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#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.
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016576_file02
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###### 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.
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## 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
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## 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.
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021691_file02
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# & 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.
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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
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045237_file02
| "## parameter\n\n& \\\\ \\hline \\(x\\) and \\(A(\\tau)\\) & rate coefficient for infection and expe(...TRUNCATED)
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053355_file02
| "## Detailed methods and R summary model output\n\n### GAMM models\n\n#### Summary model output\n\nT(...TRUNCATED)
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054338_file03
| "## Chicago, IL\n\n\n\\begin{tabular}{|l|l|} \\hline _County_ & _FIPS_ \\\\ \\hline Cook County & 17(...TRUNCATED)
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055574_file02
| "## Supplementary Table S2.\n\nThe spearman correlations between the vectors of 23 statistics, one v(...TRUNCATED)
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