associated with a decreased risk of incident all-cause dementia diagnosis for MCI patients. Statistically significant differences in cumulative survival functions by hearing aid status were found in Group 1, with accelerated cognitive decline, as indicated by change in the CDRSB score in the MCI group. The use of hearing aids was not associated with reduced risk of death in people with dementia. Three different sensitivity analyses confirmed the robustness of our findings.
* 330 So far, hearing aid usage has been linked to improvements in cognition as well as psychological, social, and emotional functioning. Amieva _et al._ showed that non-use of hearing aids was associated with faster cognitive decline as indicated by the accelerated rate of change in Mini Mental State Examination score. Yet, no significant difference in cognitive decline was observed between hearing-impaired subjects using hearing aids and healthy individuals. The recent study of Maharani _et al._ adopted a different approach in examining differences in cognitive outcomes of hearing aid use. To prevent potential residual confounding caused by demographic differences between hearing aid users and non-users, the authors analysed rates of cognitive change before and after hearing aid use in the same individuals. They reported a significantly slower decline in episodic memory scores after patients started to use hearing aids.
* 359 The potential mechanisms behind the association between the use of hearing aids and cognitive loss, in particular the decreased risk for incident dementia, remain to be determined. Possible explanations include optimized communication and increased social engagement, with resulting lower rates of depression and loneliness, caused by the use of hearing aids and/or changes to the brain associated with the reduced impact of sensory deprivation on brain function. There is also the possibility that facilitated access to auditory information for individuals using hearing aids may result in a reduction in cognitive resources consumed by listening and, hence, lead to improved cognitive ability.
* 368 We acknowledge that biases in our analysis could arise from multiple sources. First, there is selection bias associated with different recruitment strategies implemented by each ADRC. Those enrolling in ADRC cohorts are not random volunteers and therefore, are not representative of a wider population. Their level of education and income is likely above the national average and approximately 50% of subjects have a family history of dementia. These factors may limit generalizability of our findings.
Another methodological limitation of our analysis is its reliance on retrospective data.
* Even though all ADRCs use standard evaluation procedures, there might be some variation in diagnostic criteria between Centers. The lack of use of consistent diagnostic definitions due to the retrospective design of this study can lead to an increased risk of bias due to potential misclassification of the outcome. Furthermore, bias may arise from the degree of accuracy with which subjects have been classified with respect to their exposure status, i.e. hearing status and hearing aid use status. We minimized this bias by considering only participants with a consistent record of hearing impairment and use/non-use of hearing aids. In this way, we could obtain the true effect of hearing aids on incident and progression of dementia. The inclusion of participants with noisy labels could likely result in an over or underestimation of the effect between exposure (hearing aid use) and outcome (incident dementia or death).
* It is also worth highlighting that the proportion of participants wearing hearing aids in the final groups was considerably higher than the prevalence of hearing aid use in the general population. This potential selection bias might have been introduced into the study at the data-gathering stage (the education level and income of NACC volunteers may not be reflective of the general population) or during the process of identifying the study population. In fact, a large number of participants with dementia were excluded from the analysis due to the lack of consistency in reporting hearing difficulty.
* Gender, socioeconomic factors and cultural influences all play a role in the use of hearing aids. It may also be the case that unrecorded intrinsic factors that influence use of hearing aids, or lack thereof, play a significant role in the findings presentedhere. Indeed, severity of cognitive decline may influence acceptance, compliance and correct usage of hearing aids. With incremental changes and decline in cognition, the capacity to comply with the use of hearing aids is likely to significantly diminish. Despite the fact that age, education, gender, and cognitive assessment score were included in the analysis as potential confounders, other unmeasured factors may have impact on the incident and progression of dementia. For instance, hearing aids use in the U.S. is dependent on financial resources as hearing aids are expensive and generally not covered by medical insurance. Other potentially important characteristics not considered in this study due to unavailability of data include type of hearing aid used, hours of daily use, and use of other communicative strategies. Consequently, whether these factors may have a significant effect on time to incident dementia for MCI patients remains unknown and will require further study.
* Nevertheless, we implemented measures to account for the potential impact of confounding and selection bias in our study. Propensity score matching was applied to control for measured confounding; the analysis for residual confounding was implemented to assess the sensitivity of our main conclusions with respect to confounders not included in our study; and potential selection bias was addressed via the inverse probability of treatment weighting method. Our results remained robust under different assumptions.
* Finally, this study relies on self-reported hearing loss which is far less reliable than audiometric screening. The use of information on hearing impairment via self-report prevents any adjustment for the effect of degree of hearing loss when investigating the impact of hearing aid usage on incidence and progression of dementia. It is also worth noting that even though ADRCs are anticipated to enter missing codes when they have reason to believe that the cognitive test is invalid, including if they are aware that the participant is unable to hear properly, we cannot exclude the possibility that hearing impairment, rather than cognitive function, impacted the ability to complete tasks on cognitive tests in participants with hearing loss who did not have hearing aids. Since verbal instructions that are used during cognitive testing depend significantly on hearing, hearing loss might have contributed to the overestimation of the level of cognitive impairment in some hearing-impaired individuals.
* Irrespective of the limitations associated with the present analyses, the fact that significant benefit appears to be derived in delaying conversion of MCI to dementia with hearing aid use warrants further exploration. Properly designed clinical trials will definitively measure the potential benefit of hearing correction in those experiencing hearing loss.
* 5 Conclusion
* Slower conversion from MCI to dementia in individuals using hearing aids suggests that effective identification and treatment of hearing loss may reduce the cumulative incidence of dementia. The competing risk of all-cause mortality and dementia among those with MCI should be examined in future work. One of the findings reviewed above suggested that higher-level cognitive processing involving memory in hearing-impaired individuals might be compromised because of mental resources being reallocated to perception and away from storing information. We believe this hypothesis should be further tested to see if the use of hearing aids can make word identification less effortful and thus, allow for freeing resources for higher-level processing that can in turn result in improvement in cognitive function. Furthermore,more research is needed to better understand the relationship between hearing impairment, changes in cognitive ability, and the role of hearing aids in preventing milder forms of cognitive impairment. Such knowledge may provide new and novel insights into prevention of cognitive decline. Most importantly, the magnitude and causality of the effect of hearing loss treatment on cognitive decline and incident dementia can only be established by conducting a well-designed clinical trial.
* Public health campaigns are needed to demonstrate the scale and impact of hearing loss and increase awareness regarding effective prevention strategies, consequences of inaction and potential benefits of timely audiological intervention.
* The NACC database is funded by NIA/NIH Grant U01 AG016976.
* MD), P30 AG012300 (PI Roger Rosenberg, MD), P30 AG049638 (PI Suzanne Craft,
* PhD), P50 AG005136 (PI Thomas Grabowski, MD), P30 AG062715-01 (PI Sanjay
* Asthana, MD, FRCP), P50 AG005681 (PI John Morris, MD), P50 AG047270 (PI
* Stephen Strittmatter, MD, PhD)
* **Funding**
* This work was supported by the Dr George Moore Endowment for Data Science at
* Ulster University (MB); European Union INTERREG VA Programme (MB, PLM, ST,
* LPM); Global Challenge Research Fund (MB, XD, QY, DW, VH), Alzheimer's
* Research UK (MB, SB); European Union Regional Development Fund (PLM);
* Northern Ireland Public Health Agency (PLM); Dementias Platform UK (DPUK) (SB);
* Nutricia (ST); Bohringer-Ingelheim (ST); Genomics Medicine Ireland (ST); Vifor
* Pharma (ST); and Putnam Associates (ST).
* **Conflict of Interest**
* The authors declare that they have no competing interests.
* **Ethics approval and consent to participate**
* The National Alzheimer's Coordinating Center Uniform Data Set (NACC-UDS) is
* approved by the University of Washington Institutional Review Board and
* participants provided informed consent at the ADRC where they completed their
* study visits.
* work (application reference: 1026)
|
19016089 | ### Time-frequency characterization of GPFA
To quantify the time-varying properties of the manually marked GPFA events, we converted them to the time-frequency domain to reveal their joint temporal and spectral characteristics: this step was performed because the morphology of a generalized IED evolves over both time and space (i.e., scalp EEG electrodes). Additionally, its oscillations may'slow down' or become 'faster' over the course of an individual discharge. Therefore, an appropriate quantitative detection feature for generalized IEDs must take three factors into account: (_i_) variable morphology, (_ii_) time-varying spectral content before and after the event onset, and (_iii_) multi-electrode spatial distribution.
Example of a multichannel GPFA event captured during simultaneous EEG-fMRI
2-B demonstrate the average spectrograms of all manually marked GPFAs in a subset of scalp EEG electrodes selected from all LGS patients, calculated over a 6 s time window (-3 s to 3 s peri-onset). The selected EEG electrode in each dataset was chosen as the electrode with maximum spectral power across the frequency range of 8-20 Hz post-event onset. The relevance of this frequency band for generalized IEDs is discussed in section 3.1. In 10 out of 13 datasets, the selected electrode was located in the frontal scalp region. Visual inspection of these time-frequency representations suggested a characteristic pattern of time-frequency changes between the pre- and post-onset intervals in GPFA events. As shown in Figure 2-C and D, these pre-post event onset changes became more apparent after demeaning the time-frequency maps along the time axis (i.e., each frequency row in the maps was converted to have a mean value of zero). We observed a 'bimodal' burst of increased spectral power immediately following GPFA onsets that was most apparent in frontal electrodes and was seen as a simultaneous increase in spectral power in a 'low' frequency range of approximately 0.3-3 Hz and a 'high' frequency range of approximately 8-20 Hz. Based on these observations, we hypothesized a general outline for characterization of GPFA in LGS as follows:
## GPFA is an interictal EEG event associated with a burst of post-onset low to high frequency activity spanning a frequency range of ~0.3-20 Hz across multiple, particularly frontal, scalp EEG electrodes. This increased spectral power shows a bimodal pattern consisting of a low frequency patch over ~0.3-3 Hz and a higher frequency patch over ~8-20 Hz.
To test this hypothesis, we considered three subject-specific parameters for each IED type in the time-frequency domain: (_i_) a post-onset low-frequency band (\(\Delta_{LF}\) in Hz), (_ii_) a post-onset high-frequency band (\(\Delta_{HF}\) in Hz), and (_iii_) a subset of EEG electrodes with maximal high-frequency information over \(\Delta_{HF}\). The peri-onset interval was defined as one second before to two seconds after each manually marked IED onset time. To estimate the upper limit of \(\Delta_{LF}\) in each patient, we divided the mean time-frequency representation of each IED type into pre- and post-onset regions. We then projected the two time-frequency planes along the frequency axis and selected the upper cut-off frequency of \(\Delta_{LF}\) as the frequency at which the derivative of their difference changed from negative to positive. To estimate the mid-frequency of \(\Delta_{HF}\), we detected the peak of consistent spectral 'bumps' above \(\Delta_{LF}\) before and after the onset. We defined the extent of \(\Delta_{HF}\) as the full width at half maximum of the detected peak. This analysis was performed for each patient separately.
Group average time-frequency representations of GPFA events calculated in the period from 3 s before to 3 s after the onset of manually marked events over (_A_) all events and all patients (_N_=13), (_B_) the same events and patients as (_A_), but here demeaned along each frequency row (i.e., demeaning was performed along the time axis). A burst of post-onset low to high frequency activity is observed in the time-frequency maps spanning a frequency range of ~0.3-20. This increased spectral power shows a ‘bimodal’ pattern consisting of a low-frequency patch over ~0.3-3 Hz and a high-frequency patch over ~8-20 Hz.
### Validation of the time-frequency feature via automatic IED detection
To validate the utility of the identified time-frequency feature in automatically detecting GPFA events, we searched for EEG segments with similar bimodal spectral behaviour throughout the whole of each patients' in-scanner EEG recording. The rationale here was that if the time-frequency arrangement of GPFA is a reliable and general feature across patients, it should occur during both manually marked GPFA segments as well as 'GPFA-_like_' segments that were not identified in the original manual markup (as for example may occur when a'subtle' event occurs that does that pass the subjective detection threshold for a human reviewer). Hence our automatic detection procedure is likely to yield both 'true positives' (i.e., events which coincide with the manually marked GPFA segments) as well as 'false positives' (i.e., events which do not coincide with the manually marked GPFA segments but which share similar bimodal spectral behaviour). In the following sections, we describe the automatic detection procedure and explain how its true/false positives were quantified.
#### 2.4.1 Automatic detection procedure
Figure 3-A and Figure 3-B show flow diagrams of the proposed automated event detection strategy at the single-channel and multi-channel levels for a typical EEG dataset. The strategy comprises two main steps: (_i_) analysis of each EEG channel separately (Figure 3-A), and (_ii_) integration of the channel-wise analyses (Figure 3-B). At the single-channel level, band-amplitude fluctuations (\(BAF\)s) of each channel are extracted using the Hilbert transform. The BAF envelope of a signal \(X(t)\) is defined as the absolute value of the analytic associate of its filtered version within a frequency band \(\Delta f\), i.e., \(X(t,\Delta f)\)[Omidvarnia et al., 2014]. Mathematically, it is calculated by:
\[BAF_{X}(t,\Delta f)=\left|X(t,\Delta f)+i\hat{X}(t,\Delta f)\right|=\sqrt{X^ {2}(t,\Delta f)+\hat{X}^{2}(t,\Delta f)}\] (Eq. 1)
Zero-phase band-pass filtering is first performed using a Butterworth filter of order 4 in both forward and backward directions6. The BAF of a signal represents its time-varying spectral power within the selected frequency band \(\Delta f\) only (i.e., BAF extraction preserves the spectral content of an event over time within a selected frequency range while excluding other frequency components that are not of interest).
Footnote 6: Band-pass filtering was performed using the MATLAB command _filtfilt_. For more details, see [https://www.mathworks.com/help/signal/ref/filtfilt.html](https://www.mathworks.com/help/signal/ref/filtfilt.html)
**Flow diagrams showing the proposed automatic event detection procedure**Figure 3-C and Figure 3-D show, for one example dataset, the BAF envelopes for an interictal EEG segment in a typical electrode (here, C4) within a low frequency band of \(\Delta f=\) [3 8] Hz and a high frequency band of \(\Delta f=\) [15 30] Hz. The first step in the proposed spike detection approach is to extract two BAF envelopes for each EEG electrode within the pre-defined frequency bands \(\Delta_{LF}\) and \(\Delta_{HF}\). Figure 3-A illustrates the schematic of this process for a single EEG channel. For a multi-channel EEG dataset with \(N_{chan}\) number of electrodes, the per-channel BAF extraction procedure leads to \(2N_{chan}\) BAF envelopes. The per-channel BAF signals are then integrated via multiplication over all channels at each time point: this step yields what we define here as a '_scoring signal'_ with a duration equal to that of the entire EEG recording (red arrow in Figure 3-B). For each time-point, the scoring signal indicates the degree to which there is simultaneous high power within both \(\Delta_{LF}\) and \(\Delta_{HF}\) frequency bands across the intersection of all EEG channels. An increase in the scoring signal is therefore associated with the potential occurrence of a GPFA-like event with maximal information within these bands. The desired events are then detected by selecting supra-threshold time points of the scoring signal after merging adjacent events that are closer than a pre-defined time length, which we refer to as a '_merging window'_ (here, 0.5 s).
(A) Schematic of the GPFA detection at the single electrode channel level. (B) Schematic of the approach at the multi-channel level. (C) Example of a typical band amplitude fluctuation (BAF) signal for a single channel (C4) within an exemplary frequency band of 3 - 8 Hz. (D) BAF envelope of the same signal extracted within a higher frequency band of 15 - 30 Hz. (E) Schematic illustrating an example of a true positive (TP) and a false positive (FP) event for the adjacency interval \(\Delta_{\textbf{Detect}}\) of -0,5 s to 1 s peri-onset (shaded yellow rectangle). The top line illustrates a ‘true positive’ event (red arrow) with respect to \(\Delta_{\textbf{Detect}}\) (black arrow). The bottom line shows a ‘false positive’ event (red arrow) which is outside of \(\Delta_{\textbf{Detect}}\) (black arrow).
Section 2.4.2 explains the choice of our scoring signal threshold.
Given that obtaining \(\Delta_{LF}\) and \(\Delta_{HF}\) relies on an initial manual EEG markup, we first estimated these frequency bands using the manually marked datasets of our LGS cohort and then used this estimation as _a priori_ knowledge for our automatic IED detection procedure. In line with the results of the group average time-frequency maps of Figure 2, we fixed \(\Delta_{LF}\) to [0.3 3] Hz and \(\Delta_{HF}\) of [8 20] Hz.
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190348_file02 | ## S2.
### S2.1 Virus concentration in exhalation samples of Leung _et al._
Many samples in Leung _et al._ return a virus number below the detection limit (Fig. S1) (_10_). To reconstruct the whole distribution, we adopted an alternative approach, using the statistical distribution, i.e., percentage of positive cases, to calculate the virus number. Assuming that the virus number in the samples follows a Poisson distribution, the percentage of positive samples (containing \(>\) 2 viruses, i.e., Leung _et al._, 2020 used 10\({}^{0.3}\)# as undetectable values in their statistical analysis) can be calculated with pre-assumed viral load in exhaled liquids. The Poisson distribution of virus number in emitted droplets is supported by early experiments, where the amount of bioaerosols or compounds delivered in particles is proportional to its concentration in the bulk fluid used to generate particles, and it is independent of investigated particulate type (fluorescent bead, bacteria or spore) (_33_).
For a set of sufficient samples, the positive rate (percentage of samples with virus number \(>\)2) is a function of the mathematical expectation of virus number per sample (\(N_{\rm{v,sample,me}}\)). The \(N_{\rm{v,sample,me}}\) therefore can be retrieved by scanning a series of \(N_{\rm{v,sample,me}}\) until the calculated positive rate agrees with the measurement. It should be noted that the viral load in exhaled liquids and the total exhaled liquid volume may be different among individuals, which must be considered in the calculation. Therefore, the Monte Carlo approach is used in this study. We assume that the statistical number distribution of SARS-CoV-2 in nasopharyngeal and nasal swab samples (Fig. S2, Jacot _et al._, 2020 (_18_)) can represent the individual difference of viral load in exhaled liquids. The distributions can be fitted with multi-mode lognormal distribution with a low-abundance mode and a high-abundance mode. The dispersion of the high abundance mode (\(\sigma\)\(\sim\) 1) is adopted in our calculation. In the experiment of Leung _et al._, the difference of sampled liquid volume stems from the individual difference of coughing times and volume concentration of exhaled droplets. The coughing time is assumed to follow a normal distribution with a \(\sigma\) of 44.5. The exhaled droplet volume concentration is assumed to follow a lognormal distribution with a \(\sigma\) of log\({}_{10}\). The experiment in Leung _et al._ is simulated with a series of viral loads. At each viral load, the experiment with the same sample number as in Leung _et al._ is repeated for 1\(\times\)10\({}^{5}\) times to obtain a stable result. For each sample, the mathematical expectation of virus number is calculated based on randomly generated coughing time, exhaled aerosol/droplet volume concentration, andviral load. The "true virus number" in each sample is assumed to follow a Poisson distribution, and is randomly generated with its mathematical expectation equaling to the calculated value. Finally, for each pre-defined viral load, a distribution of positive rates can be obtained and fitted with a normal distribution function. When the calculated median positive rates become equal to the reported values in Leung _et al._, the viral load of coronavirus, influenza virus and rhinovirus in exhaled liquids are determined (Table S1), which is then used to calculate the distribution function and median of virus number per sample (\(N_{\text{v,sample}}\)) (Fig. S3 and Table S2).
Given the volume of exhaled liquids in each sample (\(V_{\text{p}}\)), the viral load in respiratory tract fluid, \(C_{\text{v,fluid}}\) (number of viruses per volume of respiratory tract fluid) can be calculated by:
\[C_{\nu,fluid}=\frac{N_{\nu,sample}}{\nu_{p}} \tag{1}\]
#### S2.2 Viral load in respiratory tract fluid of Jacot _et al._
Jacot _et al._ presented a large 9-week dataset of viral load in nasopharyngeal and nasal swab samples (_18_). As shown in Fig. S2, the viral load apparently exhibited a multi-mode lognormal distribution (overall \(\sigma\sim 2\)), with one low-abundance mode around \(\sim\)1\(\times\)10\({}^{3}\) to 1\(\times\)10\({}^{5}\) copies mL-1, and the other high-abundance mode \(\sim\)1\(\times\)10\({}^{5}\) to 1\(\times\)10\({}^{10}\) copies mL-1. The high-abundance mode shows a negative skew lognormal distribution, probably due to the reduced viral load over time. To represent the individual difference of viral load in exhaled liquids, we took the variability of the high abundance mode with \(\sigma\sim 1\). The low-abundance mode is not considered due to its much smaller contribution to the infection risk compared to the high-abundance mode.
### S3.
To compare the results of exhalation samples with indoor air samples, we performed model simulations for a scenario with patient density, space areas, and ventilation conditions emulating Fangcang Hospital in Wuhan:
* The total area of the ward is 500 m\({}^{2}\) with a height of 10 m. The total number of patients is 200 (_14_).
* Each patient coughed an average of 34 times per hour, and the volume of each cough is 2 L; the breath volume is 8 L min-1. The size distributions of particles emitted during coughs and breath were taken from * All patients were wearing surgical masks with penetration rates given in Fig. S4A according to the guideline of Fangcang Hospital ([https://edition.cnn.com/2020/02/22/asia/china-coronavirus-roundup-intl-hnk/index.html](https://edition.cnn.com/2020/02/22/asia/china-coronavirus-roundup-intl-hnk/index.html)). We have also calculated the case when the patients did not wear any mask.
* Natural ventilation is assumed, and the loss rate of particles is calculated according to the function given in Fig. S5 (_34_).
The median viral load in exhaled samples were assumed the same as in Leung _et al._ (Sect S2) and the variation between individual patients was assumed to follow a lognormal distribution with a \(\sigma\) of 1. After being emitted, respiratory particles lose water and is dried to half of their initial sizes (_35_).
The indoor airborne virus concentration can be calculated with
\[C_{v}=8\cdot C_{v,aerosol}\cdot\int_{0}^{2.5\;\mu m}n(D_{d})\cdot\frac{\pi\cdot D_{ d}^{\alpha}}{6}\cdot dlogD_{d}+8\cdot C_{v,droplet}\cdot\int_{2.5\;\mu m}^{\infty}n(D_{ d})\cdot\frac{\pi\cdot D_{d}^{\alpha}}{6}\cdot dlogD_{d} \tag{2}\]
where, \(C_{v,aerosol}\) and \(C_{v,droplet}\) are the virus concentration in aerosol mode and droplet mode, respectively; \(D_{d}\) is the particle dry diameter; \(n(D_{d})\) is the equilibrium indoor airborne particle number size distribution and can be determined by
\[\frac{dn(D_{d})}{dt}=\frac{R_{E}(D_{d})}{V}-\lambda(D_{d})\cdot n(D_{d})=0 \tag{3}\]
In the case when all patients were wearing surgical masks,
\[R_{E}(D_{w})=R_{E0}(D_{w})\cdot p_{mask}(D_{w}) \tag{4}\]
In this case, we assumed that exhaled liquid droplets only start to lose water after penetrating masks. In case no patients wearing masks, \(R_{E}(D_{w})=R_{E0}(D_{w})\). Based on Eq. 3, the ambient particle number size distribution can be calculated as \(n(D_{d})=\frac{R_{E}(D_{d})}{V\cdot\lambda(D_{d})}\) when reaching equilibrium.
To account for the individual differences of viral load in exhaled particles, a Monte Carlo method is used to get the possible values of airborne virus concentration. The calculation is repeated for 1\(\times\)10\({}^{7}\) times with randomly generated viral load, which follow a lognormal distribution with a \(\sigma\) of 1. The calculated indoor airborne concentrations of coronavirus, influenza virus and rhinovirus are listed in Table S3.
Our calculation does not consider the lifetime of viruses. With a fixed virus emission rate, the airborne virus concentration is proportional to \(\frac{1}{\lambda_{v}+\lambda_{dep}+k}\), where \(\lambda_{v}\), \(\lambda_{dep}\) and \(k\) are loss rates due to ventilation, deposition and virus inactivation, respectively. The value of \(k\) is similar as (or smaller than) \(\lambda_{v}\) and \(\lambda_{dep}\). Therefore, ignoring virus loss due to inactivation (\(k\)) has a minor effect on the calculated airborne virus concentrations. The other caveat is that the particle loss rate (\(\lambda_{v}+\lambda_{dep}\)) used here may differ from the real loss rate in Fangcang Hospital. According to the loss rate reviewed by Thatcher _et al._, we may expect a maximum uncertainty of one order of magnitude in the calculated airborne virus concentrations, which will not change the regimes they belong to.
## S4 Penetration rate of masks and reduction of virus airborne transmission
The size-resolved particle penetration rate of surgical and N95/FFP2 masks (Fig. S4) is calculated based on the following literature and model calculation:
* Particle diameter \(<\) 800 nm: modified from Grinshpun _et al._
* Particle diameter \(>\) 800 nm & \(<\) 5\(\mu\)m: modified from Weber _et al._
* Particle diameter \(>\) 5\(\mu\)m: model calculation based on particle impaction with following parameters:* Droplets velocity of 6.5 m s-1, calculated based on the volume flow rate of 8 L min-1 (typical breath flow rate of adults) and an air flow cross section as a circle with a diameter of 1 cm;
* Impact angle = 90 degree.
We assumed a filtration efficiency of 99% for N99/FFP3 masks. Regarding other simple masks, Drewnick _et al._ did a comprehensive evaluation of the filtration efficiency of household materials that can be used for homemade face masks and found huge differences of filtration efficiency between sample materials, spanning from \(<\)10% up to almost 100%.
The reduction of virus airborne transmission (\(P_{\rm inf}\) or \(P_{\rm inf,pop}\)) by face masks in is calculated from the change of \(N_{\rm v}\) based on the \(P_{\rm inf}\)-\(N_{\rm v}\) or \(P_{\rm inf,pop}\)-\(N_{\rm v}\) curves in Figs. 2. The change of \(N_{\rm v}\) is the sum of changes in both "aerosol mode" and "droplet mode". For each mode, the change of \(N_{\rm v}\) is assumed to be proportional to the change of volumes of respiratory particles by face masks.
## S5.
We found that the huge variability of the patient's exhaled virus concentration is an important reason for the contrast conclusions from experiments on efficacy of masks to prevent virus transmissions. This large variability requires a large number of samples to draw a robust conclusion. To illustrate the impact of the number of samples, a sensitivity experiment is conducted using a Monte Carlo approach: the virus number in samples of 30-min exhaled droplets above and below 5 um is assumed to follow a lognormal distribution with median values as given in Table S2 and a \(\sigma\) of 1. The sampling experiment is simulated with different sample numbers (2, 5, 10, 20, 50, 100, 200, 500 and 1000) and each experiment is repeated for 1\(\times\)10\({}^{4}\) times. The standard deviation (\(\sigma\)) of the derived positive rates (percentage of samples with virus number \(>\) 2) is then calculated. Moreover, to see how the sample number influences the evaluation of the efficacy of masks, the virus number is calculated with a pre-assumed set of positive rates which follow a normal distribution with \(\sigma\) shown in Fig. S6A. The frequency distributions of derived virus number in 30-min exhalation samples with and without masks at different sample numbers are given in Fig. S6B.
Figure S6A shows the variability of the positive rates under different number of samples. And Fig. S6B shows the frequency distributions of the calculated virus numbers under different sample numbers. When the number of samples is less than 10, the uncertainty of the observed positive rate is relatively large (\(\sigma\) up to \(\sim\)0.35), and the difference between the derived viral load in samples collected with and without mask use have a high chance to be indistinguishable (Fig. S6B). When the number of samples is \(\sim\) 100, the variability is small (\(\sigma\)\(\sim\) 0.05), and the efficacy of masks become visible.
## S6.
Early studies have calculated the effect of mask use on aerosol transmission and infection Risk of COVID-19 in different indoor environments (e.g., Lelieveld _et al._ 2020). Here, we evaluate the effect of wearing masks in controlling the SARS-CoV-2 virus transmission for a population.
As detailed below, wearing surgical masks may remove 82% of the SARS-CoV-2 virus. Because of the common existence of virus-limited regime, for simplicity, we assume that the percentage change of the virus transmission rate (i.e., the reproductive number) due to airborne transmissions is proportional to the percentage change of transmitted virus numbers. Given a basic reproduction number, \(R_{0}\), of \(\sim\)2.5 for COVID-19, wearing a surgical mask can reduce it to \(\sim\) 0.46 and thus allow containing the virus. For N95/FFP2 masks, the reproductive number may even drop to 0.049. This degree of effect is apparently consistent with the real conditions (Fig. S7).
### S6.1. Effect of wearing masks on reducing the reproduction number \(R\) of COVID-19
Wearing surgical or N95/FFP2 masks can reduce the emission rate of virus and further reduce the reproduction number \(R\) of COVID-19. Assuming that infectious individuals cough on average 20 times and speak for 10 minutes per hour, the volume emission rate of exhaled particles (\(E_{\text{p}}\)) can be calculated based on the size distributions shown in Fig. 4, and the number emission rate of virus (\(E_{\text{v}}\)) can be calculated with the viral load in Table S2. Table S4 shows the results for droplet size range of \(D_{\text{w}}<5\ \mu\text{m}\) and \(D_{\text{w}}<20\ \mu\text{m}\). It can be seen that wearing surgical masks and N95/FFP2 masks can reduce the emission of virus by 81.7% and 98.0% (\(D_{\text{w}}<20\ \mu\text{m}\)), respectively.
Assuming that the reproduction number \(R\) is proportional to the emission rate of viruses, the effect of wearing masks on \(R\) can be calculated. Assuming a basic reproduction number \(R_{0}\) of 2.5, all infectious individuals wearing surgical mask and N95/FFP2 mask can reduce \(R\) to 0.46 and 0.049, respectively. It should be noted that only the mask removal of virus from the emitters is considered in the calculation. If all people wear masks, the number of viruses inhaled by healthy people will be further reduced, thereby further reducing \(R\).
### S6.2. The effect of wearing masks on the outbreak and popularity of COVID-19
To evaluate the effect of wearing masks on the dynamics of the COVID-19 outbreak, the infectious disease dynamics model (SEIR model) is employed to model the number of infections:
\[\begin{cases}\frac{dS_{pop}}{dt}=-\frac{\beta_{t}S_{pop}l_{pop}}{N_{pop}}\\ \frac{dE_{pop}}{dt}=\frac{\beta_{t}S_{pop}l_{pop}}{N_{pop}}-\sigma_{i}E_{pop}\\ \frac{d_{pop}}{dt}=\sigma_{i}E_{pop}-\gamma_{r}l_{pop}\\ \frac{dR_{pop}}{dt}=\gamma_{r}l_{pop}\\ \beta_{t}=R_{0}\gamma_{r}\end{cases} \tag{5}\]
Zhang _et al._ investigated the effect of limiting social contact patterns on the reproduction number of COVID-19 in Wuhan, China. We also select Wuhan as the target city, to compare the effects of wearing a mask and limiting social contact patterns reported in Zhang _et al._. The parameters in the SEIR model are assumed as follows:
* \(N_{pop}=11080000\);
* \(\gamma_{r}=0.0556\);* \(\sigma_{i}\) = 0.1923;
* R\({}_{0}\) = 2.5;
* The first outbreak occurred on December 2, 2019: \(E_{pop}=3000\) and \(I_{pop}=10\).
Assuming that control measures start on January 24 and no control measures are implemented before January 23, the effects of the following control measures are evaluated with the SEIR model:
* Only school closure: R = 1.9;
* Reduce personnel contact (city lockdown through nonpharmaceutical interventions, such as home isolation, close public facilities, etc.): R = 0.34;
* Wearing surgical masks, no other measures: R = 0.46;
* Wearing N95/FFP2 masks, no other measures: R = 0.049.
Figure S7A shows the results of the model calculation. Table S5 shows the cumulative total number of infections and the percentage of total infections under the five scenarios. It can be seen that wearing a surgical/N95/FFP2 mask can reduce the total infection rate to below 1%, which is similar as limiting social contact patterns. As a sensitivity study, we also calculated the total infection number and infection rate based on different virus emission reduction rates of masks. Results are shown in Fig. S7B and Table S6.
## Fig. S1. Frequency distributions of observed virus load in respiratory tract fluid. (A), (B) and (C) show the measured viral load in nasal and throat swabs for coronavirus, influenza virus and rhinovirus, respectively; (D), (E) and (F) show the viral load calculated from virus number of exhalation samples (Eq. 1 in Sect S2). The unshaded bars represent samples with virus number below the detection limit (2 viruses, Leung _et al._ 2020 (_10_)).
## Fig. S2. Frequency distribution of SARS-CoV-2 viral load in Jacot _et al._ (_18_).
## Fig. S3. Frequency distributions of calculated virus number in 30-min exhalation air samples.****(A)**, **(B)** and **(C)
In each panel, the blue and red lines represent the virus number in aerosol mode and droplet mode, respectively.
## Fig. S4. Particle penetration rate of a surgical mask (A) and a N95/FFP2 mask (B).
For the particle size range of \(\sim\)50 nm to \(\sim\) 800 nm, the penetration rate (blue circle line) is modified from Grinshpun _et al._. For particle size range of \(\sim\)800 nm to \(\sim\) 3.5 \(\mu\)m, the penetration rate (red circle line) is modified from Weber _et al._. For particle size above \(\sim\)3.5 \(\mu\)m, the penetration rate (yellow circle line) is calculated based on particle impaction.
## Fig. S5. Size-resolved particle loss rate in indoor environment with natural ventilation.
The blue circles represent the measurement in Zhao _et al._. The red line shows the fit result with \(\lambda=0.703\cdot D_{P}^{2}+1.10\cdot D_{P}+0.651\).
## Fig. S6.****(A)** Standard deviation of positive rates derived based on different sample numbers. Four scenarios are tested: aerosol mode (\(D_{\rm w}<5\)\(\mu\)m) samples of 30-min exhalation by patients without wearing surgical masks (blue circle line), droplet mode (\(D_{\rm w}>5\)\(\mu\)m) samples of 30-min exhalation by patients without wearing surgical masks (red circle line), aerosol mode samples of 30-min exhalation by patients wearing surgical masks (yellow circle line), and droplet mode samples of 30-min exhalation by patients wearing surgical masks (purple circle line). The viral loads in aerosol and droplet mode particles are assumed to be the same as the coronavirus (Table S1). **(B)** Frequency distributions of derived viral load in 30-min exhalation samples at different sample numbers. The solid circle lines show the median viral load. Median \(\pm\sigma\) and median\(\pm 2\sigma\) are shown as dashed and dotted lines, respectively. The calculated viral load of coronavirus in aerosol mode (1.39# and 0.682#, Table S2) is adopted as the true viral load in the test. The positive rates of samples are assumed to follow normal distributions with \(\sigma\) shown in panel **(A)
## Fig. S7. (A) Reported daily new cases in Wuhan and simulated numbers based on different \(R\) and control measures. (B) Simulated daily new cases based on different virus emission reduction rates of masks. In panel (A) and (B), the yellow bars represent the confirmed daily new cases in Wuhan and the colored lines show the simulated daily new cases by the SEIR model with different reproduction number \(R\).
## Fig. S8.
The same as except that the ID\({}_{\nu,50}\) is assumed to be 1 or 10000.
## Fig. S9. Reduced chance of COVID-19 transmission with masks.
The same as except for using a \(\sigma\) of \(\sim 2\).
## Table S1. Viral load in exhaled liquids (# mL\({}^{\ast}\)1).
The viral loads of coronavirus, influenza virus and rhinovirus in aerosol mode (\(D_{\rm w}<5\)\(\mu\)m) and droplet mode (\(D_{\rm w}>5\)\(\mu\)m) are retrieved based on the measured positive rates of 30-min exhalation samples. The individual differences of viral load and particle emission rate are considered in the calculation.
\begin{tabular}{|l|l|l|l|} \hline & Coronavirus & Influenza virus & Rhinovirus \\ \hline \(D_{\rm w}<5\)\(\mu\)m * & 1.03\(\times\)10\({}^{6}\) & 8.49\(\times\)10\({}^{5}\) & 2.62\(\times\)10\({}^{6}\) \\ \hline \(D_{\rm w}>5\)\(\mu\)m * & 1.55\(\times\)10\({}^{3}\) & 9.69\(\times\)10\({}^{2}\) & 1.42\(\times\)10\({}^{3}\) \\ \hline \end{tabular}
* During the sampling of exhaled particles in Leung _et al._, particles with size above and below 5 \(\mu\)m are separated very close to the mouth, thus the cut size (5 \(\mu\)m) of those two groups of particles is considered as wet diameter (\(D_{\rm w}\)).
## Table S2. Virus number in the exhalation air samples (#).
The virus number in samples is calculated from the retrieved viral loads (Table S1) and total volume of exhaled particles during 30-min sampling.
## Table S3. Simulated indoor airborne virus concentration in Fangcang Hospital.
The indoor airborne concentrations of coronavirus, influenza virus and rhinovirus are simulated for two scenarios: virus emission by patients without wearing masks, and virus emission by patients wearing surgical masks. Median values and 5%, and 95% percentiles are given in the table.
\begin{tabular}{|l|c|c|c|} \hline Scenarios & Coronavirus (\# m\({}^{-3}\)) & Influenza virus (\# m\({}^{-3}\)) & Rhinovirus (\# m\({}^{-3}\)) \\ & Mean (5\%, 95\%) & Mean (5\%, 95\%) & Mean (5\%, 95\%) \\ \hline Virus emission/exhalation by patients without wearing surgical masks & 5.49 (2.80, 10.3) & 3.78 (1.95, 7.04) & 7.88 (4.14, 14.7) \\ \hline Virus emission/exhalation by patients wearing surgical masks & 0.400 (0.174, 0.837) & 0.327 (0.143, 0.675) & 1.01 (0.438, 2.10) \\ \hline \end{tabular}
## Table S4. Emission rate of droplet volume and virus number by infectious individuals.
The emission rates of droplets smaller than 5 \(\mu\)m (\(D_{\rm w}\)\(<\) 5 \(\mu\)m, \(D_{\rm d}\)\(<\) 2.5 \(\mu\)m) and smaller than 20 \(\mu\)m (\(D_{\rm w}\)\(<\) 20 \(\mu\)m, \(D_{\rm d}\)\(<\)10 \(\mu\)m) are given. Three scenarios, patients without wearing masks, patients wearing surgical masks, and patients wearing N95/FFP2 mask, are assumed in the calculation.
\begin{tabular}{|l|l|l|l|l|} \hline \multirow{2}{*}{Scenarios} & \multicolumn{2}{c|}{\(D_{\rm w}\)\(<\) 5 \(\mu\)m} & \multicolumn{2}{c|}{\(D_{\rm w}\)\(<\) 20 \(\mu\)m} \\ & \multicolumn{2}{c|}{(\(D_{\rm d}\)\(<\) 2.5 \(\mu\)m)} & \multicolumn{2}{c|}{(\(D_{\rm d}\)\(<\)10 \(\mu\)m)} \\ \cline{2-5} & \(E_{\rm p}\) (mL h\({}^{-1}\)) & \(E_{\rm v}\) (\# h\({}^{-1}\)) & \(E_{\rm p}\) (mL h\({}^{-1}\)) & \(E_{\rm v}\) (\# h\({}^{-1}\)) \\ \hline No mask & 1.42\(\times\)10\({}^{-6}\) & 20.3 & 4.16\(\times\)10\({}^{-5}\) & 21.2 \\ \hline Surgical mask & 2.69\(\times\)10\({}^{-7}\) & 3.87 & 1.27\(\times\)10\({}^{-6}\) & 3.89 \\ \hline N95/FFP2 mask & 2.91\(\times\)10\({}^{-8}\) & 0.418 & 1.26\(\times\)10\({}^{-7}\) & 0.420 \\ \hline \end{tabular}
## Table S5. Total infection number and infection rate in Wuhan calculated based on different \(R\).
The total infection number and infection rate are simulated with the SEIR model. The \(R\) for the control measures of school closure (\(R\)=1.9) and daily contacts reduced (\(R\)=0.34) are reported in Zhang _et al._. And the \(R\) for the control measures of wearing surgical masks (\(R\)=0.46) and N95/FFP2 masks (\(R\)=0.049) are calculated assuming that \(R\) is proportional to the emission rate of virus-containing droplets.
\begin{tabular}{|l|l|l|l|} \hline & \(R\) & Total infection & Total infection rate \\ & & number & \\ \hline No intervention & 2.5 & 9.89\(\times\)10\({}^{6}\) & 89.3\% \\ \hline School closure & 1.9 & 8.43\(\times\)10\({}^{6}\) & 76.1\% \\ \hline Daily contacts reduced & 0.34 & 8.69\(\times\)10\({}^{4}\) & 0.785\% \\ \hline Protected with surgical masks & 0.46 & 1.00\(\times\)10\({}^{5}\) & 0.903\% \\ \hline Protected with N95/FFP2 masks & 0.049 & 6.81\(\times\)10\({}^{4}\) & 0.614\% \\ \hline \end{tabular}
## Table S6. Total infection number and infection rate in Wuhan calculated assuming different virus reduction rates of masks.
The total infection number and infection rate are simulated with the SEIR model. The reproduction number \(R\) is assumed to be proportional to the emission rate of virus-containing droplets.
\begin{tabular}{|l|l|l|l|} \hline Reduction rate of mask & \(R\) & Total infection & Total infection rate \\ & & number & \\ \hline
10\% & 2.25 & 9.46E\(\times\)10\({}^{6}\) & 85.4\% \\ \hline
30\% & 1.75 & 7.91E\(\times\)10\({}^{6}\) & 71.4\% \\ \hline
50\% & 1.25 & 4.21E\(\times\)10\({}^{6}\) & 38.0\% \\ \hline
70\% & 0.75 & 1.82E\(\times\)10\({}^{5}\) & 1.65\% \\ \hline
90\% & 0.25 & 7.94E\(\times\)10\({}^{4}\) & 0.717\% \\ \hline \end{tabular}
## Table S7. Indoor airborne concentration (\(C_{\rm v}\)) and 30-min inhaling number (\(N_{\rm v,30}\)) of SARS-CoV-2 RNA copies in Fangcang Hospital.
The table is modified from Liu _et al._. Room 1 and 2 are Protective Apparel Removal Room, and Room 3 is Medical Staff's Office. In the calculation of \(N_{\rm v,30}\), the total volume of inhaled air in 30 min is assumed to be 240 L.
\begin{tabular}{|c|c|c|c|c|} \hline & Mode & Room 1 & Room 2 & Room 3 \\ \hline \(C_{\rm v}\) (\(\mu\) m\({}^{-3}\)) & Aerosol mode (\(D_{amb}\!<\!2.5\)\(\mu\)m) * & 41 & 13 & 10 \\ \cline{2-5} & Droplet mode (\(D_{amb}\!>\!2.5\)\(\mu\)m) * & 1 & 7 & 10 \\ \hline \(N_{\rm v,30}\) (\(\mu\)) & Aerosol mode (\(D_{amb}\!<\!2.5\)\(\mu\)m) * & 9.8 & 3.1 & 2.4 \\ \cline{2-5} & Droplet mode (\(D_{amb}\!>\!2.5\)\(\mu\)m) * & 0.24 & 1.7 & 2.4 \\ \hline \end{tabular}
* In this study, the aerosol mode and droplet mode are defined as particles with wet diameter (\(D_{\rm w}\)) smaller than 5 \(\mu\)m and lager than 5 \(\mu\)m, respectively. After being emitted, respiratory particles lose water and dry to \(\sim\) half of the initial particle size. Therefore, the boundary of these two modes for ambient particles is at ambient diameter (\(D_{\rm amb}\)) of \(\sim\)2.5 \(\mu\)m. |
190975_file07 | **Supplement 6: GEN-COVID Multicenter Study ([https://sites.google.com/dbm.unisi.it/gen-covid](https://sites.google.com/dbm.unisi.it/gen-covid))**
Francesca Montagnani\({}^{\text{\tiny\text{i,\tiny\text{o}}}}\), Chiara Fallerini\({}^{\text{\tiny\text{i}}}\), Margherita Baldassarri\({}^{\text{\tiny\text{i}}}\), Annarita Giliberti\({}^{\text{\tiny\text{i}}}\), Elisa Benetti\({}^{\text{\tiny\text{i}}}\), Floriana Valentino\({}^{\text{\tiny\text{o}}}\), Sergio Daga\({}^{\text{\tiny\text{i}}}\), Gabriella Doddato\({}^{\text{\tiny\text{o}}}\), Susanna Croci\({}^{\text{\tiny\text{i}}}\), Rossella Tita\({}^{\text{\tiny\text{i}}}\), Francesca Fava\({}^{\text{\tiny\text{i,\tiny\text{o}}}}\), Mirella Bruttini\({}^{\text{\tiny\text{i}}}\), Elisa Frullanti\({}^{\text{\tiny\text{i}}}\), Anna Maria Pinto\({}^{\text{\tiny\text{i}}}\), Francesca Mari\({}^{\text{\tiny\text{i,\tiny\text{o}}}}\), Simone Furini\({}^{\text{\tiny\text{i}}}\), Laura Di Sarno\({}^{\text{\tiny\text{i,\tiny\text{i,\tiny\text{o}}}}}\), Andrea Tommasi\({}^{\text{\tiny\text{i,\tiny\text{o}}}}\), Maria Palmieri\({}^{\text{\tiny\text{i}}}\), Arianna Emiliozzi\({}^{\text{\tiny\text{i,\tiny\text{o}}}}\), Massimiliano Fabbiani\({}^{\text{\tiny\text{i}}}\), Barbara Rossetti\({}^{\text{\tiny\text{i}}}\), Giacomo Zanelli\({}^{\text{\tiny\text{i,\tiny\text{o}}}}\), Laura Bergantini\({}^{\text{\tiny\text{i}}}\), Miriana D'Alessandro\({}^{\text{\tiny\text{i,\tiny\text{o}}}}\), Paolo Camel\({}^{\text{\tiny\text{i}}}\), David Bennet\({}^{\text{\tiny\text{i}}}\), Federico Anedda\({}^{\text{\tiny\text{i}}}\), Simona Marcantonio\({}^{\text{\tiny\text{i,\tiny\text{o}}}}\), Sabino Scolletta\({}^{\text{\tiny\text{i,\tiny\text{o}}}}\), Federico Franchi\({}^{\text{\tiny\text{i,\tiny\text{o}}}}\), Maria Antonietta Mazzei\({}^{\text{\tiny\text{i}}}\), Edoardo Conticini\({}^{\text{\tiny\text{i}}}\), Luca Cantarini\({}^{\text{\tiny\text{i}}}\), Bruno Frediani\({}^{\text{\tiny\text{i}}}\), Danilo Tacconi\({}^{\text{\tiny\text{i,\tiny\text{o}}}}\), Marco Feri\({}^{\text{\tiny\text{i,\tiny\text{o}}}}\), Raffaele Scala\({}^{\text{\tiny\text{i,\tiny\text{o}}}}\), Genni Spargi\({}^{\text{\tiny\text{i,\tiny\text{o}}}}\), Marta Corridi\({}^{\text{\tiny\text{i,\tiny\text{o}}}}\), Cesira Nencioni\({}^{\text{\tiny\text{i,\tiny\text{o}}}}\), Gian Piero Caldarelli\({}^{\text{\tiny\text{i}}}\), Maurizio Spagnesi\({}^{\text{\tiny\text{i}}}\), Paolo Piacentini\({}^{\text{\tiny\text{i}}}\)\({}^{\text{\tiny\text{i}}}\), Maria Bandini\({}^{\text{\tiny\text{i,\tiny\text{o}}}}\), Elena Desanctis\({}^{\text{\tiny\text{i,\tiny\text{o}}}}\), Anna Canaccini\({}^{\text{\tiny\text{i}}}\), Chiara Spertilli\({}^{\text{\tiny\text{i}}}\), Alice Donati\({}^{\text{\tiny\text{i,\tiny\text{o}}}}\), Luca Guidelli\({}^{\text{\tiny\text{i,\tiny\text{i}}}}\), Leonardo Croci\({}^{\text{\tiny\text{i,\tiny\text{o}}}}\), Agnese Verzuri\({}^{\text{\tiny\text{i,\tiny\text{o}}}}\), Valentina Anemoli\({}^{\text{\tiny\text{i,\tiny\text{o}}}}\), Agostino Ognibene\({}^{\text{\tiny\text{o}}}\), Massimo Vaghi\({}^{\text{\tiny\text{i,\tiny\text{n}}}}\), Antonella D'Arminio Monforte\({}^{\text{\tiny\text{i,\tiny\text{o}}}}\), Esther Merlini\({}^{\text{\tiny\text{i,\tiny\text{o}}}}\), Mario U. Mondelli\({}^{\text{\tiny\text{i,\tiny\text{i,\tiny\text{o}}}}}\), Stefania Mantovani\({}^{\text{\tiny\text{i,\tiny\text{n}}}}\), Serena Ludovisa\({}^{\text{\tiny\text{i,\tiny\text{n}}}}\), Massimo Girardis\({}^{\text{\tiny\text{i,\tiny\text{o}}}}\), Sophie Venturelli\({}^{\text{\tiny\text{i,\tiny\text{o}}}}\), Marco Sita\({}^{\text{\tiny\text{i,\tiny\text{o}}}}\), Andrea Cossarizza\({}^{\text{\tiny\text{i,\tiny\text{o}}}}\), Andrea Antinori\({}^{\text{\tiny\text{i,\tiny\text{i}}}}\), Alessandra Vergori\({}^{\text{\tiny\text{i,\tiny\text{o}}}}\), Stefano Rusconi\({}^{\text{\tiny\text{i,\tiny\text{o}}}}\), Arianna Gabrieli\({}^{\text{\tiny\text{i,\tiny\text{o}}}}\), Agostino Riva\({}^{\text{\tiny\text{i,\tiny\text{i,\tiny\text{o}}}}}\), Daniela Francisci\({}^{\text{\tiny\text{i,\tiny\text{o}}}}\), Elisabetta Schiarolli\({}^{\text{\tiny\text{i,\tiny\text{i}}}}\), Pier Giorgio Scotton\({}^{\text{\tiny\text{i,\tiny\text{o}}}}\), Francesca Andretta\({}^{\text{\tiny\text{i,\tiny\text{o}}}}\), Sandro Panese\({}^{\text{\tiny\text{i,\tiny\text{o}}}}\), Renzo Scaggiante\({}^{\text{\tiny\text{i,\tiny\text{o}}}}\), Saverio Giuseppe Parisi\({}^{\text{\tiny\text{i,\tiny\text{o}}}}\), Francesco Castelli\({}^{\text{\tiny\text{i,\tiny\text{i}}}}\), Maria Eugenia Quiros-Roldan\({}^{\text{\tiny\text{i,\tiny\text{o}}}}\), Paola Magro\({}^{\text{\tiny\text{o}}}\), Cristina Minardi\({}^{\text{\tiny\text{i,\tiny\text{o}}}}\), Deborah Castelli\({}^{\text{\tiny\text{i,\tiny\text{i}}}}\), Itala Polesini\({}^{\text{\tiny\text{i,\tiny\text{i}}}}\), Matteo Della Monica\({}^{\text{\tiny\text{i,\tiny\text{o}}}}\), Carmelo Piccopo\({}^{\text{\tiny\text{o}}}\), Mario Capasso\({}^{\text{\tiny\text{i,\tiny\text{o}}}}\), Roberta Russo\({}^{\text{\tiny\text{i,\tiny\text{o}}}}\), Immacolata Andolfo\({}^{\text{\tiny\text{i,\tiny\text{o}}}}\), Achille Iolascon\({}^{\text{\tiny\text{i,\tiny\text{o}}}}\), Massimo Carella\({}^{\text{\tiny\text{i,\tiny\text{o}}}}\), Marco Castori\({}^{\text{\tiny\text{i}}}\), Giuseppe Merla\({}^{\text{\tiny\text{i,\tiny\text{o}}}}\), Filippo Cucella\({}^{\text{\tiny\text{i,\tiny\text{o}}}}\), Pamela Raggi\({}^{\text{\tiny\text{i,\tiny\text{o}}}}\), Carmen Marciano\({}^{\text{\tiny\text{o}}}\), Rita Perna\({}^{\text{\tiny\text{i,\tiny\text{o}}}}\), Matteo Bassetti\({}^{\text{\tiny\text{i,\tiny\text{o}}}}\), Antonio Di Biagio\({}^{\text{\tiny\text{i,\tiny\text{o}}}}\), Maurizio Sanguinetti\({}^{\text{\tiny\text{i,\tiny\text{o}}}}\), Luca Mascucci\({}^{\text{\tiny\text{i,\tiny\text{o}}}}\), Chiara Gabbi\({}^{\text{\tiny\text{i,\text{o}}}}\), Serafina Valente\({}^{\text{\tiny\text{i,\tiny\text{o}}}}\), Susanna Guerrini\({}^{\text{\tiny\text{i}}}\), Ilaria Meloni\({}^{\text{\tiny\text{i,\tiny\text{o}}}}\), Maria Antonietta Mencarelli\({}^{\text{\tiny\text{i,\tiny\text{i}}}}\), Caterina Lo Rizzo\({}^{\text{\tiny\text{o}}}\), Elena Bargagli\({}^{\text{\tiny\text{i,\tiny\text{o}}}}\), Marco Mandala\({}^{\text{\tiny\text{o}}}\), Alessia Giorli\({}^{\text{\tiny\text{i}}}\), Lorenzo Salerni\({}^{\text{\tiny\text{i,\tiny\text{o}}}}\), Giuseppe Fiorentino\({}^{\text{\tiny\text{i,\text{o}}}}\), Patrizia Zucchi\({}^{\text{\tiny\text{i,\text{o}}}}\), Pierpaolo Parravicini\({}^{\text{\tiny\text{i,\tiny\text{o}}}}\), Elisabetta Menatti\({}^{\text{\tiny\text{i,\tiny\text{o}}}}\), Stefano Baratti\({}^{\text{\tiny\text{i,\tiny\text{o}}}}\), Tullio Trotta\({}^{\text{\tiny\text{i,\text{o}}}}\), Ferdinando Giannattasio\({}^{\text{\tiny\text{o}}}\), Gabriella Coiro\({}^{\text{\tiny\text{i,\tiny\text{o}}}}\), Fabio Lena\({}^{\text{\tiny\text{\text{o}}}}\), Domenico A.
* Medical Genetics, University of Siena, Italy
* Genetica Medica, Azienda Ospedaliera Universitaria Senese, Italy
* Dept of Medical Biotechnologies, University of Siena, Italy
* Dept of Specialized and Internal Medicine, Tropical and Infectious Diseases Unit
* Unit of Respiratory Diseases and Lung Transplantation, Department of Internal and Specialist Medicine, University of Siena
* Dept of Emergency and Urgency, Medicine, Surgery and Neurosciences, Unit of Intensive Care Medicine, Siena University Hospital, Italy
* Department of Medical, Surgical and Neuro Sciences and Radiological Sciences, Unit of Diagnostic Imaging, University
* Rheumatology Unit, Department of Medicine, Surgery and Neurosciences, University of Siena, Policlinico Le Scotte, Italy Italy
* Department of Specialized and Internal Medicine, Infectious Diseases Unit, San Donato Hospital Arezzo, Italy
* Dept of Emergency, Anesthesia Unit, San Donato Hospital, Arezzo, Italy
* Department of Specialized and Internal Medicine, Pneumology Unit and* III Infectious Diseases Unit, ASST-FBF-Sacco, Milan, Italy
* Department of Biomedical and Clinical Sciences Luigi Sacco, University of Milan, Milan, Italy
* Infectious Diseases Clinic, Department of Medicine 2, Azienda Ospedaliera di Perugia and University of Perugia, Santa Maria Hospital, Perugia, Italy
* Infectious Diseases Clinic, "Santa Maria" Hospital, University of Perugia, Perugia, Italy
* Department of Infectious Diseases, Treviso Hospital, Local Health Unit 2 Marca Trevigiana, Treviso, Italy
* Infectious Diseases Department, Ospedale Civile "SS.
* Infectious Diseases Clinic, ULSS1, Belluno, Italy
* Department of Molecular Medicine, University of Padova, Italy
* Department of Infectious and Tropical Diseases, University of Brescia and ASST Spedali Civili Hospital, Brescia, Italy
* Medical Genetics and Laboratory of Medical Genetics Unit, A.O.R.N. "Antonio Cardarelli", Naples, Italy
* Department of Molecular Medicine and Medical Biotechnology, University of Naples Federico II, Naples, Italy
* CEINGE Biotecnologie Avanzate, Naples, Italy
* IRCCS SDN, Naples, Italy
* Division of Medical Genetics, Fondazione IRCCS Casa Sollievo della Sofferenza Hospital, San Giovanni Rotondo, Italy
* Department of Medical Sciences, Fondazione IRCCS Casa Sollievo della Sofferenza Hospital, San Giovanni Rotondo, Italy
* Clinical Trial Office, Fondazione IRCCS Casa Sollievo della Sofferenza Hospital, San Giovanni Rotondo, Italy
* Department of Health Sciences, University of Genova, Genova, Italy
* Infectious Diseases Clinic, Policlinico San Martino Hospital, IRCCS for Cancer Research Genova, Italy
* Microbiology, Fondazione Policlinico Universitario Agostino Gemelli IRCCS, Catholic University of Medicine, Rome, Italy
* Department of Laboratory Sciences and Infectious Diseases, Fondazione Policlinico Universitario A.
* Independent Scientist, Milan, Italy
* Department of Cardiovascular Diseases, University of Siena, Siena, Italy
* Otolaryngology Unit, University of Siena, Italy
* AORN dei Colli Presidio Ospedaliero Cotugno, Italy
* Department of Internal Medicine, ASST Valtellina e Alto Lario, Sondrio, Italy
* Study Coordinator Oncologia Medica e Ufficio Flussi Sondrio, Italy
* Department of Infectious and Tropical Diseases, University of Padova, Padova, Italy
* First Aid Department, Luigi Curto Hospital, Polla, Salerno, Italy
* Local Health Unit-Pharmaceutical Department of Grosseto, Toscana Sud Est Local Health Unit, Grosseto, Italy
* U.O.C. Laboratorio di Genetica Umana, IRCCS Istituto G. Gaslini, Genoa, Italy.
* Infectious Diseases Clinics, University of Modena and Reggio Emilia, Modena, Italy. |
191676_file02 | ## S3. \(E_{p}\), \(E_{p,CO_{2}}\), and \(B\) for different activities and associated uncertainties \(E_{p}\), \(E_{p,CO_{2}}\), and \(B\) are all functions of activity according to the literature.\({}^{2-5}\) However, they have different domains in the literature studies. For \(E_{p,CO_{2}}\), level of physical activity is quantified by a continuous variable, \(M\) in MET (metabolic equivalent of task).\({}^{4}\)\(E_{p,CO_{2}}\) is also a function of basic metabolic rate, which primarily depends on age, sex, body size, and body composition of a person.\({}^{4}\) For the data of \(B\),\({}^{5}\) the levels of physical activity are discrete ("Sleep or Nap", "Sedentary/Passive", "Light Intensity", "Moderate Intensity", and "High Intensity"), and the data are also classified by age but not by sex.
To make the data of \(E_{p,CO_{2}}\) and \(B\) directly comparable, we take the averages of BMR for the males and females in the age ranges corresponding to the data of \(B\) in ref 5, except for the range of 1-3 y as a single category (two categories, i.e., 1-2 and 2-3, in ref 5), and roughly assign "Sleep or Nap", "Sedentary/Passive", "Light Intensity", "Moderate Intensity", and "High Intensity" to \(M\) = 1, 1.5, 2, 3.5, and 5 MET, respectively.\({}^{4}\) Then a quantity that involves \(E_{p,CO_{2}}\) and \(B\) and is critical for \(\Delta c^{*}_{CO_{2}}\), \(\frac{E_{p,CO_{2}}}{B}\), i.e., fraction of CO\({}_{2}\) in exhaled air, is calculated for the abovementioned discrete levels of physical activity for people in different age ranges (Fig. S3). At a specific physical activity level, \(\frac{E_{p,CO_{2}}}{B}\) does not vary strongly with age for groups with age > 11 y (BMR > 6 MJ/d). Averages are thus taken for the groups with similar \(\frac{E_{p,CO_{2}}}{B}\) at certain \(M\) (Table S4). These averages are used in the infection risk analysis for different activities in the Main Text. Buonanno et al.\({}^{2,3}\) estimated \(E_{p}\) at different levels of physical activity as well as vocalization. In their estimates, there are only four levels of physical activities, i.e., "Resting", "Standing", "Light exercise", and "Heavy exercise". These four levels roughly correspond to "Sleep or Nap", "Sedentary/Passive", "Light Intensity", and "High Intensity". An interpolation is made by taking the geometric mean of \(E_{p}\) at the "Light exercise", and "Heavy exercise" levels to generate data for \(E_{p}\) at a "Moderate exercise" level, corresponding to "Moderate Intensity" for the \(B\) data (Table S4). The dimension of vocalization for the \(E_{p}\) data from Buonanno et al. is preserved in this study, as degree of vocalization is critical in determining \(E_{p}\),\({}^{2,3}\) For all activities listed in Fig. 2\(B\) and Table S4, the data of \(E_{p}\) and \(\frac{E_{p,CO_{2}}}{B}\) are now available and the relevant infection risk analysis can be done.
Large uncertainties are associated with the data of \(E_{p}\) and \(\frac{E_{p,CO_{2}}}{B}\) in Table S4. The \(E_{p}\) estimates themselves are highly uncertain, with possible ranges often spanning over an order of magnitude.\({}^{2,3}\) The discretization of physical activity level can also be a major uncertainty source, as there are only five discrete levels to cover the domain of a continuous variable \(M\).
# Table S1. Symbols used in this study.
\begin{tabular}{|l|l|l|} \hline _Symbol_ & _Physical meaning_ & _Unit (dimension_ \\ & & _-less if no unit_ \\ & & _indicated)_ \\ \hline \(B\) & Breathing rate of the susceptible person & m\({}^{3}\) h\({}^{\text{-1}}\) \\ \hline \(c_{avg}\) & Average virus concentration in the air over the duration of the event & quanta m\({}^{\text{-3}}\) \\ \hline \(\langle c_{avg}\rangle\) & Expected value of \(c_{avg}\), when an occupant has a probability of being immune & quanta m\({}^{\text{-3}}\) \\ \hline \(\Delta c_{avg,Co_{2}}\) & Average excess CO\({}_{2}\) volume mixing ratio & \\ \hline \(\Delta c_{Co_{2}}^{*}\) & Volume mixing ratio of the excess CO\({}_{2}\) that an uninfected individual & \\ & inhales for 1 h in an environment with \(\eta_{l}=0.1\%\) for \(P=0.01\%\) & \\ \hline \(D\) & Duration of the event & h \\ \hline \(E_{p}\) & SARS-CoV-2 exhalation rate by an infector & quanta h\({}^{\text{-1}}\) \\ \hline \(E_{p,Co_{2}}\) & CO\({}_{2}\) exhalation rate per person & m\({}^{3}\) h\({}^{\text{-1}}\) \\ \hline \(\eta_{l}\) & Probability of an occupant being an infector & \\ \hline \(\eta_{im}\) & Probability of an occupant being immune & \\ \hline \(\lambda\) & First-order overall rate constant of the virus infectivity loss & h\({}^{\text{-1}}\) \\ \hline \(\lambda_{0}\) & Ventilation rate & h\({}^{\text{-1}}\) \\ \hline \(m_{ex}\) & Mask filtration efficiency for exhalation & \\ \hline \(m_{in}\) & Mask filtration efficiency for inhalation & \\ \hline \(N\) & Number of occupants & \\ \hline \(n\) & Amount of the virus infectious doses ("quanta") inhaled by a susceptible person in a given indoor environment & quanta \\ \hline \(\langle n\rangle\) & Expected value of \(n\), when an occupant has a probability of being immune & quanta \\ \hline \(n_{\Delta cO_{2}}\) & Inhaled excess (human-exhaled) CO\({}_{2}\) volume & m\({}^{3}\) \\ \hline \(P\) & Probability of infection of a susceptible person & \\ \hline \(V\) & Indoor environment volume & m\({}^{3}\) \\ \hline _(Below are the symbols that appear in the SI only)_ & \\ \hline \(\langle c\rangle\) & Expected value of virus concentration, when an occupant has a probability of being immune & quanta m\({}^{\text{-3}}\) \\ \hline \(\Delta c_{Co_{2}}\) & Excess CO\({}_{2}\) volume mixing ratio & \\ \hline \end{tabular}
\begin{tabular}{|l|l|l|} \hline \(\langle E\rangle\) & Expected value of virus emission rate & quanta h\({}^{\text{-1}}\) \\ \hline \(E_{CO_{2}}\) & Excess CO\({}_{2}\) volume emission rate & m\({}^{3}\) h\({}^{\text{-1}}\) \\ \hline \(t\) & Time & h \\ \hline \end{tabular}
\(\eta_{i}\) the values for New York City at the peak of the first COVID-19 wave in spring 2020, and the value for Boulder, CO during a period of low disease prevalence in summer 2020 are estimated based on the New York Times Coronavirus Database ([https://www.nytimes.com/article/coronavirus-country-data-us.html](https://www.nytimes.com/article/coronavirus-country-data-us.html)). A typical value in between is assumed for all other cases.
\(m_{\text{rec}}\) and \(m_{\text{h}}\): mask parameters are estimated based on Davies et al.\(m_{\text{h}}\) is assigned a value lower than reported by Davies et al. given imperfect wearing and fit in the community.
\(\lambda_{0}\): a typical value is chosen within the range reported by Bhangar et al.
\(\lambda\): see above for ventilation (\(\lambda_{0}\)). Removal rates due to virus infectivity decay and aerosol deposition are estimated based on van Doremalen et al. and Thatcher et al., respectively.
\begin{table}
\begin{tabular}{|l|c|c|c|} \hline \hline Activity & \(E_{p}\) (quanta & \(E_{p,CO_{2}}\) & \(\Delta c^{*}_{CO_{2}}\) (ppm) \\ h\({}^{-1}\)) & \(B\) & \(\Delta c^{*}_{CO_{2}}\) (ppm) \\ \hline Resting – breathing & 2 & 0.0428 & 2140 \\ \hline Resting – speaking & 9.4 & 0.0428 & 455 \\ \hline Resting – loudly speaking & 60.5 & 0.0428 & 70.7 \\ \hline Standing – breathing & 2.3 & 0.0656 & 2850 \\ \hline Standing – speaking & 11.4 & 0.0656 & 575 \\ \hline Standing – loudly speaking & 65.1 & 0.0656 & 101 \\ \hline Light exercise – breathing & 5.6 & 0.0342 & 611 \\ \hline Light exercise – speaking & 26.3 & 0.0342 & 130 \\ \hline Light exercise – loudly speaking & 170 & 0.0342 & 20.1 \\ \hline Moderate exercise – breathing & 8.7 & 0.0280 & 322 \\ \hline Moderate exercise – speaking & 40.7 & 0.0280 & 68.8 \\ \hline Moderate exercise – loudly speaking & 263 & 0.0280 & 10.7 \\ \hline Heavy exercise – breathing & 13.5 & 0.0214 & 158 \\ \hline Heavy exercise – speaking & 63.1 & 0.0214 & 33.8 \\ \hline Heavy exercise – loudly speaking & 408 & 0.0214 & 5.23 \\ \hline \hline \end{tabular}
\end{table}
Table S3: SARS-CoV-2 exhalation rate (\(E_{p}\)), fraction of CO\({}_{2}\) in exhaled air \(\frac{E_{p,CO_{2}}}{B}\), and volume mixing ratio of the excess CO\({}_{2}\) that an uninfected individual inhales for 1 h in that environment for a probability of infection of 0.01% (\(\Delta c^{*}_{CO_{2}}\)) for activities with different physical and vocal levels. \(\Delta c^{*}_{CO_{2}}\) is estimated with probability of an occupant being injector of 0.1% and ventilation accounting for all SARS-CoV-2 loss.
\begin{table}
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|} \hline \hline Case & \(N\) & \(V\) (m\({}^{3}\)) & \(\begin{array}{c}E_{p}\\ \text{(quanta}\\ \text{h}^{1}\end{array}\)) & \(\begin{array}{c}E_{p,CO_{2}}\\ \text{h}^{1}\end{array}\) & \(B\) (m\({}^{3}\) \\ \text{(m}^{2}\) h\({}^{1}\)) & \(\eta_{in}\) & \(\eta_{in}\) & \(\eta_{in}\) & \(\begin{array}{c}D\\ \text{(h)}\end{array}\) & \(m_{ex}\) & \(m_{in}\) & \(\begin{array}{c}\lambda_{0}\\ \text{(h}^{1}\end{array}\)) & \(\lambda_{1}\) & \(\begin{array}{c}\langle n\rangle\\ \text{(quanta)}\end{array}\) & \(\Delta c_{aug,CO_{2}}\) & \(\Delta c_{CO_{2}}^{*}\) \\ \hline Class & 10 & 142 & 100 & 0.0203 & 0.516 & 0 & 0.001 & 0.833 & 0.5 & 0.3 & 3 & 3.92 & 1.70E-04 & 302 & 148 \\ \hline Choir & 61 & 810 & 970 & 0.0370 & 1.56 & 0 & 0.00011 & 2.5 & 0 & 0 & 0.7 & 1.62 & 1.42E-02 & 2102 & 91.3 \\ \hline Subway & 35 & 150 & 25 & 0.0285 & 0.42 & 0.15 & 0.001 & 0.333 & 0.5 & 0.3 & 5.7 & 10.22 & 1.66E-05 & 645 & 1270 \\ \hline Super-market & 75 & 2040 & 10 & 0.0275 & 0.72 & 0 & 0.001 & 8 & 0.5 & 0.3 & 3 & 3.92 & 1.69E-04 & 322 & 1450 \\ \hline Stadium & 31000 & 255000 & 50 & 0.0248 & 0.72 & 0 & 0.001 & 1.5 & 0 & 0 & 40 & 40.92 & 1.58E-04 & 74 & 56.2 \\ \hline \hline \end{tabular}
\end{table}
Table S4: Same format as Table S2, but for different environments, i.e., a university class, the Skagit County choir superspreading event, a subway car, a supermarket (focused on a worker), and an event in a stadium. Values of parameters are typical of real environments that we have analyzed (see footnotes for detail). |
192203_file03 | ### Nursing home staff geography measures
To calculate our nursing home staff neighborhood characteristics, we first use the 2017 LODES Workplace Area Characteristics data to identify the nursing home's census block. This data records the number of workers in the education and health care sector who work on a given census block. We geocode the nursing home addresses, and compute a predicted number of nursing home workers based on the national ratio of workers to residents (1.6 million workers to 1.3 million residents), and the average number of residents for each facility from the Nursing Home Compare data. For 83% of facilities, health care employment on the coded census block is more than half the predicted employment, and we consider this a match. For the remaining 11% of facilities, we use the closest census block in the block group that meets this condition. This allows us to match an additional1 11% of facilities, leaving about 511 facilities unmatched, which we exclude from our sample.
Using the census block chosen above, we then use the LODES Origin-Destination (OD) data to identify the home census blocks of workers who work on the same census block as the nursing home and belong to the "all other services" industry group. One concern is that there may be many more service sector employers that are on the same census block as the nursing home, and these employers have staff who live in completely different neighborhoods than the nursing home's staff. We find on the median block, 92% (IQR: [.62, 1]) of the service employment on these census blocks is in the education and health care sector. This gives us reassurance that we are not mostly picking up an entirely different type of employer on these blocks and that our geocoding is likely to be fairly accurate.
However, it is still possible that there are other education or health-care employers on the same block as the nursing home. One particular case of this is nursing homes located near hospitals. Indeed, we do find some blocks with unreasonably large numbers of health care workers for a nursing home (5000+). However, in general, we find that the total employment numbers are reasonable. Using the calculation for predicted nursing home employment above, the median block in our sample has an actual service sector employment to predicted employment ratio of 1.5 (IQR [1.1, 2.7]). Thus, we believe it is likely that the measured neighborhood characteristics will be largely representative of the types of neighborhoods where a facility's employees are likely to live.
To calculate the "share frontline" measure, we define a frontline worker as a worker in an essential industry (as defined in Tomer and Kane, 2020) in an occupation that cannot work from home (as defined in Dingel and Neiman, 2020).
## Appendix 1: Data Appendix
### State COVID-19 data
We obtain publicly released facility-level data on COVID-19 infections from 18 states. We began collecting this data in mid-April and continued to do so approximately every week until the week of July 10, 2020. Since some states do not report facilities with "closed outbreaks"-i.e. facilities with no current cases-we use the historical data to build a cumulative measure of whether a facility was ever infected as if they appeared on any list. These data should largely reflect all nursing homes that have ever reported a COVID-19 infection, though data is usually self-reported by facilities and may contain errors, and states also differ in the exact data that they report. Notably, Maryland only reported facilities that had cases after April 15, four states only report nursing homes with 2+ cases. We matched the names on these lists to the administrative data on the universe of nursing homes. This allows us to calculate the share of nursing homes that have been infected, as well as compare characteristics of infected and non-infected homes. In terms of numbers of deaths, the 18 states in our sample represent over 80% of the total deaths from COVID so far and contain all of the top 10 states. The states with many deaths for whom we do not have facility-level data include Texas, Ohio, Indiana, Arizona, Texas, and Virginia.
Eight of our sample states also released easily accessible data on confirmed or probable COVID-19 cases at a finer geography than county. These states and the lowest level of geography at which they supply data on cases were: Connecticut (town), Florida (town), Illinois (zip), Louisiana (tract), Massachusetts (town), Maryland (zip), Rhode Island (zip), and South Carolina (zip). For all states except Louisiana, we use the case rates as of the date the nursing home infection data was pulled. For Louisiana, we use data from May 31, because we have not been able to obtain data from the previous week.
### Nursing home staff geography measures
To calculate our nursing home staff neighborhood characteristics, we first use the 2017 LODES Workplace Area Characteristics data to identify the nursing home's census block. This data records the number of workers in the education and health care sector who work on a given census block. We geocode the nursing home addresses, and compute a predicted number of nursing home workers based on the national ratio of workers to residents (1.6 million workers to 1.3 million residents), and the average number of residents for each facility from the Nursing Home Compare data. For 83% of facilities, health care employment on the coded census block is more than half the predicted employment, and we consider this a match. For the remaining 11% of facilities, we use the closest census block in the block group that meets this condition. This allows us to match an additional1 11% of facilities, leaving about 511 facilities unmatched, which we exclude from our sample.
Using the census block chosen above, we then use the LODES Origin-Destination (OD) data to identify the home census blocks of workers who work on the same census block as the nursing home and belong to the "all other services" industry group. One concern is that there may be many more service sector employers that are on the same census block as the nursing home, and these employers have staff who live in completely different neighborhoods than the nursing home's staff. We find on the median block, 92% (IQR: [.62, 1]) of the service employment on these census blocks is in the education and health care sector. This gives us reassurance that we are not mostly picking up an entirely different type of employer on these blocks and that our geocoding is likely to be fairly accurate.
However, it is still possible that there are other education or health-care employers on the same block as the nursing home. One particular case of this is nursing homes located near hospitals. Indeed, we do find some blocks with unreasonably large numbers of health care workers for a nursing home (5000+). However, in general, we find that the total employment numbers are reasonable. Using the calculation for predicted nursing home employment above, the median block in our sample has an actual service sector employment to predicted employment ratio of 1.5 (IQR [1.1, 2.7]). Thus, we believe it is likely that the measured neighborhood characteristics will be largely representative of the types of neighborhoods where a facility's employees are likely to live.
To calculate the "share frontline" measure, we define a frontline worker as a worker in an essential industry (as defined in Tomer and Kane, 2020) in an occupation that cannot work from home (as defined in Dingel and Neiman, 2020).
## S1 Table: Summary statistics for analysis sample
\begin{tabular}{|l|r|r|} \hline
## Variable** & **Mean** & **Std. Dev.
\\ \hline Number of beds & 119 & 67 \\ \hline For-profit &.73 & \\ \hline Non-profit &.24 & \\ \hline Public &.03 & \\ \hline Chain &.58 & \\ \hline Star rating & 3.1 & 1.4 \\ \hline - Inspection rating & 2.7 & 1.2 \\ - & Staffing rating & 2.9 & 1.1 \\ \hline - & Quality measure rating & 3.8 & 1.2 \\ \hline RN wage & 34.3 & 6.4 \\ \hline CNA wage & 15.0 & 2.7 \\ \hline Occupancy rate &.84 &.13 \\ \hline Medicaid share &.60 &.23 \\ \hline Resident share non-white &.23 &.23 \\ \hline Staff tract pop density (pp/sq mi) & 4906 & 7386 \\ \hline Staff tract pub trans use &.05 &.08 \\ \hline Staff tract share nonwhite &.28 &.17 \\ \hline Staff tract pov rate &.19 &.07 \\ \hline Staff tract share frontline &.31 &.03 \\ \hline NH tract pop density (pp/sq mi) & 4543 & 9484 \\ \hline NH tract pub trans use &.05 &.10 \\ \hline NH tract share nonwhite &.25 &.22 \\ \hline NH tract pov rate &.18 &.17 \\ \hline NH tract share frontline &.30 &.06 \\ \hline \end{tabular}
## S2 Table: Characteristics of nursing home workers from American Community Survey and BLS data
## S3 Table: Relationship of facility infection with staff characteristics compared to staff neighborhood characteristics
\begin{tabular}{l c c} \hline & & \\ \hline Staff tract pubtrans use & 1.159\({}^{***}\) & \\ & (0.266) & \\ Staff tract PT share (Ed/Health) & 0.0465 & \\ & (0.139) & \\ Staff tract share nonwhite & & 1.078\({}^{***}\) \\ & & (0.317) \\ Staff on block share nonwhite & & -0.238 \\ & & (0.208) \\ For-profit & 0.518\({}^{**}\) & 0.541\({}^{**}\) \\ & (0.193) & (0.193) \\ Chain & 0.375\({}^{*}\) & 0.363\({}^{*}\) \\ & (0.163) & (0.163) \\ Star rating & 0.0476 & 0.0470 \\ & (0.0915) & (0.0916) \\ No prior infection viol. & 0.254 & 0.253 \\ & (0.195) & (0.196) \\ Medicaid share & -0.00697 & -0.00784 \\ & (0.0880) & (0.0880) \\ Resident share nonwhite & -0.214 & -0.295\({}^{*}\) \\ & (0.121) & (0.130) \\ Avg severity & -0.0597 & -0.0516 \\ & (0.0813) & (0.0817) \\ Occupancy Rate & 0.664\({}^{***}\) & 0.672\({}^{***}\) \\ & (0.0871) & (0.0871) \\
25-50 beds & 0 & 0 \\ & (.) & (.) \\
50-100 beds & 0.540 & 0.531 \\ & (0.328) & (0.328) \\
100-150 beds & 1.109\({}^{***}\) & 1.115\({}^{***}\) \\ & (0.333) & (0.333) \\
150-200 beds & 1.732\({}^{***}\) & 1.717\({}^{***}\) \\ & (0.368) & (0.368) \\
200+ beds & 1.163\({}^{**}\) & 1.155\({}^{**}\) \\ & (0.409) & (0.409) \\ Constant & 2.053\({}^{***}\) & 2.037\({}^{***}\) \\ & (0.343) & (0.344) \\ \hline fe & County & County \\ ymean & 3.735 & 3.735 \\ r2\_a & 0.29 & 0.29 \\ N & 6146 & 6146 \\ \hline \end{tabular}
Standard errors in parentheses
\({}^{*}\)\(p\)\(<\).05, \({}^{**}\)\(p\)\(<\).01, \({}^{***}\)\(p\)\(<\).001
\begin{tabular}{l c c c} \hline & & & \\ \hline Staff tract pubtrans use & & 0.0888\({}^{***}\) & \\ & & (0.0249) & \\ NH tract pubtrans use & & -0.0245 & \\ & & (0.0127) & \\ Staff tract share nonwhite & & & 0.0638\({}^{***}\) \\ & & & (0.0169) \\ NH tract share nonwhite & & & -0.0121 \\ & & & (0.00913) \\ For-profit & 0.0404\({}^{**}\) & 0.0396\({}^{**}\) & 0.0393\({}^{**}\) \\ & (0.0139) & (0.0139) & (0.0139) \\ Chain & 0.0183 & 0.0190 & 0.0189 \\ & (0.0117) & (0.0117) & (0.0117) \\ Overall Rating & -0.0131\({}^{*}\) & -0.0129\({}^{*}\) & -0.0124 \\ & (0.00658) & (0.00658) & (0.00659) \\ No prior infection viol. & 0.0119 & 0.0116 & 0.0114 \\ & (0.0141) & (0.0141) & (0.0141) \\ Medicaid share & -0.00554 & -0.00496 & -0.00517 \\ & (0.00653) & (0.00653) & (0.00652) \\ Resident share nonwhite & 0.0292\({}^{***}\) & 0.0237\({}^{**}\) & 0.0173 \\ & (0.00845) & (0.00890) & (0.0092) \\ Avg severity & -0.0229\({}^{***}\) & -0.0217\({}^{***}\) & -0.0206\({}^{***}\) \\ & (0.00612) & (0.00613) & (0.00615) \\ Occupancy Rate & 0.0208\({}^{**}\) & 0.0203\({}^{**}\) & 0.0208\({}^{**}\) \\ & (0.00636) & (0.00636) & (0.00635) \\
25-50 beds & 0 & 0 & 0 \\ & (.) & (.) & (.) \\
50-100 beds & 0.127\({}^{***}\) & 0.130\({}^{***}\) & 0.129\({}^{***}\) \\ & (0.0236) & (0.0236) & (0.0236) \\
100-150 beds & 0.231\({}^{***}\) & 0.233\({}^{***}\) & 0.234\({}^{***}\) \\ & (0.0240) & (0.0240) & (0.0240) \\
150-200 beds & 0.301\({}^{***}\) & 0.301\({}^{***}\) & 0.300\({}^{***}\) \\ & (0.0265) & (0.0265) & (0.0265) \\
200+ beds & 0.326\({}^{***}\) & 0.325\({}^{***}\) & 0.324\({}^{***}\) \\ & (0.0295) & (0.0294) & (0.0294) \\ Constant & 0.208\({}^{***}\) & 0.207\({}^{***}\) & 0.209\({}^{***}\) \\ & (0.0247) & (0.0247) & (0.0247) \\ \hline Fixed Effects & County & County & County \\ Depvar mean & 0.455 & 0.455 & 0.455 \\ Adj R2 & 0.40 & 0.40 & 0.40 \\ N & 6132 & 6132 & 6132 \\ \hline \multicolumn{4}{l}{Standard errors in parentheses} \\ \multicolumn{4}{l}{\({}^{*}\)\(p<.05\), \({}^{**}\)\(p<.01\), \({}^{***}\)\(p<.001\)} \\ \end{tabular}
## S5 Table: Relationship of facility deaths per bed with distance to central business district and staff and nursing home neighborhood characteristics
\begin{tabular}{l c c} \hline & & \\ \hline Distance to CBD & -0.978\({}^{***}\) & -1.052\({}^{***}\) \\ & (0.251) & (0.244) \\ Staff tract pubtrans use & 0.799\({}^{*}\) & \\ & (0.336) & \\ NH tract pubtrans use & -0.0297 & \\ & (0.163) & \\ Staff tract share nonwhite & & 0.569\({}^{*}\) \\ & & (0.244) \\ NH tract share nonwhite & & -0.0255 \\ & & (0.126) \\ For-profit & 0.529\({}^{**}\) & 0.530\({}^{**}\) \\ & (0.193) & (0.193) \\ Chain & 0.374\({}^{*}\) & 0.370\({}^{*}\) \\ & (0.162) & (0.162) \\ Star rating & 0.0500 & 0.0504 \\ & (0.0915) & (0.0916) \\ No prior infection viol. & 0.263 & 0.264 \\ & (0.195) & (0.195) \\ Medicaid share & 0.0357 & 0.0291 \\ & (0.0885) & (0.0884) \\ Resident share nonwhite & -0.290\({}^{*}\) & -0.345\({}^{*}\) \\ & (0.123) & (0.137) \\ Avg severity & -0.0673 & -0.0613 \\ & (0.0813) & (0.0816) \\ Occupancy Rate & 0.656\({}^{***}\) & 0.660\({}^{***}\) \\ & (0.0876) & (0.0876) \\
25-50 beds & 0 & 0 \\ & (.) & (.) \\
50-100 beds & 0.537 & 0.528 \\ & (0.328) & (0.328) \\
100-150 beds & 1.116\({}^{***}\) & 1.114\({}^{***}\) \\ & (0.333) & (0.333) \\
150-200 beds & 1.680\({}^{***}\) & 1.663\({}^{***}\) \\ & (0.369) & (0.368) \\
200+ beds & 1.117\({}^{**}\) & 1.096\({}^{**}\) \\ & (0.409) & (0.409) \\ Constant & 2.092\({}^{***}\) & 2.095\({}^{***}\) \\ & (0.343) & (0.343) \\ \hline fe & County & County \\ ymean & 3.736 & 3.737 \\ r2\_a & 0.29 & 0.29 \\ N & 6141 & 6142 \\ \hline \end{tabular} |
192690_file02 | ### Evaluation of viral inactivation treatments on antibody testing in ELISA
Patient serum was inactivated to eliminate residual virus in serum samples. A subset of recovered COVID-19 positive (n=10) and pre-COVID-19 controls (n=5) were used to compare two viral inactivation methods in human sera: heat-treatment and treatment with the detergent Triton X-100. For heat-treatment, patient sera (0.5 mL) were incubated with rotational shaking at 56\({}^{\circ}\)C for 30 minutes and centrifuged for 10 minutes at 14,000 x g, after which the supernatant was collected. In parallel, duplicate samples were mixed with Triton X-100 to a final concentration of 1% (v/v). The non-treated and treated patient samples were tested in the SARS-CoV-2 ELISA as previously described. We however did not test whether any virus was actually present in serum samples and whether the inactivation method was effective against virus.
To confirm the specificity of antibodies detected by the ELISA, we inhibited the binding of selected serum samples with excess fluid-phase RBD. One antibody-positive pre-COVID-19 control and COVID-19 positive (n=10) patient serum samples were tested in the SARS-CoV-2 ELISA described above. Samples diluted to a working concentration (1/100) were incubated with 10 times molar excess of RBD or the equivalent volume of PBS for 1 hour at room temperature before testing for antibodies in the standard assay as described.
### Comparing the in-house SARS-CoV-2 ELISA to commercially available assays
A subset of COVID-19 positive patient samples (n=9) and COVID-19 negative patient samples (n=5) was tested in the commercially available EUROIMMUN Anti-SARS-CoV-2 ELISA that measures anti-S1 IgG and IgA and the results were compared to our in-house assay. The same set of COVID-19 positive and pre-COVID-19 controls was also tested by the Hamilton Regional Laboratory Medicine Program (HRLMP) in the Ortho Clinical Diagnostics COVID-19 IgG Antibody Test that measures anti-S protein IgG for comparison.
### Production of recombinant SARS-CoV-2 S protein and RBD
Plasmids encoding mammalian cell codon optimized sequences for SARS-CoV-2 full-length S protein and the RBD were generously gifted from the lab of Dr. Florian Krammer (Ichan School of Medicine at Mount Sinai, NY, NY, USA). In brief, proteins were produced in Expi293 cells (ThermoFisher, Waltham, MA, USA) using manufacturer instructions. Post-transfection, when culture viability dropped to 40%, supernatants were collected and centrifuged at 500 x g for 5 minutes to remove cell debris. The supernatant was then incubated with shaking overnight at 4\({}^{\circ}\)C with 1 mL of nickel-nitrilotriacetic acid (Ni-NTA) agarose resin (Qiagen, Hilden, Germany) per 25 mL of transfected cell supernatant. The following day, 10 mL polypropylene gravity flow columns (Qiagen) were used to elute the protein. S and RBD proteins were concentrated in Amicon centrifugal units (Millipore, Burlington, MA, USA), 10 kDa and 50 kDa respectively, prior to being resuspended in phosphate buffered saline (PBS). The purified proteins were then analyzed using SDS-PAGE.
### PCR Cycle count threshold (Ct) values of Resolved COVID19 samples
Samples were analyzed from nasal or throat swabs and RT-PCR was measured at the Hamilton Regional Laboratory Medicine Program virology lab using an in-house RT-PCR targeted against the 5' UTR and the E gene. The Ct values were determined by the number of cycles the PCR goes through before detection occurs. RNaseP was run on each assay to ensure specimen adequacy. The RT-PCR is a qualitative assay where the cut-offs change based on data collected over time and where the number of targets detected are also taken into consideration, along with examination of the amplification curve to determine positivity of a sample.
## Figure S1: Optimizing antigen concentration for the SARS-CoV-2 ELISA.
Binding of (A) anti-RBD and (B) anti-S protein IgG, A, and M was measured in the SARS-CoV-2 ELISA with plates coated at 1, 2, 5 or 10 mg/mL of the corresponding antigen. Black lines indicate recovered COVID-19 positive patient samples tested (n=8) and red lines represent pre-COVID-19 controls tested (n=8). RBD at 2 mg/mL and S protein at 5 mg/mL were the optimal concentrations used that yielded the greatest separation between OD values of COVID-19 positive and pre-COVID-19 controls results. The optimal serum dilution in 1% skim milk that provided the best separation between negative and positive results was 1/100.
## Figure S2: Comparing the effect of heat-treatment and Triton X-100 treatment on assay performance.
Reactivity of (A) anti-RBD and (B) anti-S protein IgG, A, and M after heat-treatment or Triton X-100 treatment was measured using the SARS-CoV-2 ELISA. Serum samples used for this study included recovered COVID-19 positive patient samples (n=10) and pre-COVID-19 controls (n=5). Values are shown as a ratio of determined optical density to the determined assay cut-off optical density. Values above 1 are considered positive in the SARS-CoV-2 ELISA. The IgG signals were decreased in 12 of 15 samples (66.7%) by an average13.54\(\pm\)6.73% after heat-treatment, but none of these samples decreased below the cut-off. Signals for IgA against RBD and S protein decreased in 12 of 15 samples (80.0%) by an average 13.85\(\pm\)9.55% after heat-treatment. With heat treatment, for IgM anti-RBD and IgM anti-S protein from COVID-19 positive patients and pre-COVID-19 controls, there was a reduction in OD by an average 21.0\(\pm\)8.06% after heat-treatment. Four of 10 COVID-19 positive samples IgM ODs decreased below the assay cut-off after heat-treatment. IgG signals in anti-RBD and anti-S protein were decreased in 14 of 15 samples by an average level of 8.03\(\pm\)7.59% after treatment with Triton X-100. ODs for IgA against RBD and S protein decreased in 7 of 15 samples by an average 4.14\(\pm\)3.38% and increased in the 8 other samples by an average level of 6.74\(\pm\)4.01% after treatment with Triton X-100. With Triton X-100 treatment, IgM anti-RBD and IgM anti-S protein had an average increase in OD by 6.4\(\pm\)5.64% in 11 of 15 samples and OD decreased by 3.11\(\pm\)2.68% in 4 of 15 samples. Treatment with Triton X-100 had minimal effect on the reactivity of the samples. None of the COVID-19 positive samples tested with Triton X-100 treatment decreased below the cut-off after treatment. None of the measured pre-COVID-19 controls became higher than the assay cut-off value after heat-inactivation or treatment with Triton X-100.
## Figure S3: Determining inter-assay variability of the SARS-CoV-2 ELISA.
Binding of anti-RBD IgG for a subset of COVID-19-positive (n=4) and pre-COVID-19 controls (n=4) were repeat tested at least 4 consecutive times to determine any variability between assays. Filled black symbols represent recovered COVID-19 positive patients and open symbols represent pre-COVID-19 controls. Values are represented as a mean optical density reading with standard deviation at 405 nm. The samples tested for variability using resulted in similar readings and low standard deviations for all repetitions. There is minimal inter-assay variability with repeat testing in anti-RBD IgG on average, results deviated by 4.86\(\pm\)3.53% in COVID-19 positive and 7.14\(\pm\)3.03% in pre-COVID-19 controls. This trend was similar for anti-RBD IgA (7.60\(\pm\)3.75% COVID-19 positive; 5.19\(\pm\)3.02% pre-COVID-19 controls) and IgM (4.21\(\pm\)2.64% COVID-19 positive; 8.58\(\pm\)4.63% pre-COVID-19 controls) and anti-S protein IgG (6.16\(\pm\)5.70% COVID-19 positive; 8.82\(\pm\)2.43% pre-COVID-19 controls), IgA (3.30\(\pm\)2.92% COVID-19 positive;12.83\(\pm\)4.17% pre-COVID-19 controls), and IgM (6.08\(\pm\)2.68% COVID-19 positive;
12.37\(\pm\)4.18% pre-COVID-19 controls).
## Figure S4: Inhibition of IgG anti-RBD binding using excess RBD in solution.
Binding of IgG anti-RBD after inhibition with excess RBD in solution to show the specificity of antibodies to RBD antigen in the SARS-CoV-2 ELISA. Black lines indicate recovered COVID-19 patient samples tested (n=10) and red line represent one antibody-positive pre-COVID-19 control tested. The one pre-COVID-19 control tested positive for IgG anti-RBD antibodies that was also inhibited using excess RBD. All COVID-19 positive patient anti-RBD binding was inhibited on average 78.73\(\pm\)10.12% using excess RBD. One pre-COVID-19 control who tested positive for an anti-RBD IgG was also inhibited to a similar degree (80.51%) as COVID-19 positive samples with excess RBD in solution.
**Figure S5:**_Cross-sectional analysis of IgG, IgA, and IgM responses to S-protein and RBD antigens of SARS-CoV-2 in serum._ Anti-S protein (A) IgG, (C) IgA, (E) IgM and anti-RBD (B) IgG, (D) IgA, and (F) IgM of the pre-COVID-19 (n=520), resolved (n=156), and RT-PCR-negative (n=53) populations were profiled by the optimized SARS-CoV-2 ELISA. Values are shown as a ratio of observed optical density to the determined assay cut-off optical density. Values above 1 ratio are considered positive in the SARS-CoV-2 ELISA. Most pre-COVID-19 controls had only background reactivity for both the full-length S protein and RBD. Of the 153resolved COVID-19 subjects tested, 131 tested positive for antibodies against SARS-CoV-2 (IgG, IgA, or IgM antibodies against the S protein or RBD, Table 2) and 22 did not have detectable anti-SARS-CoV-2 antibodies.
**Table S1: Comparing results from the in-house SARS-CoV-2 ELISA to two commercial assays**COVID-19 IgG Antibody Test measures IgG antibodies to the S protein. We found that the in-house SARS-CoV-2 ELISA agreed with the Ortho assay performed by the clinical laboratory (HLRMP), in 14/14 samples (Table 2) for IgG antibodies to the S protein. In one COVID-negative patient sample, the in-house assay detected weak IgG anti-RBD antibodies only, and no other reactivity, which correlated with the Ortho test. The EUROIMMUN assay detected SARS-CoV-2 antibodies in two COVID-19 positive patient samples where the in-house ELISA and Ortho assay did not, one of which was borderline positive for IgG anti-S1. |
192856_file03 | **Supplementary information - Early stopping in clinical PET studies: how to reduce expense and exposure**
_Figure S1. A and B) The rate of false positive stopping decisions increases but reaches an asymptote as the maximal number of subjects (Nmax) becomes higher. Three different BF decision thresholds are shown. C and D) The BF decision threshold can be adjusted to achieve a desired rate of false positives (here 5%) for different Nmax. For all figures: samples are drawn from two populations with the same mean value; testing starts at \(N\!=\!12\)/group; and BF is checked after every additional comparison pair (1 set of patient-control scans or pre-post scans). Here stop decisions for H0 are allowed and the tests are one-sided._Figure S2. The sequential BF testing, using a zero-centered Cauchy to describe the alternative hypothesis, will produce the same results as a 5% family-wise error rate corrected sequential NHST procedure when specifying the BF threshold to correspond to a 5% false positive rate (BF = 4).
Figure S4: Settings for the simulation: H1 is a two-sided cauchy(0,0.707), (Nstart = 12, Nmax = 20, BF threshold = 3.1 and 3.3 for cross-sectional and paired respectively). Panel A and B shows true positive (or “power”) curves for BF sequential testing (blue) and a fixed N approach (black). The curves denote the rate of true positive findings at different population effects. For the fixed N approach, only one test is performed at N=20 per group. For the sequential testing, 12 subjects/group are first collected, then BF is checked after each added comparison pair until 20 subjects/group is reached, using a stopping threshold of 4. Panel C and D shows the average number of subjects needed to reach a stopping decision at different population effects. Fixed N is the black line (fixed at N = 20/group); BF sequential testing is the blue line with shaded area denoting \(\pm\)1 SD.
Figure S6. Settings for the simulation: H1 is a two-sided cauchy(0,0.707), (Nstart = 12, Nmax = 100, BF threshold = 6.6 and 6.7 for cross-sectional and paired respectively). Panel A and B shows true positive (or "power") curves for BF sequential testing (blue) and fixed N approach (black). The curves denote the rate of true positive findings at different population effects. For the fixed N approach, only one test is performed at N=100 per group. For the sequential testing, 12 subjects/group are first collected, then BF is checked after each added comparison pair until 100 subjects/group is reached, using a stopping threshold of 4. Panel C and D shows the average number of subjects needed to reach a stopping decision at different population effects. Fixed N is the black line (fixed at N = 100/group); BF sequential testing is the blue line with shaded area denoting \(\pm\)1 SD.
Figure S7. Settings for the simulation: \(H1\) is a one sided cauchy(0,0.707), (Nstart = 12, Nmax = 15, BF threshold = 4). A and B) The black curve shows the proportion of studies that showed support for H1 (BF\(>\)4) during data collection, at a range of population effects (starting at no effect, \(D\) = 0). The red curve is the proportion of studies showing support for H0 (BF\(<\)\(\%\)). The blue curve is the sum of the red and black curves. C and D) shows the average number of subjects needed to reach a stopping decision at different population effects. The flat black line represents Nmax (15 subjects/group). BF sequential testing is the blue line with shaded area denoting \(\pm\) 1 SD.
Figure S8. Settings for the simulation: H1 is a one sided cauchy(0,0.707), (Nstart = 12, Nmax = 20, BF threshold = 4). A and B) The black curve shows the proportion of studies that showed support for H1 (BF\(>\)4) during data collection, at a range of population effects (starting at no effect, D = 0). The red curve is the proportion of studies showing support for H0 (BF\(<\)1/4). The blue curve is the sum of the red and black curves. C and D) shows the average number of subjects needed to reach a stopping decision at different population effects. The flat black line represents Nmax (20 subjects/group). BF sequential testing is the blue line with shaded area denoting \(\pm\) 1 SD.
Figure S9. Settings for the simulation: \(H1\) is a one sided cauchy(0,0.707), (Nstart = 12, Nmax = 50, BF threshold = 4). A and B) The black curve shows the proportion of studies that showed support for H1 (BF\(>\)4) during data collection, at a range of population effects (starting at no effect, \(D\) = 0). The red curve is the proportion of studies showing support for H0 (BF\(<\)\(\%\)). The blue curve is the sum of the red and black curves. C and D) shows the average number of subjects needed to reach a stopping decision at different population effects. The flat black line represents Nmax (50 subjects/group). BF sequential testing is the blue line with shaded area denoting \(\pm\) 1 SD.
Figure S10. Settings for the simulation: H1 is a one sided cauchy(0,0.707), (Nstart = 12, Nmax = 100, BF threshold = 4). A and B) The black curve shows the proportion of studies that showed support for H1 (BF\(>\)4) during data collection, at a range of population effects (starting at no effect, \(D=\) 0). The red curve is the proportion of studies showing support for H0 (BF\(<\)4). The blue curve is the sum of the red and black curves. C and D) shows the average number of subjects needed to reach a stopping decision at different population effects. The flat black line represents Nmax (100 subjects/group). BF sequential testing is the blue line with shaded area denoting \(\pm\) 1 SD.
Figure S12: Maximum possible support (1/BF) in favor of H0 compared to H1 when using a two-tailed BF t-test. A-D) When using the settings described in the main article (H1 is specified as a Cauchy(0,0.707), \(\text{Nstart}=12\), threshold \(=4\)) but a two-tailed test instead of a one-tailed test, it is not possible to obtained evidence in favor of H0 at smaller N. E.g., in a cross-sectional design, at least 34 subjects/group are needed before the BF can reach a threshold of 1/4. C-D) Percentage of BF showing support (1/BF \(>4\)) for H0 at different N. E.g., at 50 subjects/group, only 45% of BF will show support in favor of H0, when H0 is true. Hence, in order to stop for H0 when using commonly seen sample sizes in PET studies, we recommend to use a one-tailed BF t-test instead. This means that the researchers must make a prediction of the direction of the effect before initiating the study.
Figure S13: Recommended steps to follow in order to perform a clinical PET study using sequential BF testing, for a paired or cross-sectional design. |
192971_file02 | ### S1.2 Robustness and Control Function Models
_Robustness Model_: As a robustness check to the growth rate model discussed above, we also use an exponential smoothing model to estimate the effect of masks, social mobility and NPIs to validate the results from the base model in Equation S9. In this model, we use exponentially smoothed data for right hand side of Equation S8 for the past \(w\) days, without using the \(lag\) variable. It can be written as shown in Equation S10 where \(<x>_{w}\) is exponentially smoothed over the last \(w\) days. Smoothing function is shown in Equation S11. This method considers data in the recent future of day \(t\) instead of considering all the data leading up to day \(t\) or data observed \(lag\) days before as in the growth rate model in Equation S9. This model is analogous to counting the number of days in which a policy was active in the past \(w\) days. We use exponential smoothing to include the lag effect of masks, NPIs and mobility on the growth rate.
\[\overline{g_{j,t+shift}}=\theta_{0}+<\theta_{m}.\mathit{mask}_{j,t}>_{w}+\sum_ {p\in P}\theta_{p}<\mathit{policy}_{j,t,p>_{w}}+\sum_{m\in M}\theta_{m}<\mathit{ mobility}_{j,t,m}>_{w}\]
\[+\theta_{e}<\mathit{testing}_{j,t}>_{m}+\sum_{w\in W}\theta_{w}week_{j,t,w}+ \theta_{r}<\mathit{trend}_{j,t}>_{w}+\sum_{j\in J}\theta_{j}\mathit{countries}_ {j}+\epsilon_{t}\] (S9)
\[<x>_{w}=\frac{\sum_{l=1}^{w}0.8^{w-l}x_{t-w}}{\sum_{l=1}^{w}0.8^{w-l}}\] (S10)
Figure S1 shows the idea behind the exponentially smoothed model. In the growth rate model, we give importance to events that happened at a lag of \(shift\) days. Thus, on day \(t\), we assign 0 weights to data from \(t-shift+1\) to \(t\). In exponentially smoothed model, we assign an exponentially reducing but non-zero weights to data for days \(t-shift+1\) to \(t\).
_Control Function Model_: We also consider a control function approach to check the robustness of the mask parameter from Equation S8. Countries have had different experiences with air borne diseases due to multiple outbreaks in the past e.g. Severe Acute Respiratory Syndrome (SARS), Middle East Respiratory Syndrome Coronavirus (MERS-CoV) and H1N1 Influenza (Swine Flu). Countries with severe outbreak of these air-borne virus were quick to adopt to wearing face masks in public. This could potentially confound with the effect of mask discussed in this paper. So, we use a control function approach to isolate the effect of masks. Since the growth rate in COVID-19 is independent of number of deaths per thousand people from SARS, MERS and H1N1, it may affect the percentage of population with mask wearing \(mask_{jt}\) but does not affect the growth rate. This allows us to use deaths from previous diseases as a control function. Total deaths per thousand people for different countries is given in Figure S2.
In the control function model, we first predict average mask wearing in country \(j\overrightarrow{mask}_{j}\) using the number of deaths from SARS, H1N1 and MERS in country \(j\) as covariates in ordinary least square linear regression estimation. We use \(d_{j,dis}\) where \(dis\in\{SARS,H1N1,MERS\}\) as predictor variable where \(d\) is the number of deaths per thousand people in country \(j\). Specifically we use, \(d_{j,dis}=1\ |d_{j,dis}>median(D_{dis})\) for deaths per thousand people in country \(j\). The model to predict \(mask_{j,t}\) is shown in Equation S12. After estimating \(\overrightarrow{mask}_{j,t}\), we use the error \(mask_{j,t}-\widehat{mask}_{j}\) in Equation S9 as a covariate. Control function model is shown in Equation S13.
Figure S1: Weights given to different data points for two models – growth rate model in Equation S9 (red) and exponentially smoothed growth rate model (blue) in Equation S10. Exponentially smoothed growth rate model consider all the data points in recent history to day \(t\) instead of considering the events only on day \(t-shift\). Weights decrease as we move closer to day \(t\) to incorporate the delay in observing the effect of events in the recent future.
\[\overrightarrow{mask_{j}}=d_{j,SARS}+d_{jH1N1}+d_{j,MERS}+\epsilon_{m}\] (S11)
\[g_{j,t+shift}=\theta_{0}+\theta_{m}.mask_{j,t}+\sum_{p\in P}\theta_{p}policy_{j, t,p}+\sum_{m\in M}\theta_{m}mobility_{j,t,m}+\theta_{e}.testing_{j,t}\] \[+\sum_{w\in W}\theta_{w}week_{j,t,w}+\theta_{r}.trend_{j,t}+\sum_ {j\in J}\theta_{j}countries_{j}+\theta_{md}(mask_{j,t}-\overrightarrow{mask_{j} })+\epsilon_{t}\] (S12)
Wearing face masks in public is common in many Asian countries, as compared to countries in Europe or America. One of the reasons is due to recent experience with air borne diseases. Another reason could be air pollution or a culture of wearing face masks. We do not account for the different trends in wearing face masks among countries due to pollution or culture. However, we believe the country fixed effects could capture the country wise trends in wearing face masks.
## S2.
We model the effect of wearing face masks, change in social mobility and government enforced Non-Pharmaceutical Interventions (NPIs) in the growth rate of infection. We select the countries with publicly available dataset for wearing face masks and community mobility. We collect data from February 21, 2020 to July 8, 2020. In this Section, we discuss the different datasets used in our analysis to isolate the effect of masks, social mobility and NPIs in the spread of the contagious SARS-CoV-2 (COVID-19 virus).
### S2.1 Masks
We collect mask data from surveys conducted by YouGov. YouGov is an international internet based market research company which specializes in opinion polls through online methods. YouGov used online surveys as their COVID-19 behavior change tracker. They conducted surveys periodically in some countries of the world to estimate the propensity of the percentage of people that wear face masks when they go out in public spaces. These surveys were conducted every week. Figure S3 shows the raw survey numbers from YouGov. As the surveys were conducted periodically and not every day, we use monotonic cubic splines to estimate the percentage of population that wear face masks in public spaces (Figure S4). Note that the online survey does not include data for type (quality) of masks or how people wear masks (insufficient quality or incorrect method of covering face masks e.g. touching the surface, not covering nose or mouth -- might not be effective in controlling the spread of virus). Thus, our estimation for effect of masks in this work would be an estimation of the behavior of wearing masks. In our analysis, we normalize the number for mask wearing such that \(0\leq mask_{jt}\leq 1,\ \forall j,\forall t\).
### S2.2 Active Cases
We use the timeline for total confirmed cases and total recovered cases from Johns Hopkins Coronavirus Research Center to find the daily active cases across different countries. We use the daily active cases to calculate the outcome variable of our model -- growth rate. Cumulative confirmed cases, Cumulativerecovered cases and daily active cases for different countries is shown in Figure S5. We use a 7-day moving for daily cumulative confirmed cases and cumulative recovered cases.
### S2.3 Growth Rate
We use daily active cases to estimate the daily growth rate for these countries. Growth Rate (Equation S8) can be very volatile at the start of the pandemic due to the low number of cases in the early stages. For example, a unit increase in \(I_{jt}\) will record a growth rate of 0.4 when \(I_{jt}=2\) as compared to a growth rate of 0.0004 when \(I_{jt}=1000\) (growth rate is calculated as the first difference in log of active cases in consecutive days). Similarly, during the later stages of the pandemic (at least when the first wave is slowed down for some countries), growth rate could be affected by multiple other factors such as awareness or changed individual behavior. To avoid these issues, we use the data for first 60 days for a country (after we start collecting data for a country following the '\(th\)').
Unlike Hsiang et al., we use data for 60 days and do not restrict to the initial phase when the cases rise exponentially. In SSRobustness check, we discuss the performance of the model (and changes in model parameter estimates) as we add more/less data in the model from 24 countries. To filter out the volatile growth rate during the start of the pandemic, we consider data for each country when the daily new cases cross a threshold \(th\). We define this threshold, as the day when the 7 day average of daily new cases in a country crosses \(th=\)20% of the peak case observed in that country (till July 8, 2020). We select \(th\) based on maximum likelihood estimate of the growth rate model (mechanism for the selection of \(th\) is discussed later in the Section on SSRobustness Check). Figure S6 shows the daily new cases. Figure S7 shows the respective growth rate. Since we use data for a maximum of 60 days for a country, from the day its daily cases cross the threshold. Thus, our dataset contains an unbalanced panel data from 24 countries.
Figure S7. Growth rate across Countries. The green line marks the day when daily new cases in that country crossed the threshold. Brown line shows the end of 60 days of data collected for each country. We use cumulative confirmed cases to calculate growth rate for Norway, Sweden and United Kingdom. Collecting data after the green line allows us to filter initial noisy growth rate from that country.
Figure S6. Daily New Cases. The green line marks the day when daily new cases in that country crossed the threshold. Brown line shows the end of 60 days of data collected for each country. For countries where cases are still increasing vis-a-vis India and Philippines, we collected fewer data points than 60 days.
### S2.4 Community Mobility
Google's COVID-19 Community Mobility Reports provides information on how movement trends change over time across different types of locations in different countries. The mobility numbers are calculated based on the change in trend from the baseline (details in the report on how Google calculates the baseline). The report tracks movement trends over time by geography, across different categories of places such as retail and recreation, groceries and pharmacies, parks, transit stations, workplaces, and residential. Figure S8 shows the community mobility across different countries.
We observe high correlation between the social mobility numbers from Google across different types of locations. This may lead unstable parameter estimates due to multicollinearity in parameter estimation using ordinary least squares. Based on the correlations, we consider the mobility in Parks and Transit stations as our measure for mobility. We also confirm these two categories using a Lasso regression (more details in Section SSRobustness Check in Section 4.5.3). The Lasso regression model pushes the coefficients of correlated variables (variable which do not add much information to the model) to 0 and gives non-zero weights to only two of the mobilities: Parks and Transit stations.
The correlation matrix between the mobility across different locations is shown in Table S1. The correlation matrix shows that transit stations is highly correlated with mobility in Retail and Recreation, Grocery and Pharmacy and Residential. Mobility in transit stations is negatively correlated with mobility in Residential as - fewer people travel indicates establishes that more people are staying home. Thus, mobility in transit stations is able to capture the information from mobility across all other locations except Parks. Henceforth, we include mobility in Parks and Transit stations as a measure of mobility (and as also selected by Lasso Regression model). In our analysis, we normalize the number for social mobility such that \(0\leq mobility_{j,t,m}\leq 1\,\forall j,\forall t,\forall M\).
Summary statistics for the community mobility is shown in Table S2.
### S2.5 Non-Pharmaceutical Interventions (NPIs)
Governments (and its policies) play a critical role in fighting a pandemic. Vaccines may take a long time to be available, particularly for a new disease e.g. COVID-19. In an ongoing pandemic, we cannot depend only on the vaccines but need strong government interventions (institutional measures) to control the spread of the disease. During such times, governments must take various measures e.g. increasing testing infrastructure to control the spread of infections. These NPIs help in decreasing mobility (for example travel bans imposed restriction on travel across states/ regions/ countries while it also helped in restricting mass gatherings in places such as transit stations. Since COVID-19 spreads through person to person physical interaction (or prolonged proximity), governments introduced various policies (Non-Pharmaceutical Interventions or NPIs) for social distancing to minimize person-to-person interaction. They also introduced closures of places where people gather together at the same time e.g. schools or businesses. However, these government policies seriously affected businesses, leading to economic shutdowns which adversely affecting the poor community. The effect of these shutdowns may also lead to prolonged economic hardships e.g. closure of some businesses and employment.
Since these policies directly affect the livelihood of a majority of the population across the world, it is important to investigate the impact they have on controlling the spread of the disease. As these policies were implemented at different times across different countries, it gives us an opportunity to explore the combined effect of these policies. Estimating the combined effect of these policies could help the governments in future (or current) pandemics to introduce policies that are effective and may not necessarily lead to complete lockdown unless extremely necessary. Please note that some of these policies were introduced at the same time, or some of the policies were implemented first and some of the policies were implemented always after some other policy were implemented, we do not claim any causal effect of the policy on the growth rate. It is difficult to isolate the effect of individual policies as the implementation of policies were not randomly sequenced across countries.
We use Coronanet dataset from Cheng at al. They collected information on all the government policies introduced by different countries across the world. They categorized the policies into 19 different _policy types_. We use their categorization to build our model. The policies were implemented at different levels - National, Provincial and Municipal. In this work, we consider the policies implemented at National and Provincial level. From February 21, 2020 to July 8, 2020, we check if a policy \(p\) was implemented in a country \(j\) or not on day \(t\). If the policy was implemented, we assign a value of 1 to \(s_{j,t,p}\). If the policy was introduced at a provincial level (could be introduced by the central government or a respective state government), we increase \(s_{j,t,p}\) by the population of the state. Equation S13 explains \(s_{jt,p}\) if a policy \(p\) is employed at a provincial level where \(\widehat{N_{js}}\) is the population of state \(s\) in country \(j\). After identifying \(s_{j,t,p}\)for all countries over the period of our analysis (considering all the entries in the dataset), we use normalization using maximum value in a country such that \(s_{j,t,p}\in\ \forall j,\ \forall t,\ \forall p\) as shown in Equation S13..
\[s_{j,t,p} =\ s_{j,t,p}+\frac{\widehat{N_{js}}}{\widehat{N_{js}}+N_{j}}\] (S13)
\[s_{j,t,p} =\ \frac{s_{j,t,p}}{\max_{t,p}s_{j,t,p}}\] (S14)
The dataset contains 5816 entries on policies (some of the policies were announcements/recommendations/ new entry or an update to existing policy) at National and Provincial level. The dataset provides detailed information on the type of the data entry (e.g. policy type, description of the policy). The statistics on the types of policies is shown in Figure S10. Figure S10 also provides a count of entries of each policy type. The data set contains 20 _policy_types_. Figure S10 shows how many countries implemented (light grey bars) a particular _policy_type_. It also shows how many countries implemented a particular _policy_type_ at national or provincial level (light blue bars and dark blue bars respectively). The dark grey bars show the total number of entries (divided by 100 for visualization) for all _policy_types_.
We use the text description of the policy to identify if an entry was an update, recommendation or actual implementation. If the entry was an announcement or an update for a policy with start date and an end date, we give a weightage of 0 to that entry in the dataset because if there is policy update, it could account that policy. Note that the policies could have been implemented differently across different countries, even if they were categorized in the same policy type. For example, a country may impose Social distancing rules from 4 pm - 8 pm while another country may impose it from 6 am - 6 pm. It may differ across different states in country. However, for the purpose of this research, we do not consider the variations in implementations of policies.
As we have survey numbers for wearing face masks at a national level, we a consider policy type that were implemented across majority of the countries. Therefore, we do not consider Anti-disinformation measures, Curfew and Lockdowns. Curfew and Lockdowns are similar to Quarantine and Restrictions of Mass Gatherings (which lead to closure of places of mass gatherings) so we can ignore them for the purpose of this research. Moreover, Curfew and Lockdowns affect the community mobility, which can be accounted for by trend in social mobility from Google Community Mobility Reports (discussed in the previous Section).
We also do not consider Hygiene Announcements and New Task Force policy as these were administrative announcements and did not have much effect on the growth rate of the infection. Somepolicies did not have a start date and end date. We calculate the cumulative number of times announcements were made for such categories. Health Testing, Health Monitoring and Health Resources are administrative announcements, so we combine them in to one Health Resources policy. As we use linear models, a linear combination (addition of three policies) does not affect our analysis. It further reduces the number of parameters to be estimated. Similarly, we combined Restrictions and Regulations of Businesses and Restriction and Regulation of Government Services. Health resources can also be used as proxy for increased awareness among governments and citizens. So, we do not consider "Public Awareness Measures" announcements to avoid multicollinearity in the set of predictor variables.
Table S4 shows the correlation between different government policies implemented across countries. The correlation value between pairs of any two NPIs is not high (>0.7 as observed with community mobility across different locations in Google Community Mobility Reports), so we include all the following 8 government policies in our model in Equation S9. We also include the Social Mobility in Parks and Transit Stations to check its correlation with NPIs. Changes (reduction during the early stages of pandemic) in social mobility were induced by the introduction of NPIs. However, social mobility is a combination of institutional measures e.g. NPIs and individual measures e.g. social mobility. Correlation between social mobility and any NPIs as shown in Table S4 is not high (>0.7) so we do not reject any further NPIs.
### Lag in Observation of the Effects of Control Variables
Studies have reported a delay in observation of effects of policies on the events on a given day. This delay could be due to several reasons. One of the most prominent reasons is the incubation period (time between getting infected and onset of symptoms/knowing that individual is confirmed for COVID-19). During the incubation period, an individual may be asymptomatic. Incubation period is estimated to be 4 days to 14 days. Another reason could be the testing time - time it takes to get the confirmation ofresults. Due to limited healthcare professionals, there could be a long queue to get tested to get the results from testing centers.
To model this delay, we use as lag variable, \(shift\). We use cross validation method to find the lag with the best fit for the data. We test \(shift\in\) and observe that the model performs best at a \(shift\) of 9 days. We discuss this further in Section SSB Robustness check.
### S2.7 Testing
Testing is critical in identifying the infectious individuals. Once identified, these individuals can be quarantined or isolated from public so that they do not spread to susceptible individuals. While people can get tested when they start showing symptoms, evidence reports that even asymptomatic individuals can spread the virus (50% of cases can be attributed to asymptomatic cases) Since they do not show any symptoms, people around them (e.g. asymptomatic young adult living with family) are less cautious and may get infected through them. It is critical to identify asymptomatic individuals as they can spread the virus unknowingly. This can be done by increased testing and contact tracing the individual who have come in contact with those who tested positive for the COVID-19. Testing can be crucial in identifying COVID-19 positive individuals so that they can be quarantined (hospital or home isolation) or treated early when symptoms starts showing. In our analysis, we normalize the number for social mobility such that \(0\leq testing_{j,t}\leq 1\;\forall j,\forall t\).
As testing increases, the probability that more confirmed positive cases will be identified. This will lead to increase in empirical growth rate over time as more confirmed cases will be reported. This shows a change in testing pattern over time which could lead to bias (or underestimating the effect of NPIs and masks). To counter this time sensitive bias, we use testing data to account for increased testing over time. Figure S13 shows the data on total tests (per thousand people) in a country from ourworldindata.org.
### S2.8 Google Trends
As the number of cases start increasing, awareness increased in public (e.g. washing hands more often). We use Google Trends to account for the increase in active awareness over time (Figure S14). Google Trends numbers indicate the search interest of a topic over time as a proportion of all other searches at the same time. In our analysis, we normalize the number for Google Trends such that \(0\leq trend_{j,t}\leq 1\ \forall j,\forall t\).
### S2.9 Week Fixed Effects
Handling of COVID-19 changes over time. It includes increase in public awareness or better understanding of the virus as more studies and research comes to public attention. Not only do citizens understand how to be more careful (or more informed), healthcare providers also learn more about the disease for more efficient treatment of COVID-19 patients (e.g. creating new wards for COVID-19 patients, treating them by wearing Personal Protection Kits, PPE). It also involves improved infrastructure e.g. testing, converting existing medical facilities to dedicated COVID--19 centers. To account for all the time sensitive fixed effects (other than the controls we discuss before), we use fixed effects for weeks (from the day that country reaches \(th\) in our analysis).
Figure S14 shows how the growth rate changes across different weeks (Figure S15 provides same information across different countries). Even after removing the initial noisy data, we observe highest variance in the growth rates during week 1 in most countries (Figure S14 and Figure S15). We use one hot vector to denote week (\(week_{j,t,w}=1\)) if day \(t\) lies in week \(t\) for country \(j\). Note that due to different starting times for each country (Figure S6), a day may come under different week for different country. For example, days in week 1 for Vietnam are earlier in the calendar as compared to the days in week 1 inIndia. Note that the growth rate is higher during the initial weeks and slows down with time. To capture this effect, we use fixed effects for weeks. Results in Section SSResult show that the magnitude of coefficient for week 0 is higher than the magnitude of the coefficient for week 1 and so on.
We observe heterogeneity across countries with many aspects in handling COVID-19. Multiple factors affect the spread and handling of a disease in a country. Heterogeneity may be observed at different levels. For example, heterogeneity at government level includes difference in reporting cases, testing infrastructure, strictness is reducing social mobility and implementation of NPIs. Population wise heterogeneity includes population density in a country or percentage of population living in high density urban regions or poor neighborhoods with shared sanitation facilities. It may also include cities with international airports or international travelers (particularly from countries hard hit with COVID-19 in early 2020 e.g. China and Iran). It also includes heterogeneity at the level of education (awareness about COVID-19, responsibility in understanding the severity of precautions), poverty (health insurance, ability to purchase sanitizers or high quality masks), basic health care facilities (drinking water, sanitation, shared places) or family structure (number of young adults in a family or size of the family residing in a residential complex). To control for all this heterogeneity among countries which may lead to country level effects in the growth rate of COVID-19, we use country fixed effects.
Note that since we use a constant in our model, we consider fixed effects for 23 countries and we consider last country (Vietnam) as our base country (with 0 fixed country effect). This ensures that parameter estimates are stable.
## S3.
We use growth rate model in our analysis to study the effect of Masks, Social Mobility and Non-Pharmaceutical Interventions (NPIs). Since we do not have real numbers on how many people wear masks (or wear masks that could be effective), we use different transformations of the mask numbers from the surveys. We use growth rate model with masks transformed as \(\ln(1+mask_{jt})\) as our focal model. We use threshold \(th=0.2\) and \(shift=9\) days. Details on selection of \(th\) and \(shift\) is provided in Section S6Robustness Check. Model statistics are given in Table S5. Parameter estimates for model with different transformations is shown in Table S6.
\begin{tabular}{|l|l|l|l|l|l|l|} \hline week1 & 0.0589 & 0.009 & 6.872 & 0 & 0.042 & 0.076 \\ \hline week2 & 0.0411 & 0.008 & 5.146 & 0 & 0.025 & 0.057 \\ \hline week3 & 0.0324 & 0.007 & 4.335 & 0 & 0.018 & 0.047 \\ \hline week4 & 0.018 & 0.007 & 2.575 & 0.01 & 0.004 & 0.032 \\ \hline week5 & 0.0039 & 0.007 & 0.592 & 0.554 & -0.009 & 0.017 \\ \hline week6 & -0.0013 & 0.006 & -0.209 & 0.834 & -0.014 & 0.011 \\ \hline week7 & 0.0021 & 0.006 & 0.343 & 0.732 & -0.01 & 0.014 \\ \hline Testing & -0.0121 & 0.006 & -1.938 & 0.053 & -0.024 & 0 \\ \hline Trend & -0.0455 & 0.008 & -5.933 & 0 & -0.061 & -0.03 \\ \hline Health Resources & -0.034 & 0.012 & -2.881 & 0.004 & -0.057 & -0.011 \\ \hline Restriction and Regulation of Businesses & -0.0049 & 0.005 & -1.03 & 0.303 & -0.014 & 0.004 \\ \hline Closure and Regulation of Schools & -0.0153 & 0.006 & -2.436 & 0.015 & -0.028 & -0.003 \\ \hline External Border Restrictions & -0.0315 & 0.008 & -3.807 & 0 & -0.048 & -0.015 \\ \hline Quarantine & -0.0321 & 0.01 & -3.194 & 0.001 & -0.052 & -0.012 \\ \hline Restrictions of Mass Gatherings & -0.0066 & 0.007 & -1.007 & 0.314 & -0.019 & 0.006 \\ \hline Social Distancing & 0.0038 & 0.006 & 0.618 & 0.536 & -0.008 & 0.016 \\ \hline Internal Border Restrictions & -0.01 & 0.006 & -1.639 & 0.101 & -0.022 & 0.002 \\ \hline Australia & -0.0338 & 0.013 & -2.531 & 0.011 & -0.06 & -0.008 \\ \hline Canada & 0.0205 & 0.012 & 1.645 & 0.1 & -0.004 & 0.045 \\ \hline Denmark & 0.0167 & 0.014 & 1.23 & 0.219 & -0.01 & 0.043 \\ \hline Finland & -0.02 & 0.016 & -1.27 & 0.204 & -0.051 & 0.011 \\ \hline France & -0.032 & 0.014 & -2.209 & 0.027 & -0.06 & -0.004 \\ \hline Germany & -0.0101 & 0.014 & -0.739 & 0.46 & -0.037 & 0.017 \\ \hline India & -0.0038 & 0.013 & -0.295 & 0.768 & -0.029 &and NPIs. They also show consistency on the parameter estimates for fixed effects (week and countries). Fixed effect of week is able to capture the trend in awareness or infrastructure change over time. In the beginning of the pandemic in a country, the growth rates were higher. This is corroborated with positive and statistically significant values for the fixed effects of weeks (decreases as week increase). The coefficients for masks seem different across the different transformations but due to its transformation, it has to be interpreted differently (as we discuss next in the interpretation of results). However, we cannot claim causality from these results as the NPIs were not randomly introduced in different countries. Nonetheless, we can estimate the combined effect of different mobilities and NPIs.
### S3.1 Krinsky-Robb method
In the rest of our analysis, we use Krinsky-Robb method to estimate confidence intervals for combined effect of masks, social mobility and NPIs. We also use this method to obtain confidence bounds across the predictions of growth rate and active cases in a country. Krinsky-Robb method is a Monte Carlo simulation method used to draw samples from multivariate normal distribution. We use ordinary least square method to estimate the coefficients \(\theta\) in Equation S8. Ordinary least square method for multiple linear regression assumes multivariate normal distribution of \(\theta\). Krinsky-Robb method takes advantage of this assumption to sample random draws for \(\theta\) using Cholesky decomposition and standard normal variates. Steps in Krinsky-Robb method are:
1. Find Cholesky decomposition matrix \(\mathcal{C}\) for the covariance matrix of \(\sum_{\theta}\).
2. Draw \(|\theta|\) x \(n\) random samples from standard normal distribution (\(|\mathbf{x}|\) is the cardinality of \(\theta\)).
3. \(\theta_{samples}=\hat{\theta}+\sum_{\theta}\). \(\mathbf{x}\,|\theta|\,\mathbf{x}\,n\)
4. Calculate confidence interval based on \(\theta_{samples}\) We use this method to get confidence interval bounds for the sum of the coefficients of mobility and NPIs to get the combined effect. We also use this method to predict confidence intervals of growth rate and daily active cases under different scenarios as we discuss next. First, we discuss the model performance and then discuss the interpretation of the coefficients in Table S6.
### S3.2 Model Performance
We can use the coefficients from our model to predict the growth rate for different countries. Figure S17 shows the actual growth rate (green dots) with predicted growth rate (blue line) with its confidence interval (blue shade). We use Krinsky-Robb method to estimate the confidence interval bounds around the prediction. Results show that the model is accurately able to predict the growth rate of daily infections across different countries. Green and Brown vertical lines indicate the 60 days period for which data was collected for that country.
Since growth rate is a forward looking model, we can also use growth rates to estimate active infectious population by \(I_{j,t}=I_{j,t-1}\)x \(g_{j,t}\). Results for daily active cases are shown in Figure S18. Note that we estimate active cases using an exponential model. Thus, as the number of days in the prediction model increases, confidence interval bounds around predictions increase. However, the mean prediction for active cases closely approximates the actual active cases for different countries.
### S3.3 Effect of Masks, Social Mobility and NPIs
We model growth rate as the first difference of log of active daily infectious confirmed cases as shown in Equation S9. Thus, the exponential of the coefficients in Table S12 (other than mask as we discuss next) estimates % drop in active cases on day \(t\) (as compared to active cases on day \(t-1\)). Using the coefficients in Table S13, we can estimate the combined effect of masks, social mobility and NPIs by using Krinsky-Robb method.
Negative and statistically significant coefficient for masks show that increased mask wearing behavior may lead to decrease in the growth rate of COVID-19. As we use different transformations, the coefficient for masks should be interpreted differently. When masks are transformed as \(\ln(1+mask)\), a coefficient of \(\theta_{m}\) shows that if 100% of the population wears masks, it would lead to a daily drop of \(1-e^{\theta_{m}(\ln(1+1)-\ln(1+0))}\) % in the growth rate as compared with the scenario when no one wears face mask. For raw mask numbers, the effect of masks can be interpreted directly as \(1-e^{\theta_{m}}\) % drop in daily total infectious cases when everyone wears masks as compared to no one wearing masks. When masks are transformed as \(\surd(1+mask)\), coefficients should be interpreted as - a coefficient of \(\theta_{m}\) shows that if 100% of the population wears masks, it would lead to a daily drop of \(1-e^{\theta_{m}(\surd(1+1)-\surd(1+0))}\) % in the growth rate as compared with the scenario when no one wears face mask. Similarly, we can estimate the bounds for the effect of coefficients of masks. The estimate for decrease in daily growth rate when one percent additional population wears face masks in public spaces (under different transformations) is given in Table S7.
The effects of not wearing masks in each country is shown in Figure S19. Note that the results are not significantly different for Denmark, Finland, Norway and Sweden as these countries already had very low numbers for mass wearing in public spaces. Similarly, the effect is much stronger for countries e.g. Japan, Thailand and Vietnam, which have higher percentages of people wearing face masks.
Similar to Figure S18, we can predict daily active cases with zero percent mask wearing as shown in Figure S20. The results show that masks lead to significant reduction in total cases as without these measures, the number of cases could exponentially increase over time (more discussion later on SSCountry wise effect),We build five simulation models to further understand the impact of masks. In the first simulation model, we consider a hypothetical country with a constant value for all the covariates in the Equation S8. In the second simulation model, we check the change in active cases at the end of 60 days when mask wearing in a country is \(m\%\) where \(m\in[0,10,20,\ldots,100]\). In the third model we check the change in active cases at the end of 60 days if the current levels of mask wearing is multiplied by a factor of \(x\in[0,0.2,0.4,\ldots,2]\). In the fourth model, we present results for active cases at the end of 60 days when mask wearing percentage increases by \(a\%\) as compared to the current levels in that country where \(a\in[1,2,\ldots 10]\). In the fifth model, we exchange the mask wearing numbers between countries with minimum and maximum average mask wearing through the period of our analysis.
Simulation Model 1 helps in isolating the effect of masks as in this analysis, we do not consider any other covariates (as if no individual or institutional measures were taken apart from wearing masks in public areas). We construct data for a hypothetical country with these numbers to quantify the effect of masks in our analysis. In Simulation Model 2-4, we study country-wise association of masks with growth rate. In these models, we do not change numbers of any other covariates other than masks. These results show the potential change in active cases in that country for different percentage of people wearing masks in public. Simulation model 5 is used to build an approximate counter factual model for masks by exchanging mask wearing in countries with minimum and maximum average mask wearing during the period of our analysis. We discuss the results of these simulation models next.
We simulate a hypothetical country with no wearing (\(mask_{jt}=0\)), no active awareness \(\big{(}trend_{jt}=0\big{)}\), no testing( \(testing_{jt}=0\)) and no government implemented NPIs (\(s_{pjt}=0\)). We predict the active cases at the end of 60 days at different levels of mask wearing. We consider the average country with 0 country fixed effects for prediction. Daily active cases for this average country at different levels of mask wearing is shown in Figure S21. We assume that the average country has 100 cases on day 0 of simulation. Results show that increasing the mask number can help in flattening the curve (even when social mobility and NPIs remain unchanged). As the percentage of people wearing face masks increases, the daily active goes down as compared to no mask wearing. Results also show that social mobility along with NPI can also play significant role in flattening the curve (the daily active curve flatten even with no mask wearing, albeit slower). Cases starts rising again after initial flattening for most cases as social mobility increases and NPIs are relaxed (Figure S8). The results imply that if masks are mandated and its use widespread, complete lockdowns may be eased to help alleviate the associated economic hardships.
### Simulation Model 2: Changing mask levels
In this simulation, we predict the number of active cases in each country by changing the levels of mask wearing. Figure S22 shows the ratio of active cases at the end of 60 days under different levels of mask wearing as compared to active cases at the current levels of masks. As the mask levels increase, the ratio of active cases to the true active cases at the end of 60 days decreases (Figure S22).
#### Simulation Model 3: Multiplying a constant to current mask levels
In this simulation, we multiply the current mask wearing levels with a constant multiplication factor (0.2, 0.4,.., 2) to predict active cases at the end of 60 days as compared to actual scenario across 24 countries (Figure S23). Similar to Figure S22, we observe as we increase mask levels, ratio decreases significantly. However, the effect is different across different countries.
Similar to results in Figure S22, when the mask levels are much lower than the current levels (e.g. countries like Thailand, Vietnam, Singapore), the ratio of active cases at the end of 60 days (as compared to current levels of mask wearing) is much higher as compared to countries with lower current mask rates (e.g. Sweden, Norway).
#### Simulation Model 4: Adding a constant to current mask levels
In this simulation, we predict the ratio of active cases at the end of 60 days when mask wearing in a country is increased by different percentage points (0%, 1%, 2%,..., 9 %). Figure S24 plots the ratio of active cases at the end of 60 days with simulation for increased mask wearing to the actual active cases. This could help the government in forming policies that if \(a\) % of more people follow the guidelines of wearing face masks, which NPIs could be relaxed while still controlling the spread of the virus. Enforcing mask wearing policy could be particularly useful in countries with low mask wearing.
We present the combined effect of social mobility and NPIs. We provide a combined effect for social mobility and NPIs as it is difficult to estimate the causal analysis for individual variables. We use Krinsky-Robb method to estimate the combined effect of social mobility and NPIs. After drawing samples of coefficients of social mobility and NPIs using Krinsky-Robb method, we add the random samples draw and present the mean and confidence interval bounds of these samples as the combined effect and confidence interval bounds of that combined effect.
### Social Mobility
Parameter coefficients in Table S6 show that growth rate increases as mobility increases. This is because if people travel more or move to places with potential of public gatherings, infected individuals can spread the virus to the susceptible population. Governments therefore imposed strict restrictions to reduce mobility. We report the effect of mobility as negative of the coefficients in Table S13. Thus, we report the effect of mobility if the mobility numbers were 0 (no mobility change). Results in Figure S25 indicates that 0 change in mobility trends (no change in individual mobility trend indicates if people move around as they were before COVID-19) is associated with a daily increase in growth rate by 8.1% (5.6% - 10.6%) as compared to no mobility. Note that decrease in mobility can also be attributed to NPIs, no causality can be claimed on the effect of increase in mobility on growth rate.
The effect of full mobility across different countries is shown in Figure S25. It shows that even with mask numbers remaining unchanged and NPIs being implemented as they were implemented in that country, increasing mobility can lead to a significant increase in growth rate. Similar to Figure S20, we can predict daily active cases with full mobility as shown in Figure S26.
Similar to exchanging the mask wearing numbers among the countries with lowest and highest mask wearing percentages, we simulate for the active cases at the end of 60 days by exchanging social mobility among countries with highest and lowest social mobility. The results are shown in Table S8.
### S3.3.3 Non-Pharmaceutical Interventions (NPIs)
Negative and statistically significant estimate for the combined effect of NPIs show that NPIs helped in controlling the spread of virus. Results in Table S6 indicates that if mask wearing and mobility remains unchanged, implementing NPIs is associated to a daily drop in infectious cases by 13% (9.2% - 16.2%). Predicted growth rate and daily active cases with no NPIs is shown in Figure S27 and S28 respectively.
Similar to exchanging the mask wearing numbers among the countries with lowest and highest mask wearing percentages, we simulate for the active cases at the end of 60 days by exchanging NPI numbers among countries with highest and lowest number of NPIs introduced across the country. The results are shown in Table S8.
### S3.3.4 Combined Effect of Mask, Social Mobility and NPIs
Similar to presenting the combined effect of mobility and NPIs, we use the Krinsky-Robb method to present the effects for the combined effect of masks, social mobility and NPIs in daily drop in growth rate in Figure S29. Figure S29 also show the robustness of the model across different values of \(shift\). It also shows the Mean Absolute Percentage Error for 10 - fold cross validation used to get the \(shift\) that best fit the data. We observe best data fit for a lag of 9 days. Grey vertical lines indicate a shift of day 7 and day 11. The combined effect of masks, social mobility and NPIs is estimated to be a 28.1% (24.2%-32%) drop in daily growth rate.
Results show that the effect of masks remain consistent across different transformations and different \(shift\). We also observe consistency across different transformations of mask numbers. Furthermore, the total combined effect of masks, social mobility and NPIs remain consistent as we change \(shift\).
The results show that masks, social mobility and NPIs lead to significant reduction in total cases as without these measures, the number of cases could exponentially increase over time.
### S3.4 Testing and Google Trends
Negative and statistically significant coefficient for testing and Google Trends indicate a drop in daily growth rate as these numbers increase. As testing increases, it may show increased daily confirmed cases (as more people get tested and it can discover asymptomatic cases). However, our model uses a lag of 9 days. Thus the cases may not be affected by testing immediately. Thus, a negative coefficient with a lag shows that testing helps in achieving a daily drop in growth rate in active infectious cases. Similar to testing, as our model uses a lag of 9 days, increased google trends indicate increased awareness among the citizens regarding COVID-19 which may lead to more caution against COVID-19.
## S4.
### S4.1 Selection of \(th\) and \(shift\)
To filter the initial volatile growth rate, we use a threshold in the model (one for each country). We start collecting data for a country from the day respective countries reach their threshold. We define threshold as - the day after which the 7-day average of daily new cases were \(th\) % of the peak daily new cases observed in that country. Decreasing \(th\) will add noise to the model due to high volatility in early the growth rates. However, if the threshold is high, we miss out on important data, particularly during the initial phase when the growth in infections is exponential.
Along with \(th\), we also use \(shift\) in the growth rate model to capture the delay in effect of mask, Non-Pharmaceutical Interventions (NPIs) and mobility. First we find the value of \(th\) and then use that \(th\) to find optimal \(shift\) for our analysis. We calculate log likelihood for growth rate model under different \(th\in(0.01,0.02,...,0.3)\). For each \(th\), we run the model for different \(shift\). Using multiple \(lag\) ensures that the model performance is consisted with different values of \(shift\). It also ensures that we do not select \(th\) that performs well by chance. We select \(th\) based on maximum average log likelihood for different \(shift\). We start with threshold value of \(0.01\) and starts increasing. Figure S30 shows that the average log-likelihood for does not change much after \(th=0.18\). We use a \(th=0.20\) in the rest of the paper. We use sensitivity test to check the consistency of the model.
In the growth rate model, we use \(shift\) to estimate the parameter coefficients as shown in Equation S9. After we select \(th\), we use cross validation to find \(lag\) that best fits the data. We use 10-fold cross-validation with Mean Percentage Error (MAPE) as a metric for out of sample data points to select \(shift\) with the best fit. The average MAPE (for 10-fold cross validation) for different lags is shown in Figure S31. \(shift=9\) days shows the best fit with minimum value for average MAPE for 10-fold cross validation.
### S4.2 Model Estimation Sensitivity to \(th\) and \(shift\)
We use sensitivity test to check the consistency of the parameter estimates for different values of \(th\) and \(shift\). The performance of the model remains consistent on changing the values of \(th\) from 0.18 to 0.22 as shown from parameter estimates in Figure S32 (we use a \(shift\) of 9 days). The performance of the model remains consistent on changing the values of \(shift\) from 7 days to 9 days as shown from parameter estimates in Figure S33 (we use \(th=0.2\)). We transform masks as \(\ln\bigl{(}1+mask_{jt}\bigr{)}\).
Figure S32. Parameter Estimates for Growth Rate Model for Different \(t\)\(h\). Horizontal lines represent the upper and lower confidence interval bound for the parameter estimates. We show the results for a lag of 9 days with \(t\)\(h\)\(\in\) [0.18,0.22]. The results indicate that the model is robust to different lags as the parameter estimates show consistency. Vietnam has been kept as the base country (the fixed country effect is 0).
## S4.3 Handling Data Error in Active Cases
In Figure S5, we observe data reporting issue in Norway, Sweden and United Kingdom. We observe that the recovered cases are reported very late in Norway, not reported in Sweden and recorded very in United Kingdom. We use data from Johns Hopkins Resource Center. In our analysis, we use total confirmed cases to find active cases for these three countries. However, this may lead to bias in the results. To check the bias, we run the model without these three countries. The parameter estimates after excluding these countries is shown in Figure S34. In Figure S18, we show the parameter coefficients when \(shift=9\) days and \(th=0.2\).
The results show that the model parameter estimates are robust to exclusion of Norway, Sweden and United Kingdom from the model. However, the model slightly overestimates the coefficient of masks after excluding Norway, Sweden and United Kingdom (as compared to the growth model with data from all the 24 countries). All the three countries are in Europe where wearing face masks is not as common as Asian countries. Moreover, Norway and Sweden (along with Denmark and Finland) have the lowest percentage of people who wear face masks in public in our data set.
## S4.4 Robustness Check for Mobility
In our analysis, we used Google's community mobility report as a measure of social mobility. We used Google's Community reports numbers as a measure of social mobility as android operating devices are more common than iOS, particularly in Asian countries. Also, Apple's Community Mobility Reports record data only when an individual opens Apple Maps. To check the robustness of the combined effect of masks, social mobility and NPIs, we also consider the apple's community mobility numbers as a measure of social mobility. Apple released data for change in trend for driving and walking for all the 24 countries considered in this work. The combined effect after substituting with apple's mobility report is shown in Figure S35. Consistency of the results show that the estimates for the model are robust.
### S4.5 Alternative Specifications
We build two robustness model to check the consistency and reliability of the parameter estimates of the growth rate model. In the first robustness check, we use exponential smoothing as shown in Equation S9-S10. In the second model, we use a control function approach to identify the impact of masks on the spread of COVID-19. We discuss it in details in this Section.
#### S4.5.1 Model 1: Exponentially Smoothed Variates for Growth Rate
In the first specification, we use exponential smoothing to estimate the parameter estimates for masks, NPIs and social mobility. In our base model in Equation S8, growth rate is defined as a function of masks, NPIs, social mobility, trend and testing at a lag of \(lag\) days. On any day \(t\), this model ignores the value of the variates from days \(t-lag+1\) to \(t\) (discussed in Figure S1). In this model, we do not ignore variates between \(t-lag\) and \(t\) and use exponential smoothing average to check the robustness of our model. To check the consistency of the parameter estimates for different transformations of masks (top left), mobility (top right), NPIs (bottom left) and the combined effect of masks, social mobility and NPIs (bottom right) is shown in Figure S36.
We also show the parameter estimates from the growth model for comparison. The results show that the parameter estimates for both the models are close and consistent, thus showing the robustness of the results in Table S6.
In the next model, we use a control function approach to check the robustness of our estimates in Table S6. Control function approach considers an error variable based on an exogenous variable which is not correlated with response variable but is correlated to an instrumental variable. We use number of deaths per thousand people for SARS, H1N1 and MERS CoV ad our instrumental variables.
### S4.5.2 Model 2: Control function Approach to Growth Rate
In the control function approach, we first predict the average value of \(mask_{j,t}\) by using the number of deaths per thousand people in each country by SARS, MERS-CoV and H1N1. Results from predicting masks using disease per thousand people is shown in Table S10 and the parameter estimates are shown in Table S11.
Note that we consider all the available data set (from February 21, 2020 to July 8, 2020) to estimate the coefficients for SARS, H1N1 and MERS. We convert the numbers for deaths due to SARS, H1N1 and MERS into binary variable (1 if the number for a country is greater than the median).
We use \(mask_{jt}\) along with the residuals from prediction model, \(e=mask_{jt}-\widehat{mask}_{j}\), as control function in Equation S9. The results for the combined effect of masks, social mobility and NPIs is shown in Figure S37. We use a \(shift\) of 9 days. We also show the combined effect of masks, social mobility and NPIs without control function (focal model in this paper) to show that the combined effect of masks, social mobility and NPIs estimated in are not appreciably different.
### Lasso Regression
Governments across the world introduced NPIs to enforce social distancing through policies like quarantine, restriction on mass gatherings or closure of schools and businesses. NPIs led to decreased social mobility. For example, there were no major gathering in railway or bus stations as rails and buses were closed down. In our analysis, NPIs and social mobility across different location types are correlated. This may lead to multicollinearity that may lead to unstable coefficients. As a robustness check, we use penalized linear regression (Lasso regression) to shrink the coefficients of highly correlated variates.
Lasso regression can also handle multicollinearity in the data as it shrinks the coefficients to 0 using L1-norm. Lasso regression pushes the coefficients of insignificant variables to 0, thereby introducing sparsity in the model. Lasso regression pushes the coefficients for all the indicators of social mobility except mobility in parks and transit stations. As we observe the correlation between different indicators of social mobility in Table S2, Lasso regression provides a validation for the selection of two (out of 6) indicators of mobility. Coefficients for the growth model are shown in Figure S38. Lasso regression model is given in Equation S14 where \(n\) is sample size, \(\beta\) is a vector of coefficients and \(Y\) is outcome variable. We use 5-fold cross-validation to find \(\lambda\) that best fits the out of sample test data.
\[\beta=\ \arg\min_{\beta\in R^{p}}\left\{\frac{(Y-XB)^{2}}{n}\,+\,\lambda\big{|} \big{|}\beta\big{|}\big{|}_{1}\right\}\] (S14)
Figure S38. Parameter Estimation from Ordinary Least Square and Lasso Regression Model for growth rate. The blue dot represents the coefficients estimated from the Linear Regression model. The error bars represent the upper and lower confidence interval for the coefficients obtained from Ordinary Least Squares. The blue dot represents the coefficients estimated from the Lasso Regression model.
### Selecting Period of Analysis in the Analysis
To filter out initial volatile growth rates during the start of the pandemic, we use a threshold \(th\) as discussed before. We collect data for up to 60 days for a country, from the day it reaches \(th\) percent of peak daily cases in that country. However, the model estimates could be biased and fit to the given set of data points. To estimate the robustness of the model, we estimate the model parameters by collecting data for up to \(D\) days from the day that country reaches threshold \(th\). The results for the combined effect of mask, social mobility and NPIs for different \(D\in\) is shown in Figure S39.
### S4.7 Interpolating Mask Survey Numbers Between Survey Days
We use survey data released by the Institute of Global Health Innovation (IGHI) at Imperial College London and YouGov4 for reported mask-wearing across multiple countries. The data present global insights on people's reported behavior in response to COVID-19. The dataset provides the percentage of population in each country who report to wear a mask in public places. Because these surveys were conducted at an interval of several days, we used linear interpolation to estimate the percentage of the population that would wear masks in public spaces for days when the data were unavailable (Figure S4). To check the robustness of estimates from the model, here we use a quadratic interpolation method to estimate the percentage of population that would wear masks in public spaces for days between surveys. The estimate for stated mask wearing using quadratic interpolation is shown in Figure S40.
The results for the association of mask, social mobility, NPIs and the combined effect of masks, social mobility and NPIs on growth rate for quadratic interpolation is shown in Figure S41. We use a \(shift\) of 9 days and transformed masks as our focal model (\(\ln(1+mask)\)). We also show similar for linear interpolation (focal model in this paper) to show that the parameter estimates are not appreciably different.
Figure S41. Combined effect of Mask, Social Mobility and NPIs under different interpolation for mask survey numbers. We use growth rate model with a \(shift\) of 9 days and consider data for 60 days.
|
193532_file02 | ## Supplementary Appendix
Rahul Kalippurayil Moozhipurath*\({}^{1}\)
(Faculty of Economics and Business, Goethe University Frankfurt\({}^{1}\))
## Date:
05.10.2020
Rahul Kalippurayil Moozhipurath, PhD Student; Faculty of Economics and Business, Goethe University Frankfurt, Theodor-W.-Adorno-Platz 4, 60629 Frankfurt, Germany; Phone: +49-152-1301-0589;
Description of Methodology
In this supplementary section, we outline our methodology. We apply a Fixed-Effects log-linear regression model to estimate the effect of different weather parameters on the number of COVID-19 deaths. This fixed-effects model is closely related to the models proposed by Moozhipurath, Kraft, and Skiera, Moozhipurath, and Kraft as well as Hsiang et al.. This study extends the methodology proposed by Moozhipurath, Kraft, and Skiera, Moozhipurath, and Kraft by exploring all relevant weather factors rather than only UV Index and also includes additional weather factors such as dewpoint, wind speed, wind gust and pressure. In contrast to Moozhipurath, Kraft, and Skiera, Moozhipurath, and Kraft who use lagged values, we use a moving average of weather factors with varying time windows. A log-linear model increases the comparability of the growth rates of COVID-19 deaths across administrative regions because it considers percentage rather than the absolute changes over time. Percentage growth rates are more comparable across administrative regions rather than the absolute ones.
Our model isolates the effect of weather parameters from region-specific time-constant factors via the fixed effects. These time-constant factors consist of the location of the administrative region (as measured by its latitude and longitude) and other population factors such as demographics, age composition, gender, genetics, culture, location. They also account for mobility & lifestyle of the population, the prevalence of co-morbidities, obesity and other chronic diseases and skin pigmentation. Thus it controls for factors which may be associated with the severity of COVID-19. These fixed-effects further capture time-constant diet-related factors such as the proportion of vegans and vegetarians, consumption of dietary supplements, fortified foods and diets rich in vitamin D, which might affect the growth rates of COVID-19 deaths. Furthermore, they also capture the socio-economic situation of a population in an administrative region which are likely to remain reasonably stable over our observation period.
Further, the methodology also partially controls for the increasing pressure on the healthcare system in an administrative region over time. We do so by flexibly controlling for the time passed by, since the first reported case of COVID-19 in each administrative region. Importantly, this factor also helps to partial out any linear or quadratic change of growth rates over time that is similar across administrative regions. Therefore, the model isolates the effect of the weather factors from the typically observed exponential-shaped or S-shaped curve, which are often found in the cumulative COVID-19 daily deaths over time.
The fixed-effects also capture time-constant behaviours of individuals such as recurring habits or mobility of individuals. These time-constant behaviours might affect the likelihood of exposure to weather factors (e.g., walking to work, outdoor exercises, outdoor activities related to employment). Yet, the fixed-effects do not capture time-varying behaviours of individuals such as their varying travel patterns and thus varying exposure to weather factors.
Because weather plausibly affects deaths several weeks later, we use the moving average of the previous 42 days of the weather factors in our model. The results did not change substantially, even after increasing or decreasing the time windows. We derive the following model in equation to explain the number of COVID-19 deaths:
\[D_{i,t}=D_{i,t-1}\times e^{\gamma+W_{i,t}\beta_{W}+c_{i,t}\beta_{c}+u_{i}+e_{i, t}} \tag{1}\]
\(D_{i,t}\) represents the cumulative COVID-19 deaths in the administrative region \(i\) at time point \(t\) (in days). \(D_{i,t}\) is related to the explanatory factors via an exponential growth model on the right-hand side of the equation in line with Moozhipurath, Kraft, and Skiera and Moozhipurath, and Kraft. The exponential growth model flexibly allows different shapes of the cumulative COVID-19 deaths. The exponential growth model that we use in the study consists of five explanatory parts as shown below.
1. \(\gamma\) represents the daily growth rate of COVID-19 deaths from \(D_{t,t-1}\) to \(D_{t,t}\) that is independent of the weather variables of this model. \(\gamma\) controls for virus-specific attributes like its transmission characteristics such as basic reproductive rate R\({}_{0}\) combined with its lethality, similar to Moozhipurath, Kraft, and Skiera and Moozhipurath, and Kraft.
2. \(W_{i,t}\) represents the 42 days moving average of weather factors including ultraviolet index (UVI), precipitation, cloud index, ozone, visibility level, humidity level, the maximum and the minimum temperature for a state \(i\) at day \(t\). \(\beta_{W}\) reflects the effect of weather factors.
3. \(C_{i,t}\) stands for the set of control variables. In the main model specification, this set consists of the time passed by since the first reported COVID-19 infection for an administrative region \(i\) at day \(t\). In the specification for the robustness checks, this set also includes the moving average of additional weather variables. The vector \(\beta_{C}\) represents the effect of the control variables in the equation.
4. \(u_{i}\) represents time-constant region-specific factors influencing the growth rate of cumulative COVID-19 deaths (e.g., time-constant region-specific factors include population factors such as demographics, age composition, gender, genetics, culture, location, mobility, lifestyle, dietary pattern, dietary supplements, the prevalence of comorbidities or other chronic diseases). The fixed effects isolate the weather factors from this time-constant state-specific factor, similar to Moozhipurath, Kraft, and Skiera.
5. \(\epsilon_{i,t}\) consists of all the remaining factors which are not identified but also may have an effect on the cumulative daily COVID-19 deaths (i.e., all non-linear differences of growth rates concerning time as well as the region-specific linear differences of growth rates concerning time), similar to Moozhipurath, Kraft, and Skiera1. These unidentified factors could be the declining number of people who could potentially become infected or contagious due to acquired immunity, lockdowns in an administrative region, mutation of the virus in an administrative region over time, systematic false-reports of the dependent variable by an administrative region1,2.
An appropriate transformation of equation results in the estimable equation as given below.
\[\Delta\ln(D_{i,t})=UVI_{i,t}\beta_{UVI}+C_{i,t}\beta_{C}+u_{i}+ \gamma+\epsilon_{i,t} \tag{2}\]
If \(\gamma\) and \(u_{i}\) are correlated with past or future values of the weather factors, then the estimation of coefficients of equation will be inconsistent. Therefore, we use a fixed-effects model that isolates the weather factors from those time-constant factors via the error correction term.
Equation shows why we can only use those observations where cumulative COVID-19 deaths are greater than zero. We show an overview of how many observations per administrative region in Table S2.
## 2 Interpretation of Coefficients for Moving Average Variables
The structural model of equation consists of 42 days moving average of the weather factors that are being studied. Therefore, the model outlines the impact of a consistent unit change in each of these weather factors (for example UVI) over this moving average window (e.g., 42 days) on the daily COVID-19 deaths growth rates after 42 days. We define this effect as the long-run effect. The linearity of the model implies that the short-run effect (e.g., the effect after 14 days) of the weather factors (e.g., UVI) on the growth rates of daily COVID-19 deaths equals the number of days of the considered period (e.g., 14 days) divided by 42 days (e.g., one third) times the long-run effect.
## 3 Identification of Effect of Weather Variables
Moozhipurath, Kraft, and Skiera1outlines the key assumption that is required to identify the causal effect of the UV Index on COVID-19 deaths. The key assumption required to identify the causal effect of the relevant weather factors is similar to that of Moozhipurath, Kraft, and Skiera1, as UVI is one of the weather factors and has similar characteristics to the remaining weather factors. As such, a major threat to identification is the potential presence of a spurious correlation via time trends which could affect the weather factors as well as the growth rates of daily COVID-19 deaths. Therefore, we have to assume that all weather factors are uncorrelated to \(\epsilon_{t,s}\) at all points in time conditional on the region-specific time-constant factors and the inclusion of the time trends of the model. Given the unavailability of variation of governmental measures across regions in Brazil, we are unable to control for such measures. However, because the weather factors are independent of the governmental measures, not controlling for governmental measures should not affect the consistency of the estimates.
## 4 Model Selection to Identify the Effect of Weather
Variables on the Cumulative COVID-19 Deaths
We estimate equation for different time windows of the moving averaged weather factors from 1 to 9 weeks. We do not observe any substantial changes concerning the size or the statistical significance of the estimates of weather factors.
## 5 Robustness Checks
Table S1 outlines the estimation with additional moving averaged weather factors such as dewpoint, pressure, wind speed and wind gust. We find consistent results across these model specifications as shown in Table S1. We also report the number of observations per administrative region and the latitude and longitude information which is used to collect the weather data per administrative region in Table S2.
## 6 Supplementary Tables
## Table S1: Effect of Weather Factors on Cumulative COVID-19 Deaths in Brazil (Robustness)
\begin{tabular}{l c c} \hline & Model 1 & Model 2 \\ Dependent Variable & COVID-19 Deaths & CFR \\ UVI & -0.062*** (-5.72) & -0.048*** (-5.14) \\ Precipitation & 0.029 (0.33) & 0.25 (0.34) \\ Cloud Index & -0.168* (-2.32) & -0.14* (-2.56) \\ Ozone & -0.0020 (-1.13) & -0.0028 (-1.70) \\ Visibility Level & -0.0012 (-0.11) & 0.00078 (0.07) \\ Humidity Level & (0.0027 (0.42) & -0.0024 (-0.39) \\ Temperature Max & -0.0079 (-0.61) & -0.014 (-1.19) \\ Temperature Min & -0.0018 (-0.11) & -0.006 (-0.36) \\ Dewpoint & -0.0065 (-0.23) & 0.011 (0.39) \\ Pressure & 0.0090+ (1.87) & 0.0025 (0.39) \\ Windspeed & -0.013 (-0.51) & 0.014 (0.55) \\ Windgust & 0.011 (1.46) & 0.000084 (0.01) \\ \hline \end{tabular}
## Control Variables
\begin{tabular}{l c c} \hline Time Trend of Growth Rate & Region-specific Linear and & Region-specific Linear and \\ & Squared Time Trends & Squared Time Trends \\ \hline Time Window for Moving & 42 & 42 \\ Averages in Days & 12 (+27 FE + 54 TRSE) & 12 (+27 FE + 54 TRSE) \\ Number of Observations & 3,882 & 3,882 \\ Number of Administrative & 27 & 27 \\ Regions & 32.90\% & 9.67\% \\ \hline Note: +: p \(<\) 0.10, *: p \(<\) 0.05, **: p \(<\) 0.01. t-statistics based on robust standard errors in \\ parentheses. FE stands for region fixed-effects, TRSE stands for time region-specific effects. \\ \hline \end{tabular}
\begin{table}
\begin{tabular}{c|c|c|c|c|c|c|c} \hline
## Region** & **Obs** & **Lat** & **Long** & **Region** & **Obs.** & **Lat** & **Long
\\ \hline AC & 139 & -9.05 & -70.53 & PB & & & \\ Acre & & & & Paraiba & 140 & -7.12 & -36.72 \\ \hline AL & 146 & -9.66 & -36.65 & PE & & & \\ Alagoas & & & & & & \\ \hline AM & 144 & -4.48 & -63.52 & PI & & & \\ Amazonas & & & & & Piaui & 139 & -7.70 & -42.50 \\ \hline AP & 139 & 1.35 & -51.92 & PR & & & \\ Amapá & & & & & Paraña & 147 & -24.48 & -51.81 \\ \hline BA & 148 & -12.29 & -41.93 & RJ & & & \\ Bahia & & & & Rio de Janeiro & 154 & -22.28 & -42.42 \\ \hline CE & 142 & -5.33 & -39.72 & RN & & & \\ Ceará & & & -39.72 & Rio Grande & 146 & -5.68 & -36.48 \\ & & & & Do Norte & & \\ \hline DF & & & & & & \\ Distrito & 148 & -15.78 & -47.80 & RO & & & \\ Federal & & & & & Rondónia & 139 & -10.94 & -62.83 \\ \hline ES & & & & & & & \\ Espirito & 144 & -19.57 & -40.17 & RR & & & \\ Santo & & & & & Roraima & 137 & 2.14 & -61.36 \\ \hline GO & & & & & & & \\ Goias & 146 & -15.93 & -50.14 & RS & & & \\ \hline MA & 138 & -5.21 & -45.39 & SC & & & & \\ Maranhão & & & & & Santa Catarina & 146 & -27.06 & -51.11 \\ \hline MG & & & & & & & \\ Minas Gerais & 147 & -18.53 & -44.16 & & SE & & \\ & & & & & & \\ \hline MS & & & & & & & \\ Mato Grosso do Sul & 143 & -19.59 & -54.48 & SP & & & \\ & & & & & São Paulo & & \\ \hline MT & & & & & & & \\ Mato Grosso & 139 & -12.21 & -55.57 & TO & & & \\ & & & & & Tocantins & & \\ \hline PA & & & & & & & \\ Pará & 140 & -4.75 & -52.90 & & & & \\ \hline \multicolumn{7}{c}{Total Number of Observations} & 3,882 \\ \hline \end{tabular}
\end{table}
Table S2: Number of Observations (Obs.), Latitude (Lat.) and Longitude (Long.) of Administrative Regions Used in Analysis
|
194241_file02 | ## Patient Recruitment and Sequencing
A total of 13,451 patients were recruited from 24 regional genetics services throughout the United Kingdom and Republic of Ireland as previously described. Sequencing of families and alignment to the human reference genome (GRCh37) with bwa was performed as previously described but is repeated here in brief. Genomic DNA from all samples (probands and recruited parents, if available) recruited to DDD were fragmented to an average size of 150bp and used to create Illumina PCR-amplified paired-end libraries. Libraries were then hybridized to one of two SureSelect RNA baits (v3 or v5), captured, amplified and submitted for 75bp paired-end sequencing on an Illumina HiSeq following manufacturer instructions. All samples were sequenced to a mean depth of 90x across primary bait capture regions. Following sequencing, all samples were aligned with either bwa aln or mem to version the 1000 Genomes Project phase 2 reference (vers. hs37d5) and processed with IndelRealigner and Base Quality Score Recalibration (BQSR) available as part of the GATK resource bundle (version 2.2).
### InDelible Variant Calling Protocol
To ascertain the variants reported in this manuscript, we applied InDelible to all 13,451 recruited probands, but excluded 13 probands from further analysis due to excessive runtime, leaving 13,438 probands. This includes probands sequenced with both parents (trios, n = 9,848) or with one or both parents absent (non-trios, n = 3,590). As this was the first dataset analyzed with InDelible, we ran all steps while also training the random forest.
All probands were first run through the "Fetch" and "Aggregate" steps with default settings to identify 353,313,108 redundant split read clusters. Next, to train our random forest to perform split read cluster quality control, we randomly selected 2,000 non-redundant sites across all probands from the output of the aggregate step. We then visually inspected all 2,000 sites using the Integrative Genomics Viewer9 to build a labelled truth set of variants for training. These 2,000 manually curated sites were then provided as input to the "Train" subcommand of InDelible at various test and training sizes (_k_). We ultimately decided on a probability (_p_) of being a true variant p > 0.6 at \(k\) = 75 as a reasonable value for filtering following cross-validation (Supplementary Figure 4). We then used the trained random forest to score all sites identified with the probability of being a true variant with the InDelible "Score" command. Training data used for this study is available as part of the GitHub repository provided in the Data and Code Availability section of the main text.
We next provided all output files of the "Score" command for all probands as input to the "Database" command with default settings to build the allele frequency database required as input to the "Annotate" command. All probands and split read clusters were subsequently processed with the "Annotate" and "denovo" commands with default settings. Following initial calling, we performed additional quality control to generate our final set of putatively clinically relevant variants. Split read clusters were retained at this step based on the following criteria:
1. Breakpoint frequency < 4x10-4
2. Average MAPQ >= 20
3. Number of split reads >= 5
4. Proportion of split reads as a factor of coverage >= 0.1 (i.e. sr_total / coverage)
5. Found within coding sequence (here defined as exons >=10bp)
6. Intersected a gene with a known monoallelic, X-linked, or hemizygous mechanism with a loss of function or dominant negative consequence based off of the DDG2P database10
7. < 2 split reads in either the maternal or paternal sample if available
8. < 50% of reads with both ends split (i.e. both 5' and 3' ends with an "S" tag in the cigar string) AND
1. <= 10% of reads with both ends split OR
2. > 10% of reads with both ends split while also having a valid bwa alignment (see "Database" step)A script which performs this filtering is included at the InDelible GitHub repository (see main text Data and Code Availability). Calling and subsequent filtering left a remainder of 354 split read clusters. Split read clusters identified at the same locus within the same proband were subsequently manually merged (marked as "OTHERSIDE" in Supplementary Data 1), leaving a remainder of 260 variants, with the 5' breakpoint retained for final reporting.
Via visual inspection of read alignments, we next determined whether variants were likely to be real in the proband and inherited from a parent where possible. Variants with gnomAD non-Finnish European allele frequency >= 1x10-4 based on Karczewski et al. (variants <= 50bp) or Collins et al. (variants > 50bp) were then filtered out from further analysis (Figure 2A, Supplementary Data 1). This approach is imperfect - as the variant size range that InDelible detects is under-represented, some variants may be common in the population but may not be represented in these reference datasets. To determine the sensitivity of InDelible for DDD variants previously reported as potentially pathogenic, InDelible variants were intersected with previously reported DDD variants and with CNVs called from read-depth analysis of DDD ES data (Supplementary Data 1). Previously known variants, false negative/positive variants, variants with high DDD/gnomAD allele frequency, variants that do not actually intersect a known DD gene, and variants located in regions difficult to interpret clinically (e.g. intron or 5'/3' UTR) are annotated as such in Supplementary Data 1.
To identify a set of rare inherited variants that could plausibly be associated with patient phenotype, we repeated our above filtering as for _de novo_ variants except we restricted to variants found only in a single proband (e.g. singletons) without filtering for parental split read support. This approach identified a total of 211 breakpoints which, after collapsing identical loci as above, left a total of 145 variants for downstream analysis. We next excluded variants based on likely association with patient phenotype by removing:
* In-frame InDels inherited from an unaffected parent.
* Primarily non-coding variants.
* Variants found in patients with a more plausible variant already reported.
* Variant types of uncertain consequence such as processed pseudogenes and duplications which partially overlap coding sequence.
* Presence in any control individuals in the gnomAD database.
* Likely _de novo_ variants already ascertained by InDelible and/or other approaches This filtering left a total of 17 variants, of which 7 were already identified by an alternate approach and returned to referring clinicians. The remaining 10 variants were annotated for contribution to patient phenotype, returned to referring clinicians where relevant, and provided in Supplementary Data 3.
## Benchmarking InDelible Runtime and Memory
To benchmark InDelible, we collected usage statistics provided by the standard output of the Platform Load Sharing Facility (LSF) at the Wellcome Sanger Institute. Metrics were generated during the course of processing the 13,438 DDD individuals through the standard InDelible SV discovery pipeline. The compute cluster used consists of 105 nodes with 32 8-core 2400Ghz CPU AMD Opteron Processors with 256Gb of memory each. To generate the extrapolated curve seen in Supplementary Figure 2C, we randomly sampled individuals 100 times at each sample size to generate an average expected runtime. On average, InDelible took 92.9 CPU minutes and a maximum of 1.2Gb of memory to run one sample with mean exome-wide coverage of 90x from aligned CRAM file to reporting of candidate diagnostic variants (Supplementary Figure 2). Considering that most users would likely be utilizing InDelible to analyse multi-sample datasets, we also calculated extrapolated runtimes via down-sampling of our own DDD runtimes for datasets composed of between 1-10,000 individuals (Supplementary Figure 2).
## PCR Validation
To validate all 54 variants returned to clinicians via the DECIPHER platform, we used PCR. For small variants (<=50bp) we extracted the surrounding 300bp and used Primer313 with GC clamp turned on to automatically design an initial set of primers. Following initial design, we confirmed specificity with UCSC _in silico_ PCR. For larger variants, we manually designed primers 5' and 3' of the predicted variant breakpoint and likewise confirmed specificity with UCSC _in silico_ PCR. PCR was carried out using REDAccuTaq(r) LA DNA Polymerase (Sigma); 80ng of genomic DNA extracted from blood or saliva was amplified in the presence of 0.4 uM of each primer and 1 unit of REDAccuTaq. We used the following cycling conditions: 30s at 98\({}^{\circ}\)C followed by 6 cycles of (15s at 94\({}^{\circ}\)C, 45s at 60\({}^{\circ}\), and 60s at 68\({}^{\circ}\)C) and 24 cycles of (15s at 94\({}^{\circ}\)C, 45s at 55\({}^{\circ}\), and 60s at 68\({}^{\circ}\)C). For longer variants (i.e. \(\geq\)1Kbp) elongation time was changed from 45s to 480s. A final elongation step was carried out for 30m at 68\({}^{\circ}\)C. PCR products were visualized on a 2% or 4% agarose gel for short and long products, respectively. Following PCR, all reactions were PCR purified using a standard exosap protocol and submitted for capillary sequencing. Following sequencing, traces were examined for quality and BLAT and manual inspection used to check for presence of the predicted variant. For 28 variants we were unable to obtain conclusive validation results due to too little DNA for PCR (n = 3), failed capillary sequencing (n = 8), failed primer design (n = 6), or failed PCR (n = 11). We were unable to allocate resources during the COVID-19 pandemic to validate 3 variants prior to returning them to referring clinicians.
### Analysis of _Mecp2_ Carrier Phenotypes
For proband phenotypes reported in Figure 3B, we first collated all HPO terms as reported by the referring clinician for all probands with an InDelible-ascertained _MECP2_ variant. We then condensed these terms into 19 super-HPO groups which group related HPO terms into a more broad phenotype (e.g. the terms long toe and long fingers condense into the digital anomalies super-HPO group). Original HPO terms for all probands and the super-HPO terms to which they were assigned are available in Supplementary Data 2.
### Proportion of PTVs Called By InDelible
To determine the proportion of PTVs within a dataset attributable to InDelible as shown in Figure 4, we queried variants identified in DDD probands sequenced as a trio from three different sources: (i) GATK called SNVs and short InDels \(\leq\)100bp from DECIPHER for DDD patients (n = 1,140 variants), (ii) XHMM called CNVs from CNV data generated for DDD probands (unpublished; n = 128 deletions), and (iii) MELT called MEIs from Gardner et al. that were plausibly associated with patient symptoms (n = 4 MEIs). For all variant types, we retained only _de novo_ variants which overlapped the same set of DD genes used for InDelible ascertainment. For InDelible, we considered the 56 _de novo_ variants reported in Supplementary Data 1, regardless of novelty. InDelible Variants were then matched to each of the three other callsets, first by exact coordinate/sequence match and then by subsequent manual confirmation. Variants queried for the purpose of this exercise were also used to catalogue previously reported _MECP2_ variants.
## Benchmarking InDelible using Genome in a Bottle Consortium Data
To benchmark InDelible against GATK and Manta, we downloaded ES data for sample HG002 (Ashkenazi proband sample) provided by the Genome in a Bottle (SIAB) Consortium from the NCBI FTP site ([https://github.com/genome-in-a-bottle/giab_data_indexes](https://github.com/genome-in-a-bottle/giab_data_indexes)). We then acquired variant benchmarks for small variants from Zook et al.16 and structural variants from Zook et al.17 and limited each to variants with a REF/ALT size difference >=1bp (i.e. InDels) and at least one breakpoint within padded (i.e. +-100bps) exome bait regions used for original whole exome sequencing (SureSelect coordinate files acquired from Agilent). We then ascertained variants from HG002 using InDelible, GATK, and Manta. For InDelible, we used the "complete" pipeline with default settings. Filtering was performed identically to that outlined for _de novo_ variant discovery above, except we did not filter variants with high allele frequency, located outside coding sequence, or outside of known monoallelic DDG2P genes. For GATK we first ran HaplotypeCaller to generate a gVCF and then ran GenotypeGVCFs on the resulting output with default settings to generate a final output of genotyped sites. Default settings were used for GATK except we provided the SureSelect bait regions outlined above during the HaplotypeCaller step. We then used bcftools18 to filter sites with GQ < 20 and DP < 7 to generate a final list of sites for benchmarking. To identify structural variant breakpoints with Manta, we first ran configManta.py with default settings other than providing ES baits with '--callRegions' and setting the '--exome' flag to generate a Manta workflow file. We then ran the resulting 'runWorkflow.py' command.
We then converted all three callsets to bed format and used a custom python script to ask if any variant from HG002 as ascertained by the GIAB consortium was found within 100bps of a variant called by any of the three callers to calculate recall rate. All variants/breakpoints that were not within 100bps of a true variant were coded as false positives (Supplementary Figure 3). To calculate recall relative to InDelible, we quantified the number of variants >20bps in length recalled by InDelible, GATK, and Manta separately for deletions and insertions/duplications. We then divided calculated values for GATK and Manta by the value for InDelible as presented in the main text.
## Supplementary Figures
### Supplementary
### Feature importance from the InDelible random forest.
Shown is the mean decrease in accuracy given by random forest for each of the 17 features we used to estimate the probability of a split read cluster being a true positive variant. Error bars represent standard deviation of mean decrease in accuracy for 10 cross-validated random forests at k = 75 (Supplementary Figure 4) for the final forest generated by our active learning model (see Supplementary Methods). Features which quantify the number of reads with clipped sequence length less than/greater than 5bp (e.g. Total number of SRs \(\geq\) 5bp) represents the default setting of InDelible and can be adjusted by the end user during random forest training. Sequence entropy for all categories is calculated as in Schmitt and Herzel1.
## Supplementary
## Benchmarks of InDelible**. Using real data from the DDD study, we benchmarked the InDelible algorithm. Average memory use in megabytes (**A**) and CPU time in minutes (**B
Using the CPU times in (**B**), we extrapolated runtimes for studies of various sizes by randomly sampling the number of individuals shown on the x-axis (**C**).
## Supplementary
## InDelible benchmarks across the allele frequency spectrum.** To benchmark InDelible, we called variants using InDelible, GATK, and Manta in the genome of an Ashkanazi Jewish individual characterised for both small InDels and large structural variants by GIAB. (**A**) Recall rate of all three callers for deletions (left side of plot) and insertions/duplications (right side of plot). Each point represents the proportion of variants in the size bin depicted on the x-axis. Size-ranges for deletions and insertions/duplications are right-open and left-open, respectively. Variants with an absolute size <=20 base pairs were excluded from this analysis. Despite GATK generally being designed to identify variants <100bps in length, for a limited set of variants GATK was able to ascertain at least one breakpoint for some larger variants (i.e. > 100bps), albeit and as expected with incorrect size estimates. (**B
False positive rate for all three callers as a function of total number of sites identified by each caller. We note that these experiments likely drastically overstate the FP rates of all callers - GIAB gold-standard calls were based on a merge of several different technologies and variants that are readily identifiable with long-read sequencing (e.g. Pacific Biosciences) may be very difficult to identify with short-read based approaches which query ES data.
## Supplementary
## Filtering split read clusters in InDelible with active learning.** To estimate the probability of a variant being real, we utilized an active learning approach (see Supplementary Methods). (**A**) Cross validated ROC curves at various inputs of \(k\) as well as for a traditional machine learning model where data was split into 50% training and test data without active learning. (**B**) Total number of original redundant split read clusters in 0.05 p-value bins. By default, InDelible filters all split read clusters with a probability of being a true variant <0.6 (red dashed line). (**C
Cumulative density plot of the redundant clusters from (**B**).
## Supplementary
### Breakpoint resolution of InDelible as a factor of allele frequency and coverage.
Lower-left plot represents the proportion of sites within each bin on the X (cluster frequency - proportion of individuals a given site has been identified in) and Y (cluster mean coverage - mean sequencing coverage within individuals with a given cluster) axes which have resolved variant type and/or breakpoints. The lighter the shade of blue, the higher proportion of sites within that bin that have resolved breakpoints. Marginal histograms represent the total number of clusters within each bin on the X and Y-axes.
## Supplementary
## Supplementary
Other Unclassified Repetitive Ins. (1.88%)
SVA MEI Ins. (0.30%)
Alu MEI Ins. (2.16%)
L1 MEI Ins. (1.47%)
Translocation/Seg. Dup. (9.65%)
Complex-DUP/INS (8.03%)
Complex-DEL/INS (10.68%)
Simple Ins. (0.17%)
Duplication (30.08%)
## Variant types identified by InDelible.
InDelible identifies a wide range of genetic rearrangement classes using a re-alignment of split read sequences to the reference genome. Each slice of the pie represents the proportion of breakpoints exhibiting the annotated structure among sites that have both 5'/3' breakpoints resolved or align to a known human repeat element (total n = 199,932 breakpoints). Translocations and segmental duplications (Translocation/Seg. Dup. above) are grouped together as discerning between these variant types is difficult with available sequencing data.
## Supplementary
## Supplementary
## Proportion of in-frame versus out-of-frame insertions for trio versus non-trio data.
Shown is the proportion of variants \(\leq\)50bp which are in-frame (blue) or out-of-frame (orange) separated by whether the variant was called in a proband sequenced with/without parental samples.
## Supplementary Tables
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194639_file03 | ## Figure S1 Genomic distribution of methylated and hydroxymethylated sites
We classified loci as methylated/hydroxymethylated vs. non-methylated/hydroxy, and genomic features as present vs. absent. Using these 2 by 2 tables as input for the colocalization tests described below, we calculated the odds ratios that indicated whether sites in the studied feature were more likely to methylated/hydroxymethylated compared to sites not in this feature. We plotted the odds ratio on the x-axis. Thus, a value of 1, indicated by the dashed lines in the figure, means no enrichment of methylated/hydroxymethylated sites at that feature. The full list of tested features is provided in Supplemental Table S#.
### Cell type specific MWAS
It is practically not feasible to isolate all common cell types also and perform methylation assays for each type for all study samples. We therefore used a statistical approach to perform cell type specific MWAS. Thus, we first estimated the cell type proportions for each sample using Houseman's method\({}^{4,5}\) and then, following Shen-Orr et al.\({}^{6}\), used the estimated cell type proportions to test the null hypothesis that mean methylation of a given site is equal for AUD cases and controls for each cell type.
In the notation to describe the statistical approach, we indicate constants/parameters with lower case letters and vectors/variables with upper case letters. Furthermore, subscript \(i\) is used for the \(n\) subjects and subscript \(j\) for the \(m\) methylation sites. Note that whereas analyses in step 1 use all methylation sites for a single subject concurrently, step 2 uses all subjects for a single site concurrently. This is the reason that formulas for step 1 only have subscript \(i\) (all sites are represented by vectors) and those for step 2 only have subscript \(j\) (all subjects are represented by vectors).
The amount of methylation in bulk tissue is a weighted sum of the average methylation levels for each cell type with weights being equal to the proportion of cells of each type. For example, if we know the methylation levels for each of the \(c\) = 1..\(n_{c}\) cell types we can calculate bulk methylation levels as follows:
\[\overline{Y}_{i}^{\mathit{bulk}} = \sum_{c = 1}^{n_{c}}p_{i}^{c}M_{i}^{c}\]
To avoid performing cell counts forall subjects in the study, the cell type proportions \(p_{i}^{c}\)are estimated using "reference" methylomes generated with DNA from sorted nuclei/cells using the following regression model:
\[Y_{i}^{bulk}=\sum_{c=1}^{n_{c}}p_{i}^{c}R^{c}+E_{i}\]
Thus, the methylation levels assayed in bulk tissue for subject \(i\) is again a weighted sum of the average methylation levels in the cell type specific methylomes but we replace \(M_{i}^{c}\)with the reference samples. The weights or cell type proportions are the estimated coefficients of the regression model. The reference methylomes will not perfectly match the true cell type methylation profiles for subject \(i\) and reference methylomes may not be available for rare cell types. The model account for that through estimated residuals.
In the second step we use the estimated cell type proportions to fit a regression model that allows us to test the null hypothesis that cell type means are the same in cases and controls (_H_0:_m_j(_AUD_) =0):
\[Y_{j}^{bulk}=\sum_{c=1}^{n_{c}}m_{j}^{c}p^{c}+\sum_{c=1}^{n_{c}}m_{j(AUD)}^{c }(AUD\times P^{c})+E_{j}\]
The _n_x1 vector AUD is coded 1 for cases and 0 for controls where parameter _m_j(_AUD_) represents the case-control difference for cell type \(c\) and site \(j\). _Ei_ is a _n_x1 vector with residuals. Thus, the bulk methylation levels for site \(j\) are regressed on the cell type proportions \(P^{c}\). This will estimate the mean for each cell type in controls \(m_{j}^{c}\). The effect of the product AUDx \(P^{c}\), that is zero in controls but \(m_{j(AUD)}^{c}\) in cases, captures the case control difference for cell type \(c\).
### Cross-tissue Overlap and Colocalization Testing
We used circular permutations in the cross-tissue overlap tests to account for dependency between sites. In other words, as the permutations are performed on a per site basis (i.e., individual mCG or hmCG sites), they account for gene size (i.e., genes with more CpGs are more likely to be among the top results in the permutations) and correlations between neighboring sites (e.g., linkage disequilibrium). To perform permutations of overlap between datasets we map the two datasets to each other based on chromosomal location. Next, the P-values for each site are used to cross-classify each mapped marker in the two datasets as being in the top or bottom. Based on the resulting 2 by 2 tables as input, we test the null hypothesis that the enrichment odds ratio equals 1. To perform these tests, we use circular permutations that shifts the mapping of the two datasets by a single random integer in each permutation. This approach to generate the empirical test statistic distribution under the null hypothesis preserves the correlational structure of the data. Multiple thresholds can be specified to define "top findings" (i.e., for our cross-tissue analyses we used the top 0.1%, and 0.5%). To account for this "multiple testing", the same thresholds are used in the permutations where the test statistic distribution under the null hypothesis is generated from the most significant (combination of) thresholds.
For co-localization analyses such as those involving genomic features and chromatin states, we used a site-based test (i.e., individual mCG or hmCG sites), as these features may not necessarily involve genes. Tests were performed using our R package shiftR ([https://cran.rproject.org/web/packages/shiftR/index.html](https://cran.rproject.org/web/packages/shiftR/index.html)) that performs circular permutations through bitwise operations. shiftR was used as these bitwise operations are faster for CpGbased tests. We first mapped the CpGs of MWAS to the other data set based on chromosomal location. Next, the state values are used to cross-classify each mapped site in the two data sets as being in the top or bottom. Based on the resulting 2 by 2 tables as input, shiftR tests uses Cramer's V to test the null hypothesis that the enrichment odds ratio equals one. To perform these tests, shiftR uses circular permutations. Specifically, through these fast, bitwise operations, it shifts the mapping of the two data sets by a single random integer in each permutation. If multiple thresholds are specified to define "top findings", the same thresholds are used in the permutations where the empirical test statistic distribution under the null hypothesis is generated from most significant (combination of) thresholds.
For the co-localization analyses, we tested whether the overlap across blood and brain colocalized with basic genomic feature tracks that were downloaded from the UCSC Browser Annotation Database and Roadmap Epigenomics Project chromHMM 15-state chromatin state consensus tracks. All co-localization analyses were performed using shiftR using 100,000 permutations. For the chromatin state colocalization analyses, we used Quiescent/Low as the reference state. To study overlap between the 15 histone states, we used the E073 track from the Dorsolateral Prefrontal Cortex for the enrichment testing.
## Quality control of the transcript expression data
After read alignment with HiSat2 there was an average of 63.4 million reads per sample (S.D. = 6.3 million). Reads were assembled into transcripts and quantified using StringTie. Transcripts were then compared against known transcripts and genes using gffcompare utility of StringTie. Further quality control was conducted using custom R scripts. In total, RNA-seq data was obtained from the same 50 samples for which we generated methylation and hydroxymethylation.
After assembly, there were 227,442 unique transcripts of which 195,811 (86.1%) were located in known transcripts. After removing unknown transcripts and retaining those on the autosomal chromosomes, 188,192 transcripts remained. Following similar quality control procedures to what was used in Gtex (cite), we retained transcripts that had TPM > 0.1 in at least 20% of the samples, greater than or equal to 5 reads per sample, and average TPM > 1. This left 40,090 high quality transcripts for analysis. Transcripts were then logged plus one and quantile normalized.
## Replication Sample: Great Smokey Mountain Study
## Participants
The Great Smoky Mountain Study (GSMS) is an ongoing, prospective longitudinal, representative study of children in 11 predominantly-rural counties in the southeast United States, which began in 1993. Three cohorts of children, age 9 to 13 years, were recruited resulting in N=1,420 participants. Details about the GSMS design, recruitment and data collection are published elsewhere. As part of a larger methylation study on childhood and young adult exposures, 525 participants were selected that were 9-21 years of age and had a bloodspot taken at the time of assessment available. Of the 525 participants, 412 had bloodspots included from additional older time points (age 21 years or older). Only data from participants that were 18 years of age or older were used in this study to be comparable to the discovery sample. Participants provided their informed consent and the current study was approved by Institutional Review Boards at Duke University and Virginia Commonwealth University.
Participant substance involvement was assessed during an in-person interview. At each interview assessment the participant completed a full structured clinical interview about substance involvement using the Young Adult Psychiatric Assessment (YAPA). The substance use module of the YAPA included assessments of DSM-IV abuse and dependence. AlthoughDSM-5 alcohol use disorder (AUD) symptoms of craving and withdrawal were not part of the DSM-IV abuse or dependence diagnostic criteria, these data have been collected since the start of GSMS is 1993. Further details about the study sample, and the demographic and clinical characteristics of participants used for the present study are in Table S17.
### Assaying the Methylome
The same MBD-seq approach, which was previously used to generate mCG data for the discovery blood samples was also used to generate mCG data for the independent replications samples. Specifically, we used an optimized protocol for the MBD-seq approach that achieves near-complete coverage of the 28 million possible mCG sites at a cost comparable to commonly used methylation arrays that assay only 2-3% of all mCG sites. Briefly, genomic DNA was sheared into 150 bp fragments using the Covaris(tm) E220 focused ultrasonicator system. We performed enrichment with MethylMiner(tm) (Invitrogen) to capture the methylated fraction of the genome. Next, dual-indexed sequencing library for each methylation capture was prepared using the Accel-NGS(r) 2S Plus DNA Library Kit (Swift Biosciences) and sequenced on a NextSeq500 instrument (Illumina). The sequence reads were aligned to the human reference genome (hg19/GRCh37) using Bowtie2. Following quality control, libraries were pooled in equal molarities and sequenced with 75 cycles (i.e., 1 x 75 base pair reads) on a NextSeq500 instrument (Illumina).
### Data Processing and Methylation Score Calculation
As in the discovery, data quality control and analyses were performed in RaMWAS and followed the same steps used for the discovery sample. Methylation scores were calculated by estimating the number of fragments covering the CpG using a non-parametric estimate of the fragment size distribution. These scores provide a quantitative methylation measure for each individual at that specific site.
## Methylome-wide Association Study in Whole Blood
The methylome-wide association study (MWAS) in whole blood was performed using multiple regression analyses with four sets of covariates. First, we regressed out assay-related variables (i.e., potential technical artifacts) such as sample batches and peak. Second, we regressed out biological sex, age, age squared, race and regular cigarette use. Third, to avoid false positives due to cell type heterogeneity in whole blood, we regressed out cell type proportions as estimated from the methylation data. Fourth, principle component analysis (PCA) was used to capture any remaining unmeasured sources of variation. One principal component was selected based on the Scree test. A false discovery rate (FDR) of 10% (q-value < 0.1) was used to classify sites as differentially methylated.
## Cell-type Specific MWAS
We used the same epigenomic deconvolution approach used in the discovery (described above) to perform cell-type specific MWAS for the major nucleated cell types found in blood: granulocytes (CD15+), T-cells (CD3+), B-cells (CD19+) and monocytes (CD14+). Assay-related variables, demographic variables (sex, age, age squared, race, regular cigarette use), and one principal component were included as covariates in the cell-type specific MWAS. Cell-type proportions were also included as main effects in cell-type specific MWAS as the epigenomic deconvolution is essentially an interaction model.
### Block-based Association Testing
To potentially reduce the multiple testing burden in the brain association analyses, the sites were adaptively combined by collapsing highly inter-correlated coverage estimates at adjacent sites into a single mean coverage estimate. This was done separately for mCG and hmCG. This resulted in 10,082,773 "blocks" for mCG and 17,755,251 for hmCG, which were then tested for association with AUD. The brain mCG and hmCG block association testing was conducted separately for mCG and hmCG, and included measured technical variables, sex, age at death, post-mortem interval, estimated cell type proportions, and one principal component.
## Figure S2 Quantile-Quantile plot for block-based association testing in brain mCG
The observed p-values (red dots), on a -log10 scale, are plotted against their expected values (grey main diagonal line) under the null hypothesis assuming none of the sites have an effect. Orange lines indicate the 95% confidence bands (Cl). A deviation of the observed p-values from the main diagonal indicates that there are sites associated with AUD. Coefficient lambda (\(\lambda\)) will be close to one if the vast majority of sites behave as expected under the null hypothesis.
## Figure S3 Quantile-Quantile plot for block-based association testing in brain hmCG
The observed p-values (red dots), on a -log10 scale, are plotted against their expected values (grey main diagonal line) under the null hypothesis assuming none of the sites have an effect. Orange lines indicate the 95% confidence bands (Cl). A deviation of the observed p-values from the main diagonal indicates that there are sites associated with AUD. Coefficient lambda (\(\lambda\)) will be close to one if the vast majority of sites behave as expected under the null hypothesis.
|
196048_file02 | ### Effective reproductive number (\(R(t)\))
We used the daily cases, incubation period, and serial interval previously estimated. This allowed us to estimate the effective reproduction number for each county. The effective reproduction number \(R(t)\) represents the mean number of secondary cases generated by a primary infector at time \(t\). This measure is useful to track the effectiveness of performed control measures, which aims to push it below the epidemic threshold (corresponding to \(R(t)=1\)). \(R(t)\) incorporates factors affecting the spread of the epidemic (e.g., individual's behavior and susceptible depletion.
To estimate \(R(t)\), we use the same methodology described previously to distinguish between locally acquired and imported cases.
\[C(t)Pois(R_{t}\sum_{s=1}^{t}\phi(s)C(t-s)) \tag{1}\]
To estimate the time between consecutive generations of cases, we adopted the serial interval (which measures the time difference between the symptom onset of the infectors and of their infected) estimated from the literature, namely a gamma distribution with mean 5.0 days and standard deviation 3.4 days (shape=4.87, rate=0.65).
The likelihood \(\lambda\) of the observed time series cases from day 1 to \(T\) can be written as:
\[\lambda=\Pi_{t=1}^{T}P\left(C(t)Pois(R_{t}\sum_{s=1}^{t}\phi(s)C(t-s))\right) \tag{2}\]
We then use Metropolis-Hastings MCMC sampling to estimate the posterior distribution of \(R(t)\). The Markov chains were run for 100,000 iterations, considering a burn-in period of 10,000 steps, and assuming non-informative prior distributions of \(R(t)\) (flat distribution in the range (0-1000]). Convergence was checked by visual inspection by running multiple chains starting from different starting points.
### Constructing exposure measures
We constructed a measure of a colleges exposure to different geographic areas using movement data from 2020. For each county and college campus we estimated the average number of devices from the source county on each campus by week and computed the change from 20 to 14 days before reopening to 0 to 6 days after reopening. Because in some cases the net flow went in the opposite direction, we truncated the change in devices at 0.
We then estimated, for each county, 7-day incidence of COVID-19 ending 14 days before campus reopened. Finally, we used the truncated number of devices moving from each county to a given campus to constructthe weighted average of all counties that had net movement towards a college campus. The resulting exposure metric is the average 7-day incidence for the period ending two weeks before campus reopened.
## 2 Robustness checks and alternative specifications
We discuss our robustness checks, which are presented in table 4 below. The first row of table 4 repeats our baseline results as a reference.
### Balanced panel
Using a balanced panel, which incorporates data from periods that are significantly earlier and later than in the trimmed panel, we find consistent effects of reopening on mobility. However, our results for incident cases are almost uniformly negative, which may reflect the effect of comparisons between counties with earlier versus later reopening dates.
### Group-specific time trends
We also estimated modified versions of our outcome variables in which we removed a linear time trend that we estimated based on data from July 5 2020 to August 1 2020, the four-week period before the first campus reopened. This approach, which is recommended in the modern DID literature, allows for counties that were assigned to the same reopening date to be on similar trajectories before they reopened, relative to counties without a college or university. Using these adjusted outcome variables we find that reopening a college was associated with an increase in mobility and significant increases in COVID-19 incidence, including incident cases resulting in hospitalizations and deaths.
### Weighting by county population
When we weight counties by population several of our results vanish, which is what one should expect since in larger counties colleges and universities should have a smaller effect on COVID-19 incidence. The exception is for incident cases estimated from the CDC data, for which we find a similar increase in COVID-19 incidence with versus without population weighting and may reflect the set of counties that are included in the CDC sample.
### Restricting to counties with a college
Restricting our sample to counties with a college or university reduces the change in mobility that we observed and leaves only the increase in COVID-19 incidence using CDC data and the increase in \(R_{t}\).
### Including all colleges in a county
Including all colleges in a county and weighting each college by it's share of total college enrollment in a county leaves our results essentially unchanged when we use USAFacts-derived variables.
### Timing-group specific estimates
We also estimated timing-group specific difference-in-difference models and aggregated those estimates using the share of colleges with a given reopening date. These results, which are robust to concerns about differential trends, time varying treatment effects, and staggered adoption of policies, are consistent with our main estimates and, in some cases, larger in magnitude.
|
196097_file13 | ### Protein purification.
Cell lysates were incubated for 2h at 4\({}^{\circ}\)C on Ni-NTA beads (Qiagen, #30210) previously equilibrated with lysis buffer. Then, beads were washed three times with 50 times bed volume of washing buffer (20 mM HEPES pH 7.5, 500 mM NaCl, 5 mM MgCl\({}_{2}\), 0.01% NP-40, 10% glycerol, 40 mM Imidazole, 5 mM b-mercaptoethanol, 0.1 mM AEBSF, 0.5 mg/L leupeptin/pepstatin A, 2 mg/L aprotinin). Bound proteins were eluted with 8 times bed volume of elution buffer (20 mM HEPES pH 7.5, 500 mM NaCl, 5 mM MgCl\({}_{2}\), 10% glycerol, 300 mM imidazole, 5 mM b-mercaptoethanol,). The elution fractions were subsequently analyzed for the presence of the target protein by SDS-PAGE and Coomassie blue staining. Afterwards the fractions of interest were pooled and sample was concentrated using concentrators (Vivaspin(tm) _500_, MWCO 10 000). 2 - 5 mg of the concentrated sample was further purified by size exclusion chromatography (Superdex 75) with the Akta(tm) purifier system (GE Healthcare). Fractions were analyzed for the presence of the target protein by SDS-PAGE and Coomassie staining. Samples were quantified from the Coomassie stained gel using the ImageJ software.
### _In vitro_ synthesis of RNA molecules.
To test the RNA unwinding activity of DHX30, a \({}^{32}\)P-Labeled RNA duplex was synthesized using the T7 RNA polymerase from a linearized DNA template designed by (Tseng-Rogenski and Chang, 2004). The _in vitro_ transcription reaction mix was prepared as follows: 1X transcription buffer (40 mM Tris-HCl pH 7.9, 1 mM Spermidine, 26 mM MgCl2, 0,01% Triton X, 5mM DTT), NTPs (GTP 8 mM, ATP 5 mM, CTP 5 mM, UTP 2 mM, 50 uCi of \({}^{32}\)P-UTP), 3 uM DNA template, 3 uM top strand primer (5'-TAATACGACTCATAG-3'), 7 U of T7 RNA polymerase. Transcription reactions were incubated for 2h at 37\({}^{\circ}\) C. RNA was precipitated by adding 0.1 volumes of 3M NaAc (pH 5.5) and 3 volumes of ethanol for 30 min at -20\({}^{\circ}\)C. Then, samples were centrifuged at 13 000 g, 30 min at 4\({}^{\circ}\)C. RNA pellets were rinsed with 70 % ethanol and resuspended in H\({}_{2}\)O.
RNA samples were mixed with 2X denaturing RNA loading dye (1X Tris-Borate-EDTA pH 8.3, 95% formamide, 0.1% bromophenol blue, 0.1% xylene cyanol FF) and analyzed on 8% UREA-PAGE in 1X TBE. Radioactive signals were detected by autoradiography and the RNA band was excised from the gel.
The RNA product was extracted from the gel in RNA extraction buffer (200 mM Tris-HCl pH 7.0, 0.1% SDS, 1 mM EDTA). Subsequently, RNA was precipitated as described above and the RNA pellets were resuspended in 100 mM KCl.
To promote the formation of the RNA duplex, the RNA sample was boiled at 95\({}^{\circ}\)C for 5 min and cooled down over 2h. The sample was mixed with 2X non-denaturing loading dye (1X TBE, 20% glycerol, 0.1% bromophenol blue, 0.1% xylene cyanol FF) and separated on 8% native PAGE. The RNA duplexwas excised from the gel and purified as described before. The RNA concentration was determined by measuring absorbance at 260 nm.
### RNA unwinding assay
The helicase activity was measured in 20 ul of reaction mixture containing 0.13 pmol of purified protein (=20 ng of full length protein), 25 fmol radioactively labeled RNA duplex, 17 mM HEPES-KOH pH 7.5, 150 mM NaCl, 1 mM MgCl\({}_{2}\), 2 mM DTT, 1 mM spermidine, 0.3% PEG8000, 5% glycerol, 150 mM KCl, 20 units of RNasin(tm) Plus (Promega), 1 mM ATP. The mixture was incubated for 1h at 37\({}^{\circ}\)C and subsequently mixed with 2X non-denaturing loading dye and subjected to gel electrophoresis through non-denaturing 8% PAGE (19:1) in 0.5X TBE at 4\({}^{\circ}\)C. Reaction products were visualized by autoradiography.
## Supplementary Figures 1 - 7
## Supplementary Identified missense variants affect highly conserved amino acids. (a)
Evolutionary conservation of the missense variants within motifs of the helicase core region. The position of the missense variants identified are shown in red. Amino acid residues affecting novel missense variants are noted in brackets. Non conserved amino acid are shown in yellow. Nucleotide-interacting motifs (I, II and VI) are shown in purple, nucleic acid-binding motifs (Ia, Ib and IV) in orange, motif V, which binds nucleic acid and interacts with nucleotides, in purple and orange, and motif III, which couples ATP hydrolysis to RNA unwinding, in blue (as previoulsy described by Lessel et al., 2017). (b) Evolutionary conservation of the missense variants p.(Arg725His) and p.(Arg08Gln) not located within motifs of the helicase core region. The position of the missense variants are shown in red. Note that the affected amino acids are evolutionary highly conserved from humans to zebrafish.
**Supplementary _De novo_ mosaicism in individual 6.Sanger sequence electropherograms of parts of _DHX30_ after PCR amplification of genomic DNA of the affected individual 6 and her parents, confirming _de novo_ mosaicism. The amino acid translation is shown in the three-letter code above the DNA sequence. The red arrow indicates the variant at c.2201C\(>\)A, p.(Ala734Asp) present only in the DNA sample of the affected individual.
## Supplementary Whole gene deletion in individual 24.
Adapted from Chromosome Analysis Suite 3.3 (ChAS 3.3) showing loss of oligonucleotide probes at 3p21.31. Each dot represents one single nucleotide polymorphism that are distributed on the x-axis which shows the genomic positions.
## Supplementary DHX30 WT acts as an ATP-dependent RNA helicase.
Top: Increasing amounts of His6-SUMO-tagged DHX30 WT protein were incubated with a 32P-labelled RNA substrate in the presence (lane 3-7) or absence (lane 8) of ATP and analyzed by native PAGE. The position of the RNA duplex and the single-stranded RNA are indicated in the first and second lane respectively. Their schematic representation is shown at the right side. Bottom: RNA duplex containing a central GC sequence flanked by single-stranded regions of 53 nucleotides at the 5' end and 21 nucleotides at the 3' end.
## Supplementary Recombinant protein variants of DHX30 induce the formation of cytoplasmic clusters. (a)** Immunocytochemical detection of DHX30-GFP fusion proteins (GFP, green) and endogenous ATXN2 (magenta) in transfected U2OS cells. Upper panel: wild-type DHX30-GFP preferentially resides throughout the cytoplasm and GFP accumulates in nuclei, similar to recombinant protein variants of DHX30 harboring amino acid substitutions V556I, R725H and E948K (upper panel). Lower panel: recombinant protein variants of DHX30 harboring amino acid substitutions in the helicase core region G462E, A734D, S737F and T739A induce the genesis of cytoplasmic foci containing endogenous SG-marker ATXN2 (arrowheads), Notably R908Q amino acid substitution lead to the formation of clusters co-localizing with the SG-marker ATXN2 in only 50% of transfected cells. Nuclei are identified via DAPI staining (blue). Scale bars indicate 10 um. (b) Bar graph indicating the percentage of transfected cells, in which recombinant proteins induce the emergence of clusters. (*****:
## Supplementary Representative images of zebrafish embryos.** (**a**) Injected with Tol2 mRNA and pTol2pA2-cmlc2:EGFP;tuba1a:DHX30 wild-type or (**b**) DHX30 harboring mutations R493H, (**c**) R725H, (**d**) R785C, or (**e
Scale bars show 1000uM or 500 uM per unit. Embryos injected with wild-type DHX30 showed apparently normal development at day 7. Embryos injected with mutated DHX30 showed sign of severe developmental defects before day 7.
## Supplementary Generation of zebrafish CRISPR-Cas9-mediated dhx30 stable knockout line.****(a)** Shown are genomic regions of zebrafish dhx30 targeted by CRISPR-Cas9. Red indicates gRNA-binding site with the protospacer-adjacent motif (underlined) in wild-type (WT) sequence. The mutant animals carry an 8 bp-deletions generated by CRISPR-Cas9. **(b)** Dhx30-targeted PCR products were analyzed by high-resolution melting analysis (HRM) to distinguish wild-type (+/+), heterozygous (+/-), and homozygous (-/-) animals. Two different melting peaks were shown in heterozygous PCR product (top). To distinguish wild-type and homozygous animals, wild-type DNA samples are mixed with DNA from the 'test' animals. Homozygous DNA hence become heterozygous-like, resulting in two melting peaks (bottom). **(c)** Analyses of dhx30 transcript levels in dhx30 mutant animals at 5 days post fertilization. Data are presented as means \(\pm\) standard error of mean and are based on 3 replications. *, *
significantly different from DHX30+/+ (*p\(<\)0.05, ***p\(<\)0.001; n=3; One-way ANOVA, followed by the Holm-Sidak multiple comparison test). |
197640_file05 | ### The detailed method of the manuscript
Trial design and participant
The study used a randomised, double-blind, placebo-controlled, parallel-group design. We recruited eligible children from outpatient clinics at the Xinhua Hospital affiliated to Shanghai Jiao Tong University School of Medicine. Participants were considered eligible if they were diagnosed with ASD according to the Diagnostic and Statistical Manual of Mental Disorders, Fifth Edition (DSM-5); aged between 3 to 6 years; confirmed diagnosis with the Autism Diagnostic Interview-Revised (ADIR) and/or Autism Diagnostic Observation Schedule (ADOS), a CARS total score of no less than 30 and had no access to any behavioural intervention. We excluded patients if they had liver or kidney dysfunction; a history of allergy to sulfa drugs; abnormal electrocardiogram; genetic or chromosomal abnormalities; were diagnosed with neurological disease (e.g. epilepsy, Rett syndrome), or psychiatric disorder (e.g. very early-onset schizophrenia) other than ASD; severe hearing or visual impairment; were currently using melatonin for the treatment of sleep disorders or cessation of such treatment for less than 3 weeks. Additional exclusion criteria for neuroimaging were any contraindications of magnetic resonance imaging (MRI) scanning and any previous reports of traumatic brain injury. In regard to intellectual functioning,intelligence quotients (IQ), or developmental quotients (DQ) was assessed using the Wechsler Intelligence Scale for Children-Revised (WISC-R, Chinese version) for subjects \(\geq 6\) years old and the Wechsler Preschool and Primary Scale of Intelligence (WPPSI, Chinese version) for subjects \(<6\) but \(\geq 4\) years old, and the Gesell Developmental Schedules Chinese version for subjects \(<48\) months old.
The study was conducted in accordance with the guidelines for Good Clinical Practice and the principles of the Declaration of Helsinki and was reviewed and approved by the Ethics Committee of Xinhua Hospital affiliated to Shanghai Jiao Tong University School of Medicine (XHEC-C-2016-103). Parents or legal guardians of all participants provided written informed consent. The trial was registered with ClinicalTrials.gov (NCT03156153).
### Randomisation and masking
Participants were randomly assigned in a 1:1 ratio to receive bumetanide or placebo by use of a block randomisation scheme, with a block size of six. The generation of random allocation sequence and the preparation of trial medication were done by investigators in an external consultancy who do not participate in other aspects of the study. The study medication (bumetanide or placebo tablet) was provided in sequentially numbered envelopes. Bumetanide and placebo tablets were identical in appearance, smell and taste. Patients and their caregivers, investigators, experienced psychiatrists, and data analysts remained masked for the treatment allocation until the study database was locked. To reduce the possibility of differences in the incidence of polyuria between the two groups (bumetanide and placebo) potentially compromising the blinding effectiveness, a pediatrician was involved in the treatment of polyuria, but not in any other aspect of the study. This meant that the psychiatrist conducting the clinical ratings remained blind throughout the study.
Participants were given 0.5 mg oral bumentanide or placebo tablets twice daily for 3 months. Before that, a pretreatment education session of potential side effects of bumentanide (polyuria, hypokalemia, and hyperuricemia) and common symptoms (thirsty, fatigue, and loss of appetite) was delivered to the caregivers of the participants in both bumentanide and control groups. In addition, to minimize the impact of diuretic actions of bumentanide in blinding, a dietary supplement plan (adequate daily drinking water and potassium-rich diet) was encouraged for the applicants of both groups.
### Outcome measures
The primary outcome was the change from baseline to 3-month in CARS (the total score ranges from 15 to 60 by summing up the 15 subscales items, with a higher score indicating more severe autism). Confirmatory secondary outcomes were the change from baseline to 3-month in ADOS, SRS and the Clinical Global Impression-Improvement (CGI-I) to rate how much the patient's illness has improved or worsened relative to a baseline measurement (a seven-point scale; 1 = "very much improved" to 7 = "very much worse"). The exploratory outcomes were the changes from baseline to 3-month in neurotransmitter (e.g. GABA and glutamate) concentrations within the IC. Additional secondary and exploratory outcome measures included Symbolic Play Test, Chinese Communicative Development Inventory, and Short Sensory Profile Report scores as secondary outcomes, and electroencephalogram (EEG) recording, plasma metabolites, and GWAS as exploratory outcomes. These additional outcome measures will be reported in a subsequent study.
### Adverse effect monitoring
Participants who received at least one dose of the study medication or placebo were assessed for safety. Symptoms (thirst, diuresis, nausea, vomiting, diarrhea, constipation, rash, palpitation, headache, dizziness, shortness of breath, and any other self-reported symptoms) were telephone interviewed at 1 week and 1 month. Bloodparameters (serum potassium, uric acid, and creatine) were monitored via laboratory tests at 1 week and 1 month after the initiation of treatment and at the end of the treatment period. Adverse events that occurred on or after initiation of the study medication or placebo or preexisting medical condition that worsened during the treatment period were assessed and graded according to the World Health Organization standard.
### MRI acquisition
Participants were scanned using a Siemens Verio 3.0-Tesla MRI scanner (Siemens Medical Solutions, Munich, Germany) with 32-channel head coil and four-channel neck coil. Scans were performed at chloral-hydrate-induced-sleep. The dosage of chloral hydrate was 50 mg/kg up to a maximum dose of 1g administered rectally. Earplugs, earphones, and extra foam padding were provided to the subjects to reduce the sound of the scanner during the scan. The potential confounding effects of chloral hydrate were controlled for both by experimental design and analyses used.
The insula voxel (\(20\times 40\times 20\) mm, Figure 2A) was placed along the anterior-posterior direction of the insular cortex and covered the anterior and posterior limits of the insula. To ensure the consistency of volume-of-interest (VOI) positioning in the longitudinal experiments, we used the first-scanned VOI of each participant as a reference to locate the same VOI in the follow-up scan. For each participant, a three-plane localizer image was first acquired, followed by a high-resolution anatomical T1-weighted magnetization-prepared rapid gradient echo image (192 sagittal slices; voxels \(=1\times 1\times 1\) mm; repetition time [TR] \(=2300\) ms; echo time [TE] \(=2.28\) ms; inversion time \(=1100\) ms; flip angle \(=8^{\circ}\), field of view \(=192\times 192\times 192\) mm) to guide the spectroscopic VOI. For GABA measurement, Mescher-Garwood point-resolved spectroscopy (MEGA-PRESS) scan (256 spectra for the insular cortex were acquired with on-/off-resonance frequency \(=1.9/7.5\) ppm using TR/TE \(=1500/68\) ms)was performed in the VOI. The difference spectrum was obtained by subtracting the edit-ON and -OFF spectra, yielding a spectrum for total GABA and glutamate.
### Image processing
We first used the LCModel software with a simulated MEGA-PRESS basis set to fit the MRS data, and then determined the n-acetylaspartate (NAA), n-acetylaspartyl-Glx, GABA, glutamine, and glutathione concentrations using the difference spectra, where GABA was actually GABA plus macromolecules around 3ppm and the NAAs we used was actually NAA plus NAAG. To ensure an acceptable signal-to-noise ratio (SNR) for the MRS voxel, we excluded those participants with SNR \(\leq\) 15, full-width at half-maximum \(\geq\) 0.05 ppm, and Cramer-Rao lower bounds in the fitted spectrum equal to or higher than 20% for GABA from the neuroimaging analyses. shows representative MRS spectra of the target VOI analyzed with the LCmodel.
We focused on GABA in this study, since our previous open-label study of bumetanide for children with ASD identified that the most significant change after the treatment was the decrease in GABA. This decrease in GABA was also found to relate to symptom improvement We used the NAA concentration as an internal reference for the GABA concentration. Due to the individual variation in the tissue composition of the VOI, we further performed a tissue correction for the GABA-edited MRS to adjust the GABA measurements. In this paper, the GABA concentration refers to the corrected GABA metabolite concentration, i.e. GABA/NAA ratio corrected for tissue composition. As NAA was the only available peak acquired simultaneously to GABA in the MEGA-PRESS scans, we chose to use the GABA/NAA ratio as a proxy to the GABA concentration. To further test its validity, we calculated a GABA/Creatine ratio by combining GABA/NAA from the difference spectra with the NAA/Creatine from the edit-off spectra using the LCModel. Using the Statistical Parametric Mapping (SPM12) software, we estimated both the grey matter volume fraction (frGM) and the white matter volume fraction (frWM) within the VOI using the T1-weighte images. Therefore, the corrected GABA metabolite concentration was calculated by Metabolite-raw / NAA-observed \(\times\) (1/[frGM + 0.5 \(\times\) frWM]).
### Statistical analysis
To detect a between-group difference of two or more points on CARS total score after 3-months treatment (primary outcome), a change from baseline of 3.1 SD and an alpha of 0.05, we required 51 participants per group to attain a power of 90%. Accounting for an expected no more than 15% drop out during follow-up period, we sought to include 120 patients (group size 60). Fifty-nine (98%) patients in the bumetanide group and 60 (100%) in the placebo group received at least one dose of the study medication, all of whom were included in the modified intention-to-treat population of primary outcome analysis and safety analysis, which was performed when the last trial participant reached 3 months.
The treatment effect of bumetanide was assessed by the change of the total score of CARS from baseline to 3-month using a mixed model. In this model, we assumed individualized random intercepts, and tested the treatment effect by the interaction term, treatment (0, placebo; 1, bumetanide) \(\times\) time (0, baseline before treatment; 1, 3 months after treatment). The normality of the model residuals was assessed with the Shapiro-Wilk normality test, and homogeneity of variance across groups was evaluated with Levene's test. If at least one of the two tests were significant, a permutation-based mixed-effects model was established by 3000 random permutations of the group label using the permlmer function in the R package "predictmeans" v.1.0.1. If the treatment effect was significant on the total score of CARS, we further tested the effects on 6 CARS items separately as suggested by our previous open-label study, including item 1 (Impairment in human relationships), item 3 (Inappropriate affect ), item 4 (Bizarre use of body movement and persistence of stereotypes), item 5 (Peculiarities in relating to nonhuman objects), item 7 (Peculiarities of visual responsiveness), item 13 (Activity level: abnormal apathy or hyperactivity). Adjustment for multiple comparisons was performed at p = 0.05 using the false discovery rate approach (Benjamin-Hochberg adjusted-p value). For CGI-I, the Kruskal-Wallis chi-squared test was applied to assess the significance level of the inter-group difference. Similarly, the treatment effects of bumetanide on the neurotransmitters in the insular cortex were tested by mixed models adjusted for age, sex, and intelligent (1, DQ\(<\)75 or IQ\(<\)70; 0, otherwise). A permutation-based linear model was used to study the association between the changes of the neurotransmitter concentrations and the change of the CARS total scores, conducted by treatment group, adjusted for age, sex, intelligence, baseline CARS scores and neurotransmitter concentrations, using the lmp function in the R package. If a significant association was detected, associations between the change in MRS measurement and subscales of the CARS items which showed significant treatment effects were further investigated and FDR correction was applied to control for multiple comparisons with items.
All analyses were conducted with the use of R v.3.5.1. To facilitate reproducibility of our analysis, we have provided all data analytic code on GitHub in the following webpage: [https://github.com/qluo2018/RCT](https://github.com/qluo2018/RCT).
## Rational to examining 6 subscales of CARS
The primary goal of this RCT was to test whether bumetanide had any treatment effect on the overall severity of ASD. The secondary goal was to test which symptom dimensions of ASD were significantly affected by bumetanide. Given that an open-label RCT without placebo control often shows larger treatment effect compared with a double-blinded RCT with placebo control, we focused on those 6 subscales of CARS that were significantly improved following the treatment with bumetanide in our previous open-label trial."
#### Power calculation of the sample size
This study was powered to detect a 3.8-point (SD 3.1) reduction in CARS total scored after 3-month bumetanide treatment, based on our preliminary intervention trial on 15 ASD patients, compared with 1.8-point in placebo group based on a previous publication, assuming the same SD as treatment. Setting the type I error rate to 0.05, a sample of 51 participants per group was deemed necessary to attain a power of 90%. Accounting for an expected no more than 15% drop out during follow-up period, we sought to include 120 patients (group size 60).
#### Analysis of CGI-I interpreted as responder/non-responder
We performed chi-squared test using CGI-I to categorize subjects as responders/non-responders. With 22 responders and 37 non-responders in bumetanide group and 13 responders and 47 non-responders in placebo group, the result only indicated a trend (p=0.061) between two groups.
#### Change of ADOS from baseline to 3-month follow-up
The Autism Diagnostic Observation Schedule (ADOS), designed as a diagnostic tool for ASD, is a semi-structured, standardized observation instrument, including domains of reciprocal social interaction, communication, and repetitive and stereotyped behaviours. All domains with higher scores indicate greater severity. The ADOS was assessed at baseline and after 3-month treatment. To test the treatment effect on ADOS, we used a mixed-effects model similar to that described in the main text for CARS. However, we did not observe significant difference in ADOS comparing before and after 3-month treatment.
#### Change of RBS-R from baseline to 3-month follow-up
The RBS-R (Repetitive Behavior Scale-Revised) is a scale to assess patient's repetitive behavior severity based on parent report. The RBS-R quantifies repetitive behavior in six behavioral subcategories: stereotypy, self-injury, compulsive behavior, ritualisticbehavior, sameness, and restricted behavior. The RBS-R was assessed at baseline and after 3-month treatment. To test the treatment effect on RBS-R, we used a mixed-effects model similar to that described in the main text for CARS. However, we did not observe significant difference in RBS-R comparing before and after 3-month treatment.
## Change of SRS from baseline to 3-month follow-up
The SRS is a quantitative measure of autistic traits in 4-18 years old. The SRS was assessed at baseline and after 3-month treatment on participants above 4 years old (25 in bumentanide group and 30 in placebo group). To test the treatment effect on SRS, we used a mixed-effects model similar to that described in the main text for CARS.
## Training programs prior to MRS scans
Home training program: Carers were asked to help acclimatise the ASD children to using ear plugs and sleeping on their backs. Home training started 2 weeks prior to the MRI visit.
On-site training: 1) children were shown around the MRI scanning room to familiarise themselves with the new environment and various MRI sounds for 2-3 hours, prior to the actual scans; 2) children were brought to the MRI scanning room, they sat/lay on MRI scanner for around 10 min to become acclimatised to the MRI scanner and the room temperature, before falling asleep.
## Strategies to control the possible effects of chloral hydrate on MRS measurements
The possible effects of chloral hydrate were controlled for both by experimental design and the analyses used. In the experimental design, both the children in the placebo group and the drug group received chloral hydrate. Therefore, the chloral hydrate was administered at both time points to both groups. In addition, in the analysis of the data, we used a mixed effect model instead of repeated measures ANOVA. By using this approach, we were able to subtract out the "time-invariant" effect of chloral hydrate.
### Testing the treatment effect of bumetanide on the glutamate concentration
We also tested the treatment effect of bumetanide on the glutamate concentration. This concentration was measured by the Glx / NAA \(\times\) (1/[frGM + 0.5 x fWM]), where Glx = Glutamate + Glutamine, and NAA = NAA + NAAG. The treatment effect was tested by the same mixed effect model as described in the main text. The change in the glutamate concentration in the bumetanide group after the 3-months treatment did not significantly different from that in the placebo group (t39 = -1.50, p = 0.143).
### MRI findings were not affected by a biased sampling due to the image quality
We compared the bumetanide and placebo groups in terms of signal to noise ratio and other quality control parameters. No significant differences were observed (supplementary Table 2). We also compared the clinical features between the subjects with the MRS images which met and did not meet the quality control criteria. Again, no significant differences were detected (supplementary Table 3). Therefore, the MRS findings were strictly quality controlled and unlikely to be affected by a biased sampling, due to the image quality.
### The estimation of GABA+/creatine ratios
GABA levels were firstly quantified relative to NAA as described in Method. Then the ratio of NAA to creatine was determined by fitting the spectral peaks in the edit-off spectrum with LCModel software. A set of metabolite basis spectra specific to the PRESS sequence (TE=68 ms) was used, provided by the MR Spectroscopy Lab ([http://purcell.healthsciences.purdue.edu/mrslab/basis](http://purcell.healthsciences.purdue.edu/mrslab/basis) sets.html). The ratios of GABA/NAA and NAA/creatine were combined to yield a GABA/creatine ratio (GABA/Cr), as previous reports. Of the subjects who had qualified GABA/NAA measurement, one was dropped when estimating GABA/Cr due to the missing of edit-off spectrum at baseline.
1: E Lemonnier et al. A randomised controlled trial of bumetanide in the treatment of autism in children.
2. Donahue MJ, Near J, Blicher JU, Jezzard P. Baseline GABA concentration and fMRI response. Neuroimage. 2010;53:392-398. doi:10.1016/j.neuroimage.2010.07.017
3. Mullins PG, McGonigle DJ, O'Gorman RL, et al. Current practice in the use of MEGA-PRESS spectroscopy for the detection of GABA. Neuroimage. 2014;86:43-52. doi:10.1016/j.neuroimage.2012.12.004 |
198424_file02 | ## DIAN
Data collection and sharing for this project were supported by The Dominantly Inherited Alzheimer Network (DIAN, U19AG032438), funded by the National Institute on Aging (NIA), the Alzheimer's Association (SG-20-690363-DIAN), the German Center for Neurodegenerative Diseases (DZNE), Raul Carrea Institute for Neurological Research (FLENI), Partial support by the Research and Development Grants for Dementia from Japan Agency for Medical Research and Development, AMED, and the Korea Health Technology R&D Project through the Korea Health Industry Development Institute (KHIDI), Spanish Institute of Health Carlos III (ISCIII), Canadian Institutes of Health Research (CIHR), Canadian Consortium of Neurodegeneration and Aging, Brain Canada Foundation, and Fonds de Recherche du Quebec - Sante. DIAN Study investigators have reviewed this manuscript for scientific content and consistency of data interpretation with previous DIAN Study publications. We acknowledge the altruism of the participants and their families and the contributions of the DIAN research and support staff at each of the participating sites for their contributions to this study.
## DIAN study group
Sarah Adams, Ricardo Allegri, Aki Araki, Nicolas Barthelemy, Randall Bateman, Jacob Bechara,Tammie Benzinger, Sarah Berman, Courtney Bodge, Susan Brandon, William (Bill) Brooks, Jared Brosch, Jill Buck, Virginia Buckles, Kathleen Carter, Lisa Cash, Charlie Chen, Jasmeer Chhatwal, Patricio Chrem, Jasmin Chua, Helena Chui, Carlos Cruchaga, Gregory S Day, Chrismary De La Cruz, Darcy Denner, Anna Diffenbacher, Aylin Dincer, Tamara Donahue, Jane Douglas, Duc Duong, Noelia Egido, Bianca Esposito, Anne Fagan, Marty Farlow, Becca Feldman, Colleen Fitzpatrick, Shaney Flores, Nick Fox, Erin Franklin, Nelly Friedrichsen, Hisako Fujii, Samantha Gardener, Bernardino Ghetti, Alison Goate, Sarah Goldberg, Jill Goldman, Alyssa Gonzalez, Brian Gordon, Susanne Graber-Sultan, Neill Graff-Radford, Morgan Graham, Julia Gray, Emily Gremminger, Miguel Grilo, Alex Groves, Christian Haass, Lisa Hasler, Jason Hassenstab, Cortaiga Hellm, Elizabeth Herries, Laura Hoechst-Swisher, Anna Hofmann, David oltzman, Russ Hornbeck, Yakushev Igor, Ryoko Ihara, Takeshi Ikeuchi, Snezana Ikonomovic, Kenji Ishii, Clifford Jack, Gina Jerome, Erik Johnson, Mathias Jucker, Celeste Karch, Stephan Kaser, Kensaku Kasuga, Sarah Keefe, William (Bill) Klunk, Robert Koeppe, Deb Koudelis, Elke Kuder-Buletta, Christoph Laske, Allan Levey, Johannes Levin, Yan Li, Oscar Lopez, Jacob Marsh, Rita Martinez, Ralph Martins, Neal Scott Mason, Colin Masters, Kwasi Mawuenyega, Austin McCullough, Eric McDade, Arlene Mejia, Estrella Morenas-Rodriguez, John Morris, James MountzMD, Cath Mummery, Neelesh Nadkarni, Akemi Nagamatsu, Katie Neimeyer, Yoshiki Niimi, James Noble, Joanne Norton, Brigitte Nuscher, Antoinette O'Connor, Ulricke Obermuller, Riddhi Patira, Richard Perrin, Lingyan Ping, Oliver Preische, Alan Renton, John Ringman, Stephen Salloway, Peter Schofield, Michio Senda, Nick Seyfried, Kristine Shady, Hiroyuki Shimada, Wendy Sigurdson, Jennifer Smith, Lori Smith, Beth Snitz, Hamid Sohrabi, Sochenda Stephens, Kevin Taddei, Sarah Thompson, Jonathan Voglein, Peter Wang, Qing Wang, Elise Weamer, Chengjie Xiong, Jinbin Xu, and Xiong Xu.
### Igap
We thank the International Genomics of Alzheimer's Project (IGAP) for providing summary results data for these analyses. The investigators within IGAP contributed to the design and implementation of IGAP and/or provided data but did not participate in analysis or writing of this report. IGAP was made possible by the generous participation of the control subjects, the patients, and their families. The i-Select chips was funded by the French National Foundation on Alzheimer's disease and related disorders. EADI was supported by the LABEX (laboratory of excellence program investment for the future) DISTALZ grant, Inserm, Institut Pasteur de Lille, Universite de Lille 2 and the Lille University Hospital. GERAD/PERADES was supported by the Medical Research Council (Grant no 503480), Alzheimer's Research UK (Grant no 503176), the Wellcome Trust (Grant no 082604/2/07/Z) and German Federal Ministry of Education and Research (BMBF): Competence Network Dementia (CND) grant no 01GI0102, 01GI0711, 01GI0420. CHARGE was partly supported by the NIH/NIA grant R01 AG033193 and the NIA AG081220 and AGES contract N01-AG-12100, the NHLBI grant R01 HL105756, the Icelandic Heart Association, and the Erasmus Medical Center and Erasmus University. ADGC was supported by the NIH/NIA grants: U01 AG032984, U24 AG021886, U01 AG016976, and the Alzheimer's Association grant ADGC-10-196728.
### Adds
The results published here are in whole or in part based on data obtained from the AD Knowledge Portal ( [https://adknowledgeportal.org](https://adknowledgeportal.org) ). Study data were provided by G. H. Sergievsky Center and the Taub Institute for Research for Alzheimer's Disease and the Aging Brain at the Columbia University Irving Medical Center. Omic data collection was supported by funding from the National Institutes of Health [R56 AG061837 (Lee and Krinsky-McHale) generated GWAS, whole genome sequencing, targeted proteomic, and untargeted metabolomic data; P01HD035897 (Silverman) and R01 AG014673 (Schupf) generated demographic and clinical phenotype data] and from the Alzheimer's Association (IIRG-08-90655 (Schupf) generated targeted proteomic data) as well as by funds from the New York State Office for People with Developmental Disabilities. Additional phenotypic data can be requested by contacting the PIs: Drs Joseph H Lee ) and Sharon Krinsky-McHale ( ).
### ADGC (from ADGC website, [https://www.adgenetics.org/](https://www.adgenetics.org/))
The National Institutes of Health, National Institute on Aging (NIH-NIA) supported this work through the following grants: ADGC, U01 AG032984, RC2 AG036528; Samples from the National Cell Repository for Alzheimer's Disease (NCRAD), which receives government support under a cooperative agreement grant (U24 AG21886) awarded by the National Institute on Aging (NIA), were used in this study.
We thank contributors who collected samples used in this study, as well as patients and their families, whose help and participation made this work possible; Data for this study were prepared, archived, and distributed by the National Institute on Aging Alzheimer's Disease Data Storage Site (NIAGADS) at the University of Pennsylvania (U24-AG041689-01); NACC, U01 AG016976; NIA LOAD, U24 AG026395, R01AG041797; Banner Sun Health Research Institute P30 AG019610; Boston University, P30 AG013846, U01 AG10483, R01 CA129769, R01 MH080295, R01 AG017173, R01 AG025259, R01AG33193; Columbia University, P50 AG008702, R37 AG015473; Duke University, P30 AG028377, AG05128; Emory University, AG025688; Group Health Research Institute, U01 AG006781, U01 HG004610, U01 HG006375; Indiana University, P30 AG10133; Johns Hopkins University, P50 AG005146, R01 AG020688; Massachusetts General Hospital, P50 AG005134; Mayo Clinic, P50 AG016574; Mount Sinai School of Medicine, P50 AG005138, P01 AG002219; New York University, P30 AG08051, UL1 RR029893, 5R01AG012101, 5R01AG022374, 5R01AG013616, 1RC2AG036502, 1R01AG035137; Northwestern University, P30 AG013854; Oregon Health & Science University, P30 AG008017, R01 AG026916; Rush University, P30 AG010161, R01 AG019085, R01 AG15819, R01 AG17917, R01 AG30146; TGen, R01 NS059873; University of Alabama at Birmingham, P50 AG016582; University of Arizona, R01 AG031581; University of California, Davis, P30 AG010129; University of California, Irvine, P50 AG016573; University of California, Los Angeles, P50 AG016570; University of California, San Diego, P50 AG005131; University of California, San Francisco, P50 AG023501, P01 AG019724; University of Kentucky, P30 AG028383, AG05144; University of Michigan, P50 AG008671; University of Pennsylvania, P30 AG010124; University of Pittsburgh, P50 AG005133, AG030653, AG041718, AG07562, AG02365; University of Southern California, P50 AG005142; University of Texas Southwestern, P30 AG012300; University of Miami, R01 AG027944, AG010491, AG027944, AG021547, AG019757; University of Washington, P50 AG005136; University of Wisconsin, P50 AG033514; Vanderbilt University, R01 AG019085; and Washington University, P50 AG005681, P01 AG03991. The Kathleen Price Bryan Brain Bank at Duke University Medical Center is funded by NINDS grant \(\ |
199562_file04 | ## Title and Abstract
Title and 1 \(\bullet\)Information on how unit were allocated to interventions
Abstract
\(\bullet\)Structured abstract recommended
\(\bullet\)Information on target population or study sample
## Introduction
Background 2 \(\bullet\)Scientific background and explanation of rationale
\(\bullet\)Theories used in designing behavioral interventions
## Methods
Participants 3 \(\bullet\)Eligibility criteria for participants, including criteria at different levels in recruitment/sampling plan (e.g., cities, clinics, subjects)
Method of recruitment (e.g., referral, self-selection), including the sampling method if a systematic sampling plan was implemented
\(\bullet\)Recruitment setting
\(\bullet\)Settings and locations where the data were collected
\(\bullet\)Details of the interventions intended for each study condition and how
and when they were actually administered, specifically including:
\(\circ\)Content: what was given?
\(\circ\)Delivery method: how was the content given?
\(\circ\)Unit of delivery: how were the subjects grouped during delivery?
\(\circ\)Deliverer: who delivered the intervention?
\(\circ\)Setting: where was the intervention delivered?
\(\circ\)Exposure quantity and duration: how many sessions or episodes or
events were intended to be delivered? How long were they
intended to last?
Time span: how long was it intended to take to deliver the
intervention to each unit?
Activities to increase compliance or adherence (e.g., incentives)
\(\circ\)Activities to increase compliance or adherence (e.g., incentives)
\(\bullet\)Specific objectives and hypotheses
\(\bullet\)Clearly defined primary and secondary outcome measures
\(\bullet\)Methods used to collect data and any methods used to enhance the
quality of measurements
\(\bullet\)Information on validated instruments such as psychometric and biometric
properties
\(\bullet\)How sample size was determined and, when applicable, explanation of any
interim analyses and stopping rules
\(\bullet\)Methods used to collect data and any methods used to enhance the
quality of measurements
\(\bullet\)Information on validated instruments such as psychometric and biometric
properties
\(\bullet\)How sample size was determined and, when applicable, explanation of any
interim analyses and stopping rules
\(\bullet\)Method used to assign units to study conditions, including details of any
restriction (e.g., blocking, stratification, minimization)
Inclusion of aspects employed to help minimize potential bias induced due
to non-randomization (e.g., matching)
## TREND Statement Checklist
\begin{tabular}{p{56.9pt}|p{28.5pt}|p{28.5pt}|p{28.5pt}|p{28.5pt}} \hline Numbers & 16 & \(\bullet\) & Number of participants (denominator) included in each analysis for each study condition, particularly when the denominators change for different outcomes; statement of the results in absolute numbers when feasible & 7 \\ & & \(\bullet\) & Indication of whether the analysis strategy was "intention to treat" or, if not, description of how non-compliers were treated in the analyses & & 7 \\ \hline Outcomes and estimation & 17 & \(\bullet\) & For each primary and secondary outcome, a summary of results for each estimation study condition, and the estimated effect size and a confidence interval to indicate the precision & 7 \\ & & \(\bullet\) & Inclusion of null and negative findings & & \\ & & & Inclusion of results from testing pre-specified causal pathways through which the intervention was intended to operate, if any & & \\ \hline Ancillary analyses & 18 & \(\bullet\) & Summary of other analyses performed, including subgroup or restricted analyses, indicating which are pre-specified or exploratory & & 7 \\ \hline Adverse events & 19 & \(\bullet\) & Summary of all important adverse events or unintended effects in each study condition (including summary measures, effect size estimates, and confidence intervals) & & 7 \\ \hline
## DISCUSSION
& & & & \\ Interpretation & 20 & \(\bullet\) & Interpretation of the results, taking into account study hypotheses, sources of potential bias, imprecision of measures, multiplicative analyses, and other limitations or weaknesses of the study & & 7 - 8 \\ & & & Discussion of results taking into account the mechanism by which the intervention was intended to work (causal pathways) or alternative mechanisms or explanations & & 8 \\ & & & Discussion of the success of and barriers to implementing the intervention, fidelity of implementation & & \\ & & \(\bullet\) & Discussion of research, programmatic, or policy implications & & \\ \hline Generalizability & 21 & \(\bullet\) & Generalizability (external validity) of the trial findings, taking into account the study population, the characteristics of the intervention, length of follow-up, incentives, compliance rates, specific sites/settings involved in the study, and other contextual issues & & 9 \\ \hline Overall Evidence & 22 & \(\bullet\) & General interpretation of the results in the context of current evidence and current theory & & 9 \\ \hline \end{tabular}
_From:_ Des Jarlais, D. C., Lyles, C., Crepaz, N., & the Trend Group. Improving the reporting quality of nonrandomized evaluations of behavioral and public health interventions: The TREND statement. _American Journal of Public Health_, 94, 361-366. For more information, visit: [http://www.cdc.gov/trendstatement/](http://www.cdc.gov/trendstatement/) |
199828_file04 | ## Document Number
## Version Number
## Date Last Updated
## (See Revision History table on last page)
## Project Management
## Workstream
## Introduction
## Context
The Aerosol Assessment Study involves the assessment of exhaled aerosol particles among the employees of No Evil Foods, administered by the Sensory Cloud team, overseen by the PI, Dr. David Edwards. Volunteers who participate in the study will be roughly 20 minutes away from their daily work routine, to assess their exhaled aerosol particles. Volunteers will be asked to sign a consent form prior to the study that clarifies the safety and purpose of the assessment with a potential side effect of a dry mouth. Participants will be able to observe the measurement in real time.
## Goals and Outcomes
The goal of the study is to determine exhaled aerosol variation between subjects
## 2 Scope
### This process document contains information on the following:
1.1.Suggested protocol for the measurement of exhaled and emitted aerosolized particles, by size of particles
2.1.2.This version of the study focuses on the _variations of particle aerosolization in participants over the course of multiple, closely timed measurements_ (e.g., daily over the course of a week, with multiple measurements taken each day).
2.1.2.1.1.1.e., there are two assessments performed
2.1.2.2.
2.1.2.3.Additionally, this study design varies is other ways:
2.1.2.4.This study is meant to be _administered for a single household at a given time_, given the risk of communicable illness, like COVID-19. Because of this, the study should be done for all individuals willing to participate from that household, and all participants should be tested for COVID-19. The study can be repeated, but _separately_ with cleaned equipment for _other participating households_ at _different date_
2.1.2.5.The participants will also NOT participate in a control administration with saline.
2.1.2.6.Test administrators will track the participant's COVID-19 status (i.e., COVID-positive or COVID-negative), noting the days from the onset of COVID-like symptoms (i.e., Day 0
2.1.2.6.1.The timing of same-day measurement administrations will be measured
2.1.3.Suggested directions for participants and administrators to effectively and consistently administer this process and inform participants of the test's mechanics to aid their understanding and successful participation of study requirements
2.1.4.Required inventory list of equipment, supporting inventory, and study administration materials for successful deployment (see Appendix A)References
The following documents are referred to in the text in such a way that some or all of their content constitutes requirements of this document. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies.
### For the purposes of this document, the following terms and definitions apply.
#### Nebulizer Kits
This is the apparatus that allows the exhaled particles from the participant's airway to be counted by the particle counter.
This device filters the ambient air of particles, so that the particle counter is measuring only those particles exhaled from the participant. Because it serves this purpose, the Hema filter and all joints and connections for between the parts of the Nebulizer kit must be tight and secure. This is also why the Particle Counter Administrator must perform a baseline to ensure that the seals are tight and the Hema filter is filtering properly. See study administration protocol, Particle Counter, to see the minimum required readings for the Hema Filter Baseline Test.
#### T-Connector Valve Caps (Used for Hema Filter Testing / Baseline)
Every Nebulizer Kit includes a cap that is a small convex plastic cap, that fits snugly over the ends of the T-Connector Valve. When properly connected, one end of the top of the T-Connector Valve is connected to the particle counter; the bottom valve is connected to the Joint Connector Tube (which connects to the Hema filter). The cap will be fitted to the other top valve of the T-Connector Valve before the participant attaches their mouthpiece to perform the baseline test. The cap seals tightly to the T-Connector Valve blocking airflow through that side.
#### Particle Counter Receipt Paper
Each particle counter machine measures counts over a 6-second period. The results of this count are measured in real time, and the results are captured on physical thermal print paper (much like a cash register at a store). Each participant will have ONE printout of their results over the ~2-3 minutes of breathing (with results measured for each 6 second interval), for each administration of the particle test. These printed results are the only physical record of the participant's results, and therefore are critical to capture, organize, and store securely. The machines should have rolls of paper in the device, with many extras nearby.
Roles and responsibilities
For the purposes of this document, the following roles apply with the responsibilities listed besides each.
### Study Project Manager
Managing all study related logistics, collaborating cross-functionally within Sensory Cloud and externally with the partner organization to ensure all information/materials required for the study are arranged for in time.
### Study Site Point of Contact (POC)
Responsible to manage relationships with the site owners, hosts, or "client" (depending on the nature of the test administration), and to oversee and engage other SC team members to drive successful execution
### Registration Administrator
Responsible for staffing the Registration Station, which includes the following: Checking in participants, assigning participants a Participant Number, confirming participants have signed Informed Consent Waiver, provision participants with their Ziplock bag, mouthpiece, and cap; direct them to the particle test station, receive them when they complete the aerosolization station; collect, sanitize, and store (in numeric order) participants nebulizer kit bags; write down and inform participant of their next test; and finally collect their nebulizer kits (once again sanitizing) and thanking participant for their time.
### Particle Test Administrator
Responsible for staffing the Particle Counter Machines, facilitating the participant through the particle test. BEFORE each participant is received at the counter, the Administrator should wipe/spray down the chair, separator screen, and table; secure an UNUSED nebulizer assembly (with cap) to the particle counter; and check the machine has sufficient paper. WHEN PARTICIPANT ARRIVES, Administrator will welcome participant; instruct the participant about the process they will take; guide the participant through the exhalation test process (and correct for any errors); mark the receipt paper with any errors; thank the participant for their time; direct them to the Aerosolization station (or the Registration Table).
### Runner to Coordinate with Participants
Responsible for informing participants to come to the registration desk and make sure that only the set number of participants (i.e., 3) are brought into the testing space for registration at a single time. This is part of the protocol to reduce the risk of inter-personal transmission.
### Trial participants
Willful and informed participant in the study, and for this study are parts of the same household, given the presence and tracking of COVID-19 positivity within the household. Participants must sign consent form, provide basic data as solicited on the Informed Consent Form, and follow the instruction of all study administrators.
Process
### Pre-Work / Things Done in Advance
6.1.1.Gather/Acquire all materials required as per materials list (see full inventory list in Appendix A)
6.1.1.1.Gather materials in inventory
6.1.1.2.List out materials in transit or yet to be purchased
6.1.1.3.Place orders/ track delivery
6.1.1.4.Ensure all travel arrangements made
6.1.2.Organize Dry-Run Before Trial
6.1.2.1.Setup room exactly as per layout
6.1.2.2.Have all materials laid out next to each station as planned
6.1.2.3.Run-through the entire process with the team
### Visit Study Location
6.2.1.Room Setup for Trial
6.2.1.1.Set up each trail station as described below. There are 4 stations for each administration, all trial stations with materials (_Note_: This list is illustrative only; please refer to Appendix A for complete inventory pack list)
6.2.1.1.1.Registration/Check-in/Check-out Station
6.2.1.1.1.1.Consent Forms
6.2.1.1.2.Pens
6.2.1.1.1.3.Labels for allotting number to participants
6.2.1.1.1.4.Mouthpiece in resealable bags
6.2.1.1.1.5.Participant check-in/check-out list
6.2.1.1.1.6.Bin to store consent forms
6.2.1.1.7.Bin to store sealed kit bags
6.2.1.1.2.Particle Testing Station
6.2.1.1.2.1.Particle Counter Machine with plexiglass separator screen
6.2.1.1.2.2.Pre-assembled filter kit
6.2.1.1.2.3.Envelopes to store receipts (i.e., particle test results)
6.2.1.1.2.4.Fine point pens
6.2.1.1.2.5.Bin to store numbered envelopes in
6.2.1.1.2.6.Extra receipt roles for particle counter
6.2.1.1.2.7.Dry- Run at study location
6.2.1.1.2.8.Take them through all stations and explain the testing cycle
6.2.1.2.Locate materials and resources to be organized and offered by study host location
6.2.1.2.1.Runner to help communicate with employees
6.2.1.2.2.Identify go-to person for any logistical questions
### Overview of Particle Exhalation Baseline
6.3.1.Participants will proceed through several measurements, taking place over several days. Please defer to the study Principle Investigator (i.e., PI) to determine the final protocol for the specific study administration.
6.3.2.In this study, participants within the same household will be tested at the same sequence.
6.3.2.1.
### Phase A: Registration
6.4.1.Participant comes into the test administration room. The Registration Administrator (Admin) welcomes them: _Thank you for making time to participate in this study. Can I please have your First and Last Names?_
6.4.1.1.Admin completes the Online Form (or if no internet connection is available, enter into pre-formatted table) with the participant's name and the number they are assigned. Each participant should be assigned a number; the numbers do not have to be assigned in ascending order. However, each participant's number must be documented with their name in order to track the completion of Informed Consent Waivers and the completion of all 4 tests of the study protocol.
6.4.1.2.The Admin will put one sticker with the participant's number on their bag, and another on an envelope.
6.4.2.Admin should also ask the participant if they have tested positive for COVID-19. If so, the administrator should make a note, and ask when the participant was tested, and when their symptoms were first observed.
6.4.2.1.Admin should write these facts legibly on the consent form, rather than leaving it for the participant to complete themselves.
6.4.3.Admin says _Have you had a chance to review and sign our informed consent waiver?_
6.4.3.1.(If not) _Here is a consent form that you can go through and sign on page 2. On the last page, you will be required to fill in some basic information about yourself such as age, gender, smoking habits and history of lung disease._
6.4.3.2.Participant should sign and complete their consent form. If there is another participant behind them waiting, kindly ask the participant to step aside while the next participant checks in.
6.4.3.3.(If yes) _Thank you for completing the form_
6.4.4.Overview of process: _The test process will take about 20 minutes. You will be asked to breathe into the particle counter machine using your own new filter kit assembly. We want to measure the number and size of particles our participants give off, when you breath or create when talking._
6.4.5.Participant is handed their Ziploc bag with the mouthpiece inside. Admin says: _At the next station, our Administrations will guide you through how to use the particle counter. To reduce the risk of any transmission of illness, only you will touch the component that will go in your mouth. This bag was packaged by our team, on clean surfaces, wearing gloves, to make sure it is clean for you._
6.4.5.1._At the station, the administrator will have attached your filter to the machine. They will guide you through how to attach the mouthpiece you see in this bag._6.4.6. The particle count test will run for about 5 minutes. When you are done, our team will direct you back to me at the registration desk. At that time, I will collect and sanitize the bag with your Nebulizer Assembly (including your mouthpiece) to be kept by the desk. I will also let you know what time to be back at the registration desk.
6.4.7. Do you have any questions before we begin?
6.4.8.Admin will hand the participant three items
6.4.8.1.Bag with the sticker (with participant's number on it), and a sharpie-written number on the bag in the corner
6.4.8.2.Envelope with the participant's number and name in the corner
6.4.8.3.Sticker with the participant's number and name to put on their shirt / uniform
6.4.9.Admin will say: Please proceed to the next station (indicating where it is). When you arrive, please give your envelope to the administrator at the station. It will have been sanitized before you arrive.
6.4.10.Admin can then proceed to address the following participant in line.
### Phase A: Particle Exhalation
5.1.Before the participant arrives, the admin will come around from the particle counter and the separator screen. They will sanitize with wipes the seat, screen, and tabletop.
5.1.Station administrator (admin) will attach a pre-assembled nebulizer filter kit (with the red cap in place; stored in a bin at the station)
5.1.2.They will also have to remove the two labels that cover the HEPA filter (i.e., blue hard plastic box) and discard the sticker labels.
5.2.When the participant arrives, the admin will direct them to kindly sit down in the chair in front of the machine. Admin: _Thank you for participating! At this station, we will measure the number and size of the particles you produce while breathing. At the registration table, you were given a bag and an envelope. Can I please have the envelope?_
#### 6.5.2.1.Participant should then give their envelope to the administrator. Admin: _Thank you_
5.3.To begin, I will activate the machine so you get a sense for how it sounds and work. Right now, you will see the red cap is sealing where your mouthpiece and mouth will go. This will help us make sure the machine is properly working--and give us a baseline against which to measure your particle counts and sizes._
5.3.1.Admin will activate the machine by quickly pressing the POWER button, and hitting start (the yellow icon in the bottom LEFT HAND corner of the screen). This activates the vacuum motor and will begin to draw air in through the HEPA filter. Admin will run the machine so at least 4 printed intervals (i.e., a 6-second interval printed on a receipt).
5.4.During this test, if the >0.3 mm count (the lowest of the four numbers) on the particle counter machine screen is > 40 for more than ten seconds, AND/OR if the>0.3 mm count is variable (i.e., the count jumps), let the machine run for 20 seconds (~3-4 6-second intervals). If the count continues to exceed the number above, or is variable, the admin should take the following steps to remediate:
5.4.1.Slowly and with small movements, move around with nebulizer assembly and the particle machine connector tube to see if the numbers jump more.
5.4.2.First come around the plexiglass screen and make sure that every seal between Nebulizer Assembly parts is tight. This is especially true for the red cap, which may have become loosened during transit.
5.4.3.Move around the connections between the components of the assembly, to migrate them a little bit relative to one another. If the numbers on the counter jump, there are joints that need to be tightened.
5.4.4.Check the connection between the nebulizer kit and the machine connection nozzle. Since this is attached by hand, it can require some force to make a seal.
5.4.5.Restart the machine and check particle counts; if the >0.3 mm count on the particle counter machine screen is > 40 do the following:
5.4.6.Disconnect the entire Nebulizer Assembly and discard. Retrieve a new one from the bin, and redo the test. If numbers still exceed threshold, repeat the whole baseline test.
6.5.5.If the numbers **do not exceed** thresholds, the Admin should turn off the counter (but hitting STOP on the bottom left hand yellow button) for machine. The test can begin. The Admin will then facilitate the participant to attach their mouthpiece. 6.5.5.1.Admin: _For safety, please sanitize your hands before we begin. Please remove the red cap from the Nebulizer Assembly and place if back in your bag. 6.5.5.2.Now please remove your mouthpiece from the bag and attach it firmly around the valve opening where the red cap was. Kindly press firmly; it should be a snug fit--and might need more force than you think._ 6.5.5.3.Participant follows instructions; Admin will visually inspect the mouthpiece from behind the screen. If the participant needs any assistance, the Admin will come around to help them, wearing mask, face shield, and gloves. 6.5.6.Admin will then provide instruction for how the test will run, and answer any questions the participant has. 6.5.6.1.Admin: _As you might remember, this test measures the number and size of particles you breath out. While it might feel weird, we actually want you to breath as normally as possible, breathing in and out of the mouthpiece. 6.5.6.2.The machine measures the particle size and count in 6 second intervals, so we will ask you to keep your mouth on the mouthpiece, breathing normally for up to 3 minutes. A few things to keep in mind: 6.5.6.3.Keep a tight but comfortable seal between your lips and the mouthpiece until I tell you the test is complete. If the seal is broken, we may have to restart the test. 6.5.6.4.We will require that you pinch your nose for that whole time as well, so that all air inhaled comes through the HEPA filter. This is to make sure particles above a certain size to not enter the machine--and that all your exhaled air goes into the machine (and not out of your nose). If you have any issues with this, please let me know. 6.5.6.5.When you first put your mouth over the mouthpiece, take two deep inhales and exhalations with your nose UNPINCHED. These breaths will clear your lungs of air that is in your lungs from before the filtered air enters. These should be deep exhalations. 6.5.6.6.Once those two breaths are complete, please proceed to pinch your nose, and breath normally while maintaining the pinch on your nose. 6.5.6.7.Again, we will ask you to breath normally for the whole 2-3 minutes. Please do not stop or remove your mouth or stop pinching your nose until I let you know. Do you have any questions?_ 6.5.6.8.Admin will pause to answer any questions the participant has. 6.5.7.If none, or all are answered, Admin will power on the machine by pressing the POWER button quickly one time (note: The power button should be hit with one quick depression/push should be sufficient. A sustained push on the button might result in the machine to cycle back to OFF). 6.5.8.The Admin should tell participant: _Please put your mouth on the machine. First you should exhale twice with your nose open and un-pinched. After that, you should pinch your nose and breathe normally until I tell you we're all set._6.5.8.1.The participant should put their lips on the mouthpiece, and take two deep exhalations. The Admin should then make sure the participant pinches their nose, and continues to breathe.
6.5.8.2.During the 2-3 minutes, the Admin should periodically encourage the participant and remind them that they are doing well. The admin should **NOT** ask any questions or make jokes that might encourage the participant to remove their mouth to respond or react in any way. Consider the following:
6.5.8.2.1.You are doing great; exactly as you're doing
6.5.8.2.2.Thanks for keeping your nose pinched; this is going perfectly.
6.5.8.2.3.Nice work; just keep breathing normally. This is exactly how it should work.
6.5.8.3.After 60 seconds, the Admin should check the printing receipt and confirm that the results are satisfactory. If they are, the machine motor should be deactivated. Administrators should confirm that the receipt paper indicates the following data were acquired:
6.5.8.3.1.5-8x 6-second interval printed results with relatively consistent particle counts across all four size categories
6.5.8.3.2.If any intervals appear to "jump" with high particle counts, the admin should continue the test for another 5-6x 6-second interval results. The "jump" can often be attributed to latent atmospheric (i.e., unfiltered) air within the lungs being expelled.
6.5.8.4.At no point should the participant be allowed to remove their lips from the machine, or to un-pinch their nose after the two initial breaths.
6.5.9.Once the results are considered satisfactory, the admin should tear the piece of paper and place the result in the envelope. The admin can inform the participant to remove their mouth from the machine, but to not remove their mouthpiece.
### Post-Phase A: Particle Exhalation Test Close and Clean-Up
6.1.Once all Exhalation Tests are complete, the Admin will ask the Participant to remove the mouthpiece from their device and place it in the bag. The admin should also ask the participant to put the cap back on the end where the mouthpiece was, and encourage them to firmly attach the cap.
6.1.1.Administrator should then come around the separator to remove the Nebulizer Assembly from the nozzle, and hand it to the participant.
6.1.2.Participant is asked to put the remaining filter assembly handed over by the administrator in the resealable bag. The admin will thank the participant for their time and direct them to the following station (FEND administration)
6.2.Administrator should tear the printer receipt from the participant, and prepare it with the appropriate information:
#### 6.6.2.1.On the paper, the admin should write the participant's number (from the envelope).
6.2.2.Administrator draws line on receipt paper printed from particle counter where the particle exhalation stabilizes (e.g., after the two initial exhalations when the particle counts have ceased to "jump"). The printed particle counts above this line will be considered baseline, while those printed number below will be considered the test administration.
6.2.3.The admin should also write on the receipt paper the name of the study phase for which the receipt:
#### 6.6.2.3.1.Baseline
6.2.4. The receipt paper should be folded (NOT ROLLED) and slipped into the envelope, in order to keep the receipts as flat as possible. Do NOT SEAL the envelope.
6.2.5.Administrator will put the participant's envelope in the box for their station (NOTE: each machine station should have its OWN box of envelopes).
6.3.The administrator should come around to the front of the protector screen, wipe down the screen, table, and chair with a sanitizing wipe.
6.3.1.The admin should also attach another (as of yet unused) Nebulizer Assembly from the bin (with the cap attached) to the machine nozzle. The administrator should check and tighten the connections between joints in the Nebulizer Assembly and the machine nozzle, and in the joints in the Nebulizer Assembly (e.g., on the T-Connector Valve; the HEPA filter; the joint connector tube.
#### 6.6.4.Administrator will now be ready to for another participant at their station.
### Phase A: Return to Registration / Check-out
7.1.Participant returns back to the Registration Table to the "Check Out" side. Once there, the participant will hand their Nebulizer Assembly bag (with the assembly, mouthpiece, and cap inside). At the station the administrator says to the participant: _"Thank you for your time. I will take your filter bag, sanitize it and store it hear for you to use it again._
7.2.The admin will take note of the time, and on a 3x5 note card or sticker, the admin will write the time at which the participant should return (i.e., the current time + 30 mins). The admin will write the participant's number on the card with the time, and hand it to the participant.
7.3.The admin will then say to the participant: _Thank you so much for your time. We kindly ask that you please return for the next test (indicating to the card with the time and number).._6.7.3.1.When you return to the test room at the designated time, please come straight to the registration desk, and hand this card (indicating to the card with the time and participant number) back to me or the person at this station. We will sanitize and keep this bag safely at our station.
6.7.3.2.Do you have any questions?
6.7.3.3.If the participant has any questions, the admin will answer them to the best of their ability
6.7.4.The admin will write the current time on the table with the participant's name, noting that they received the bag and that the participant completed the first cycle.
6.7.5.The admin will then spray the participant's bag with sanitizing spray (being careful to NOT spray the number written on the bag or on the sticker--so that they do not fall off). The admin places the bag in the container, in ascending number order (to facilitate the participants return.
6.9.3.Admin will say: _Same as before, I will activate the machine so you get a sense for how it sounds and works. Right now, you will see the red cap is sealing where your mouthpiece and mouth will go. This will help us make sure the machine is properly working--and give us a baseline against which to measure your particle counts and sizes._
6.9.3.1.Admin will activate the machine by quickly pressing the POWER button, and hitting start (the yellow icon in the bottom LEFT HAND corner of the screen). This activates the vacuum motor and will begin to draw air in through the HEPA filter. Admin will run the machine so at least 4 printed intervals (i.e., a 6-second interval printed on a receipt).
6.9.3.2.During this test, if the >0.3 mm count (the lowest of the four numbers) on the particle counter machine screen is > 40 for more than ten seconds, AND/OR if the>0.3 mm count is variable (i.e., the count jumps), let the machine run for 20 seconds (~3-4 6-second intervals). If the count continues to exceed the number above, or is variable, the admin should take the following steps to remediate:
6.9.3.3.Play with the tube to see if the numbers jump more; making it clear that there is a leak
6.9.3.4.First come around the plexiglass screen and make sure that every seal between Nebulizer Assembly parts is tight. This is especially true for the red cap, which may have become loosened during transit.
6.9.3.5.Move around the connections between the components of the assembly, to migrate them a little bit relative to one another. If the numbers on the counter jump, there are joints that need to be tightened.
6.9.3.6.Check the connection between the nebulizer kit and the machine connection nozzle. Since this is attached by hand, it can require some force to make a seal.
6.9.3.7.Restart the machine and check particle counts; if >0.3 mm count on the particle counter machine screen is > 40 do the following:
6.9.3.8.Disconnect the entire Nebulizer Assembly and discard. Retrieve a new one from the bin, and redo the test. If numbers still exceed threshold, repeat the whole baseline test.
6.9.4.If the numbers **do not exceed** thresholds, the Admin turn off the counter (but hitting STOP on the bottom left yellow button) for machine. The test can begin. The Admin will then facilitate the participant to attach their mouthpiece.
6.9.4.1.Admin: _For safety, please sanitize your hands before we begin. Please remove the red cap from the Nebulizer Assembly and place if back in your bag._
6.9.4.2._Now please remove your mouthpiece from the bag and attach it firmly around the valve opening where the red cap was. Kindly press firmly; it should be a snug fit--and might need more force than you think.
6.9.4.3.Participant follows instructions; Admin will visually inspect the mouthpiece from behind the screen. If the participant needs any assistance, the Admin will come around to help them, wearing mask, face shield, and gloves.
6.9.5.Admin will then provide instruction for how the test will run, and answer any questions the participant has.
6.9.5.1.Admin: _As you might remember, this test measures the number and size of particles you breath out. While it might feel weird, we actually want you to breath as normally as possible, breathing in and out of the mouthpiece._
6.9.5.2._The machine measures the particle size and count in 6 second intervals, so we will ask you to keep your mouth on the mouthpiece, breathing normally for up to 3 minutes. A few things to keep in mind:_
6.9.5.3._Keep a tight but comfortable seal between your lips and the mouthpiece until I tell you the test is complete. If the seal is broken, we may have to restart the test._
6.9.5.4._We will require that you pinch your nose for that whole time as well, so that all air inhaled comes through the HEPA filter. This is to make sure particles above a certain size to not enter the machine--and that all your exhaled air goes into the machine (and not out of your nose). If you have any issues with this, please let me know._
6.9.5.5._When you first put your mouth over the mouthpiece, take two deep inhales and exhalations with your nose UNPINCHED. These breaths will clear your lungs of air that is in your lungs from before the filtered air enters. These should be deep exhalations._
6.9.5.6._Once those two breaths are complete, please proceed to pinch your nose, and breath normally while maintaining the pinch on your nose._
6.9.5.7._Again, we will ask you to breath normally for the whole 2-3 minutes. Please do not stop or remove your mouth or stop pinching your nose until I let you know. Do you have any questions?_
6.9.5.8.Admin will pause to answer any questions the participant has.
6.9.6.If none, or all are answered, Admin will power on the machine by pressing the POWER button quickly one time (note: The power button should be hit with one quick depression/push should be sufficient. A sustained push on the button might result in the machine to cycle back to OFF).
6.9.7.The Admin should tell participant: _Please put your mouth on the machine. First you should exhale twice with your nose open and un-pinched. After that, you should pinch your nose and breathe normally until I tell you we're all set._
6.9.7.1.The participant should put their lips on the mouthpiece, and take two deep exhalations. The Admin should then make sure the participant pinches their nose, and continues to breathe.
6.9.7.2.During the 2-3 minutes, the Admin should periodically encourage the participant and remind them that they are doing well. The admin should **NOT** ask any questions or make jokes that might encourage the participant to remove their mouth to respond or react in any way. Consider the following:
6.9.7.2.1._You are doing great; exactly as you're doing 6.9.7.2.2.Thanks for keeping your nose pinched; this is going perfectly. 6.9.7.2.3._Nice work; just keep breathing normally. This is exactly how it should work.
6.9.7.3.After 60 seconds, the Admin should check the printing receipt and confirm that the results are satisfactory. If they are, the machine motor should be deactivated. Administrators should confirm that the receipt paper is the following:
6.9.7.3.1.5-8 6-second interval results with relatively consistent particle counts6.9.7.3.2.If any intervals appear to "jump" with high particle counts, the admin should continue the test for another 5-6 6-second interval results. The "jump" can often be attributed to latent atmospheric (i.e., unfiltered) air within the lungs being expelled.
6.9.7.3.3.At no point should the participant be allowed to remove their lips from the machine, or to un-pinch their nose after the two initial breaths.
6.9.7.4.Once the results are considered satisfactory, the admin asks the Participant to remove the mouthpiece from their device and place it in the bag. **The admin should also ask the participant to put the cap back on the end where the mouthpiece was, and encourage them to firmly attach the cap.**
6.9.7.5.Administrator should then come around the separator to remove the Nebulizer Assembly from the nozzle, and hand it to the participant.
6.9.7.6.Participant is asked to put the remaining filter assembly handed over by the administrator in the resealable bag. The admin will thank the participant for their time and direct them to the following station (FEND administration)
6.9.8.Administrator should tear the printer receipt from the participant, and prepare it with the appropriate information:
6.9.8.1.On the paper, the admin should write the participant's number (from the envelope).
6.9.8.2.Administrator draws line on receipt paper printed from particle counter where the particle exhalation stabilizes (e.g., after the two initial exhalations when the particle counts have ceased to "jump"). The printed particle counts above this line will be considered baseline, while those printed number below will be considered the test administration.
6.9.8.3.The admin should also write on the receipt paper the name of the study phase for which the receipt
6.9.8.4.The receipt paper should be folded (NOT ROLLED) and slipped into the envelope, in order to keep the receipts as flat as possible. Do NOT SEAL the envelope.
6.9.8.5.Administrator will put the participant's envelope in the box for their station (NOTE: each machine station should have its OWN box of envelopes).
6.9.9.The administrator should come around to the front of the protector screen, wipe down the screen, table, and chair with a sanitizing wipe.
6.9.9.1.The admin should also attach another (as of yet unused) Nebulizer Assembly from the bin (with the cap attached) to the machine nozzle. The administrator should check and tighten the connections between joints in the Nebulizer Assembly and the machine nozzle, and in the joints in the Nebulizer Assembly (e.g., on the T-Connector Valve; the HPA filter; the joint connector tube.)
6.9.10.Administrator will now be ready to for another participant at their station.
6.10.Close Out
6.10.1.Admin: Thank you for participating in the study.
6.10.1.1.(If Day 1) We appreciate that you can come back in tomorrow at this same location and approximate time, to have the control study completed.
6.10.2.Admin will ask for the participant's nebulizer assembly bag. The admin will sanitize the bag, by spraying the bag with alcohol cleaner, taking care to not spray the number or the sticker (which could become dislodged or wiped from the bag). If it does, the admin should rewrite the number on the bag, so that it does not lose its participant number.
6.10.3.The admin will put the bag in the bin, in ascending numeric order with the stickers and numbers in the same corner.
6.10.4.Participant may exit.
## Chapter 4 Physical Inventory Checklist
## 1 Materials to Be Printed Checklist
## Item
## Staples Laser/Inkjet Address Labels, 1" x 2 5/8", White, 30 Labels/
## Sheet, 100 Sheets/Box (18057/SIWO100)
## Printed with ascending numbers at left side of stickers (to the max number of anticipated participants +20%), no names
|
20016832 | ## Results:
Additionally, the two-stage Cox-nnet complex model combining histopathology image and transcriptomics RNA-Seq data achieves better prognosis prediction, with a median C-index of 0.75 and log-rank p-value of 6e-7 in the testing datasets. The results are much more accurate than PAGE-Net, a CNN based complex model (median C-index of 0.68 and log-rank p-value of 0.03). Imaging features present additional predictive information to gene expression features, as the combined model is much more accurate than the model with gene expression alone (median C-index0.70). Pathological image features are modestly correlated with gene expression. Genes having correlations to top imaging features have known associations with HCC patient survival and morphogenesis of liver tissue.
## Conclusion:
This work provides two-stage Cox-nnet, a new class of biologically relevant and relatively interpretable models, to integrate multi-modal and multiple types of data for survival prediction.
## Key words:
prognosis, survival, prediction, neural network, modelling, Cox proportional hazards, pathology, image, gene expression, omics, RNA-Seq, data integration
## Introduction
Prognosis prediction is important for providing effective disease monitoring and management. Various biomaterials have been proposed as potential biomarkers to predict patient survival. Among them, hematoxylin and eosin (H&E) stained histopathological images, are very attractive materials to extract biomarker features. Compared to genomics materials, such as RNA-Seq transcriptomics, these images are much more easily accessible and cheaper to obtain, through processing archived formalin-fixed paraffin-embedded (FFPE) Blocks. In H&E staining, the hematoxylin is oxidized into phenatein, a basic dye which stains acidic (basophilic) tissue components (ribosomes, nuclei, and rough endoplasmic reticulum) into darker purple color. Whereas acidic eosin dye stains other protein structures of the tissue (stroma, cytoplasm, muscle fibers) into a pink color. As patients' survival information is retrospectively available in electronic medical record data and FFPE blocks are routinely collected clinically, the histopathology images can be generated and used for highly valuable and predictive prognosis models.
Previously, we developed a neural network model called Cox-nnet to predict patient survival, using transcriptomics data. Cox-nnet is an alternative to the conventional methods, such as Cox proportional hazards (Cox-PH) methods with LASSO or ridge penalization. We have demonstrated that Cox-nnet is more optimized for survival prediction from high throughput gene expression data, with comparable or better performance than other conventional methods, including Cox-PH, Random Survival Forests and Coxboost. Moreover, Cox-nnet reveals much richer biological information, at both the pathway and gene levels, through analysing the survival related "surrogate features" represented as the hidden layer nodes in Cox-nnet. A few other neural network based models were also proposed around the same time as Cox-nnet, such as DeepSurv. It remains to be explored if Cox-nnet can take input features from other data types that are less biologically intuitive than genomics data, such as histopathology imaging data. It is also important to benchmark Cox-nnet with the other above mentioned methods. Moreover, some neural network based models were reported to handle multi-modal data. For example, PAGE-Net is a complex neural network model that has a convolutional neural network (CNN) layer followed by pooling and a genomics model involved in transformation of the gene layer to pathway layer. The genomics neural network portion is followed by two hidden layers, the latter of which is combined with the image neural network model to predict glioblastoma patient survival. Though PAGE-Net uses CNN, the resulting predictive C-index value based on imaging data raises concern of overfitting (train C-index\(=\)0.97; test C-index\(=\)0.68). It is therefore important to test if a model built upon Cox-nnet, using pre-extracted, biologically informative features, can combine multiple types of data, eg. imaging and genomics data, and if so, how well it performs relative to models such as PAGE-Net.
In this study, we extend Cox-nnet to take up pathological image features extracted from imaging processing tool _CellProfiler_, and compare the predictive performance of Cox-nnet relative to Cox proportional hazards, the standard method for survival analysis, which was also the second best method in the previous survival prediction study using pan-cancer datasets. We further used the pathology image data to compare Cox-nnet with two other methods CoxBoost and Random SurvivalForests, which we had compared before on genomics data, as well as the start of the art method DeepSurv []. Moreover, we propose a new type of two-stage complex Cox-nnet model, which combines the hidden node features from multiple first-stage Cox-nnet models, and then use these combined features as the input nodes to train a second stage Cox-nnet model. We applied the models on TCGA hepatocellular carcinoma (HCC), which we had previously gained domain experience on []. Hepatocellular carcinoma (HCC) is the most prevalent type of liver cancer that accounts for 70%-90% of all liver cancer cases. It is a devastating disease with poor prognosis, where the 5-year survival rate is only 12% []. And the prognosis prediction becomes very challenging due to the high level of heterogeneity in HCC as well as the complex etiologic factors. Limited treatment strategies in HCC, relative to other cancers, also imposes an urgent need to develop tools for patient survival prediction. As comparison, we also evaluated the performance of another CNN based model called PAGE-Net, and showed that Cox-nnet achieves higher accuracy in testing data.
## Material & Methods
### Datasets
The histopathology images and their associated clinical information are downloaded from The Cancer Genome Atlas (TCGA). A total of 384 liver tumor images are collected. Among them 322 samples are clearly identified with tumor regions by pathology inspection. Among these samples, 290 have gene expression RNA-Seq data, and thus are selected for pathology-gene expression integrated prognosis prediction. The gene expression RNA-Seq dataset is also downloaded from TCGA, each feature was then normalized into RPKM using the function _ProcessRNASeqData_ by TCGA-Assembler [].
### Tumor Image Pre-processing
For each FFPE image stained with H&E, two pathologists at University of Michigan provide us with the ROI (tumor regions). The tumor regions are then extracted using Aperio software _ImageScope_[]. To reduce computational complexities, each extracted tumor region is divided into non overlapping 1000 by 1000 pixel tiles. The density of each tile is computed as the summation of red, green and blue values, and 10 tiles with the highest density are selected for further feature extraction, following the guideline of others []. To ensure that the quantitative features are measured under the same scale, the red, green and blue values are rescaled for each image. Image |
20017426 | ## Results:
The four genetic variant groups differed in autism severity, autism subdomain profile as well as IQ profile. However, we found substantial variability in phenotypic outcome within individual genetic variant groups (74% to 97% of the variance depending on the trait), whereas variability between groups was low (1% to 21% depending on trait). We compared CNV carriers who met autism criteria, to individuals with heterogeneous autism, and a range of profile differences were identified. Using clinical cut-offs, we found that 54% of individuals with one of the 4 CNVs who did not meet full autism diagnostic criteria nonetheless had elevated levels of autistic traits.
## Conclusion:
Many CNV carriers do not meet full diagnostic criteria for autism, but nevertheless meet clinical cut-offs for autistic traits. Although we find profile differences between variants, there is considerable variability in clinical symptoms within the same variant.
## Introduction
Autism is a behaviourally defined condition characterized by deficits in social interaction and communication, as well as the presence of restricted, repetitive behaviours and interests. There is considerable heterogeneity in the clinical presentation of autism, in terms of symptom profile, cognitive function and developmental trajectories. Studies of large genotyped cohorts of individuals with autism and typically developing controls have identified several chromosomal copy number variants (CNVs) (deletions and duplications >1 kilobase (kb)) as genetic risk factors for autism, and have been demonstrated in clinical settings to have predictive value. Although individually rare, collectively pathogenic CNVs are identified in 15% of patients with neurodevelopmental disability. A number of researchers have advocated that the time is ripe for a reverse strategy based on a genetics-first rather than a phenotype-first approach, in order to better understand the clinical heterogeneity of autism.
Deletions and duplications at the 16p11.2 (600kb, break points 4 and 5 (BP4-BP5) critical region 29.6-30.2 Mb, build hg19) and 22q11.2 (3 Mb, break points A and D, critical region 19.0-21.5 Mb, build hg19) loci have been identified as risk factors for autism, both from phenotype-first studies that find these variants occur with greater frequency in cohorts of individuals with autism versus controls, and genetics-first studies which find that patients diagnosed with 16p11.2 and 22q11.2 CNVs in medical genetics clinics have an elevated frequency of autism diagnosis relative to the frequency in the general population of 1%. It is important to determine whether these variants confer risk for the same autism phenotype or whether the presentation differs by genotype. The former would indicate that genomic risk for autism has common phenotypic effects, whilst the latter would suggest that genetic heterogeneity underpins clinical heterogeneity. Within the autism field, there is a strong notion that the condition is dissociable by genetics, with some researchers using the term "autisms". Early evidence indicates that the 22q11.2 deletion and duplication may have unique autism profiles, however, the profiles of the two groups have not been directly compared within the same study, and hence the differences reported could be due to methodologicalinconsistencies. For the 16p11.2 locus, it has been reported that duplication carriers with autism have lower IQ compared to deletion carriers with autism, however the autism profiles of the two groups have not been compared. It is also important to investigate the extent to which the autism profile of these variants differs from individuals without these variants who have autism (referred to as heterogeneous autism from here onwards).
Comprehensive clinical phenotyping of individuals with autism-risk genetic variants requires large integrated networks of researchers and clinicians using the same clinical instruments. The present study brings together patient data from several international genetics-first consortia of individuals with rare chromosomal conditions associated with high risk of autism. Individuals with deletions and duplications that span critical regions at the 22q11.2 and 16p11.2 loci were ascertained clinically via medical genetics clinics and patient organisations. We aimed to: 1) Characterise and contrast the phenotypes of different autism risk genetic variants, in terms of autism prevalence, severity, symptom domain profile, subdomain profile and IQ; 2) Investigate whether CNV carriers with autism differ in phenotype from individuals with autism of heterogeneous origins.
## Methods
### Participants
#### Genetics-first cohorts
We identified several clinical research sites and consortia which had independently established genetic-first cohorts, and had utilised the Autism Diagnostic Interview - Revised (ADI-R) to assess autism, thus allowing data to be easily combined. Data on 566 clinically ascertained CNV carriers were available but 19 cases were removed due to insufficient genotypic information (n=18) and cohort overlap (n=1). This resulted in 547 CNV carriers (12.3 years (SD=4.2), 54% male) ; 82 with 16p11.2 deletion, 50 with 16p11.2 duplication, 370 with 22q11.2 deletion and 45 with 22q11.2 duplication was provided from the ECHO (ExperiCes of people with tOpy number variants
These individuals were not included in the genomic condition groups given the different ascertainment strategies. The remaining 2027 individuals represent a group of individuals with autism for whom the underlying aetiology is heterogeneous (See Table 1 for demographics). Following previous authors, we refer to this cohort as " heterogeneous autism", rather than "idiopathic."
### Autism assessment
All individuals were assessed using the Autism Diagnostic Interview - Revised (ADI-R) by a research reliable assessor (further information on assessors and assessment sites in Supplementary Table 3). The ADI-R is a semi-structured interview conducted with the primary caregiver about a child's symptoms both currently and during early development. Total ADI-R score was used as an index of autism severity. Autism domain scores for "Social Interaction", "Communication" and "Restricted, Repetitive, and Stereotyped Behaviours (RRBs)" were extracted, as well as autism subdomain scores (further details on ADI-R scores in Supplementary Materials). To meet autism criteria on the ADI-R an individual had to meet the clinical cut-offs on each domain (score of 10 for social, 8 (7 if nonverbal) for communication, and 3 for RRB) and there must also have been evidence of developmental abnormality before the age of 36 months.
### Cognitive assessment
Full Scale IQ (FSIQ), Verbal IQ (VIQ) and Performance IQ (PIQ) scores were derived from age and developmentally appropriate standardized IQ measures as described elsewhere.
### Statistical Analysis
## Aim 1:
Characterising and contrasting the phenotypes of different autism risk genetic variants
_Autism prevalence within genetic variant groups_Autism prevalence was determined on the basis of the ADI-R diagnostic algorithm. A logit mixed model was performed to determine whether genetic variant group (22q11.2 deletion, 22q11.2 duplication, 16p11.2 deletion, 16p11.2 duplication) was a predictor of autism diagnosis, whilst accounting for gender and age. Following previous international studies of the 16p11.2 duplication, we included site (European vs United States) as a covariate. Post-hoc contrasts were conducted to establish autism prevalence differences between genetic variant groups with Tukey adjustment for multiple comparisons. The percentage of individuals who did not meet autism criteria but did meet the clinical cut-off in one or more domains was additionally calculated.
### Autism profiles between genetic variant groups
To investigate possible differences in autism profiles between genetic variant groups, a series of analysis of covariance (ANCOVA) models were conducted with group as a predictor and the following phenotypic variables as outcome measures: ADI-R total as an index of _autism severity_ (ADI-R total score), _autism domain profile, autism subdomain profile_ and _IQ profile_, whilst accounting for gender, age and site (see Supplementary Materials for full information). Tukey's method was used to conduct post-hoc contrasts between genetic variant groups, producing p-values adjusted for the number of contrasts. Eta-squared values were calculated to estimate the proportion of variance explained by genetic variant group (between group differences). We also calculated the variance that is explained by variable expressivity within the four genetic variant groups, i.e. variance not explained by genetic variant group, age, gender and site. Analyses of ADI-R total score, domain and subdomain scores were repeated including FSIQ as a covariate, to investigate whether differences in autism phenotype were driven by FSIQ.
Aim 2: Symptom profiles of individuals with autism within the genetic variant groups and individuals with "heterogeneous autism"To compare autism in the genetic variant groups to _heterogeneous autism_ (i.e., individuals from the AGP dataset who did not have 16p11.2 and 22q11.2 CNVs; n=2027), we conducted analyses leaving out individuals within the genetic variant groups who did not meet ADI-R criteria for autism, and compared the profiles to individuals with heterogenous autism. This resulted in 5 groups: _16p11.2 deletion + autism; 16p11.2 duplication + autism; 22q11.2 deletion + autism; 22q11.2 duplication + autism;_ and _heterogeneous autism_ (Table 1).
MANCOVA analysis was conducted with group as a predictor and phenotypic scores as the outcomes, whilst accounting for gender, age and site. As in aim 1, analyses were run for _autism severity_ (ADI-R total score), _autism domain profile, autism subdomain profile_ and _IQ profile_. Post hoc contrasts to investigate the difference between CNV + autism groups in relation to the autism group were conducted with Tukey adjustment for multiple comparisons.
To investigate whether male-to-female ratios differed between the five groups, we used a logit model with gender as a binary outcome, and group as a predictor, whilst taking account of fixed effects of age, and the random effect of site.
For aims 1 and 2 a Benjamini-Hochberg False Discovery Rate (B-H FDR) multiple testing correction of 0.05 was applied to p-values.
## Results
### Aim 1:
Characterising and contrasting the phenotypes of different autism risk genetic variants
#### Autism prevalence within genetic variant groups
Within our cohort of CNV carriers ascertained clinically via medical genetics clinics and patient organisations; 43% of individuals with 16p11.2 deletion, 58% of individuals with 16p11.2 duplication, 23% of individuals with 22q11.2 deletion and 44% of individuals with 22q11.2 duplication met ADI-R criteria for autism (Table 1). Genetic variant group was a significant predictor of autism diagnosis (p<0.001). Post-hoc contrasts revealed that autism prevalence in the 22q11.2 deletion carrier group (23%) was significantly lower compared to the 16p11.2 deletion (43%, p=0.004), 16p11.2 duplication (58%, p<0.001) groups; the remaining genetic variant group differences were not significant.
Within CNV carriers who did not meet formal autism diagnosis, we examined the proportion who met clinical cut-off criteria for one or more domains on the ADI-R. Amongst the 378/547 (69%) individuals who did not meet criteria for autism, 205/378 (54%) were found to meet the clinical cut-off for at least one domain, indicating a significant domain-based impairment; 38/47 (81%) of 16p11.2 deletion, 19/21 (90%) of 16p11.2 duplication, 135/285 (47%) of 22q11.2 deletion and 13/25 (52%) of 22q11.2 duplication carriers. Supplementary Table 4 and Supplementary show for each CNV the proportion of individuals who met the clinical cut-offs for each domain.
### Autism profiles between genetic variant groups
Genetic variant group predicted autism severity (7% of the variance, p<0.001), autism domain profile (5% of the variance, p<0.001), autism subdomain profile (1% of the variance, p<0.001). In terms of individual domain scores, genetic variant group predicted 5% of the social domain total score, 3% of the communication domain score, and 15% of the RRB domain (Table 2, Figure 1). For subdomain scores the proportion of variance predicted by genetic variant group varied between 1% (social interaction) and 21% (motor mannerisms). In addition to motor mannerisms, the proportion of variance explained was also high for sensorimotor interests (19%). Genetic group variant predicted 12% of variance in FSIQ (p<0.001), 12% of variance in PIQ (p<0.001) and 4% of the variance in VIQ (p<0.001). Findings for autism severity, domain scores and subdomain scores remained significant after controlling for FSIQ, and the eta-squared values remained relatively unchanged (Supplementary Table 5). Age accounted for 0-3% of variance in phenotypic traits (see Supplementary Table 6).
After accounting for between group variability, age, gender and site, a large proportion of variability remained; 74% to 97% within group variability depending on trait (final column, Table 2). This is visualised in and Supplementary Figure 2, which shows that although group differences exist, there is much more variability within all groups across traits. For IQ we found greater variability for duplications than deletions for both 16p11.2 (Levene's test, p=0.001) and 22q11.2 (Levene's test, p<0.001) loci. For autism severity we found greater variability in outcome for duplications than deletions for the 22q11.2 locus (Levene's test, p<0.001) but not for the 16p11.2 locus (Levene's test, p=0.071).
Supplementary Table 7 details which post hoc Tukey contrasts between groups were significant (p-values adjusted for multiple contrasts). To briefly summarise phenotypic profiles; 16p11.2 deletion carriers had relatively moderate autism severity scores and moderate cognitive impairment (IQ= 81.3); 16p11.2 duplication carriers had relatively greater autism severity scores and greater cognitive impairment (IQ= 70.9); 22q11.2 deletion carriers had relatively lower autism severity scores but greater cognitive impairment (IQ=70.3); and 22q11.2 duplication carriers had relatively higher autism severity scores but less cognitive impairment (IQ=88.1).
## Aim 2:
Symptom profiles of individuals with autism within the genetic variant groups and individuals with "heterogeneous autism"
Supplementary Table 8 details mean scores for each phenotypic trait for each group (heterogeneous autism, 16p11.2 deletion + autism, 16p11.2 duplication + autism, 22q11.2 deletion + autism, 22q11.2 duplication + autism). With the exception of VIQ and "routines and rituals" domain, all phenotypic traits and subdomains were found to differ between the five groups (last column Supplementary Table 5). These findings remained significant after a B-H FDR 0.05 correction for multiple testing. Age accounted for 0-5% of variance in phenotypic traits (see Supplementary Table 9). visualises the profile of each "genetic variant + autism" group relative to each other and visualises the profile of each "genetic variant+ autism" group relative to the heterogeneous autism group. Supplementary Table 8 details which aspects of the phenotypic profile showed significant contrasts between the heterogeneous autism group and the genetic variant groups.
To briefly summarise phenotypic profile differences relative to the heterogeneous autism group: the 16p11.2 deletion + autism group had relatively less impairment in autism score severity but had a similar level of cognitive impairment; the 16p11.2 duplication + autism group had greater PIQ deficits but did not differ on any of the other phenotypic measures; the 22q11.2 deletion + autism group had greater cognitive impairment but relatively less severity in autism scores; the 22q11.2 duplication + autism group did not significantly differ from the heterogeneous autism group on any phenotypic measure.
#### Sex
Male CNV carriers (all groups combined) were at increased risk of autism (OR = 2.3, p<0.001) compared to female CNV carriers. However, male to female ratios were lower within CNV carriers with autism (2.3:1) compared to the heterogeneous autism group (6.4:1) (p<0.001).
## Discussion
This study is the result of a collaboration between several international genetics-first consortia and the Autism Genome Project. The availability of a large sample of individuals with one of four autism risk CNVs allowed us to use a genetics-first approach which meant we were not constrained by ascertaining patients on the basis of autism diagnosis, allowing examination of the impact of genotype on autism severity and domain profiles across the spectrum. The use of the widely accepted research diagnostic ADI-R interview across all sites represents a methodological strength, enabling us to directly compare the autism profiles of 22q11.2 and 16p11.2 CNVs. Our findings indicate that although autism risk genetic variants differ in several aspects of the autism phenotype, including autism severity, symptom domain profile and cognitive profile, only 1-21% of the variance is explained by genetic variant group, depending on autism measure. In contrast, variation within each of the four genetic variant groups is much greater, explaining between 74%-97% of the variability, depending on autism measure. This highlights that even within individuals with the same autism risk genetic variant, the autism profile is difficult to predict on the basis of CNV alone and that phenotypic profiles overlap, providing evidence against a 'highly specific" model whereby each genotype leads to a unique autism phenotype (see Supplementary Figure 3), instead our findings support a partially specific model whereby autism profiles are distinct but overlapping.
Severity of autism phenotype differed by genetic variant group. In terms of autism prevalence; fewer 22q11.2 deletion carriers met criteria for autism (23%) than 22q11.2 duplication (44%), 16p11.2 deletion (43%) and 16p11.2 duplication (58%) carriers. These figures represent autism prevalence within a clinically ascertained cohort of CNV carriers, and should not be taken as the prevalence for CNV carriers in the wider population. Among CNV carriers with autism we found that 22q11.2 deletion and 16p11.2 deletion carriers with autism had relatively less severe profiles compared to individuals with heterogeneous autism. On the other hand individuals with 16p11.2 duplication and 22q11.2 duplication with autism had a profile more consistent with individuals with heterogeneous autism. Our findings complement genome wide CNV studies which find the strength of association and penetrance for autism varies by genetic variant, in particular the association of 22q11.2 deletion is relatively weaker.
We found evidence that the four genetic variant groups were associated with differences in autism severity, the three autism domains as well as nine out of the 10 subdomains we studied, FSIQ, VIQ and PIQ. However, the proportion of variance explained by genetic variant group for each subdomain varied between 1-21%. It was only the social interaction subdomain that did not differ, indicating that this trait is a universal aspect of autism across the 4 genetic variant groups. The subdomains for which genetic variant group explained the greatest proportion of variance were motor aspects of the RRB domain, motor mannerisms (21%) and sensorimotor interests (19%), indicating that genetic variant group particularly distinguishes motor aspects of the autism phenotype.
Cognitive profile was also influenced by genetic variant group; 22q11.2 deletion and 16p11.2 duplication carriers had greater cognitive impairments in FSIQ, VIQ and PIQ relative to 22q11.2 duplication and 16p11.2 deletion carriers. There was evidence at both the 22q11.2 and 16p11.2 loci that cognitive outcomes are more variable for duplication carriers than deletion carriers. This has been previously been reported for 16p11.2 duplication carriers and our findings indicate the same may be true for the 22q11.2 locus. Autism severity of a genetic variant did not covary with magnitude of cognitive deficit, 22q11.2 duplication carriers had the highest mean IQ (88.1) out of the CNV groups, yet had high symptom severity scores. 22q11.2 deletion carriers had the greatest cognitive impairment yet were at less risk of autism compared to the other genetic variants. Furthermore, when we controlled for IQ, differences in autism domain and subdomains scores between CNVs remained relatively unchanged. These findings suggest that the mechanisms underlying autism and cognitive impairment are at least partially distinct among carriers of pathogenic CNVs.
However, although specific group differences exist, it is clear that phenotypic profiles overlap (Supplementary Figure 2), and we find greater variability between individuals with the same CNV than between CNVs. Overall, our findings provide most support for a "partially specific model" whereby autism profiles are distinct but highly overlapping. Though the magnitude of these differences is closer to the "non-specific effect" end of the scale whereby all genotypes lead to similar autism phenotypes, than the "highly specific effect" end of the scale whereby genotypes lead to discrete autism subtypes. These findings highlight that it will be important for behavioural phenotyping research to move beyond a focus on average differences between variants, and to investigate the genetic (including additional rare variants and polygenic risk, which we were not able to analyse in this study) and environmental factors that contribute to variation in clinical phenotypes. There is already evidence that family background is important to consider in a genetic counselling context; parental IQ has been found to predict the IQ impairment in 16p11.2 and 22q11.2 deletion carriers.
There was a male preponderance for autism across all genetic variant groups, and gender significantly influenced domain and subdomain profiles. However, the male to female ratio in CNV carriers is approximately 2.3:1 which is considerably less pronounced than in the heterogeneous autism group (6.4:1). It may be that the genetic variants we studied have such a large effect on neurodevelopment that they partially override the protective effect of being female. Age did influence phenotypic traits, however the proportion of variance age explained in analyses was low (\(\lesssim\)5%).
Using a genetics-first approach, we identified a significant proportion of CNV carriers (54%) who did not meet autism criteria but did meet clinical cut-offs for diagnosis related impairments. Furthermore, the profile of CNV carriers with autism does to some extent present differently from heterogeneous autism. This has the potential implication that the clinical needs of patients with genomic conditions may be overlooked because they fail to meet diagnostic criteria despite exhibiting a range of impairments across domains. Parents of children with CNVs at 16p11.2 or 22q11.2 who have taken part in our studies in the UK have anecdotally reported that their child's genetic diagnosis can be a barrier to receiving an autism diagnosis and support, with some service providers having stated that a child with a genetic diagnosis cannot also have a secondary diagnosis of autism despite DSM 5 specifying that autism can be diagnosed when "associated with a known medical or genetic condition or environmental factor". It is important that clinicians are aware of the risk of autism associated with certain genetic variants to improve the opportunities that these children receive of an early diagnosis and access to interventions.
Further clinical implications arise from our finding that there are not highly specific genotype-phenotype relationships between individual CNVs and autism, at least for 16p11.2 and 22q11.2 deletion and duplication variants. This indicates that, although CNVs are pre-symptomatically predictive of autism and therefore can inform early intervention, individual genotypes are not specific in predicting symptom subtypes. Rather our findings indicate an overlap in clinical phenotypes between these CNVs, suggesting that neurodevelopmental service provision for different CNVs could be grouped together. Our genetics-first approach reveals great variability within CNV groups, highlighting that autism risk variants are not deterministic for autism. It is important that in genomic counselling that pathogenic CNVs are considered as one factor within a broader biopsychosocial context, rather than being the only causative factor for autism.
Identification of genetic and environmental modifiers of phenotypes of autism risk CNVs has potential for informing clinical care and intervention.
Our study benefits from several features, including a large sample size by combining data from individuals with these rare genetic conditions from a number of international cohorts, and synchronisation of phenotyping measures across sites allowing for analysis extending beyond categorical diagnosis, allowing for autism domains and subdomains to be analysed. However, there are potential limitations. Firstly, ascertainment bias needs to be considered as our study focuses on individuals who received a clinical genetic diagnosis, and our findings therefore do not necessarily extend to individuals with these CNVs in the population who are affected below a clinical threshold and as a consequence not referred for genetic testing. As one of the main indications for genetic testing currently is often developmental delay, our findings may not be representative for individuals with these CNVs with a more typical developmental pattern. However, despite these ascertainment considerations, not all CNV carriers in this study met autism criteria or had cognitive impairment, thus allowing us to study the impact of genotype across a broad spectrum of abilities. Another source of possible ascertainment bias is that referral reason for genetic testing may differ by genetic variant. For instance it has been reported that 22q11.2 deletion carriers are more likely to be referred due to physical abnormalities, such as heart defects, in comparison to 22q11.2 duplication carriers who are more likely to be referred for developmental reasons. However, this may actually reflect true phenotypic differences as a recent population based study which was able to identify individuals in the population undiagnosed with a 22q11.2 CNV, as well as individuals with a diagnosis through a clinic, reported higher frequency of congenital abnormalities in the deletion carriers. Before taking part in the study, individuals had a variety of diagnostic experiences, where some had a pre-existing autism diagnosis before the ADI-R assessment, whilst others had had no interaction with autism diagnostic services. This potentially introduces caregiver reporter bias, but this is partly mitigated by the semi-structured nature of the ADI-R. That is, although the ADI-R interview is based on caregiver report, the scoring of a particular trait is based on concrete descriptions coded by a trained interviewer. We were not able to conduct cross-site reliability of ADI-R administration as it was not pre-planned that ADI-R data would be combined across several international sites, however all assessors underwent ADI-R formal training and were research reliable. Finally, we were not able to control for ethnicity, and socio-economic and environmental factors, as these data were not available at all sites, and/or were not internationally comparable. Future studies would benefit from greater alignment of measurement of environmental factors across international sites.
## Conclusion
The genetics-first approach we employed represents a novel method for investigating genotype-phenotype relationships unconstrained by categorical diagnostic criteria. We found that the phenotypic profiles of 16p11.2 and 22q11.2 CNVs differ in terms of severity, symptom profile and cognitive profile. However, although genetic variants have specific effects, within variant variability is much greater than between variant variability, thus indicating that the phenotypic consequences of genomic risk factors for autism fit a "partial specific model" rather than a "highly specific" model. It will be important that future studies of autism risk variants consider the genetic and environmental factors that contribute to clinical variability within autism risk variant carriers. An important message from our work is that individuals with genomic conditions are likely to present with clinically significant symptoms of autism but not meet diagnostic criteria. Clinical services need to adapt as individuals without a formal autism diagnosis are unlikely to access support and interventions.
# RRB domain** & 82 & 3.3 & 2.2 & 50 & 5.3 & 2.6 & 370 & 2.1 & 2.3 & 45 & 3.3 & 2.9 & **<0.001*** & 14.7 & 81.7 \\ _subdomains_ & & & & & & & & & & & & & & & \\ Unusual interests & 82 & 0.8 & 1.0 & 50 & 1.6 & 1.1 & 370 & 0.8 & 1.0 & 45 & 0.9 & 1.0 & **<0.001*** & 4.2 & 92.8 \\ Routines \& rtuals & 82 & 0.5 & 0.9 & 50 & 1.1 & 1.3 & 370 & 0.5 & 1.0 & 45 & 0.8 & 1.1 & **<0.001*** & 3.2 & 96.2 \\ Motor mannerisms & 82 & 0.9 & 0.9 & 50 & 1.2 & 0.9 & 370 & 0.2 & 0.5 & 45 & 0.8 & 0.9 & **<0.001*** & 20.9 & 77.8 \\ Sensorimotor interests & 82 & 1.2 & 0.8 & 50 & 1.5 & 0.7 & 370 & 0.5 & 0.7 & 45 & 0.8 & 0.9 & **<0.001*
& 18.8 & 74.0 \\ \hline \end{tabular} |
20018929 | ### The observed association summary statistics
Let us now assume that we observe univariable association summary statistics for these two traits from two (potentially overlapping) finite samples \(N_{x}\) and \(N_{y}\) of size \(n_{x},n_{y}\), respectively. In the following, we will derive observed summary statistics in sample \(N_{x}\) and then we will repeat the analogous exercise for sample \(N_{y}\). Let the realisations of \(X,Y\) and \(U\) be denoted by \(\mathbf{x},\mathbf{y}\) and \(\mathbf{u}\in\mathcal{R}^{n_{x}}\). The genome-wide genetic data is represented by \(\mathsf{G}_{x}\in\mathcal{R}^{n_{x}\times M}\) and the genetic data for a single nucleotide polymorphism (SNP) \(k\) tested for association is \(\mathbf{g_{k}}\in\mathcal{R}^{n_{x}}\). Note the distinction between the \(k\)-th column of \(\mathsf{G}_{x}\), which is the \(k\)-th sequence variant, in contrast to \(\mathbf{g_{k}}\), which is the \(k\)-th SNP tested for association in the GWAS. We assume that all SNP genotypes have been standardised to have zero mean and unit variance. The marginal effect size estimate for SNP \(k\) of trait \(X\) can then be written as \(\widehat{\beta}_{k}^{x}=\mathbf{g}_{k}^{\prime}\cdot\mathbf{x}/n_{x}\), which is a special case of univariable standard normal linear regression when both the outcome and the predictor is standardised to have zero mean and unit variance[\(\overline{\texttt{i}}\)2]. Note that \(\mathbf{x}^{\prime}\) denotes the transposed of the column vector \(\mathbf{x}\).
\[\widehat{\beta}_{k}^{x} = \mathbf{g}_{k}^{\prime}\cdot\mathbf{x}/n_{x}\] \[= \frac{q_{x}+\alpha_{y\to x}\cdot q_{y}}{1-\alpha_{y\to x} \alpha_{y\to x}}\cdot\mathbf{g}_{k}^{\prime}\cdot\mathsf{G}_{x}\cdot\mathbf{\gamma_{u }}/n_{x}+\frac{\alpha_{y\to x}}{1-\alpha_{y\to x}\alpha_{y\to x}} \cdot\mathbf{g}_{k}^{\prime}\cdot\mathsf{G}_{x}\cdot\mathbf{\gamma_{y}}/n_{x}\] \[+ \frac{1}{1-\alpha_{y\to x}\alpha_{y\to x}}\cdot\mathbf{g}_{k}^{ \prime}\cdot\mathsf{G}_{x}\cdot\mathbf{\gamma_{x}}/n_{x}+\mathbf{g}_{k}^{\prime}\cdot \mathbf{\epsilon_{x}}/n_{x}\]
By denoting the linkage disequilibrium (LD) between variant \(k\) and all markers in the genome with \(\mathbf{\rho_{k}}=\mathsf{G}_{x}^{\prime}\cdot\mathbf{g}_{k}/n_{x}\) we get
\[\widehat{\beta}_{k}^{x} = \frac{q_{x}+\alpha_{y\to x}\cdot q_{y}}{1-\alpha_{y\to x} \alpha_{y\to x}}\cdot\mathbf{\rho}_{k}^{\prime}\cdot\mathbf{\gamma_{u}}+\frac{\alpha_ {y\to x}}{1-\alpha_{y\to x}\alpha_{y\to x}}\cdot\mathbf{\rho}_{k}^{\prime}\cdot \mathbf{\gamma_{y}}+\frac{1}{1-\alpha_{y\to x}\alpha_{y\to x}}\cdot\mathbf{\rho}_{k}^{ \prime}\cdot\mathbf{\gamma_{x}}+\eta_{k}^{x}\]
Given the above-defined genetic effect size distribution the equation becomes
\[\widehat{\beta}_{k}^{x} = \frac{q_{x}+\alpha_{y\to x}\cdot q_{y}}{1-\alpha_{y\to x} \alpha_{y\to x}}\cdot\underbrace{\rho_{k}^{\prime}\cdot(\mathsf{G}_{u} \odot\mathbf{\kappa_{u}})}_{z_{k}^{(u)}}+\frac{\alpha_{y\to x}}{1-\alpha_{y\to x} \alpha_{y\to x}}\cdot\underbrace{\rho_{k}^{\prime}\cdot(\mathsf{G}_{y} \odot\mathbf{\kappa_{y}})}_{z_{k}^{(y)}}\] \[+ \frac{1}{1-\alpha_{y\to x}\alpha_{y\to x}}\cdot\underbrace{\rho_{k}^{ \prime}\cdot(\mathsf{G}_{x}\odot\mathbf{\kappa_{x}})}_{z_{k}^{(x)}}+\eta_{k}^{x}\] \[= \frac{q_{x}+\alpha_{y\to x}\cdot q_{y}}{1-\alpha_{y\to x} \alpha_{y\to x}}\cdot z_{k}^{(u)}+\frac{\alpha_{y\to x}}{1-\alpha_{x\to y} \alpha_{y\to x}}\cdot z_{k}^{(y)}+\frac{1}{1-\alpha_{x\to y}\alpha_{y\to x}} z_{k}^{(x)}+\eta_{k}^{x}\]Similarly, assuming that the LD structures \((\mathbf{\rho_{k}})\) in the two samples are comparable, for \(\widehat{\beta}_{k}^{y}\) estimated in the other sample (\(N_{y}\)) we obtain
\[\widehat{\beta}_{k}^{y} = \frac{\alpha_{x\to y}\cdot q_{x}+q_{y}}{1-\alpha_{x\to y}\alpha_{y \to x}}\cdot z_{k}^{(u)}+\frac{\alpha_{x\to y}}{1-\alpha_{x\to y}\alpha_{y \to x}}\cdot z_{k}^{(x)}+\frac{1}{1-\alpha_{x\to y}\alpha_{y \to x}}z_{k}^{(y)}+\eta_{k}^{y}\]
Therefore, the joint effect size estimates can be written as
\[\left(\begin{array}{c}\widehat{\beta}_{k}^{x}\\ \widehat{\beta}_{k}^{y}\end{array}\right) = \frac{1}{1-\alpha_{x\to y}\alpha_{y\to x}}\left(\left( \begin{array}{c}(\alpha_{y\to x}\cdot q_{y}+q_{x})\\ (\alpha_{x\to y}\cdot q_{x}+q_{y})\end{array}\right)z_{k}^{(u)}+\left( \begin{array}{c}1\\ \alpha_{x\to y}\end{array}\right)z_{k}^{(x)}+\left(\begin{array}{c}\alpha_{y \to x}\\ 1\end{array}\right)z_{k}^{(y)}\right)+\left(\begin{array}{c}\eta_{k}^{x}\\ \eta_{k}^{y}\end{array}\right)\]
Following the same rational as the cross-trait LD score regression(\(\frac{1}{2}\)), the noise term distribution is readily obtained
\[\left(\begin{array}{c}\eta_{k}^{x}\\ \eta_{k}^{y}\end{array}\right)\sim\mathcal{N}\left(\left(\begin{array}{c}0\\ 0\end{array}\right),\left(\begin{array}{cc}i_{x}/n_{x}&\frac{n_{x}\cap y}{n_{ x}\cdot n_{y}}\cdot r_{x,y}\\ \frac{n_{x}\cap y}{n_{x}\cdot n_{y}}\cdot r_{x,y}&i_{y}/n_{y}\end{array}\right)\right)\]
Since both \(n_{x\cap y}\) and \(r_{x,y}\) cannot be estimated, we simply denote \(i_{x,y}:=r_{x,y}\cdot\frac{n_{x\cap y}}{\sqrt{n_{x}\cdot n_{y}}}\) as the only estimated parameter and parameterise the covariance term as \(\frac{i_{x,y}}{\sqrt{n_{x}\cdot n_{y}}}\). Note that \(i_{x,y}\) is the cross-trait LD score regression intercept.
The bivariate probability density function (PDF) of these summary statistics cannot be obtained analytically, but in the following we demonstrate that the characteristic function can be derived. Let us first compute the characteristic function of this two-dimensional random variable, knowing that \(z_{k}^{(x)},z_{k}^{(u)},z_{k}^{(y)}\) and \((\eta_{k}^{x},\eta_{k}^{y})\) are independent, hence the characteristic function can be factorised:
\[\varphi_{\left(\widehat{\beta}_{k}^{x},\widehat{\beta}_{k}^{y} \right)}(v,w) = E\left[\exp\left(i\cdot(v\cdot\widehat{\beta}_{k}^{x}+w\cdot \widehat{\beta}_{k}^{y}\right)\right]\] \[= E\left[\exp\left(i\cdot\left(v\cdot\left(\frac{z_{k}^{(x)}+( \alpha_{y\to x}\cdot q_{y}+q_{x})\cdot z_{k}^{(u)}+\alpha_{y\to x}\cdot z_{k}^ {(y)}}{1-\alpha_{x\to y}\alpha_{y\to x}}+\eta_{k}^{x}\right)+\right.\right.\right.\] \[+ \left.\left.\left.w\cdot\left(\frac{z_{k}^{(y)}+(\alpha_{x\to y} \cdot q_{x}+q_{y})\cdot z_{k}^{(u)}+\alpha_{x\to y}\cdot z_{k}^{(x)}}{1- \alpha_{x\to y}\alpha_{y\to x}}+\eta_{k}^{y}\right)\right)\right]\right.\] \[= E\left[\exp\left(i\cdot z_{k}^{(u)}\cdot\frac{v\cdot(\alpha_{y \to x}\cdot q_{y}+q_{x})+w\cdot(\alpha_{x\to y}\cdot q_{x}+q_{y})}{1-\alpha _{x\to y}\alpha_{y\to x}}\right)\right]\] \[\times E\left[\exp\left(i\cdot z_{k}^{(x)}\cdot\frac{v+\alpha_{x\to y} \cdot w}{1-\alpha_{x\to y}\alpha_{y\to x}}\right)\right]\cdot E\left[\exp \left(i\cdot z_{k}^{(y)}\cdot\frac{w+\alpha_{y\to x}\cdot v}{1-\alpha_{x\to y }\alpha_{y\to x}}\right)\right]\] \[\times E\left[\exp\left(i\cdot\left(v\cdot\eta_{k}^{x}+w\cdot\eta_{k}^{ y}\right)\right)\right]\] \[= \varphi_{z_{k}^{(u)}}\left(\frac{v\cdot(\alpha_{y\to x}\cdot q_{y}+q_{x })+w\cdot(\alpha_{x\to y}\cdot q_{x}+q_{y})}{1-\alpha_{x\to y}\alpha_{y\to x}}\right)\] \[\times \varphi_{z_{k}^{(u)}}\left(\frac{v+\alpha_{x\to y}\cdot w}{1-\alpha_{x \to y}\alpha_{y\to x}}\right)\cdot\varphi_{z_{k}^{(y)}}\left(\frac{w+\alpha_{y \to x}\cdot v}{1-\alpha_{x\to y}\alpha_{y\to x}}\right)\cdot\varphi_{(\eta_{k}^{x}, \eta_{k}^{y})}(v,w)\]
In the following we will work out each of the characteristic functions on the right hand side.
Finally, we apply a first order Taylor series approximation (around 1) of the log of the characteristic function in order to speed up computation and improve numerical accuracy
\[\log(\varphi_{z_{k}^{(u)}}(t)) = m_{0}\cdot\log\left(\frac{\pi_{k}\cdot\pi_{u}}{\sqrt{\sigma_{u}^{2 }\cdot\sigma_{k}^{2}\cdot t^{2}+1}}+(1-\pi_{k}\cdot\pi_{u})\right)\] \[= m_{0}\cdot\log\left(1-\pi_{k}\cdot\pi_{u}\cdot\left(1-\frac{1}{ \sqrt{\sigma_{u}^{2}\cdot\sigma_{k}^{2}\cdot t^{2}+1}}\right)\right)\] \[\approx -m_{0}\cdot\pi_{k}\cdot\pi_{u}\cdot\left(1-\frac{1}{\sqrt{\sigma_{ u}^{2}\cdot\sigma_{k}^{2}\cdot t^{2}+1}}\right)\]
Analogously, the approximation of the logarithm of the characteristic functions of \(z_{k}^{(x)}\) and \(z_{k}^{(y)}\) is
\[\log(\varphi_{z_{k}^{(x)}}(t)) \approx -m_{0}\cdot\pi_{k}\cdot\pi_{x}\cdot\left(1-\frac{1}{\sqrt{\sigma _{x}^{2}\cdot\sigma_{k}^{2}\cdot t^{2}+1}}\right)\] \[\log(\varphi_{z_{k}^{(y)}}(t)) \approx -m_{0}\cdot\pi_{k}\cdot\pi_{y}\cdot\left(1-\frac{1}{\sqrt{\sigma _{y}^{2}\cdot\sigma_{k}^{2}\cdot t^{2}+1}}\right)\]
Since the characteristic function of a centred multivariate Gaussian with variance-covariance matrix \(\Sigma\) is \(\exp(-(1/2)\cdot\mathbf{t}^{\prime}\cdot\Sigma\cdot\mathbf{t})\) we have
\[\log\left(\varphi_{\left(\eta_{k}^{x},\eta_{k}^{y}\right)}(v,w)\right)=-\frac{ 1}{2}\cdot\left(\frac{i_{x}}{n_{x}}\cdot v^{2}+2\cdot\frac{i_{x,y}}{\sqrt{n_{x} \cdot n_{y}}}\cdot v\cdot w+\frac{i_{y}}{n_{y}}\cdot w^{2}\right)\]
### From characteristic function to probability density function
The final form of the logarithm of the joint characteristic function of the transformed summary statistics is
\[\log\left(\varphi_{\left(\widehat{\beta}_{k}^{x},\widehat{\beta}_{k}^ {y}\right)}(v,w)\right) = \log\left(\varphi_{z_{k}^{(x)}}\left(\frac{v+\alpha_{x\to y}w}{1- \alpha_{x\to y}\alpha_{y\to x}}\right)\right)+\log\left(\varphi_{z_{k}^{(y)}} \left(\frac{w+\alpha_{y\to x}v}{1-\alpha_{x\to y}\alpha_{y\to x}}\right)\right)\] \[+ \log\left(\varphi_{z_{k}^{(u)}}\left(\frac{v\cdot(\alpha_{y\to x} \cdot q_{y}+q_{x})+w\cdot(\alpha_{x\to y}\cdot q_{x}+q_{y}}{1-\alpha_{x\to y} \alpha_{y\to x}}\right)\right)\] \[+ \log\left(\varphi_{\left(\eta_{k}^{x},\eta_{k}^{y}\right)}(v,w)\right)\] \[\approx -m_{0}\cdot\pi_{k}\cdot\pi_{x}\cdot\left(1-\frac{1}{\sqrt{\frac{ \sigma_{q}^{2}\cdot\sigma_{k}^{2}\cdot(v+\alpha_{x\to y}w)^{2}}{(1-\alpha_{x \to y}\alpha_{y\to x})^{2}}+1}}\right)\] \[- m_{0}\cdot\pi_{k}\cdot\pi_{y}\cdot\left(1-\frac{1}{\sqrt{\frac{ \sigma_{q}^{2}\cdot\sigma_{k}^{2}\cdot(w\cdot(\alpha_{y\to x}\cdot q_{y}+q_{x}) +w\cdot(\alpha_{x\to y}\cdot q_{x}+q_{y}))^{2}}{(1-\alpha_{x\to y}\alpha_{y\to x })^{2}}+1}}\right)\] \[- m_{0}\cdot\pi_{k}\cdot\pi_{u}\cdot\left(1-\frac{1}{\sqrt{\frac{ \sigma_{u}^{2}\cdot\sigma_{k}^{2}\cdot(v\cdot(\alpha_{y\to x}\cdot q_{y}+q_{x}) +w\cdot(\alpha_{x\to y}\cdot q_{x}+q_{y}))^{2}}{(1-\alpha_{x\to y}\alpha_{y\to x })^{2}}+1}}\right)\] \[- \frac{1}{2}\cdot\left(\frac{i_{x}}{n_{x}}\cdot v^{2}+2\cdot\frac{ i_{x,y}}{\sqrt{n_{x}\cdot n_{y}}}\cdot v\cdot w+\frac{i_{y}}{n_{y}}\cdot w^{2}\right)\]
Using the inversion theorem for characteristic functions we can express the joint distribution of \(\left(\widehat{\beta}_{k}^{x},\widehat{\beta}_{k}^{y}\right)\) as
\[f_{\left(\widehat{\beta}_{k}^{x},\widehat{\beta}_{k}^{y}\right)} (x,y) = \left(\frac{1}{2\pi}\right)^{2}\cdot\int_{-\infty}^{\infty}\int_ {-\infty}^{\infty}\exp(-i\cdot(x\cdot v+y\cdot w))\cdot\varphi_{\left( \widehat{\beta}_{k}^{x},\widehat{\beta}_{k}^{y}\right)}(v,w)\ dv\ dw\]
This integral can be efficiently computed by Fast Fourier Transformation (FFT, see and references within). To speed up computation, we bin SNPs according to their \(\pi_{k}\) and \(\sigma_{k}\) values (\(10\times 10\) bins with equidistant centres) and for SNPs in the same bin the PDF function is evaluated over a fine grid (\(2^{7}\times 2^{7}\) combinations) using the FFT.
To reduce the number of parameters we define \(t_{x}:=\sigma_{u}\cdot q_{x}\) and \(t_{y}:=\sigma_{u}\cdot q_{y}\) since \(\sigma_{u}\) and \(q_{x}\) are separately not identifiable, but only their product is. Similarly \(\pi_{u}\) is unidentifiable, and is set to an arbitrary value of \(0.1\). For improved interpretability, we slightly reparameterise the likelihood function by using \(h_{x}^{2}:=\pi_{x}\cdot M\cdot\sigma_{x}^{2},h_{y}^{2}:=\pi_{y}\cdot M\cdot \sigma_{y}^{2}\). Since different SNPs are correlated we have to estimate the over-counting of each SNP. We choose the same strategy as LD score regression and weigh each SNP by the inverse of its restricted LD score, i.e. \(w_{k}=1/\sum_{j=1}^{m_{0}}r_{jk}^{2}\), where \(r_{jk}\) is the correlation between GWAS SNPs \(k\) and \(j\).
\[\log\left(\mathcal{L}\left(\boldsymbol{\theta}|\left(\begin{array}{c} \widehat{\boldsymbol{\beta}}^{\boldsymbol{x}}\\ \widehat{\boldsymbol{\beta}}^{\boldsymbol{y}}\end{array}\right)\right)\right) \propto\sum_{k=1}^{K}w_{k}\cdot f_{k}\left(\widehat{\beta}_{k}^{x},\widehat{ \beta}_{k}^{y}\right) \tag{2}\]
Parameters \(\{n_{x},n_{y},m,\sigma_{k=1,\ldots,K},\pi_{k=1,\ldots,K}\}\) are known and the other \(11\) parameters
\[\boldsymbol{\theta}=\{\pi_{x},\pi_{y},h_{x}^{2},h_{y}^{2},t_{x},t_{y},\alpha_{x \to y},\alpha_{y\to x},i_{x},i_{y},i_{x,y}\}\]are to be estimated from the observed association summary statistics. In order to speed up computation, we can estimate the 11 parameters in two separate steps: the first estimates for each trait the parameters \(\pi_{x},i_{x}\) and \(\pi_{y},i_{y}\) (SNP polygenicity and LD-score intercept) and the total heritability (unlike the direct heritability obtained by the full-model of LHC-MR) by using a simplified model with only the trait of interest, without a second trait or confounder, e.g. we fit only \(\pi_{x},h_{x}^{2}\) and \(i_{x}\) using \(\widehat{\boldsymbol{\beta}}^{\boldsymbol{x}}\) and assume that \(\pi_{x}\) and \(i_{x}\) do not change when two traits are taken into account. Note that \(\pi_{x}\) may change slightly (decreasing from the total- to direct polygenicity), but its value has little impact on the likelihood function. The estimates from the first step can then be fixed for the parameter estimation of trait pairs. Since only \(\pi_{x},i_{x}\) and \(\pi_{y},i_{y}\) are fixed, the remaining parameters to estimate are now:
\[\boldsymbol{\theta}=\{h_{x}^{2},h_{y}^{2},t_{x},t_{y},\alpha_{x\to y}, \alpha_{y\to x},i_{x,y}\}\]
It is key to note that our approach does not aim to estimate individual (direct or indirect) SNP effects, as these are handled as random effects. By replacing \(U\) with \(-U\) we swap the signs of both \(t_{x}\) and \(t_{y}\), therefore these parameters are unique only if the sign of one of them is fixed. Thus, we will have the following restrictions on the parameter ranges: \(h_{x}^{2},h_{y}^{2},t_{x}\) are in \(\), \(t_{y},\alpha_{x\to y},\alpha_{y\to x},i_{x,y}\) are in \([-1,1]\).
### Likelihood maximisation and standard error calculation
Our method, termed _Latent Heritable Confounder Mendelian Randomisation (LHC-MR)_, maximises this likelihood function to obtain the maximum likelihood estimate (MLE). Due to the complexity of the likelihood surface, we initialise the maximisation using 50 different starting points, where they come from a uniform distribution within the parameter-specific ranges mentioned above. We then choose parameter estimates corresponding to the highest likelihood of the 50 runs. Run time depends on the number of iterations during the maximisation procedure, and is linear with respect to the number of SNPs. It takes \(\sim 0.25\) CPU-minute to fit the complete model to 50,000 SNPs with a single starting point.
Given the particular nature of the underlying directed graph, two different sets of parameters lead to an identical fit of the data, resulting in two global optima. The reason for this is the difficulty in distinguishing the ratio of the confounder effects \((t_{y}/t_{x})\) from the causal effect \((\alpha_{x\to y})\), as illustrated in Figure S2 by the slopes belonging to different SNP-clusters.
\[h_{x}^{\prime} = t_{x}+t_{y}\cdot\alpha_{y\to x}\] \[h_{y}^{\prime} = h_{y}\] \[\alpha_{x\to y}^{\prime} = \frac{\alpha_{x\to y}+w}{1+\alpha_{y\to x}\cdot w}\] \[\alpha_{y\to x}^{\prime} = \alpha_{y\to x}\] \[t_{x}^{\prime} = h_{x}\cdot(1+\alpha_{y\to x}\cdot w)\] \[t_{y}^{\prime} = -h_{x}\cdot w\]
This allows us to directly obtain both optima, even if the optimisation only revealed one of them. It happens very often that one of these parameter sets are outside of the allowed ranges and hence can be automatically excluded. If not, we keep track of both parameter estimates maximising the likelihood function. Note that, we call the one for which the direct heritability is larger than the indirect one, i.e. \(h_{x}^{2}>t_{x}^{2}\), the primary solution. We show that for real data application this solution is far more plausible than the alternative optimum. Finally, note that such bimodality can be observed at different levels: (i) For one given data generation, using multiple starting points leads to different optima; (ii) LHC-MR applied to multiple different data generations for a fixed parameter setting can yield different optima. Both of these situations are signs of the same underlying phenomenon and most often co-occur.
We implemented the block jackknife procedure that is also used by LD score regression to calculate the standard errors. For this we split the genome into 200 jackknife blocks and compute MLE in a leave-one-block-out fashion yielding \(\widehat{\mathbf{\theta}}^{(-i)},i=1,\ldots,200\) estimates. The variance of the full SNP MLE is then defined as \(Var(\widehat{\theta}):=\frac{m-\langle 1/200\rangle}{m-\langle 1/200\rangle} \cdot\frac{1}{200-1}\sum_{i=1}^{200}(\widehat{\mathbf{\theta}}^{(-i)}-\widehat{ \mathbf{\theta}})^{2}=\sum_{i=1}^{200}(\widehat{\mathbf{\theta}}^{(-i)}-\widehat{\mathbf{ \theta}})^{2}\).
### Decomposition of genetic correlation
Given the starting equations for \(X\) and \(Y\) we can calculate their genetic correlation.
\[\mathbf{\delta_{x}} = q_{x}\cdot\mathbf{\gamma_{u}}+\alpha_{y\to x}\mathbf{\delta_{y}}+\mathbf{ \gamma_{x}}\] \[\mathbf{\delta_{y}} = q_{y}\cdot\mathbf{\gamma_{u}}+\alpha_{x\to y}\mathbf{\delta_{x}}+\mathbf{ \gamma_{y}}\]
Substituting the second equation to the first yields
\[\mathbf{\delta_{x}} = q_{x}\cdot\mathbf{\gamma_{u}}+\alpha_{y\to x}(q_{y}\cdot\mathbf{ \gamma_{u}}+\alpha_{x\to y}\mathbf{\delta_{x}}+\mathbf{\gamma_{y}})+\mathbf{\gamma_{x}}\] \[= (q_{x}+\alpha_{y\to x}q_{y})\cdot\mathbf{\gamma_{u}}+(\alpha_{y\to x} \alpha_{x\to y})\mathbf{\delta_{x}}+\alpha_{y\to x}\mathbf{\gamma_{y}}+\mathbf{\gamma_{x}}\] \[= \left((q_{x}+\alpha_{y\to x}q_{y})\cdot\mathbf{\gamma_{u}}+\alpha_{y \to x}\mathbf{\gamma_{y}}+\mathbf{\gamma_{x}}\right)/(1-\alpha_{y\to x}\alpha_{x\to y})\]
Similarly,
\[\mathbf{\delta_{y}} = \left((q_{y}+\alpha_{x\to y}q_{x})\cdot\mathbf{\gamma_{u}}+\alpha_{x \to y}\mathbf{\gamma_{x}}+\mathbf{\gamma_{y}}\right)/(1-\alpha_{y\to x}\alpha_{x\to y})\]
Thus the genetic covariance is
\[E[\mathbf{\delta_{x}}\cdot\mathbf{\delta_{y}}] = \left((q_{x}+\alpha_{y\to x}q_{y})\cdot\mathbf{\gamma_{u}}+\alpha_{y \to x}\mathbf{\gamma_{y}}+\mathbf{\gamma_{x}}\right)\left((q_{y}+\alpha_{x\to y}q_{x}) \cdot\mathbf{\gamma_{u}}+\alpha_{x\to y}\mathbf{\gamma_{x}}+\mathbf{\gamma_{y}}\right)/(1- \alpha_{y\to x}\alpha_{x\to y})^{2}\] \[= \left((q_{x}+\alpha_{y\to x}q_{y})(q_{y}+\alpha_{x\to y}q_{x})h_{u}^{2} +\alpha_{y\to x}h_{y}^{2}+\alpha_{x\to y}h_{x}^{2}\right)/(1-\alpha_{y\to x} \alpha_{x\to y})^{2}\] \[= \left((t_{x}+\alpha_{y\to x}t_{y})(t_{y}+\alpha_{x\to y}t_{x})+ \alpha_{y\to x}h_{y}^{2}+\alpha_{x\to y}h_{x}^{2}\right)/(1-\alpha_{y\to x} \alpha_{x\to y})^{2}\]
and the heritabilities are
\[E[\mathbf{\delta_{x}^{2}}] = \left((t_{x}+\alpha_{y\to x}t_{y})^{2}+\alpha_{y\to x}^{2}h_{y}^{2}+h_{x}^{2 }\right)/(1-\alpha_{y\to x}\alpha_{x\to y})^{2}\] \[E[\mathbf{\delta_{y}^{2}}] = \left((t_{y}+\alpha_{x\to y}t_{x})^{2}+\alpha_{x\to y}^{2}h_{x}^{2}+h_{y}^{2 }\right)/(1-\alpha_{y\to x}\alpha_{x\to y})^{2}\]
Therefore the genetic correlation takes the form
\[corr(\mathbf{\delta_{x}},\mathbf{\delta_{y}})=\frac{(t_{x}+\alpha_{y\to x}t_{y})(t_{y}+ \alpha_{x\to y}t_{x})+\alpha_{y\to x}h_{y}^{2}+\alpha_{x\to y}h_{x}^{2}}{\sqrt{ \left((t_{x}+\alpha_{y\to x}t_{y})^{2}+\alpha_{y\to x}^{2}h_{y}^{2}+h_{x}^{2} \right)\left((t_{y}+\alpha_{x\to y}t_{x})^{2}+\alpha_{x\to y}^{2}h_{x}^{2}+h_{y}^{2 }\right)}} \tag{3}\]
These values can be compared to those obtained by LD score regression.
### Computation of the LD scores
We first took 4,773,627 SNPs with info (imputation certainty measure) \(\geq\) 0.99 present in the association summary files from the second round of GWAS by the Neale lab. This set was restricted to 4,650,107 common, high-quality SNPs, defined as being present in both UK10K and UK Biobank, having MAF \(>\) 1% in both data sets, non-significant (\(P_{diff}>0.05\)) allele frequency difference between UK Biobank and UK10K and residing outside the HLA region (chr6:28.5-33.5Mb). For these SNPs, LD scores and regression weights were computed based on 3,781 individuals from the UK10K study. To estimate the local LD distribution for each SNP (\(k\)), characterised by \(\pi_{k},\sigma_{k}^{2}\), we fitted a two-component Gaussian mixture distribution to the observed local correlations (focal SNP +/\(-\) 2'500 markers with MAF\(\geq\) 0.5% in the UK10K): one Gaussian component corresponding to zero correlations, reflecting only measurement noise (whose variance is proportional to the inverse of the reference panel size) and a second component with zero mean and a larger variance than the first component (encompassing measurement noise plus non-zero LD).
### Simulation settings
First, we tested LHC-MR using realistic parameter settings with a mild violation of the classical MR assumptions. These standard parameter settings consisted of simulating \(m\) = 234,000 SNPs for two non-overlapping cohorts of equal size (for simplicity) of \(n_{x}=n_{y}\) = 50,000 for each trait. \(X,Y\) and \(U\) were simulated with moderate polygenicity (\(\pi_{x}=5\times 10^{-3},\pi_{y}=1\times 10^{-2},\pi_{u}=5\times 10^{-2}\)), and considerable direct heritability (\(h_{x}^{2}=0.25,h_{y}^{2}=0.2,h_{u}^{2}=0.3\)). \(U\) had a confounding effect on the two traits as such, \(q_{x}=0.3,q_{y}=0.2\) (resulting in \(t_{x}=0.16,t_{y}=0.11\)), and \(X\) had a direct causal effect on \(Y\) (\(\alpha_{x\to y}=0.3\)), while the reverse causal effect from \(Y\) to \(X\) was set to null. Note that in this setting the total heritability of each of these traits is principally driven by direct effects and less than 10% of the total heritability is through a confounder and in case of \(Y\) less than an additional 8% of its total heritability is through \(X\).
It is important to note that for each tested parameter setting, we generated 50 different data sets, and each data generation underwent a likelihood maximisation of Eq. using 50 starting points, and produced estimated parameters corresponding to the highest likelihood (simplified schema in Figure S3).
In the following simulations, we changed various parameters of these standard settings to test the robustness of the method. We explored how increased sample size (\(n_{x}=n_{y}=500,000\)) or differences in sample sizes (\((n_{x},n_{y})=\) and \((n_{x},n_{y})=\)) influence causal effect estimates of LHC-MR and other MR methods. We also simulated data with no causal effect (or with no confounder) and then examined how LHC-MR estimates those parameters. Next, we varied our causal effects between the two traits by lowering \(\alpha_{x\to y}\) to 0.1, and in another setting by introducing a reverse causal effect (\(\alpha_{y\to x}=-0.1\)). In addition, we tried to create extremely unfavourable conditions for all MR analyses by varying the confounding effects. We did this in several ways: (i) increasing \(q_{x}\) and \(q_{y}\) (\(q_{x}=0.75,q_{y}=0.50\)), (ii) having a confounder with causal effects of opposite signs on \(X\) and \(Y\) (\(q_{x}=0.3,q_{y}=-0.2\)). We also drastically increased the proportion of SNPs with non-zero effect on traits \(X\), \(Y\) and \(U\) (\(\pi_{x}\), \(\pi_{y}\) and \(\pi_{u}=0.1,0.15,0.2\) respectively). We also simulated data whereby the confounder has lower (\(\pi_{u}\) = 0.01) polygenicity than the two focal traits.
Finally, we explored various violations of the assumptions of our model (see Section). First, we introduced two confounders in the simulated data, once with causal effects on \(X\) and \(Y\) that were concordant (\(t_{x}^{}=0.16,t_{y}^{}=0.11,t_{x}^{}=0.22,t_{y}^{}=0.16\)) in sign, and another with discordant effects (\(t_{x}^{}=0.16,t_{y}^{}=0.11,t_{x}^{}=0.22,t_{y}^{}=-0.16\)), while still fitting the model with only one \(U\). Second, we breached the assumption that the non-zero effects come from aGaussian distribution. By design, the first three moments of the direct effects are fixed: they have zero mean, their variance is defined by the direct heritabilities and they must have zero skewness because the effect size distribution has to be symmetrical. Therefore, to violate the normality assumption, we varied the kurtosis (2, 3, 5, and 10) of the distribution drawn from the Pearson's distribution family. Third, we tested the assumption of the direct effects on our traits coming from a two-component Gaussian mixture by introducing a third component and observing how the estimates were effected. In this simulation scenario we introduced a large effect third component for \(X\) while decreasing the polygenicity of \(U\) (\(\pi_{x1}=1\times 10^{-4},\pi_{x2}=1\times 10^{-2},h_{x1}^{2}=0.15,h_{x2}^{2}=0.1, \pi_{u}=1\times 10^{-2}\)).
### Application to real summary statistics
Once we demonstrated favourable performance of our method on simulated data, we went on to apply LHC-MR to summary statics obtained from the UK Biobank and other meta-analytic studies (Table S1) in order to estimate pairwise bi-directional causal effect between 13 complex traits. The traits varied between conventional risk factors (such as low education, high body mass index (BMI), dislipidemia) and diseases (including diabetes and coronary artery disease among others). SNPs with imputation quality greater than 0.99, and minor allele frequency (MAF) greater than 0.5% were selected. Moreover, SNPs found within the human leukocyte antigen (HLA) region on chromosome 6 were removed due to the abundance of SNPs associated with autoimmune and infectious diseases as well as the complicated LD structure present in that region. For traits with total heritability below 2.5%, the outgoing causal effect estimates were ignored since instrumenting such barely heritable traits is questionable.
In order to perform LHC-MR between trait pairs, a set of overlapping SNPs was used as input for each pair. The effects of these overlapping SNPs were then aligned to the same effect allele in both traits. To decrease computation time further (while only minimally reducing power), we selected every 10th QC-filtered SNP as input for the analysis. We calculated regression weights using the UK10K panel, which may be sub-optimal for summary statistics not coming from the UK Biobank, but we have previously shown that estimating LD in a ten-times larger data set (UK10K) outweighs the benefit of using smaller, but possibly better-matched European panel (1000 Genomes).
We also ran IVW for each trait pair in both directions to estimate bi-directional causal effects as well as LD score regression to get the cross trait intercept term. We then added uniformly distributed (\(\sim U(-0.1,0.1)\)) noise to these pre-estimated parameters to generate starting points for the second step of the likelihood optimisation. These closer-to-target starting points did not change the optimisation results, simply sped up the likelihood maximisation and increased the chances to converge to the same (primary) optimum. The LHC-MR procedure was run for each pair of traits 100 times, each using a different set of randomly generated starting points within the ranges of their respective parameters. For the optimisation of the likelihood function (Eq. 2), we used the R function 'optim' from the'stats' R package. Once we fitted this _complete_ model estimating 11 parameters in two steps \(\{i_{x},i_{y},\pi_{x},\pi_{y},h_{x}^{2},h_{y}^{2},t_{x},t_{y},\alpha_{x\!-\!y },\alpha_{y\!-\!x},i_{xy}\}\), we then ran block jackknife to obtain the SE of the parameters estimated in the second step: \(\{h_{x}^{2},h_{y}^{2},t_{x},t_{y},\alpha_{x\!-\!y},\alpha_{y\!-\!x},i_{xy}\}\).
To support the existence of the confounders identified by LHC-MR, we used EpiGraphDB to systematically identify those potential confounders. The database provided for each potential confounder of a causal relationship, a causal effect on trait \(X\) and \(Y\) (\(r1\), and \(r3\) in their notation), the sign of the ratio of which (\(sign(r_{3}/r_{1})\)) was compared to the sign of the LHC-MR estimated \(t_{y}/t_{x}\) values representing the strength of the confounder acting on the two traits. We restricted our comparison to the sign only, since the \(r1,r3\) values reported in EpiGraphDB are not necessarily on the same scale.
### Comparison against conventional MR methods and CAUSE
We compared the causal parameter estimates of the LHC-MR method to those of five conventional MR approaches (MR-Egger, weighted median, IVW, mode MR, and weighted mode MR) using a Z-test. The 'TwoSampleMR' R package was used to get the causal estimates for all the pairwise traits as well as their standard errors from the above-mentioned MR methods. The same set of genome-wide SNPs that were used by LHC-MR, were used as input for the package. SNPs associated with the exposure were selected to various degrees (for simulation we selected SNPs over a range of thresholds: absolute P-value \(<5\times 10^{-4}\) to \(<5\times 10^{-8}\)), and SNPs more strongly associated with the outcome than with the exposure (P-value \(<0.05\) in one-sided t-test) were removed. The default package settings for the clumping of SNPs (\(r^{2}=0.001\)) were used and the analysis was run with no further changes. We tested the agreement between the significance and direction of our estimates and that of standard MR methods, with the focus being on finding differences in statistical conclusions regarding causal effect sizes.
We compared our causal estimates from all our simulation settings to the causal estimates obtained by running MR-RAPS also using the 'TwoSampleMR' R package, once by using the entire set of SNPs, and another by filtering for SNPs with a significance threshold of \(<5\times 10^{-4}\). We also compared both our simulation as well as real data results against those of CAUSE. We first generated simulated data under the LHC model and used them as input to estimate the causal effect using CAUSE. We then generated simulated data using the CAUSE framework and inputted them to LHC-MR (as well as standard MR methods) to estimate the causal parameters. Lastly, we compared causal estimates obtained for the 78 trait pairs (156 bi-directional causal effects) from LHC-MR to those obtained when running CAUSE.
## 3 Results
### Overview of the method
We fitted an 11-parameter structural equation model (SEM) to genome-wide summary statistics of two studied complex traits in order to estimate bi-directional causal effects between them (for details see Methods). Additional model parameters represent direct heritabilities for \(X\) and \(Y\), confounder effects, cross-trait and individual trait LD score intercepts and the polygenicity for \(X\) and \(Y\). All SNPs associated with the heritable confounder (\(U\)) are indirectly associated with \(X\) and \(Y\) with effects that are proportional (ratio \(t_{y}/t_{x}\)). SNPs that are directly associated with \(X\) (and not with \(U\)) are also associated with \(Y\) with proportional effects (ratio \(1/\alpha_{x\to y}\)). Finally, SNPs that are directly \(Y\)-associated are also \(X\)-associated with a proportionality ratio of \(1/\alpha_{y\to x}\). These three groups of SNPs are illustrated on the \(\beta_{x}\)-vs-\(\beta_{y}\) scatter plot (Figure S2). In simple terms, the aim of our method is to identify the different clusters, estimate the slopes and distinguish which corresponds to the causal- and confounder effects. In this paper, we focus on the properties of the maximum likelihood estimates (and their variances) for the bi-directional causal effects arising from our SEM.
### Simulation results
We started off with a realistic simulation setting of 234,000 SNPs on chromosome 10 (LD patterns used from the UK10K panel) and 50,000 samples for both traits. Traits \(X,Y\) and confounder \(U\) had average polygenicity (\(\pi_{x}=5\times 10^{-3},\pi_{y}=1\times 10^{-2},\pi_{u}=5\times 10^{-2}\)), with substantial direct heritability for \(X\) and \(Y\) (\(h_{x}^{2}=0.25,h_{y}^{2}=0.2\)), mild confounding (\(t_{x}=0.16,t_{y}=0.11\)) and a causal effect between \(X\) and \(Y\) (\(\alpha_{x\to y}=0.3,\alpha_{y\to x}=0\)). Note that with these settings, SNPs associated with \(U\) would violate the InSIDE assumption but might still be used by conventional MR methods. Under this standard setting, there were no genome-wide significant SNPs for standard MR methods, and estimates derived using SNPs with a p-value \(<5\times 10^{-6}\) showed a downward bias for all MR methods (panel _a_). MR-RAPS using filtered SNPs (p-value \(<5\times 10^{-4}\)) was similarly downward biased whereas MR-RAPS using the entire set of SNPs was upward biased with the least amount of variance compared to all methods including LHC-MR. LHC-MR in this scenario slightly over estimated the causal effect in comparison but had the smallest RMSE after MR-RAPS (0.13 vs 0.06, Supplementary Table S2).
We ran all our simulation scenarios with a smaller and a larger sample size (50,000 and 500,000) and observed that the relative performance of the methods were in some cases sample size specific. Smaller sample sizes often meant that standard MR methods had little to no IVs reaching genome-wide (GW) significance and hence we were forced to use IVs from less stringent thresholds (\(<5\times 10^{-4}\) and \(<5\times 10^{-6}\)). Therefore, the causal effects were estimated with a substantial downward bias due to weak instrument bias (and winner's curse). LHC-MR in these cases was able to estimate the causal effect with less bias but with a larger variance compared to most standard MR methods - still outperforming them in terms of RMSE in most settings. In the larger sample size setting, standard MR methods had IVs for every threshold cutoff. However, a pattern also observed with smaller sample sizes, but to a lesser extent, the causal estimates of some methods changed (either in mean or in variance, most noticeably observed in weighted median and IVW) as the threshold became more stringent. This is of particular concern and highlights that while in this simulation setting the \(5\times 10^{-8}\) threshold may have optimally cancelled out the different biases for IVW (downward bias due to winner's curse and weak instrument bias, upward bias due to genetic confounding), its estimate remains strongly setting-dependent. LHC-MR has performed reasonably well, exhibiting lower RMSE than most other methods, except for IVW and MR-RAPS for the \(5\times 10^{-4}\) threshold (panel _a_). However, we observed that the performance of MR-RAPs is particularly setting- and threshold dependent.
Furthermore, unequal sample sizes for the two traits showed an underestimation of the causal effects for almost all MR methods, while LHC-MR remained the most accurate in the case where \(n_{x}\) was smaller than \(n_{y}\). However, the performances in the reverse scenario, where \(n_{x}\) was larger in size, were akin to the large sample size standard setting, where only IVW and filtered MR-RAPS (\(<5\times 10^{-4}\)) showed superior performance to LHC-MR both in terms of bias and variance (see Figure 5).
When testing scenarios in the absence of a causal- or a confounder effect (imitating the classical MR assumptions), with a smaller causal effect (\(\alpha_{x\to y}=0.1\)), or with both forward- and reverse causal effects, we note that LHC-MR outperforms the standard MR methods as well as MR-RAPS in all these scenarios.
When there was no causal effect (\(\alpha_{x\to y}=0\)), LHC-MR had the smallest bias out of all the methods in both sample sizes (0.004 in both, panel \(a\) and panel _a_). The variance of the LHC-MR estimates in the larger sample size was much lower (0.0001 vs 0.01), similarly the other methods had a smaller variance in larger sample sizes and had more clearly seen upward biased estimates. The increased upward bias of standard MR methods is due to the fact that confounder-associated SNPs could only be detected in larger sample size and those lead to positive bias (due to the concordant effect of the confounder on the two traits). Note that the variance of standard MR methods are low simply because, in these settings, we were forced to lower the instrument selection threshold, hence artificially included many (potentially invalid) instruments, which lowers the estimator variance while increasing bias. MR-RAPS greatly overestimates the causal effects when the sample size is larger.
**Simulation results under various scenarios.** These Raincloud boxplots represent the distribution of parameter estimates from 50 different data generations under various conditions. For each generation, standard MR methods as well as our LHC-MR were used to estimate a causal effect. The true values of the parameters used in the data generations are represented by the blue dots/lines. **a** Estimation under standard settings (\(\pi_{x}=5\times 10^{-3},\pi_{y}=1\times 10^{-2},\pi_{u}=5\times 10^{-2},h_{x}^{2}=0.25,h_{y}^{2}=0.2,h_{u}^{2}=0.3,t_{x}=0.16,t_{y}=0.11\)). **b** Addition of a reverse causal effect \(\alpha_{y\to x}=-0.2\). **c** Confounder with opposite causal effects on \(X\) and \(Y\) (\(t_{x}=0.16,\overset{\text{R}}{\underset{y}{\text{R}}}=-0.11\)).
In the absence of a confounder effect, there is not much of a difference between the two sample sizes; standard MR methods have a large variance and are downward biased, LHC-MR is less biased compared to them but MR-RAPS performs best with the least bias and variance when all the SNPs are used as instruments (Figure S6 panel \(b\) and Figure S7 panel _b_). Trying a smaller causal effect led to an upward bias for all MR methods including both filterings of MR-RAPS in the larger sample size. Alternately, when \(n_{x}=n_{y}=50,000\), the MR methods are downward biased (Figures S6 panel \(c\) and Figures S7 panel _c_). Lastly, when a (negative) reverse causal effect is introduced, all MR methods and MR-RAPS are negatively biased in their estimation of the causal effect (see panel _b_). LHC-MR has a much smaller bias for the forward causal effect estimate in this case, and a generally small bias for the reverse causal effect in both sample sizes (\(0.05\) for \(n=50,000\) and \(0.03\) for \(n=500,000\), Figure S4 panel _b_).
Increasing the indirect genetic effects, by intensifying the contribution of the confounder to \(X\) and \(Y\) (\(t_{x}=0.41,t_{y}=0.27\)), led to a general over estimation of the causal effects by all methods including LHC-MR, though more drastically seen in standard MR methods and MR-RAPS in larger sample sizes, when there is sufficient power to pick up these confounder-associated SNPs. The causal effect estimates of standard MR methods in the smaller sample size were much less affected by the presence of a strong confounder compared to LHC-MR and MR-RAPS (Figure S8). The reason for this is that the confounder-associated SNPs remain undetectable at lower sample size and hence instruments will not violate the classical MR assumptions.
Further testing the effects of the confounder trait on the causal estimation, we tested the impact of confounders with opposite effects on \(X\) and \(Y\). We observe a major underestimation of the causal effects for standard MR methods as well as MR-RAPS, whereas LHC-MR performs better for both sample sizes (RMSE = 0.01 and 0.1 for larger and smaller \(n\) respectively), see Figures 2 panel \(c\) and 4 panel \(c\).
Our LHC-MR method is influenced by the unlikely scenario of extreme polygenicity for traits \(X,Y\) and \(U\), and it suffers from increased bias and variance regardless of sample size (see Figure S9). Standard MR methods as well as filtered MR-RAPS underestimated the causal effect when \(n=50,000\). Some also underestimated \(\alpha_{x\to y}\) when \(n=500,000\), with the exception of IVW, Mode and filtered MR-RAPS, that outperformed the rest. Decreasing the proportion of confounder-associated SNPs to 1% only, does not seem to affect our method and shows similar results to the standard setting (Figure S10).
Furthermore, we simulated summary statistics, where (contrary to our modelling assumptions) the \(X-Y\) relationship has two confounders, \(U_{1}\) and \(U_{2}\). When the ratio of the causal effects of these two confounders on \(X\) and \(Y\) (\(q_{x}^{}/q_{y}^{}\) and \(q_{x}^{}/q_{y}^{}\) respectively) agreed in sign, the corresponding causal effects of standard MR methods were over-estimated in larger sample sizes and, conversely, underestimated in smaller sample sizes (Figures S11 and S12 panels _a_). LHC-MR and weighted median performed better however in larger sample sizes and had a bias of 0.03 and 0.07 respectively. However, when the signs were opposite (\(q_{x}^{}=0.3,q_{y}^{}=0.2\) for \(U_{1}\) and \(q_{x}^{}=0.3,q_{y}^{}=-0.2\) for \(U_{2}\)), conventional MR methods and MR-RAPS in this case almost all underestimated the causal effect regardless of sample size. LHC-MR outperformed them both in the larger sample size (bias of \(0.007\)) and in the smaller sample size (bias of \(-0.003\)), see Figures S11 and S12 panels \(b\).
Finally, we explored how sensitive our method is to different violations of our modelling assumptions. First, we simulated summary statistics when the underlying non-zero effects come from a non-Gaussian distribution. Interestingly, we observed that, for smaller sample sizes, the variance of the causal effect estimate was dependent on the kurtosis for most MR methods. LHC-MR estimations yielded slightly more pronounced upward bias than IVW, while still exhibiting the lowest RMSE among all methods (Figure S1 panel _a_). Similar results are seen in larger sample **Simulation results under various scenarios.** These Raincloud boxplots represent the distribution of parameter estimates from 50 different data generations under various conditions. For each generation, standard MR methods as well as our LHC-MR were used to estimate a causal effect. The true values of the parameters used in the data generations are represented by the blue dots/lines. **a** The different coloured boxplots represent the underlying non-normal distribution used in the simulation of the three \(\gamma_{x},\gamma_{x},\gamma_{u}\) vectors associated to their respective traits. The Pearson distributions had the same zero mean and skewness, however their kurtosis ranged between 2 and 10, including the kurtosis of 3, which corresponds to a normal distribution assumed by our model. The standard MR results reported had IVs selected with a p-value threshold of \(5\times 10^{-6}\). **b** Addition of a third component for exposure \(X\), while decreasing the strength of \(U\). True parameter values are in colour, blue and red for each component (\(\pi_{x1}=1\times 10^{-4},\pi_{x2}=1\times 10^{-2},h_{x1}^{2}=0.15,h_{x2}^{2}=0.1\)).
Second, we simulated effect sizes coming from a three-component Gaussian mixture distribution (null/small/large effects), instead of the classical spike-and-slab assumption of our model. The smaller sample size estimates mirror those of the standard setting with \(n\) also equal to \(50,000\) (see Figure S panel _b_). However, in the larger sample size, LHC-MR overestimates the causal effect. This bias could be due to the merging of true effect estimates with confounder effect leading to an overestimation of \(\alpha_{x\to y}\) (Figure S13 panel _b_). MR-Egger, IVW and filtered MR-RAPS have the smallest RMSE in this case.
#### 3.2.1 Comparing CAUSE and LHC-MR
When running CAUSE on data simulated using the LHC-MR model framework in order to estimate a causal effect (\(\gamma\) in their notation), we investigated three different scenarios, each with multiple data generations: one where the underlying model has a shared factor/confounder with effect on both exposure and outcome only, another where the underlying model has a causal effect of \(0.3\) only, a third where the underlying model has both a causal effect and a shared factor. The data generated using the LHC-MR model was done under the standard settings (\(\pi_{x}=5\times 10^{-3},\pi_{y}=1\times 10^{-2},\pi_{u}=5\times 10^{-2}\), \(h_{x}^{2}=0.25,h_{y}^{2}=0.2,h_{u}^{2}=0.3\), \(t_{x}=0.16,t_{y}=0.11\), \(\alpha_{x\to y}=0.3,\alpha_{y\to x}=0\), \(m=234,000,n_{x}=n_{y}=50,000\)). For each setting, \(50\) different replications were investigated.
In the case of an underlying shared effect only, CAUSE preferred the sharing model \(100\%\) of the time, and thus there was no causal estimation, however it underestimated both \(eta\) and \(q\). When there was an underlying causal effect only, CAUSE preferred the causal model only \(4\%\) of the times, where it slightly underestimated the causal effect (\(\widehat{\gamma}=0.241\)). Although the true values of \(\eta\) and \(q\) are null in this scenario, the sharing model returned estimates for these two parameters overestimating them both (probably driven by their priors), as seen in Figure S14. In the third case, and in the presence of both, CAUSE preferred the sharing model in \(48\) of the \(50\) simulations, yet it underestimated \(\eta\) (corresponding to \(t_{y}/t_{x}\) for our model) but overestimated \(q\) (\(t_{x}^{2}/(t_{x}^{2}+h_{x}^{2})\) in our model) (mean of \(0.566\) and \(0.222\) respectively where the true values are \(0.667\) and \(0.097\)) showing a similar estimation pattern to the second case. Interestingly, in larger sample sizes, CAUSE selects the correct model \(100\%\) of the time, but still underestimates \(\gamma\), see Figure S15.
In the reverse situation, where data was generated using the CAUSE framework (with parameters \(h_{1}=h_{2}=0.25,m=97,450,N1=N2=50,000\)) and LHC-MR was used to estimate the causal effect, we saw the following results (see Figure S16). First, when we generated data in the absence of causal effect (\(\gamma=0,\eta=\sqrt{0.05},q=0.1\)), CAUSE does extremely well in estimating a null causal effect \(100\%\) of the time. Standard MR methods yield a slight overestimation of the (null) causal effect with varying degrees of variance, whereas LHC-MR shows both a greater variance and an upward bias - still leading to a causal effect compatible with zero. Second, in the absence of a confounder combined with non-zero causal effect (\(\gamma=\sqrt{0.05}=0.22,\eta=0,q=0\)), CAUSE underestimates the causal effect (\(\widehat{\gamma}=0.18\)) compared to LHC-MR which overestimates the causal effect: the mean of the estimates was \(0.38\) (over the \(50\) runs). Finally, in the presence of both a confounder and a causal effect (\(\gamma=\sqrt{0.05},\eta=\sqrt{0.05},q=0.1\)), CAUSE slightly underestimates the causal effect (\(\widehat{\gamma}=0.20\)), whereas LHC-MR overestimates the effects and shows estimates reaching the boundaries \(11\) out of \(50\) times (mean of the converged \(\widehat{\gamma}=0.39\) over the \(39\) data simulations, see Figure S16 panel _c_) - indicating that this setting of the CAUSE model is not compatible with the LHC-MR model framework. Interestingly, classical MR methods outperform CAUSE in this case. Note that in the interest of run time we used less SNPs (than usual) for parameter estimations. The analysis was repeated for a larger sample size of \(500,000\) (Figure S17), with more favourable results for LHC-MR. In the absence of a causal effect, we had similar results to smaller sample sizes, whereas in the absence of a shared effect, LHC-MR estimates the causal effect accurately with a mean of \(0.22\), CAUSE underestimates it and the rest of the MR methods are less biased. In the presence of both causal and shared factor, CAUSE recovers the causal effect. IVW, unlike the other MR methods and CAUSE, is more affected by the presence of the confounder, while LHC-MR exhibits upward bias with a mean estimate of \(0.27\).
### Application to association summary statistics of complex traits
We applied our LHC-MR and other MR methods to estimate all pairwise causal effects between \(13\) complex traits (\(156\) causal relationships in both directions). Our results are presented as a heatmap in (and are detailed in Supplementary Table S3). Further, we calculated the alternate set of estimated parameters that naturally results from our model (for reference see Sections 2.2 and Supplementary materials [1.1]). Among trait pairs for which the exposure had sufficient heritability (\(>2.5\%\)), the alternate parameters of a \(102\) trait pairs were within the possible ranges mentioned in methods (i.e. the confounder and the exposure are interchangeable). However, for all of these pairs, the alternative parameter optima lead to lower direct-than indirect heritability, which we deem unrealistic. Therefore, we report only the primary set of estimated optimal parameters in the main results and provide the alternative parameters in the Supplementary Table S4. The comparison of the results obtained by LHC-MR and standard MR methods is detailed below and more extensively in Supplementary Tables S5-S6. In summary, LHC-MR provided reliable causal effect estimates for \(132\) out of \(156\) exposure traits (i.e. those exposures had an estimated total heritability greater than \(2.5\%\)). These estimates were compared to five different MR methods. Seventy-four causal relationships were deemed significant by LHC-MR. Furthermore, for \(117\) out of those \(132\) comparable causal relationships, our LHC-MR causal effect estimates were concordant (not significantly different) with at least two out of five standard MR methods' estimates.
By simply comparing the significance status and the direction of the causal effects between the methods, we see that LHC-MR agrees in sign and significance (or the lack there of) with at least \(3\) MR methods \(77\) times. For \(31\) relationships, LHC-MR results lead to different conclusions than those of standard MR methods. For \(28\) of those, LHC-MR identified a causal effect missed by all standard MR methods. For the other three, we observed a disagreement in sign: LDL has a negative effect on BMI according to weighted mode and weighted median, whereas we show a positive effect, HDL and LDL show a negative bi-directional causal effect for weighted mode but a positive bi-directional effect with LHC-MR. Despite the conflicting evidence for the causal relationship of LDL on BMI, studies have shown that the relationship between them is non-linear, possibly explaining the discrepancy between the results.
LHC-MR agreed with most MR estimates and confirmed many previous findings, such as increased BMI leading to elevated blood pressure, diabetes mellitus (DM), myocardial infarction (MI) and coronary artery disease (CAD). Furthermore, we confirmed previous results that diabetes increases SBP (\(\hat{\alpha}_{x\to y}=0.39\ -P=1.70\times 10^{-9}\)).
Interestingly, it revealed that higher BMI increases smoking intensity, concordant with other studies. It has also shown the protective effect of education against a range of diseases (e.g. CAD and diabetes,) and risk factors such as smoking, in agreement with previous observational and MR studies. Probably reflecting lifestyle change recommendations by medical doctors upon disease diagnosis, statin use is greatly increased when being diagnosed with CAD, (systolic) hypertension, dislipidemia, and diabetes as is shown by both LHC-MR and standard MR methods.
Furthermore, causal effects of height on CAD, DM and SBP have been previously examined in large MR studies. LHC-MR, agreeing with these claims, did not find significant evidence to support the effect of height on DM, but did find a significant protective effect on CAD and SBP. However, unlike the first two, the relationship between height and SBP also revealed the existence of a confounder with causal effects \(0.14\,(P=9.2\times 10^{-11})\) and \(0.11\,(P=3.39\times 10^{-8})\) on height and SBP respectively. Another example of a trait pair for which LHC-MR found an opposite sign confounder effect is HDL and its protective effect on SBP. The confounder had a positive effect ratio of \(t_{y}/t_{x}=0.84\), opposing the negative causal effect of \(\hat{\alpha}_{x\to y}=-0.13\) supported by observational studies. This causal effect was not found by any other MR method.
It is important to note that while the effects of parental exposures on offspring outcomes can be seen as genetic confounding, LHC-MR would not be able to distinguish parental and offspring causal effects, because the LHC-MR model assumes that there is no correlation between the genetic effects on the exposure and the genetic effects on the confounder (which is not the case of parental vs offspring traits). Thus, LHC-MR causal effect estimates are just as likely to reflect parental effects as any other MR method.
**Heatmap representing the bi-directional causal relationship between the 13 UK Biobank traits.** The causal effect estimates in coloured tiles all have a significant p-values surviving Bonferroni multiple testing correction with a threshold of \(3.2\times 10^{-4}\). We did not report an estimated causal effects for exposures with an estimated total heritability less than 2.5%. White tiles show an absence of a significant causal effect estimate.
Abbreviations: BMI: Body Mass Index, BWeight: Birth Weight, CAD: coronary artery disease, DM: Diabetes Mellitus, Edu: Years of Education, HDL: High-density Lipoprotein LDL: Low-density Lipoprotein, MI: Myocardial Infarction, PSmoke: # of Cigarettes Previously Smoked, SBP: Systolic Blood Pressure, SHeight: Standing Height, SVstat: Medication Simvastatinfor the detrimental effect of increased (parental) BMI on education (supported by longitudinal studies), the positive effect of (parental) height on birth weight, or on education. There are also some associations identified only by LHC-MR that might reflect parental effects: the negative causal effect of CAD on education or on birth weight, the positive impact of HDL on birth weight, or DM reducing height. All these pair associations uniquely found by LHC-MR are examples of LHC-MR's use of whole-genome SNPs instead of GW-significant SNPs only, as our estimates are of larger magnitude than those found by standard MR. Interestingly, for the CAD\(\rightarrow\)birth weight relationship, LHC-MR revealed a confounder of opposite causal effects, which could have masked/mitigated the causal effect of standard MR methods.
A systematic comparison between IVW and LHC-MR has shown generally good agreement between the two methods, which is illustrated in To identify discrepancies between our causal estimates and those of the standard MR results, we grouped the estimates into several categories, either non-significant p-value for both or either, significant with an agreeing sign for the causal estimate, or significant with a disagreeing sign. The diagonal (seen in Figure 5) representing the agreement in significance status and sign between the two methods, is heavily populated. On the other hand, 34 pairs have causal links that are significantly non-zero according to LHC-MR, but are non-significant for IVW, while the opposite is true for seven pairs. We believe that many of these seven pairs may be false positives, since four of them are picked up by no other MR method, two are confirmed by only one other method and the last one by two methods. Further comparisons of significance between LHC-MR estimates and the remaining standard MR methods can be found in Table 5.
LHC-MR identified a confounder for 16 trait pairs out of the possible 78.
A scatter plot of the causal effect estimates between LHC-MR and IVW. To improve visibility, non-significant estimates by both methods are placed at the origin, while significant estimates by both methods appear on the diagonal with 95% CI error bars.
EpiGraphDB could identify reliable confounders for ten out of the 16 trait pairs. Notably, for the birth weight - diabetes pair, the average epigraph confounder-effect ratio \((r_{3}/r_{1})\) clearly agreed in sign with our \(t_{y}/t_{x}\) ratio, indicating that the characteristics of the confounder(s) evidenced by LHC-MR agree with those found in an exhaustive confounder search, and are mainly obesity-related traits (Figure S18 panel \(a\)). Six other trait pairs showed mixed signs of different confounders, indicating the possibility of having heterogeneous confounders (Figure S18 panels \(b\)-\(e\)). Finally, three trait pairs showed a disagreement between our estimated confounder effect ratio and the bulk of those found by epigraphDB as seen in Supplementary Figure S18 panels \(f\)-\(j\). However, at least one of the top ten potential confounders showed effects that are in agreement with our ratio for each of these pairs. Note that since the reported causal effects of the confounders on \(X\) and \(Y\) reported in EpiGraphDB are not necessarily on the same scale, we do not expect the magnitudes to agree.
As described in the methods (Eq. 3), genetic correlation can be computed from our estimated model parameters. To verify that the fitted LHC-MR model leads to a genetic correlation similar to the one obtained from LD score regression (LDSC), we compared whether the two approaches produce similar genetic correlation estimates. We did this by taking the estimated parameters obtained from the 200 block jackknife to estimate the genetic correlations between traits (and their standard errors), and plotted them against LD score regression values as seen in As expected, we observe an overall good agreement between the estimates of the two methods, with only six trait pairs differing in sign. Of these six, only 2 were nominally significantly different between the two methods (LDL\(\rightarrow\)Asthma and LDL\(\rightarrow\)DM).
Scatter plot comparing the genetic correlation for each trait obtained from LDSC against the value calculated using parameter estimates from the LHC-MR model. A 95% CI is shown for each point. Values from both methods are reported in Supplementary Table S9.
A reason for this could be that confounders would need to have very strong effects to substantially contribute to the genetic correlation (\(\approx t_{x}\cdot t_{y}\)) compared to the bi-directional causal effects (\(\approx\alpha_{x\to y}^{2}\cdot h_{x}^{2}+\alpha_{y\to x}^{2}\cdot h_{y}^{2}\)).
As for the comparison of LHC-MR against CAUSE for real trait pairs, we ran CAUSE on all 156 trait pairs (bi-directional), and extracted the parameter estimates that corresponded to the methods winning model. The p-value threshold was corrected for multiple testing and was equivalent to 0.05/156. Based on that threshold, the p-value that compared between the causal and the sharing model of CAUSE was used to choose one of the two. Then the parameters estimated from the winning model, \(\gamma\) (only for causal model), \(\eta\) and \(q\), were compared to their counterparts in LHC-MR. A visual comparison of LHC-MR's causal estimates and those of CAUSE can be seen in Figure S19
Whenever the causal effect estimates were significant both for CAUSE and LHC-MR (30 causal relationships), they always agreed in sign (Table S8) with a high Pearson correlation of 0.592. Calculating the correlation for their estimates regardless of significance yielded a smaller value of 0.377. When compared to the causal effect estimate from IVW, LHC-MR was strongly correlated (0.585), whereas CAUSE had a slightly weaker correlation (0.471) using all estimates.
Similarly, the significant confounder effect ratio of LHC-MR (\(t_{y}/t_{x}\)) can be compared to the significant confounder effect estimate of CAUSE (\(\eta\)) when a sharing model is chosen. These 12 confounding quantities by CAUSE and LHC-MR disagreed in sign for all but one trait pair (Height\(\rightarrow\)MI), with a Pearson correlation compatible with zero (\(-0.357\) (95% CI [-0.77, 0.27]))
## 4 Discussion
We have developed a structural equation (mixed effect) model to account for a latent heritable confounder (\(U\)) of an exposure (\(X\)) - outcome (\(Y\)) relationship in order to estimate bi-directional causal effects between the two traits (\(X\) and \(Y\)). The method, termed LHC-MR, fits this model to association summary statistics of genome-wide genetic markers to estimate various global characteristics of these traits, including bi-directional causal effects, confounder effects, direct heritabilities, polygenicities, and population stratification.
We first demonstrated through simulations that in most scenarios, the method produces causal effect estimates with substantially less bias and variance (in larger sample sizes) than other MR tools. The direction and magnitude of the bias of classical MR approaches varied across scenarios and sample sizes. This bias was mainly influenced by two often opposite forces: downward bias resulting from winner's curse and weak instruments, and upward bias due to a positive confounder of the \(X-Y\) relationship, evident in larger sample sizes. In the scenario lacking a confounder (thus respecting all MR assumptions), MR methods were distinctly underestimating the causal effect, except for LHC-MR and to a better extent MR-RAPS. However, under standard settings with an added small heritable confounder and no reverse causality present, all classical MR methods still slightly underestimated the causal effect in smaller sample sizes, except for the MR-RAPS estimate which was now overestimated. For the same standard setting scenario but in a larger sample size where confounder effects were more detectable, IVW had an estimation that was close to the true causal value chosen (\(\alpha_{x\to y}=0.3\)) due to the opposite biases cancelling out. However, when the causal effect was set to be smaller (\(\alpha_{x\to y}=0.1\)), the estimates of IVW became biased. More substantial violations of classical MR assumptions, such as the presence of negative-effect confounder or a negative reverse causal effect, led to more substantial biases that impacted all methods (including MR-RAPS) except LHC-MR.
Interestingly, in smaller sample sizes, standard MR methods showed a slight decreasing trend in the variance of the causal effect estimate as the kurtosis of the underlying effect size distribution went up from 2 to 10. On the other hand, LHC-MR did not show a similar trend with growing kurtosis, and estimated the causal effect with a smaller bias. As confounder causal effects (\(q_{x}\), \(q_{y}\)) increased, classical MR methods (except weighted ones) were prone to produce overestimated causal effects with at least twice the bias than that of LHC-MR, especially in larger sample sizes where the confounder-associated SNPs make it to the set of GW-significant instruments for all methods. Furthermore, mode-based estimators were robust to the presence of two concordant confounders, yet their bias was still 10-fold higher than LHC-MR's, and they did not perform as well in the presence of discordant confounders. In summary, LHC-MR was robust to a wide range of violations of the classical MR assumptions and was less impacted than standard MR methods. Thus it outperformed all MR methods in virtually all tested scenarios, many of which violated even its own modelling assumptions.
We then applied our method to summary statistics of 13 complex traits from large studies, including the UK Biobank. We observed a general trend in our results that (in agreement with epidemiological studies) higher BMI and LDL are risk factors for most diseases such as diabetes and CAD. We also note the protective effect HDL has on these same diseases. Moreover, we observe many disease traits increasing the intake of lipid-lowering medication (simvastatin), reflecting the recommendation/treatment of medical personnel following the diagnosis.
LHC-MR can have discordant results compared to other MR methods for many possible reasons. The positive causal effect of smoking on MI, diabetes on asthma, the protective impact of higher birth weight on asthma, or higher education on smoking intensity, all of which were missed by standard MR could reflect the increased power of LHC-MR with its use of full-genome SNPs as opposed to genome-wide significant SNPs of classical MR approaches. Estimates from classicalMR methods could also be impacted by sample overlap between the exposure and outcome datasets, whereas LHC-MR takes this into account. However, when using large sample sizes, the bias due to sample overlap is expected to be very small, and therefore not sufficient to explain any discrepancy in the results. Another possible reason for the discrepancy between our findings and those of standard MR methods is the presence of a significant heritable confounder found by LHC-MR with opposite effect to the estimated causal effect between the pair. These two opposite forces lead to association summary statistics that may be compatible with reduced (or even null) causal effect when the confounder is ignored. Possible examples of this scenario can be observed for when (parental) traits, e.g. diabetes and CAD, act on birth weight. These pairs have a confounder of opposite effects, possibly related to (parental) obesity. Similarly, standard MR methods show little evidence for a causal effect of SBP on height, while our LHC-MR estimate is \(-0.37\) (\(P=4.81\times 10^{-8}\)) which most probably reflects parental (maternal) effects as seen in previous studies. The protective effect of HDL on SBP is another example where a confounder of opposite sign to that of the causal effect allows it to be uniquely found by LHC-MR. LHC-MR assumes no genetic correlation between the confounder and the direct effects on the exposure, which may be violated when the confounder is the same trait as the exposure, but in the parent. Such parental effects can mislead most MR methods, including ours, and hence we may observe biased results for traits such as BMI\(\rightarrow\)education and HDL\(\rightarrow\)birth weight.
Sixteen trait pairs showed a strong confounder effect, in the form of significant \(t_{x}\) and \(t_{y}\) estimates. These pairs were investigated for the presence of confounders using EpiGraphDB, and 10 of them returned possible confounders. The bulk of such pairs returned confounders with both agreeing and disagreeing effect directions on \(X\) and \(Y\), making it difficult to pinpoint a group of concordant and dominant confounders. However, for the birth weight-DM pair, where LHC-MR identifies a negative reverse causal effect and a confounder with effects \(t_{x}=0.10(P=6.77\times 10^{-8})\) and \(t_{y}=0.15(P=3.13\times 10^{-7})\) on birth weight and DM respectively, EpigraphDB confirmed several confounders related to body fat distribution and weight that matched in sign with our estimated confounder effect (Figure S18 panel _a_). Note that EpiGraphDB causal estimates are not necessarily on the scale of SD outcome difference upon 1 SD exposure change scale, hence they are not directly comparable with the \(t_{y}/t_{x}\) ratio, but are rather indicative of the sign of the causal effect ratio of the confounder. Furthermore, if EpigraphDB does not find a causal relationship between the trait pair in either directions, then it does not return any possible confounders of the two, a reason why only 10 out of 16 confounder-associated trait pairs returned any hits.
Lastly, our comparison of the genetic correlations calculated from our estimated parameters against those calculated from LD score regression showed good concordance, confirming that the detailed genetic architecture proposed by our model is compatible with the observed genetic covariance. The major difference between the genetic correlation obtained by LD score regression \(vs\) LHC-MR is that our model approximates all existing confounders by a single latent variable, which may be inaccurate when multiple ones exist with highly variable \(t_{y}/t_{x}\) ratios. Furthermore, LHC-MR decomposed the observed genetic correlation into confounder and bi-directional causality driven components, revealing that most genetic correlations are primarily driven by bi-directional causal effects. Note that we have much higher statistical power to detect situations when the confounder effects are of opposite sign compared to the causal effects, because opposing genetic components are more distinct.
To our knowledge only two recent papers use similar models and genome-wide summary statistics. The LCV approach is a special case of our model, where the causal effects are not included in the model, but they estimate the confounder effect mixed with the causal effect to estimate a quantity of genetic causality proportion (GCP). In agreement with others, we would not interpret non-zero GCP as evidence for causal effect. Moreover, in other simulation settings, LCV has shown very low power to detect causal effects (by rejecting GCP=0) (Fig S15 in Howey et al.). Another very recent approach, CAUSE, proposes a structural equation mixed effect model similar to ours. However, there are several differences between LHC-MR and CAUSE: (a) we allow for bi-directional causal effects and model them simultaneously, while CAUSE is fitted twice for each direction of causal effect; (b) they first use an adaptive shrinkage method to integrate out the multivariable SNP effects and then go on to estimate other model parameters, while we fit all parameters at once; (c) CAUSE estimates the correlation parameter empirically; (d) we assume that direct effects come from a two-component Gaussian mixture, while they allow for larger number of components; (e) their likelihood function does not explicitly model the shift between univariate vs multivariate effects (i.e. the LD); (f) CAUSE adds a prior distribution for the causal/confounder effects and the proportion \(\pi_{u}\), while LHC-MR does not; (g) to calculate the significance of the causal effect they estimate the difference in the expected log point-wise posterior density and its variance through importance sampling, whereas we use a simple block jackknife method. Because of point (a), the CAUSE model can be viewed as a special case of ours when there is no reverse causal effect. We have the advantage of fitting all parameters simultaneously, while they only approximate this procedure. Although they allow for more than a two-component Gaussian mixture, for most traits with realistic sample sizes we do not have enough power to distinguish whether two or more components fit the data better. Therefore, we believe that a two component Gaussian is a reasonable simplification. Due to the more complicated approach described in points (e-g), CAUSE is computationally more intense than LHC-MR, taking up to 1.25 CPU-hours in contrast to our 2.5 CPU-minute run time for a single starting point optimisation (which is massively parallelisable).
When we compared the performance of CAUSE and LHC-MR, we found that for large sample sizes both LHC-MR and CAUSE performed well not only when applied to data simulated by their own model, but also by the model of the other method. For smaller sample sizes, both methods performed poorly when applied to data generated by the other model. However, LHC-MR was less biased when applied to data generated by its own model than CAUSE was on data simulated based on its own model, where it provided rather conservative estimates. This is somewhat expected, since the primary aim of CAUSE is model selection and it is less geared towards parameter estimation, especially for settings where both sharing and causal effects are present (leading to very broad estimates). Also, CAUSE parameter estimates have shown to be somewhat sensitive to the choice of the prior.
Finally, when applying both LHC-MR and CAUSE to 156 complex trait pairs, we observed that the causal effects are reasonably well correlated (0.38 for all estimates, 0.59 for significant estimates) and agree in sign for trait pairs deemed significantly causal by either or both methods. In addition, LHC-MR causal estimates were more similar to those of IVW than the estimates provided by CAUSE. Surprisingly, when a confounding factor was identified by both methods, the confounder effects (LHC-MR \(t_{y}/t_{x}\) ratio and CAUSE \(\eta\) parameter) were uncorrelated. There are two possible explanations for this: (i) CAUSE may confuse/merge the confounder with the reverse causal effect, since it does not explicitly model the latter one. (ii) The two models assume different marginal effect size distributions, hence when multiple heterogeneous confounders exist, one method may detect one of the confounders, while the other method picks up the other confounder, depending on which has more similar genetic architecture to the assumed one.
Our approach has its own limitations, which we list below. Like any MR method, LHC-MR provides biased causal effect estimates if the input summary statistics are flawed (e.g. not corrected for complex population stratification, parental/dynasty effects). As mentioned in the Methodssection, our model is strictly-speaking unidentifiable and two distinct sets of parameters fit the data equally well, if the alternate set of parameters fall within the parameter ranges. As opposed to classical MR methods that give a single (biased) causal effect estimate, ours can detect and calculate the competing model. Due to biological considerations, from these competing models, we chose the one which yielded larger direct heritability than confounder-driven (indirect) heritability. Additional pointers to decide which parameter optimum we choose can be to pick the one with smaller magnitude of causal effects (large causal effects are unrealistic) or pick the one that includes causal effects that agree better with those of other MR methods.
LHC-MR is not an optimal solution for traits whose genetic architecture substantially deviates from a two-component Gaussian mixture of effect sizes. Also, for traits with low heritability (\(<2.5\%\)), it is particularly important to compare the causal effect estimates to those from standard MR methods as results from LHC-MR may be less robust. In addition, trait pairs with multiple confounders with heterogeneous effect ratios can violate the single confounder assumption of the LHC model and can lead to biased causal effect estimates. Finally, LHC-MR, like other methods, is not immune to parental effects that are correlated with offspring effects. In such cases, the parental effect is grouped with the exposure (due to their strong genetic correlation) and not viewed as a confounder of the exposure-outcome relationship.
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20019091 | ## Key Characteristics** & **eICU** & **MIMIC-III
\\ \hline Unique ICU types (n) & 8 & 5 \\ Final cohort (n) & 3,816 & 5,975 \\ The incidence of AKI within the first week (n(\%)) & 1,988 (52.1\%) & 1,870 (31.3\%) \\ AKI cases were determined based on urine output criteria (n(\%)) & 1722 (45.1\%) & 1486 (24.9\%) \\ Age, years (mean (s.d.)) & 60 (18.0) & 60 (18.3) \\ Male gender (n(\%)) & 2,169 (56.8\%) & 3,404 (57.0\%) \\ Comorbidities (n(\%)): Hypertension & 1,625 (42.6\%) & 2,430 (40.7\%) \\ \hline \end{tabular}
Diabetes 527 (13.8%) 1,253 (21.0%) Congestive heart failure 593 (15.5%) 1,172 (19.6%) Chronic pulmonary disease 550 (14.4%) 795 (13.3%) Chronic kidney disease 379 (10.0%) 395 (6.6%) Chronic liver disease 201 (5.3%) 108 (1.8%) **Primary ICD-9 diagnosis (n(%)):** Sepsis, including pneumonia 713 (18.7%) 2,290 (38.3%) Cardiovascular 1,367 (35.8%) 1,531 (25.6%) Other Respiratory 670 (17.6%) 642 (10.7%) Neurological 401 (10.5%) 280 (4.7%) Others 665 (17.4%) 1,232 (20.6%) **Ethnicity (n(%)):** Black 264 (6.9%) 420 (7.0%) Hispanic 66 (1.7%) 273 (4.6%) Asian 38 (1.0%) 202 (3.4%) White 3,234 (84.8%) 4,140 (69.3%) Other 214 (5.6%) 940 (15.7%) Initial SOFA (mean (s.d.)) 5.8 (3.3) 4.1 (3.0) Cardiac surgery (n(%)) 149 (3.9%) 122 (2.0%) Mechanical ventilation (n(%)) 1,276 (33.4%) 2,830 (47.4%) Vasopressors (n(%)) 1,006 (26.4%) 1,666 (27.9%) Need for renal replacement therapy (RRT) 68 (1.8%) 57 (0.95%) Length of stay, days (median, (IQR)) 2.6 (1.6-4.8) 2.8 (1.8-5.0) ICU mortality rate 10.00% 8.60%* Table 2. Description of the datasets. Ethnicity of Black includes African American, Cape 293 Verdean, Haitian, and African. Ethnicity of Hispanic includes Latino (central American), Latino (Cuban), Latino (Puerto Rican), Latino (Honduran), Latino (Guatemalan), Latino (Mexican), 295 Latino (Dominican), Latino (Salvadoran), Latino (Colombian), and Portuguese. Ethnicity of Asia includes Vietnamese, Thai, Asian Indian, middle Eastern, Korean, Chinese, Filipino, 297 Cambodian, Japanese, Asian other. White includes Eastern European, Brazilian, Russian, and other European. Ethnicity of Other includes Unknown, not specified, multi race, patient declined 299 to answer, and unable to obtain. s.d.: Standard deviation in short. IQR: interquartile range in short.
*
*
## *Model Development and Evaluation in eICU Cohort
* Compared with the baseline algorithm (logistic regression algorithm) in eICU cohort, we found that AdaBoost and Gradient Boosting Machine (GBM) achieved higher AUC than other algorithms in predicting task of all four configurations of the time-series models. The model 6-6 configuration in general yielded the highest performance. Using model 6-6, the AUC of logistic regression is 0.8385, while the AUC was higher in the AdaBoost (0.8859) and GBM (0.8522).
* AUC results of all five-fold cross validation across four different configurations of the time-series models and eight different machine learning algorithms are shown in Precision and Recall of the models are also demonstrated in Figure S1A and Figure S2A. The model performance (mean values) on eICU cohort testing sets is shown in Table 3. Other performance * metrics on eICU cohort testing sets MIMIC-III such as F1 score, negative predictive value (NPV), and specificity are also available at Table S3.
* **Model External Validation and Evaluation in MIMIC-III Cohort**
* After external validation on four configurations of the time-series models which developed by eight different machine learning algorithms, we found model 12-6 developed by AdaBoost achieved the highest AUC (0.9228) on external validation set. For some models, the higher performance is noted on external validation than model development stage due to the differences between eICU and MIMIC-III cohorts (for example, the onset of AKI in MIMIC-III is more imbalanced), yet the evaluations are comparable within each database cohorts. AUC results of all five-folds results across four different configurations of the time-series models and eight different machine learning algorithms on MIMIC-III external validation set are presented in The model performances (mean values) on external validation cohort MIMIC-III of AUC, precision, and recall are shown in Table 4. Other performance metrics on external validation cohort MIMIC-III such as F1 score, negative predictive value (NPV), and specificity are also available at Table S4.
Performance of four different configurations of the time-series models (model 6-6, model 6-12, model 12-6, model 12-12) and eight different machine learning algorithms on eICU for model development (A) and MIMIC-III for external validation (B). Abbreviations: DT: Decision Tree; GBM: Gradient Boosting Machine; LR: Logistic Regression; NN: Neural Networks; NN (L2): Neural Networks with L2 regularization; RF: Random Forest; LSTM: Long short-term memory networks.
* Table 3. Comparison of model performance (mean values across five-fold validation results) on eICU internal validation. Abbreviations: AUC: area under the ROC curve. L2 stands for Ridge regularization.
*
* 359 Table 5. Secondary outcomes of eICU and MIMIC-III databases. s.d.: standard deviation in short.
* 360 IQR: interquartile range in short. *P-value is derived according to alternative hypothesis: true Spearman \(\rho\) is not equal to 0 when comparing the variable with the onset of AKI.
* 362
* 363
* 364 Relationships between Prediction Performances and Different Time-Series Models
* 365 As eight different algorithms with five-fold cross-validation produces 40 results per each time series model (model 6-6, model 6-12, model 12-6, model 12-12), violin plot and pairwise paired t-test (Table 6) are used to compare the overall performances across time series models.
* 382 Table 6.
* 384 four different time-series models.
* 385
* 386 **Identifying Feature Importance**
* 387 The feature importance identified by the AdaBoost algorithm is determined by the average
* 388 feature importance over all ensembled trees.
* 389 analyzed feature importance by Gini importance (mean decrease impurity).
* 390 categorized groups is shown in Table 1.
* 391 To gain insights into the relevance of each feature, summarized and ranked the
* 392 most critical variables in model 6-6 based on the averaged Gini feature importance using
* 393 AdaBoost algorithm in model development (eICU database).
* 394 static data are important for the prediction task, and the most important group of features was
* 395 vital signs. Specifically, fluid balance-related features (OUTPUT_12HR, OUTPUT_6HR,
* 396 INPUT_12HR, OUTPUT_24HR), AST, AG, SCr, UN, CA_ION, K_ION in the class of * laboratory values, SYS_BP, RR, HR in the class of vital signs, HOURS in the class of others, and WEIGHT in the class of Demographic, are the most important predictors for the early AKI prediction.
*
Identified top important features in eICU database. Values and rankings are based on time-series model 6-6 and the averaged Gini importance from AdaBoost algorithm. Features are colored group-wisely according to the categories listed in Table 1. The higher value indicates the higher significance of the feature.
* Electronic healthcare systems (EHR) provides real-world clinical data not only for secondary analysis, but also for developing the artificial intelligence-based platform to assist clinicians to identify potential critical events, such as the onset of AKI. Since there is no effective treatment of AKI, the prevention of AKI becomes more critical, thus an early warning system which may reduce the risk of exacerbating injury is necessary and in urgent demand.
* Though some studies on early warning system have been successfully reduced the nephrotoxic medication in AKI and prevented the contrast-induced AKI, several other studies showed the failure of those methods, which mainly due to the lack of external validation. Therefore, the study with external validation are necessary before any developed method be applied to the clinical setting, especially the externally validated prediction models are relatively rare.
* In this paper, we have integrated most of the routinely available ICU data based on two large ICU databases with general population to developed and externally validated an ideal artificial intelligence assisted early warning system for predicting the onset of AKI within the first week of ICU stay. Our workflow and time-series models addressed several topics that have been discussing over these days. For example, we used both oliguric and SCr as diagnostic criteria of the KDIGO to identify the onset of AKI and included most of physiological and laboratory parameters as predictors, which contained different clinical commonly used urine output trends. As a result, we have got an ideal incidence of AKI in both eICU and MIMIC-III cohort, which would minimize the potential mistakes and maximize the accuracy and improving of predicting model performance in clinical situation. Moreover, we fully made use of all * 428 routinely available ICU and clinical features as predictors, to optimize and improve the model performances.
* 429 Using multiple types of ICU and clinical features to predict AKI, a complex clinical syndrome, is very challenging and difficult as any feature or small changes may cause great impact on outcomes. Machine learning technique has been successfully applied to predict critical events under a fast-paced, data-overloaded setting of ICU, which could provide new insights into evidence-based decision support. Different machine learning algorithms usually used to capture the real relationships across different data types which may provide advantages for predicting AKI far in advance of onset with high sensitivity and specificity. As previous studies, many machine learning algorithms have been used training many ideal models in predicting AKI, such as random forest, multivariate regression model, boosted ensembles of decision trees, etc.. Based on these previous studies, we take a further step by fully utilizing two independent databases and applied eight machine learning algorithms with 52 comprehensive features of different data types for a large-scale model assessments and analyses.
* 430 Our current study has several strengths. First, we integrated most of the routinely available ICU data, including 52 features under different data types, which would be considered containing the largest number of predictors. Second, we not only used both urine output and SCr as diagnostic criteria to identify the onset of AKI, but also included physiological (especially urine output) and laboratory trends as predictors to improve model performance. Third, we compared 8 modern machine learning algorithms for further analysis to select the best model of predicting task. Fourth, we developed and externally validated an ideal model based on two independent general population ICU databases. Last but not least, we did not only rely on usingdata at a single time point (admission to hospital), but also combining static and time-varying variables as a time series dataset to achieve accurate prediction model performance.
* 452 From the results and performances across four time-series models and various machine learning algorithms, we proved the feasibility of deploying artificial intelligence assisted early warning system for AKI prediction. We also showed that AdaBoost, one of the ensemble machine learning algorithms, could be a desired model to predict the onset of AKI. The performances measured by AUC is decent and could be applied in real-time to assist clinicians' decision in the future. While the across-model performances demonstrated that increasing the lag (feature collecting window), or in another word, how many hours we look back, doesn't help improve the performance, justified that model 6-6 with 6 hours feature collecting window is enough for the future AKI inference.
* 461 For feature importance ranking of AKI prediction, the top 15 features are critical and closely related to AKI development. We justified and validated that the fluid balance and laboratory values are not only the AKI criteria of the KDIGO, but also directly associated with the kidney function (such as OUTPUT_12HR, OUTPUT_6HR, INPUT_12HR, SCr, UN, CA_100, K_ION, etc.) 54. Most vital signs, which are used to assess patients' physiological stability, are important for prediction as the AKI prediction should be in real-time. Hours stayed in ICU and weight are also indicated as the most important features which have already been reported that both of them have a great association with AKI 102. The model developed has the potential capability of serving as an "alert" for early warning of AKI, which would make the electronic healthcare systems more artificially intelligence and enable bedside application.
- with well-performed AUC and precision, the recall is not so promising due to some positive samples (AKI) are misclassified. 484 Fifth, although we used two non-overlapping general population ICU databases, both are from the United States hospitals. Thus, cross-national and multi-background validations are necessary. 486 Sixth, we only evaluated two feature windows (6 and 12 hours), two gap windows (6 and 12 hours) and one prediction window (1 hour) due to the data and computational limitation. In the future, we may put more efforts on various time-series models. Last but not the least, study design in this work relied on retrospective data investigation which may cause missing some important information than a prospective study and could not have any result about the impact analysis between model prediction and patients' outcomes. Therefore, the model also requires further external validation based on different background populations and may only be used inside the research arena.
* **Conclusion**
* Recent reviews and comments showed that the prediction of AKI in the ICU is relatively difficult and with several limitations. To answer these limitations and problems, We have developed an artificial intelligence assisted early warning model for predicting the onset of AKI within the first week of ICU stay, which identified by using both oliguric and SCr diagnostic criteria in multi-center eICU database and externally validated in single-center MIMIC-III database. We integrated most routinely available ICU data and demonstrated the model with 6 hours feature and 6 hours gap developed by AdaBoost achieved optimal performances measured with AUC, precision, and recall among 8 prevalent machine learning algorithms.
* **Author Contributions:**
* SH, CF designed the study, conducted the data collection, data analysis, data interpretation, and wrote the manuscript. SH, CF conducted the data analysis, data interpretation and wrote the manuscript. LC and WW conducted the data interpretation and reviewed the manuscript. ZZ and TL designed the study and reviewed the manuscript. KL, LW, and XC conducted the data interpretation and reviewed the manuscript.
* **Data Availability Statement*** Datasets are used from the publically available collection of eICU(r) Collaborative Research
* Database (eICU, [https://eicu-crd.mit.edu/](https://eicu-crd.mit.edu/)) (v1.2) and Medical Information Mart for Intensive
* Care III (MIMIC-III, [https://mimic.physionet.org/](https://mimic.physionet.org/)) (v1.4).
*
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