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Using the output in Figure [7.18,](#page-354-0) write the overall model equation, the model equation for nondiabetics, and the model equation for diabetics. The overall model equation is TotChol = 4 .70 + 0.0096(Age) + 1.72(DiabetesYes) <sup>−</sup> <sup>0</sup>.034(Age <sup>×</sup> DiabetesYes). For no...	{ "Header 1": "7.7 Interaction in regression", "Header 3": "EXAMPLE 7.12", "token_count": 1392, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
Previously, multiple regression modeling was shown in the context of estimating an association while adjusting for possible confounders. Another application of multiple regression is explanatory modeling, in which the goal is to construct a model that explains the observed variation in the response variable. In this co...	{ "Header 1": "7.8 Model selection for explanatory models", "token_count": 506, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
Habitat fragmentation is the process by which a habitat in a large contiguous space is divided into smaller, isolated pieces; human activities such as agricultural development can result in habitat fragmentation. Smaller patches of habitat are only able to support limited populations of organisms, which reduces genetic...	{ "Header 1": "7.8 Model selection for explanatory models", "Header 3": "Abundance of forest birds: introduction", "token_count": 674, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
The response variable for the model is abundance. Numerical summaries calculated from software show that abundance ranges from 1.5 to 39.6. Figure [7.21](#page-359-0) shows that the distribution of abundance is bimodal, with modes at small values of abundance and at between 25 and 30 birds. The median (21.0) and mean (...	{ "Header 1": "7.8 Model selection for explanatory models", "Header 3": "Data exploration", "token_count": 876, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
The variables log.dist.nearest and log.dist.larger appear strongly associated; a model may only need one of the two, as they may be essentially "redundant" in explaining the variability in the response variable.[22](#page-362-0) In this case, however, since both are only weakly associated with abundance, both may be un...	{ "Header 1": "7.8 Model selection for explanatory models", "Header 3": "7.8. MODEL SELECTION FOR EXPLANATORY MODELS 363", "token_count": 577, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
Based on the data exploration, the initial model should include the variables log.area, altitude, log.yrs.isolation, and grazing.intensity; a summary of this model is shown in Figure [7.26.](#page-362-2) The R <sup>2</sup> and adjusted R 2 for this model are, respectively, 0.728 and 0.688. The model explains about ...	{ "Header 1": "7.8 Model selection for explanatory models", "Header 3": "Initial model fitting", "token_count": 616, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
First, fit models excluding the predictors that were not statistically significant: altitude and log.yrs.isolation. Models excluding either variable have adjusted R <sup>2</sup> of 0.69, and a model excluding both variables has an adjusted R <sup>2</sup> of 0.70, a small but noticeable increase from the initial mod...	{ "Header 1": "7.8 Model selection for explanatory models", "Header 3": "Model comparison", "token_count": 1076, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
The fit of a model can be assessed using various residual plots. Figure 7.29 shows a histogram and normal probability plot of the residuals for the final model. Both show that the residuals follow the shape of a normal density in the middle range (between -10 and 10) but fit less well in the tails. There are too many l...	{ "Header 1": "7.8 Model selection for explanatory models", "Header 3": "Model assessment", "token_count": 517, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
The relatively large R 2 for the final model (0.72) suggests that patch area and extent of grazing (either heavy or not) explain a large amount of the observed variability in bird abundance. Of the features measured in the study, these two are the most highly associated with bird abundance. Larger area is associated ...	{ "Header 1": "7.8 Model selection for explanatory models", "Header 3": "Conclusions", "token_count": 374, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
Might a model including all the predictor variables be better than the final model with only log.area and grazing.binary? The model is shown in Figure [7.31.](#page-366-0) The R 2 for this model is 0.729 and the adjusted R 2 is 0.676. While the R 2 is essentially the same as for the final model, the adjusted R ...	{ "Header 1": "7.8 Model selection for explanatory models", "Header 3": "Final considerations", "token_count": 1102, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
Regression with categorical variables and ANOVA are essentially the same method, but with some important differences in the information provided by the analysis. Earlier in this chapter, the strength of the association between RFFT scores and educational level was assessed with regression. Figure [7.33](#page-367-1) sh...	{ "Header 1": "7.9 The connection between ANOVA and regression", "token_count": 682, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
Why use ANOVA at all if fitting a linear regression model seems to provide more information? A case can be be made that the most important first step in analyzing the association between a response and a categorical variable is to compute and examine the F-statistic for evidence of any effect, and that only when the ...	{ "Header 1": "7.9 The connection between ANOVA and regression", "Header 3": "7.9. THE CONNECTION BETWEEN ANOVA AND REGRESSION 369", "token_count": 455, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
- Keep a clear view of the purpose. Is the goal of constructing the model to understand the relationship between the response and a particular predictor after adjusting for confounders? Or is the goal to understand the joint association between a response and a set of predictors? - Avoid rushing into model fitting....	{ "Header 1": "7.10 Notes", "Header 3": "Important ideas", "token_count": 309, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
- Stepwise model selection. Many introductory texts recommend using "stepwise" regression. Forward stepwise regression adds predictors one by one according to a set criterion (usually by smallest p-value). Backward stepwise regression eliminates variables one by one from a larger model until a criterion is met. Ste...	{ "Header 1": "7.10 Notes", "Header 3": "Related topics", "token_count": 732, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
[7.1](#page-454-0) PREVEND, Part I. The summary table below shows the results of a multiple regression model of RFFT score versus statin use and age. \| \| Estimate \| Std. Error \| t value \| Pr(> t ) \| \|-------------\|----------\|------------\|---------\|----------\| \| (Intercept) \| 137.8822 \| 5.1221 \| 26...	{ "Header 1": "7.11 Exercises", "Header 3": "7.11.2 Simple versus multiple regression", "token_count": 789, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
7.4 Wolbachia, Part I. Wolbachia is a microbial symbiont estimated to be hosted by about 40% of all arthropod species, transmitted primarily from females to their offspring through the eggs. Researchers conducted a study on a wasp species to understand the effect of Wolbachia on the lifetime reproductive succes...	{ "Header 1": "7.11 Exercises", "Header 3": "7.11. EXERCISES", "token_count": 440, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
7.5 Baby weights, Part III. We considered the variables smoke and parity, one at a time, in modeling birth weights of babies in Exercise 7.3. A more realistic approach to modeling infant weights is to consider all possibly related variables at once. Other variables of interest include length of pregnancy in days (g...	{ "Header 1": "7.11 Exercises", "Header 3": "7.11.3 Evaluating the fit of a multiple regression model", "token_count": 2044, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
- (a) Suppose a numerical variable x has a coefficient of b1 = 2.5 in the multiple regression model. Suppose also that the first observation has x1 = 7.2, the second observation has a value of x1 = 8.2, and these two observations have the same values for all other predictors. Then the predicted value of...	{ "Header 1": "7.11 Exercises", "Header 3": "7.11.3 Evaluating the fit of a multiple regression model", "token_count": 250, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
[7.10](#page-454-9) Cherry trees. Timber yield is approximately equal to the volume of a tree, however, this value is difficult to measure without first cutting the tree down. Instead, other variables, such as height and diameter, may be used to predict a tree's volume and yield. Researchers wanting to understand t...	{ "Header 1": "7.11 Exercises", "Header 3": "7.11.4 The general multiple linear regression model", "token_count": 1958, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
Exercises [5.35](#page-283-1) and [5.47](#page-288-0) introduced an experiment conducted with the goal of identifying a treatment that reduces subjects' psychopathic deviant T scores on the MMPI test. Exercise [5.35](#page-283-1) evaluated the success of each individual treatment, and in exercise [5.47,](#page-288-0) A...	{ "Header 1": "7.11 Exercises", "Header 3": "[7.15](#page-455-4) Prison isolation experiment, Part III.", "token_count": 1862, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
[7.19](#page-456-0) Prison isolation experiment, Part V. Exercise [7.17](#page-379-0) used regression to predict a post-intervention score based on pre-intervention score and a particular intervention. The following table shows a model incorporating interaction between pre-intervention score and intervention. \|...	{ "Header 1": "7.11 Exercises", "Header 3": "7.11.7 Interaction in regression", "token_count": 1519, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
[7.27](#page-456-8) Prison isolation experiment, Part VI. Problem [7.15](#page-378-0) used a regression model to examine the effect of the interventions on possibly reducing psychopathic deviant T scores on prisoners. The regression model is shown in the problem statement. - (a) The value of the F-statistic is ...	{ "Header 1": "7.11 Exercises", "Header 3": "7.11.9 The connection between ANOVA and regression", "token_count": 401, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
- [8.1](#page-387-0) [Inference for a single proportion](#page-387-0) - [8.2](#page-394-0) [Inference for the difference of two proportions](#page-394-0) - [8.3](#page-400-0) [Inference for two or more groups](#page-400-0) - *[8.4](#page-413-0) [Chi-square tests for the fit of a distribution](#page-413-0)...	{ "Header 1": "Inference for categorical data", "token_count": 658, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
Advanced melanoma is an aggressive form of skin cancer that until recently was almost uniformly fatal. In rare instances, a patient's melanoma stopped progressing or disappeared altogether when the patient's immune system successfully mounted a response to the cancer. Those observations led to research into therapies t...	{ "Header 1": "8.1 Inference for a single proportion", "token_count": 492, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
The sampling distribution for pˆ, calculated from a sample of size n from a population with a success proportion p, is nearly normal when - 1. the sample observations are independent and - 2. at least 10 successes and 10 failures are expected in the sample, i.e. np ≥ 10 and n(1−p) ≥ 10. This is called the...	{ "Header 1": "8.1 Inference for a single proportion", "Header 3": "CONDITIONS FOR THE SAMPLING DISTRIBUTION OF pˆ BEING NEARLY NORMAL", "token_count": 225, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
Using the normal approximation, construct an approximate 95% confidence interval for the response probability for patients with advanced melanoma who were administered the combination of nivolumab and ipilimumab. The independence and success-failure assumptions should be checked first. Since the outcome of one patien...	{ "Header 1": "8.1 Inference for a single proportion", "Header 3": "EXAMPLE 8.2", "token_count": 364, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
In New York City on October 23rd, 2014, a doctor who had recently been treating Ebola patients in Guinea went to the hospital with a slight fever and was subsequently diagnosed with Ebola. Soon after, a survey conducted by the Marist Poll, an organization with a carefully designed methodology for drawing random samples...	{ "Header 1": "8.1 Inference for a single proportion", "Header 3": "GUIDED PRACTICE 8.3", "token_count": 420, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
Just as with inference for population means, confidence intervals for population proportions can be used when deciding whether to reject a null hypothesis. It is useful in most settings, however, to calculate the p-value for a test as a measure of the strength of the evidence contradicting the null hypothesis. When...	{ "Header 1": "8.1 Inference for a single proportion", "Header 3": "Hypothesis testing for a proportion", "token_count": 462, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
Suppose that out of a cohort of 120 patients with stage 1 lung cancer at the Dana-Farber Cancer Institute (DFCI) treated with a new surgical approach, 80 of the patients survive at least 5 years, and suppose that National Cancer Institute statistics indicate that the 5-year survival probability for stage 1 lung cancer ...	{ "Header 1": "8.1 Inference for a single proportion", "Header 3": "EXAMPLE 8.4", "token_count": 498, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
When the normal approximation to the distribution of $\hat{p}$ may not be accurate, inference is based on exact binomial probabilities. Calculating confidence intervals and p-values based on the binomial distribution can be done by hand, with tables of the binomial distribution, or (more easily and accurately) with...	{ "Header 1": "8.1 Inference for a single proportion", "Header 3": "8.1.2 Inference using exact methods", "token_count": 259, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
(E) In 2009, the FDA Oncology Drug Advisory Committee (ODAC) recommended that the drug Avastin be approved for use in glioblastoma, a form of brain cancer. Tumor shrinkage after taking a drug is called a response; out of 85 patients, 24 exhibited a response. Historically, response probabilities for brain cancer drugs...	{ "Header 1": "8.1 Inference for a single proportion", "Header 3": "EXAMPLE 8.7", "token_count": 650, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
Whenever possible, a sample size for a study should be estimated before data collection begins. Section 5.4 explored the calculation of sample sizes that allow a hypothesis test comparing two groups to have adequate power. When estimating a proportion, preliminary sample size calculations are often done to estimate a s...	{ "Header 1": "8.1 Inference for a single proportion", "Header 3": "8.1.3 Choosing a sample size when estimating a proportion", "token_count": 882, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
A 2015 estimate of Congress' approval rating was 19%.[9](#page-0-0) Using this estimate, how large should an additional survey be to produce a margin of error of 0.04 with 95% confidence?[10](#page-393-0) $$1.96 \times \sqrt{\frac{p(1-p)}{n}} \approx 1.96 \times \sqrt{\frac{0.19(1-0.19)}{n}} \le 0.04 \qquad \to \qqua...	{ "Header 1": "8.1 Inference for a single proportion", "Header 3": "GUIDED PRACTICE 8.10", "token_count": 243, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
The normal model can be applied to $\hat{p}_1 - \hat{p}_2$ if the sampling distribution for each sample proportion is nearly normal and if the samples are independent random samples from the relevant populations. CONDITIONS FOR THE SAMPLING DISTRIBUTION OF $\hat{P}_1 - \hat{P}_2$ to be approximately Normal The ...	{ "Header 1": "8.2 Inference for the difference of two proportions", "Header 3": "8.2.1 Sampling distribution of the difference of two proportions", "token_count": 348, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
The way a question is phrased can influence a person's response. For example, Pew Research Center conducted a survey with the following question:[11](#page-395-0) As you may know, by 2014 nearly all Americans will be required to have health insurance. [People who do not buy insurance will pay a penalty] while [People...	{ "Header 1": "8.2 Inference for the difference of two proportions", "Header 2": "8.2.2 Confidence intervals for p<sup>1</sup> − p<sup>2</sup>", "Header 3": "EXAMPLE 8.12", "token_count": 789, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
Hypothesis tests for $p_1 - p_2$ are usually testing the null hypothesis of no difference between $p_1$ and $p_2$ ; i.e. $H_0: p_1 - p_2 = 0$ . Under the null hypothesis, $\hat{p}_1 - \hat{p}_2$ is normally distributed with mean 0 and standard deviation $\sqrt{p(1-p)(\frac{1}{n_1} + \frac{1}{n_2})}$ , where un...	{ "Header 1": "8.2 Inference for the difference of two proportions", "Header 2": "8.2.2 Confidence intervals for p<sup>1</sup> − p<sup>2</sup>", "Header 3": "8.2.3 Hypothesis testing for $p_1 - p_2$", "token_count": 1965, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
The standard error for the estimated difference uses the individual estimates of the probability of a death: $$SE \approx \sqrt{\frac{0.01113(1-0.01113)}{44,925} + \frac{0.01125(1-0.01125)}{44,910}} = 0.0007.$$ The 95% confidence interval is given by −0.00012 ± (1.96)(0.0007) = (−0.0015,0.0013). ...	{ "Header 1": "8.2 Inference for the difference of two proportions", "Header 2": "8.2.2 Confidence intervals for p<sup>1</sup> − p<sup>2</sup>", "Header 3": "8.2.3 Hypothesis testing for $p_1 - p_2$", "token_count": 202, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
The comparison of the proportion of breast cancer deaths between the two groups can also be approached using a two-way contingency table, which contains counts for combinations of outcomes for two variables. The results for the mammogram study in this format are shown in Figure 8.3. Previously, the main question of i...	{ "Header 1": "8.3 Inference for two or more groups", "token_count": 373, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
If type of breast cancer screening had no effect on outcome in the mammogram data, what would the expected results be? Recall that if two events A and B are independent, then $P(A \cap B) = P(A)P(B)$ . Let A represent assignment to the mammogram group and B the event of death from breast cancer. Under indepe...	{ "Header 1": "8.3 Inference for two or more groups", "Header 3": "8.3.1 Expected counts", "token_count": 413, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
Calculate expected counts for the data in Figure [8.3.](#page-400-1) $$E_{1,1} = \frac{44,925 \times 1,005}{89,835} = 502.6 \qquad E_{1,2} = \frac{44,925 \times 88,830}{89,835} = 44,422.4$$ $$E_{2,1} = \frac{2,922 \times 1,005}{89,835} = 502.4 \qquad E_{2,2} = \frac{7,078 \times 88,830}{89,835} = 44,407.6$$ \| Death...	{ "Header 1": "8.3 Inference for two or more groups", "Header 3": "EXAMPLE 8.17", "token_count": 378, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
If a newborn is HIV<sup>+</sup> , should he or she be treated with nevirapine (NVP) or a more expensive drug, lopinarvir (LPV)? In this setting, success means preventing virologic failure; i.e., growth of the virus. A randomized study was conducted to assess whether there is an association between treatment and outcome...	{ "Header 1": "8.3 Inference for two or more groups", "Header 3": "EXAMPLE 8.18", "token_count": 624, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
Previously, test statistics have been constructed by calculating the difference between a point estimate and a null value, then dividing by the standard error of the point estimate to standardize the difference. The χ 2 statistic is based on a different idea. In each cell of a table, the difference observed - *expe...	{ "Header 1": "8.3 Inference for two or more groups", "Header 3": "8.3.2 The χ 2 test statistic", "token_count": 336, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
Two conditions that must be checked before performing a χ 2 test: - Independence. Each case that contributes a count to the table must be independent of all the other cases in the table. - Sample size. Each expected cell count must be greater than or equal to 10. For tables larger than 2×2, it is appropriate to use...	{ "Header 1": "8.3 Inference for two or more groups", "Header 3": "CONDITIONS FOR THE χ <sup>2</sup> TEST", "token_count": 346, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
The chi-square distribution is often used with data and statistics that are positive and rightskewed. The distribution is characterized by a single parameter, the degrees of freedom. Figure [8.7](#page-403-1) demonstrates three general properties of chi-square distributions as the degrees of freedom increases: the dist...	{ "Header 1": "8.3 Inference for two or more groups", "Header 3": "8.3.3 Calculating p-values for a χ <sup>2</sup> distribution", "token_count": 258, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
The χ 2 statistic from a contingency table has a sampling distribution that approximately follows a χ <sup>2</sup> distribution with degrees of freedom df = (r − 1)(c − 1), where r is the number of rows and c is the number of columns. Either statistical software or a table can be used to calculate pvalu...	{ "Header 1": "8.3 Inference for two or more groups", "Header 3": "8.3. INFERENCE FOR TWO OR MORE GROUPS 405", "token_count": 768, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
Calculate an approximate p-value for the mammogram data, given that the χ 2 statistic equals 0.02. Assess whether the data provides convincing evidence of an association between screening group and breast cancer death. The degrees of freedom in a 2 × 2 table is 1, so refer to the values in the first column of the...	{ "Header 1": "8.3 Inference for two or more groups", "Header 3": "EXAMPLE 8.21", "token_count": 256, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
If the p-value from a χ 2 test is small enough to provide evidence to reject the null hypothesis of no association, it is important to explore the results further to understand direction of the observed association. This is done by examining the residuals, the standardized differences of the observed - expected...	{ "Header 1": "8.3 Inference for two or more groups", "Header 3": "8.3.4 Interpreting the results of a χ 2 test", "token_count": 1873, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
Confirm the conclusions reached in Example 8.24 by analyzing the residuals.<sup>17</sup> $<sup>1^{7}</sup>R_{1,1} = \frac{(44.6-60)}{\sqrt{44.6}} = 2.31; R_{1,2} = \frac{(42.4-27)}{\sqrt{27}} = -2.37; R_{2,1} = \frac{(87-102.4)}{\sqrt{102.4}} = -1.53; R_{2,2} = \frac{(113-97.6)}{\sqrt{97.6}} = 1.56$ . The positive re...	{ "Header 1": "8.3 Inference for two or more groups", "Header 3": "GUIDED PRACTICE 8.25", "token_count": 241, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
Chapter [1](#page-9-0) started with the discussion of a study examining whether exposure to peanut products reduce the rate of a child developing peanut allergies. Children were randomized either to the peanut avoidance or the peanut consumption group; at 5 years of age, each child was tested for peanut allergy using a...	{ "Header 1": "8.3 Inference for two or more groups", "Header 3": "GUIDED PRACTICE 8.26", "token_count": 1450, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
Of the 17 patients cured, 13 were in the fecal infusion group and 4 were in the vancomycin group. Assume that the marginal totals are fixed (i.e., 17 patients were cured, 12 were uncured, and 16 patients were in the fecal infusion group, while 13 were in the vancomycin group). Enumerate all possible sets of results tha...	{ "Header 1": "8.3 Inference for two or more groups", "Header 3": "EXAMPLE 8.27", "token_count": 613, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
Suppose that researchers were interested in testing the null hypothesis against the one-sided alternative, $H_A : p_1 > p_2$ . To calculate the one-sided p-value, sum the probabilities of each table representing results as or more extreme than those observed; specifically, sum the probabilities of observing Figure 8...	{ "Header 1": "8.3 Inference for two or more groups", "Header 3": "Calculating a one-sided p-value", "token_count": 318, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
Calculate the probability of observing Figure 8.15, assuming the margin totals are fixed. $$P(13,3,4,9) = \frac{\binom{16}{13}\binom{13}{4}}{\binom{29}{17}} = \frac{16!\ 13!\ 17!\ 12!}{13!\ 3!\ 4!\ 9!\ 29!} = 7.71 \times 10^{-3}.$$ The value 0.0077 represents the probability of observing 13 cured patients out of 16...	{ "Header 1": "8.3 Inference for two or more groups", "Header 3": "EXAMPLE 8.28", "token_count": 762, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
There are various methods for calculating a two-sided p-value in the Fisher's exact test setting. When the test is calculated by hand, the most common way to calculate a two-sided p-value is to double the smaller of the one-sided p-values. One other common method used by various statistical computing packages suc...	{ "Header 1": "8.3 Inference for two or more groups", "Header 3": "Calculating a two-sided p-value", "token_count": 810, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
The χ 2 test can also be used to examine the appropriateness of hypothesized distribution for a dataset, most commonly when a set of observations falls naturally into categories as in the examples discussed in this section. As with testing in the two-way table setting, expected counts are calculated based on the assu...	{ "Header 1": "8.4 Chi-square tests for the fit of a distribution", "token_count": 287, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
The participants in the FAMuSS study were volunteers at a university, and so did not come from a random sample of the US population. The participants may not be representative of the general United States population. The χ 2 test can be used to test the null hypothesis that the participants are racially representativ...	{ "Header 1": "8.4 Chi-square tests for the fit of a distribution", "Header 3": "EXAMPLE 8.31", "token_count": 1326, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
The techniques so far in this chapter have often relied on the assumption that the data were collected using random sampling from a population. When cases come from a random sample, the sample proportion of observations with a particular outcome should accurately estimate the population proportion, given that the sampl...	{ "Header 1": "8.5 Outcome-based sampling: case-control studies", "Header 3": "8.5.1 Introduction", "token_count": 552, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
In 2006, Chambers, et. al reported a case-control study examining the association of SSRI use and persistent pulmonary hypertension in newborns.[21](#page-416-0) The study team enrolled 337 women whose infants suffered from PPHN and 836 women with similar characteristics but whose infants did not have PPHN. Among the w...	{ "Header 1": "8.5 Outcome-based sampling: case-control studies", "Header 3": "8.5.2 χ 2 tests of association in case-control studies", "token_count": 767, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
For data in a 2×2 table, correct point estimates of association depend on the mechanism used to gather the data. In the example of a clinical trial of nevirapine versus lopinarvir discussed in Section [8.3.1,](#page-400-3) the population proportion of children who would experience virologic failure after treatment with...	{ "Header 1": "8.5 Outcome-based sampling: case-control studies", "Header 3": "8.5.3 Estimates of association in case-control studies", "token_count": 444, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
In a study like the PPHN case-control study, the natural population parameter of interest would be the relative risk of PPHN for infants exposed to an SSRI during after week 20 of gestation compared to those who were not exposed. However, in the design of this study, participating mothers were sampled and grouped accor...	{ "Header 1": "8.5 Outcome-based sampling: case-control studies", "Header 3": "P (virologic failure\|treatment with nevirapine) <sup>P</sup> (virologic failure\|treatment with lopinarvir) .", "token_count": 1160, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
Two-way tables are often used to summarize data from medical research studies, and entire texts have been written about methods of analysis for these tables. This chapter covers only the most basic of those methods. Until recently, Fisher's exact test could only be calculated for 2×2 tables with small cell counts. Re...	{ "Header 1": "8.6 Notes", "token_count": 734, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
[8.8](#page-457-7) Legalization of marijuana, Part I. The General Social Survey asked 1,578 US residents: "Do you think the use of marijuana should be made legal, or not?" 61% of the respondents said it should be made legal.[29](#page-422-0) - (a) Is 61% a sample statistic or a population parameter? Explain. - (b...	{ "Header 1": "8.7 Exercises", "Header 3": "8.7. EXERCISES 423", "token_count": 1801, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
[8.17](#page-458-6) Social experiment, Part I. A "social experiment" conducted by a TV program questioned what people do when they see a very obviously bruised woman getting picked on by her boyfriend. On two different occasions at the same restaurant, the same couple was depicted. In one scenario the woman was dre...	{ "Header 1": "8.7 Exercises", "Header 3": "8.7.2 Inference for the difference of two proportions", "token_count": 1798, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
[8.24](#page-459-3) Prenatal vitamins and Autism. Researchers studying the link between prenatal vitamin use and autism surveyed the mothers of a random sample of children aged 24 - 60 months with autism and conducted another separate random sample for children with typical development. The table below shows the nu...	{ "Header 1": "8.7 Exercises", "Header 3": "8.7. EXERCISES 427", "token_count": 1054, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
[8.31](#page-459-10) PREVEND, Part IV. In the PREVEND data, researchers measured various features of study participants, including data on statin use and highest level of education attained. A two-way table of education level and statin use is shown below. \| \| Primary \| LowerSec \| UpperSec \| Univ \| Sum \| ...	{ "Header 1": "8.7 Exercises", "Header 3": "8.7. EXERCISES 429", "token_count": 1915, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
The National Health Care Anti-Fraud Association estimates that approximately \$68 billion is lost to health care fraud each year. Often when fraud is suspected, an audit of randomly selected billings is conducted. The selected claims are reviewed by experts and each claim is classified as allowed or not allowed. The cl...	{ "Header 1": "8.7 Exercises", "Header 3": "8.7. EXERCISES 429", "token_count": 1304, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
[1.1](#page-74-3) (a) Treatment: 10/43 = 0.23 → 23%. (b) Control: 2/46 = 0.04 → 4%. (c) A higher percentage of patients in the treatment group were pain free 24 hours after receiving acupuncture. (d) It is possible that the observed difference between the two group percentages is due to chance. **[1.3](...	{ "Header 1": "End of chapter exercise solutions", "Header 3": "1 Introduction to data", "token_count": 2019, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
2.1 (a) False. These are independent trials. (b) False. There are red face cards. (c) True. A card cannot be both a face card and an ace. 2.3 (a) $\frac{1}{4}$ . Solution 1: A colorblind male has genotype $X^-Y$ . He must have inherited $X^-$ from his mother (probability of $\frac{1}{2}$ ) and Y ...	{ "Header 1": "End of chapter exercise solutions", "Header 3": "2 Probability", "token_count": 2014, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
2.21 Mumps is the most likely disease state, since $P(B_3\|A) = 0.563$ , $P(B_1\|A) = 0.023$ , and $P(B_2\|A) = .415$ . $P(B_i\|A) = \frac{P(A\|B_i)P(B_i)}{P(A)}$ . $P(A) = P(A \text{ and } B_1) + P(A \text{ and } B_2) + P(A \text{ and } B_3) = P(A\|B_1)P(B_1) + P(A\|B_2)P(B_2) + P(A\|B_3)P(B_3)$ . 2.23 (a) Le...	{ "Header 1": "End of chapter exercise solutions", "Header 3": "2 Probability", "token_count": 1964, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
$$P(D_1\|M_2, R) = \frac{P(M_2 \cap D_1 \cap R)}{P(M_2 \cap R)} = \frac{0.045}{(0.10)(0.60)} = 0.75$$ $$P(D_2\|M_2, R) = \frac{P(M_2 \cap D_2 \cap R)}{P(M_2 \cap R)} = \frac{0.012}{(0.10)(0.60)} = 0.20$$ Back to the original question ... $$P(M_2 \cap D^C \cap R) = P(D^C \| M_2, R) P(M_2 \| R) P(R)$$ $$= \frac{P(D^C \|...	{ "Header 1": "End of chapter exercise solutions", "Header 3": "2 Probability", "token_count": 1179, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
[3.1](#page-184-1) (a) 13. (b) No, these 27 students are not a random sample from the university's student population. For example, it might be argued that the proportion of smokers among students who go to the gym at 9 am on a Saturday morning would be lower than the proportion of smokers in the university as a wh...	{ "Header 1": "End of chapter exercise solutions", "Header 3": "3 Distributions of random variables", "token_count": 2017, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
![](_page_442_Figure_17.jpeg) (b) P ercV R = 0.9007 ≈ 90%, P ercQR = 0.6990 ≈ 70%. 100% − 90% = 10% did better than her on VR, and 100% − 70% = 30% did better than her on QR. (c) 159. (d) 147. [3.25](#page-189-0) (a) 0.115. (b) The coldest 10% of days are colder than 70.59◦F. **[3.27](#page-189-1)...	{ "Header 1": "End of chapter exercise solutions", "Header 3": "3 Distributions of random variables", "token_count": 1477, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
P (X = 4) = 0.09435. (c) P (X ≤ 2) = 0.663. (d) 0.09437, from the binomial distribution. With a large sample size, sampling with replacement is highly unlikely to result in any particular individual being sampled again. In this case, the hypergeometric and binomial distributions will produce equal proba...	{ "Header 1": "End of chapter exercise solutions", "Header 3": "3 Distributions of random variables", "token_count": 1596, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
4.1 (a) $\overline{x} = 0.6052$ . (b) s = 0.0131. (c) $Z_{0.63} = \frac{0.63 - 0.6052}{0.0131} = 1.893$ . No, this level of BGC is within 2 SD of the mean. (d) The standard error of the sample mean is given by $\frac{s}{\sqrt{n}} = \frac{0.0131}{\sqrt{70}} = 0.00157$ . 4.3 (a) This is the sampling di...	{ "Header 1": "End of chapter exercise solutions", "Header 3": "4 Foundations for inference", "token_count": 2028, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
There is sufficient evidence to reject the null hypothesis and conclude that the mean birthweight of babies from inner-city teaching hospitals is lower than 3,260 grams. 4.21 (a) $H_0$ : Anti-depressants do not help symptoms of fibromyalgia. $H_A$ : Anti- depressants do treat symptoms of fibromyalgia. (b) Concl...	{ "Header 1": "End of chapter exercise solutions", "Header 3": "4 Foundations for inference", "token_count": 309, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
5.1 (a) df = 6 - 1 = 5, $t_5^{\star} = 2.02$ (column with two tails of 0.10, row with df = 5). (b) df = 21 - 1 = 20, $t_{20}^{\star} = 2.53$ (column with two tails of 0.02, row with df = 20). (c) df = 28, $t_{28}^{\star} = 2.05$ . (d) df = 11, $t_{11}^{\star} = 3.11$ . 5.3 On a z-distribution, the cut...	{ "Header 1": "End of chapter exercise solutions", "Header 3": "5 Inference for numerical data", "token_count": 2021, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
<sup>H</sup><sup>A</sup> : <sup>µ</sup>dif f , 0. Independence: random sample from less than 10% of population. Sample size of at least 30. The skew of the differences is, at worst, slight. Z = 2.72 → p-value = 0.0066. Since p-value < 0.05, reject H0. The data provide strong evidence that the average IQ s...	{ "Header 1": "End of chapter exercise solutions", "Header 3": "5 Inference for numerical data", "token_count": 2041, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
Furthermore, the data indicate patients in the distracted eating (treatment) group consume more food than patients in the control group. [5.35](#page-283-1) Let <sup>µ</sup>dif f <sup>=</sup> <sup>µ</sup>pre <sup>−</sup>µpost. <sup>H</sup><sup>0</sup> : <sup>µ</sup>dif f = 0: Treatment has no effect. *<...	{ "Header 1": "End of chapter exercise solutions", "Header 3": "5 Inference for numerical data", "token_count": 1659, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
[6.1](#page-316-1) (a) Strong relationship, but a straight line would not fit the data. (b) Strong relationship, and a linear fit would be reasonable. (c) Weak relationship, and trying a linear fit would be reasonable. (d) Moderate relationship, but a straight line would not fit the data. (e) Strong relationship, a...	{ "Header 1": "End of chapter exercise solutions", "Header 3": "6 Simple linear regression", "token_count": 1315, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
where the explanatory variable is a binary variable taking on value 1 if the diamond is 1 carat. [6.23](#page-325-1) (a) The relationship is positive, moderate-to-strong, and linear. There are a few outliers but no points that appear to be influential. (b) weight <sup>=</sup> <sup>−</sup>105.0113 + 1.<sup...	{ "Header 1": "End of chapter exercise solutions", "Header 3": "6 Simple linear regression", "token_count": 746, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
(h) No, a 95% confidence interval for $\beta_1$ would not be expected to contain the null value 0, since the p-value is less than 0.05. 6.27 (a) The point estimate and standard error are $b_1 = 0.9112$ and SE = 0.0259. We can compute a T-score: T = (0.9112 - 1)/0.0259 = -3.43. Using df = 168, the p-value ...	{ "Header 1": "End of chapter exercise solutions", "Header 3": "6 Simple linear regression", "token_count": 1096, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
7.1 Although the use of statins appeared to be associated with lower RFFT score when no adjustment was made for possible confounders, statin use is not significantly associated with RFFT score in a model that adjusts for age. After adjusting for age, the estimated difference in mean RFFT score between statin users ...	{ "Header 1": "End of chapter exercise solutions", "Header 3": "7 Multiple linear regression", "token_count": 2002, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
[7.19](#page-380-0) (a) post <sup>d</sup> <sup>=</sup> <sup>−</sup>17.58+1.28(pre)+67.75(neutral)+64.42(therapeutic)−0.99(pre×neutral)−1.01(pre×therapeutic) (b) The coefficient for pre is the predicted increase in post score associated with a 1 unit increase in pre-score for individual...	{ "Header 1": "End of chapter exercise solutions", "Header 3": "7 Multiple linear regression", "token_count": 1479, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
[8.1](#page-420-3) (a) False. Doesn't satisfy success-failure condition. (b) True. The success-failure condition is not satisfied. In most samples we would expect pˆ to be close to 0.08, the true population proportion. While pˆ can be much above 0.08, it is bound below by 0, suggesting it would take on a right ...	{ "Header 1": "End of chapter exercise solutions", "Header 3": "8 Inference for categorical data", "token_count": 2021, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
[8.19](#page-424-4) (a) Standard error: $$SE = \sqrt{\frac{0.79(1 - 0.79)}{347} + \frac{0.55(1 - 0.55)}{617}} = 0.03$$ Using z ? = 1.96, we get: $$0.79 - 0.55 \pm 1.96 \times 0.03 \rightarrow (0.181, 0.299)$$ We are 95% confident that the proportion of Democrats who support the plan is 18.1% to 29.9% ...	{ "Header 1": "End of chapter exercise solutions", "Header 3": "8 Inference for categorical data", "token_count": 1405, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
\| \| Mosqu \| \| \| \| \| \| \|------------\|-------\|--------\|-----\|--\|--\|--\| \| \| No \| No Yes \| \| \| \| \| \| Malaria \| 30 \| 22 \| 52 \| \| \| \| \| No Malaria \| 70 \| 78 \| 148 \| \| \| \| \| Total \| 100 \| 100 \| 200 \| \| \| \| (b) Expected number of infected chil...	{ "Header 1": "End of chapter exercise solutions", "Header 3": "8.35 (a) One possible $2 \\times 2$ contingency table:", "token_count": 2041, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
(c) The easiest way of calculating the OR for the table is the cross-product of the diagonal elements of the table: [(10)(4000)]/ [(2000)(7)] = 2.86. Using the definition, it can be calculated as: $$\hat{OR} = \frac{\frac{\hat{P}(\text{CNS}\|\text{Usage})}{1-\hat{P}(\text{CNS}\|\text{Usage})}}{\frac{\hat{P}(\text...	{ "Header 1": "End of chapter exercise solutions", "Header 3": "8.35 (a) One possible $2 \\times 2$ contingency table:", "token_count": 453, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
\| Definition of Epidemiology<br> \| 1-2 \| \|-----------------------------------------\|------\| \| Historical Evolution of Epidemiology \| 1-7 \| \| Uses \| 1-12 \| \| Core Epidemiologic Functions<br> \| 1-15 \| \| The Epidemiologic Approach \| 1-21 \| \| Descriptive ...	{ "Header 1": "Major Sections", "token_count": 346, "source_pdf": "datasets/websources/Med_v1/med_textbook/cdc_6914_DS1.pdf" }
Epidemiology is a scientific discipline with sound methods of scientific inquiry at its foundation. Epidemiology is data-driven and relies on a systematic and unbiased approach to the collection, analysis, and interpretation of data. Basic epidemiologic methods tend to rely on careful observation and use of valid compa...	{ "Header 1": "Definition of Epidemiology", "Header 2": "Study", "token_count": 262, "source_pdf": "datasets/websources/Med_v1/med_textbook/cdc_6914_DS1.pdf" }
Epidemiology is concerned with the frequency and pattern of health events in a population: > Frequency refers not only to the number of health events such as the number of cases of meningitis or diabetes in a population, but also to the relationship of that number to the size of the population. The result...	{ "Header 1": "Definition of Epidemiology", "Header 2": "Distribution", "token_count": 220, "source_pdf": "datasets/websources/Med_v1/med_textbook/cdc_6914_DS1.pdf" }
In the mid-1800s, an anesthesiologist named John Snow was conducting a series of investigations in London that warrant his being considered the "father of field epidemiology." Twenty years before the development of the microscope, Snow conducted studies of cholera outbreaks both to discover the cause of disease and to ...	{ "Header 1": "Historical Evolution of Epidemiology", "Header 2": "1854", "token_count": 1698, "source_pdf": "datasets/websources/Med_v1/med_textbook/cdc_6914_DS1.pdf" }
In the mid- and late-1800s, epidemiological methods began to be applied in the investigation of disease occurrence. At that time. most investigators focused on acute infectious diseases. In the 1930s and 1940s, epidemiologists extended their methods to noninfectious diseases. The period since World War II has seen an e...	{ "Header 1": "Historical Evolution of Epidemiology", "Header 2": "19th and 20<sup>th</sup> centuries", "token_count": 447, "source_pdf": "datasets/websources/Med_v1/med_textbook/cdc_6914_DS1.pdf" }
When investigating a disease outbreak, epidemiologists rely on health-care providers and laboratorians to establish the proper diagnosis of individual patients. But epidemiologists also contribute to physicians' understanding of the clinical picture and natural history of disease. For example, in late 1989, a physician...	{ "Header 1": "Historical Evolution of Epidemiology", "Header 2": "Making individual decisions", "Header 3": "Completing the clinical picture", "token_count": 230, "source_pdf": "datasets/websources/Med_v1/med_textbook/cdc_6914_DS1.pdf" }
Public health surveillance is the ongoing, systematic collection, analysis, interpretation, and dissemination of health data to help guide public health decision making and action. Surveillance is equivalent to monitoring the pulse of the community. The purpose of public health surveillance, which is sometimes called "...	{ "Header 1": "Core Epidemiologic Functions", "Header 2": "Public health surveillance", "token_count": 476, "source_pdf": "datasets/websources/Med_v1/med_textbook/cdc_6914_DS1.pdf" }
As noted above, surveillance provides information for action. One of the first actions that results from a surveillance case report or report of a cluster is investigation by the public health department. The investigation may be as limited as a phone call to the healthcare provider to confirm or clarify the circumstan...	{ "Header 1": "Core Epidemiologic Functions", "Header 2": "Public health surveillance", "Header 3": "Field investigation", "token_count": 505, "source_pdf": "datasets/websources/Med_v1/med_textbook/cdc_6914_DS1.pdf" }
Surveillance and field investigations are usually sufficient to identify causes, modes of transmission, and appropriate control and prevention measures. But sometimes analytic studies employing more rigorous methods are needed. Often the methods are used in combination — with surveillance and field investigations provi...	{ "Header 1": "Core Epidemiologic Functions", "Header 2": "Analytic studies", "token_count": 496, "source_pdf": "datasets/websources/Med_v1/med_textbook/cdc_6914_DS1.pdf" }
Epidemiologists, who are accustomed to using systematic and quantitative approaches, have come to play an important role in evaluation of public health services and other activities. Evaluation is the process of determining, as systematically and objectively as possible, the relevance, effectiveness, efficiency, and im...	{ "Header 1": "Core Epidemiologic Functions", "Header 2": "Evaluation", "token_count": 247, "source_pdf": "datasets/websources/Med_v1/med_textbook/cdc_6914_DS1.pdf" }
As with all scientific endeavors, the practice of epidemiology relies on a systematic approach. In very simple terms, the epidemiologist: - Counts cases or health events, and describes them in terms of time, place, and person; - Divides the number of cases by an appropriate denominator to calculate rates; and...	{ "Header 1": "The Epidemiologic Approach", "token_count": 272, "source_pdf": "datasets/websources/Med_v1/med_textbook/cdc_6914_DS1.pdf" }
Before counting cases, the epidemiologist must decide what to count, that is, what to call a case. For that, the epidemiologist uses a case definition. A case definition is a set of standard criteria for classifying whether a person has a particular disease, syndrome, or other health condition. Some case definition...	{ "Header 1": "The Epidemiologic Approach", "Header 3": "Defining a case", "token_count": 439, "source_pdf": "datasets/websources/Med_v1/med_textbook/cdc_6914_DS1.pdf" }
Clinically compatible illness with L. monocytogenes isolated - From a normally sterile site - In a resident of Winston-Salem, North Carolina - With onset between October 24, 2000 and January 4, 2001 Source: MacDonald P, Boggs J, Whitwam R, Beatty M, Hunter S, MacCormack N, et al. Listeria-associated birth complicat...	{ "Header 1": "The Epidemiologic Approach", "Header 3": "Case definition", "token_count": 239, "source_pdf": "datasets/websources/Med_v1/med_textbook/cdc_6914_DS1.pdf" }
Suspected: Any febrile illness accompanied by rash Probable: A case that meets the clinical case definition, has noncontributory or no serologic or virologic testing, and is not epidemiologically linked to a confirmed case Confirmed: A case that is laboratory confirmed or that meets the clinical case definition and...	{ "Header 1": "The Epidemiologic Approach", "Header 2": "Criteria in case definitions", "Header 3": "Case classification", "token_count": 526, "source_pdf": "datasets/websources/Med_v1/med_textbook/cdc_6914_DS1.pdf" }

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Using the output in Figure [7.18,](#page-354-0) write the overall model equation, the model equation for nondiabetics, and the model equation for diabetics. The overall model equation is TotChol = 4 .70 + 0.0096(Age) + 1.72(DiabetesYes) <sup>−</sup> <sup>0</sup>.034(Age <sup>×</sup> DiabetesYes). For no...	{ "Header 1": "7.7 Interaction in regression", "Header 3": "EXAMPLE 7.12", "token_count": 1392, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
Previously, multiple regression modeling was shown in the context of estimating an association while adjusting for possible confounders. Another application of multiple regression is explanatory modeling, in which the goal is to construct a model that explains the observed variation in the response variable. In this co...	{ "Header 1": "7.8 Model selection for explanatory models", "token_count": 506, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
Habitat fragmentation is the process by which a habitat in a large contiguous space is divided into smaller, isolated pieces; human activities such as agricultural development can result in habitat fragmentation. Smaller patches of habitat are only able to support limited populations of organisms, which reduces genetic...	{ "Header 1": "7.8 Model selection for explanatory models", "Header 3": "Abundance of forest birds: introduction", "token_count": 674, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
The response variable for the model is abundance. Numerical summaries calculated from software show that abundance ranges from 1.5 to 39.6. Figure [7.21](#page-359-0) shows that the distribution of abundance is bimodal, with modes at small values of abundance and at between 25 and 30 birds. The median (21.0) and mean (...	{ "Header 1": "7.8 Model selection for explanatory models", "Header 3": "Data exploration", "token_count": 876, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
The variables log.dist.nearest and log.dist.larger appear strongly associated; a model may only need one of the two, as they may be essentially "redundant" in explaining the variability in the response variable.[22](#page-362-0) In this case, however, since both are only weakly associated with abundance, both may be un...	{ "Header 1": "7.8 Model selection for explanatory models", "Header 3": "7.8. MODEL SELECTION FOR EXPLANATORY MODELS 363", "token_count": 577, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
Based on the data exploration, the initial model should include the variables log.area, altitude, log.yrs.isolation, and grazing.intensity; a summary of this model is shown in Figure [7.26.](#page-362-2) The R <sup>2</sup> and adjusted R 2 for this model are, respectively, 0.728 and 0.688. The model explains about ...	{ "Header 1": "7.8 Model selection for explanatory models", "Header 3": "Initial model fitting", "token_count": 616, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
First, fit models excluding the predictors that were not statistically significant: altitude and log.yrs.isolation. Models excluding either variable have adjusted R <sup>2</sup> of 0.69, and a model excluding both variables has an adjusted R <sup>2</sup> of 0.70, a small but noticeable increase from the initial mod...	{ "Header 1": "7.8 Model selection for explanatory models", "Header 3": "Model comparison", "token_count": 1076, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
The fit of a model can be assessed using various residual plots. Figure 7.29 shows a histogram and normal probability plot of the residuals for the final model. Both show that the residuals follow the shape of a normal density in the middle range (between -10 and 10) but fit less well in the tails. There are too many l...	{ "Header 1": "7.8 Model selection for explanatory models", "Header 3": "Model assessment", "token_count": 517, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
The relatively large R 2 for the final model (0.72) suggests that patch area and extent of grazing (either heavy or not) explain a large amount of the observed variability in bird abundance. Of the features measured in the study, these two are the most highly associated with bird abundance. Larger area is associated ...	{ "Header 1": "7.8 Model selection for explanatory models", "Header 3": "Conclusions", "token_count": 374, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
Might a model including all the predictor variables be better than the final model with only log.area and grazing.binary? The model is shown in Figure [7.31.](#page-366-0) The R 2 for this model is 0.729 and the adjusted R 2 is 0.676. While the R 2 is essentially the same as for the final model, the adjusted R ...	{ "Header 1": "7.8 Model selection for explanatory models", "Header 3": "Final considerations", "token_count": 1102, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
Regression with categorical variables and ANOVA are essentially the same method, but with some important differences in the information provided by the analysis. Earlier in this chapter, the strength of the association between RFFT scores and educational level was assessed with regression. Figure [7.33](#page-367-1) sh...	{ "Header 1": "7.9 The connection between ANOVA and regression", "token_count": 682, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
Why use ANOVA at all if fitting a linear regression model seems to provide more information? A case can be be made that the most important first step in analyzing the association between a response and a categorical variable is to compute and examine the F-statistic for evidence of any effect, and that only when the ...	{ "Header 1": "7.9 The connection between ANOVA and regression", "Header 3": "7.9. THE CONNECTION BETWEEN ANOVA AND REGRESSION 369", "token_count": 455, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
- Keep a clear view of the purpose. Is the goal of constructing the model to understand the relationship between the response and a particular predictor after adjusting for confounders? Or is the goal to understand the joint association between a response and a set of predictors? - Avoid rushing into model fitting....	{ "Header 1": "7.10 Notes", "Header 3": "Important ideas", "token_count": 309, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
- Stepwise model selection. Many introductory texts recommend using "stepwise" regression. Forward stepwise regression adds predictors one by one according to a set criterion (usually by smallest p-value). Backward stepwise regression eliminates variables one by one from a larger model until a criterion is met. Ste...	{ "Header 1": "7.10 Notes", "Header 3": "Related topics", "token_count": 732, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
[7.1](#page-454-0) PREVEND, Part I. The summary table below shows the results of a multiple regression model of RFFT score versus statin use and age. \| \| Estimate \| Std. Error \| t value \| Pr(> t ) \| \|-------------\|----------\|------------\|---------\|----------\| \| (Intercept) \| 137.8822 \| 5.1221 \| 26...	{ "Header 1": "7.11 Exercises", "Header 3": "7.11.2 Simple versus multiple regression", "token_count": 789, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
7.4 Wolbachia, Part I. Wolbachia is a microbial symbiont estimated to be hosted by about 40% of all arthropod species, transmitted primarily from females to their offspring through the eggs. Researchers conducted a study on a wasp species to understand the effect of Wolbachia on the lifetime reproductive succes...	{ "Header 1": "7.11 Exercises", "Header 3": "7.11. EXERCISES", "token_count": 440, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
7.5 Baby weights, Part III. We considered the variables smoke and parity, one at a time, in modeling birth weights of babies in Exercise 7.3. A more realistic approach to modeling infant weights is to consider all possibly related variables at once. Other variables of interest include length of pregnancy in days (g...	{ "Header 1": "7.11 Exercises", "Header 3": "7.11.3 Evaluating the fit of a multiple regression model", "token_count": 2044, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
- (a) Suppose a numerical variable x has a coefficient of b1 = 2.5 in the multiple regression model. Suppose also that the first observation has x1 = 7.2, the second observation has a value of x1 = 8.2, and these two observations have the same values for all other predictors. Then the predicted value of...	{ "Header 1": "7.11 Exercises", "Header 3": "7.11.3 Evaluating the fit of a multiple regression model", "token_count": 250, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
[7.10](#page-454-9) Cherry trees. Timber yield is approximately equal to the volume of a tree, however, this value is difficult to measure without first cutting the tree down. Instead, other variables, such as height and diameter, may be used to predict a tree's volume and yield. Researchers wanting to understand t...	{ "Header 1": "7.11 Exercises", "Header 3": "7.11.4 The general multiple linear regression model", "token_count": 1958, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
Exercises [5.35](#page-283-1) and [5.47](#page-288-0) introduced an experiment conducted with the goal of identifying a treatment that reduces subjects' psychopathic deviant T scores on the MMPI test. Exercise [5.35](#page-283-1) evaluated the success of each individual treatment, and in exercise [5.47,](#page-288-0) A...	{ "Header 1": "7.11 Exercises", "Header 3": "[7.15](#page-455-4) Prison isolation experiment, Part III.", "token_count": 1862, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
[7.19](#page-456-0) Prison isolation experiment, Part V. Exercise [7.17](#page-379-0) used regression to predict a post-intervention score based on pre-intervention score and a particular intervention. The following table shows a model incorporating interaction between pre-intervention score and intervention. \|...	{ "Header 1": "7.11 Exercises", "Header 3": "7.11.7 Interaction in regression", "token_count": 1519, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
[7.27](#page-456-8) Prison isolation experiment, Part VI. Problem [7.15](#page-378-0) used a regression model to examine the effect of the interventions on possibly reducing psychopathic deviant T scores on prisoners. The regression model is shown in the problem statement. - (a) The value of the F-statistic is ...	{ "Header 1": "7.11 Exercises", "Header 3": "7.11.9 The connection between ANOVA and regression", "token_count": 401, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
- [8.1](#page-387-0) [Inference for a single proportion](#page-387-0) - [8.2](#page-394-0) [Inference for the difference of two proportions](#page-394-0) - [8.3](#page-400-0) [Inference for two or more groups](#page-400-0) - *[8.4](#page-413-0) [Chi-square tests for the fit of a distribution](#page-413-0)...	{ "Header 1": "Inference for categorical data", "token_count": 658, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
Advanced melanoma is an aggressive form of skin cancer that until recently was almost uniformly fatal. In rare instances, a patient's melanoma stopped progressing or disappeared altogether when the patient's immune system successfully mounted a response to the cancer. Those observations led to research into therapies t...	{ "Header 1": "8.1 Inference for a single proportion", "token_count": 492, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
The sampling distribution for pˆ, calculated from a sample of size n from a population with a success proportion p, is nearly normal when - 1. the sample observations are independent and - 2. at least 10 successes and 10 failures are expected in the sample, i.e. np ≥ 10 and n(1−p) ≥ 10. This is called the...	{ "Header 1": "8.1 Inference for a single proportion", "Header 3": "CONDITIONS FOR THE SAMPLING DISTRIBUTION OF pˆ BEING NEARLY NORMAL", "token_count": 225, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
Using the normal approximation, construct an approximate 95% confidence interval for the response probability for patients with advanced melanoma who were administered the combination of nivolumab and ipilimumab. The independence and success-failure assumptions should be checked first. Since the outcome of one patien...	{ "Header 1": "8.1 Inference for a single proportion", "Header 3": "EXAMPLE 8.2", "token_count": 364, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
In New York City on October 23rd, 2014, a doctor who had recently been treating Ebola patients in Guinea went to the hospital with a slight fever and was subsequently diagnosed with Ebola. Soon after, a survey conducted by the Marist Poll, an organization with a carefully designed methodology for drawing random samples...	{ "Header 1": "8.1 Inference for a single proportion", "Header 3": "GUIDED PRACTICE 8.3", "token_count": 420, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
Just as with inference for population means, confidence intervals for population proportions can be used when deciding whether to reject a null hypothesis. It is useful in most settings, however, to calculate the p-value for a test as a measure of the strength of the evidence contradicting the null hypothesis. When...	{ "Header 1": "8.1 Inference for a single proportion", "Header 3": "Hypothesis testing for a proportion", "token_count": 462, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
Suppose that out of a cohort of 120 patients with stage 1 lung cancer at the Dana-Farber Cancer Institute (DFCI) treated with a new surgical approach, 80 of the patients survive at least 5 years, and suppose that National Cancer Institute statistics indicate that the 5-year survival probability for stage 1 lung cancer ...	{ "Header 1": "8.1 Inference for a single proportion", "Header 3": "EXAMPLE 8.4", "token_count": 498, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
When the normal approximation to the distribution of $\hat{p}$ may not be accurate, inference is based on exact binomial probabilities. Calculating confidence intervals and p-values based on the binomial distribution can be done by hand, with tables of the binomial distribution, or (more easily and accurately) with...	{ "Header 1": "8.1 Inference for a single proportion", "Header 3": "8.1.2 Inference using exact methods", "token_count": 259, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
(E) In 2009, the FDA Oncology Drug Advisory Committee (ODAC) recommended that the drug Avastin be approved for use in glioblastoma, a form of brain cancer. Tumor shrinkage after taking a drug is called a response; out of 85 patients, 24 exhibited a response. Historically, response probabilities for brain cancer drugs...	{ "Header 1": "8.1 Inference for a single proportion", "Header 3": "EXAMPLE 8.7", "token_count": 650, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
Whenever possible, a sample size for a study should be estimated before data collection begins. Section 5.4 explored the calculation of sample sizes that allow a hypothesis test comparing two groups to have adequate power. When estimating a proportion, preliminary sample size calculations are often done to estimate a s...	{ "Header 1": "8.1 Inference for a single proportion", "Header 3": "8.1.3 Choosing a sample size when estimating a proportion", "token_count": 882, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
A 2015 estimate of Congress' approval rating was 19%.[9](#page-0-0) Using this estimate, how large should an additional survey be to produce a margin of error of 0.04 with 95% confidence?[10](#page-393-0) $$1.96 \times \sqrt{\frac{p(1-p)}{n}} \approx 1.96 \times \sqrt{\frac{0.19(1-0.19)}{n}} \le 0.04 \qquad \to \qqua...	{ "Header 1": "8.1 Inference for a single proportion", "Header 3": "GUIDED PRACTICE 8.10", "token_count": 243, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
The normal model can be applied to $\hat{p}_1 - \hat{p}_2$ if the sampling distribution for each sample proportion is nearly normal and if the samples are independent random samples from the relevant populations. CONDITIONS FOR THE SAMPLING DISTRIBUTION OF $\hat{P}_1 - \hat{P}_2$ to be approximately Normal The ...	{ "Header 1": "8.2 Inference for the difference of two proportions", "Header 3": "8.2.1 Sampling distribution of the difference of two proportions", "token_count": 348, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
The way a question is phrased can influence a person's response. For example, Pew Research Center conducted a survey with the following question:[11](#page-395-0) As you may know, by 2014 nearly all Americans will be required to have health insurance. [People who do not buy insurance will pay a penalty] while [People...	{ "Header 1": "8.2 Inference for the difference of two proportions", "Header 2": "8.2.2 Confidence intervals for p<sup>1</sup> − p<sup>2</sup>", "Header 3": "EXAMPLE 8.12", "token_count": 789, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
Hypothesis tests for $p_1 - p_2$ are usually testing the null hypothesis of no difference between $p_1$ and $p_2$ ; i.e. $H_0: p_1 - p_2 = 0$ . Under the null hypothesis, $\hat{p}_1 - \hat{p}_2$ is normally distributed with mean 0 and standard deviation $\sqrt{p(1-p)(\frac{1}{n_1} + \frac{1}{n_2})}$ , where un...	{ "Header 1": "8.2 Inference for the difference of two proportions", "Header 2": "8.2.2 Confidence intervals for p<sup>1</sup> − p<sup>2</sup>", "Header 3": "8.2.3 Hypothesis testing for $p_1 - p_2$", "token_count": 1965, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
The standard error for the estimated difference uses the individual estimates of the probability of a death: $$SE \approx \sqrt{\frac{0.01113(1-0.01113)}{44,925} + \frac{0.01125(1-0.01125)}{44,910}} = 0.0007.$$ The 95% confidence interval is given by −0.00012 ± (1.96)(0.0007) = (−0.0015,0.0013). ...	{ "Header 1": "8.2 Inference for the difference of two proportions", "Header 2": "8.2.2 Confidence intervals for p<sup>1</sup> − p<sup>2</sup>", "Header 3": "8.2.3 Hypothesis testing for $p_1 - p_2$", "token_count": 202, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
The comparison of the proportion of breast cancer deaths between the two groups can also be approached using a two-way contingency table, which contains counts for combinations of outcomes for two variables. The results for the mammogram study in this format are shown in Figure 8.3. Previously, the main question of i...	{ "Header 1": "8.3 Inference for two or more groups", "token_count": 373, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
If type of breast cancer screening had no effect on outcome in the mammogram data, what would the expected results be? Recall that if two events A and B are independent, then $P(A \cap B) = P(A)P(B)$ . Let A represent assignment to the mammogram group and B the event of death from breast cancer. Under indepe...	{ "Header 1": "8.3 Inference for two or more groups", "Header 3": "8.3.1 Expected counts", "token_count": 413, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
Calculate expected counts for the data in Figure [8.3.](#page-400-1) $$E_{1,1} = \frac{44,925 \times 1,005}{89,835} = 502.6 \qquad E_{1,2} = \frac{44,925 \times 88,830}{89,835} = 44,422.4$$ $$E_{2,1} = \frac{2,922 \times 1,005}{89,835} = 502.4 \qquad E_{2,2} = \frac{7,078 \times 88,830}{89,835} = 44,407.6$$ \| Death...	{ "Header 1": "8.3 Inference for two or more groups", "Header 3": "EXAMPLE 8.17", "token_count": 378, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
If a newborn is HIV<sup>+</sup> , should he or she be treated with nevirapine (NVP) or a more expensive drug, lopinarvir (LPV)? In this setting, success means preventing virologic failure; i.e., growth of the virus. A randomized study was conducted to assess whether there is an association between treatment and outcome...	{ "Header 1": "8.3 Inference for two or more groups", "Header 3": "EXAMPLE 8.18", "token_count": 624, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
Previously, test statistics have been constructed by calculating the difference between a point estimate and a null value, then dividing by the standard error of the point estimate to standardize the difference. The χ 2 statistic is based on a different idea. In each cell of a table, the difference observed - *expe...	{ "Header 1": "8.3 Inference for two or more groups", "Header 3": "8.3.2 The χ 2 test statistic", "token_count": 336, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
Two conditions that must be checked before performing a χ 2 test: - Independence. Each case that contributes a count to the table must be independent of all the other cases in the table. - Sample size. Each expected cell count must be greater than or equal to 10. For tables larger than 2×2, it is appropriate to use...	{ "Header 1": "8.3 Inference for two or more groups", "Header 3": "CONDITIONS FOR THE χ <sup>2</sup> TEST", "token_count": 346, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
The chi-square distribution is often used with data and statistics that are positive and rightskewed. The distribution is characterized by a single parameter, the degrees of freedom. Figure [8.7](#page-403-1) demonstrates three general properties of chi-square distributions as the degrees of freedom increases: the dist...	{ "Header 1": "8.3 Inference for two or more groups", "Header 3": "8.3.3 Calculating p-values for a χ <sup>2</sup> distribution", "token_count": 258, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
The χ 2 statistic from a contingency table has a sampling distribution that approximately follows a χ <sup>2</sup> distribution with degrees of freedom df = (r − 1)(c − 1), where r is the number of rows and c is the number of columns. Either statistical software or a table can be used to calculate pvalu...	{ "Header 1": "8.3 Inference for two or more groups", "Header 3": "8.3. INFERENCE FOR TWO OR MORE GROUPS 405", "token_count": 768, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
Calculate an approximate p-value for the mammogram data, given that the χ 2 statistic equals 0.02. Assess whether the data provides convincing evidence of an association between screening group and breast cancer death. The degrees of freedom in a 2 × 2 table is 1, so refer to the values in the first column of the...	{ "Header 1": "8.3 Inference for two or more groups", "Header 3": "EXAMPLE 8.21", "token_count": 256, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
If the p-value from a χ 2 test is small enough to provide evidence to reject the null hypothesis of no association, it is important to explore the results further to understand direction of the observed association. This is done by examining the residuals, the standardized differences of the observed - expected...	{ "Header 1": "8.3 Inference for two or more groups", "Header 3": "8.3.4 Interpreting the results of a χ 2 test", "token_count": 1873, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
Confirm the conclusions reached in Example 8.24 by analyzing the residuals.<sup>17</sup> $<sup>1^{7}</sup>R_{1,1} = \frac{(44.6-60)}{\sqrt{44.6}} = 2.31; R_{1,2} = \frac{(42.4-27)}{\sqrt{27}} = -2.37; R_{2,1} = \frac{(87-102.4)}{\sqrt{102.4}} = -1.53; R_{2,2} = \frac{(113-97.6)}{\sqrt{97.6}} = 1.56$ . The positive re...	{ "Header 1": "8.3 Inference for two or more groups", "Header 3": "GUIDED PRACTICE 8.25", "token_count": 241, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
Chapter [1](#page-9-0) started with the discussion of a study examining whether exposure to peanut products reduce the rate of a child developing peanut allergies. Children were randomized either to the peanut avoidance or the peanut consumption group; at 5 years of age, each child was tested for peanut allergy using a...	{ "Header 1": "8.3 Inference for two or more groups", "Header 3": "GUIDED PRACTICE 8.26", "token_count": 1450, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
Of the 17 patients cured, 13 were in the fecal infusion group and 4 were in the vancomycin group. Assume that the marginal totals are fixed (i.e., 17 patients were cured, 12 were uncured, and 16 patients were in the fecal infusion group, while 13 were in the vancomycin group). Enumerate all possible sets of results tha...	{ "Header 1": "8.3 Inference for two or more groups", "Header 3": "EXAMPLE 8.27", "token_count": 613, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
Suppose that researchers were interested in testing the null hypothesis against the one-sided alternative, $H_A : p_1 > p_2$ . To calculate the one-sided p-value, sum the probabilities of each table representing results as or more extreme than those observed; specifically, sum the probabilities of observing Figure 8...	{ "Header 1": "8.3 Inference for two or more groups", "Header 3": "Calculating a one-sided p-value", "token_count": 318, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
Calculate the probability of observing Figure 8.15, assuming the margin totals are fixed. $$P(13,3,4,9) = \frac{\binom{16}{13}\binom{13}{4}}{\binom{29}{17}} = \frac{16!\ 13!\ 17!\ 12!}{13!\ 3!\ 4!\ 9!\ 29!} = 7.71 \times 10^{-3}.$$ The value 0.0077 represents the probability of observing 13 cured patients out of 16...	{ "Header 1": "8.3 Inference for two or more groups", "Header 3": "EXAMPLE 8.28", "token_count": 762, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
There are various methods for calculating a two-sided p-value in the Fisher's exact test setting. When the test is calculated by hand, the most common way to calculate a two-sided p-value is to double the smaller of the one-sided p-values. One other common method used by various statistical computing packages suc...	{ "Header 1": "8.3 Inference for two or more groups", "Header 3": "Calculating a two-sided p-value", "token_count": 810, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
The χ 2 test can also be used to examine the appropriateness of hypothesized distribution for a dataset, most commonly when a set of observations falls naturally into categories as in the examples discussed in this section. As with testing in the two-way table setting, expected counts are calculated based on the assu...	{ "Header 1": "8.4 Chi-square tests for the fit of a distribution", "token_count": 287, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
The participants in the FAMuSS study were volunteers at a university, and so did not come from a random sample of the US population. The participants may not be representative of the general United States population. The χ 2 test can be used to test the null hypothesis that the participants are racially representativ...	{ "Header 1": "8.4 Chi-square tests for the fit of a distribution", "Header 3": "EXAMPLE 8.31", "token_count": 1326, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
The techniques so far in this chapter have often relied on the assumption that the data were collected using random sampling from a population. When cases come from a random sample, the sample proportion of observations with a particular outcome should accurately estimate the population proportion, given that the sampl...	{ "Header 1": "8.5 Outcome-based sampling: case-control studies", "Header 3": "8.5.1 Introduction", "token_count": 552, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
In 2006, Chambers, et. al reported a case-control study examining the association of SSRI use and persistent pulmonary hypertension in newborns.[21](#page-416-0) The study team enrolled 337 women whose infants suffered from PPHN and 836 women with similar characteristics but whose infants did not have PPHN. Among the w...	{ "Header 1": "8.5 Outcome-based sampling: case-control studies", "Header 3": "8.5.2 χ 2 tests of association in case-control studies", "token_count": 767, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
For data in a 2×2 table, correct point estimates of association depend on the mechanism used to gather the data. In the example of a clinical trial of nevirapine versus lopinarvir discussed in Section [8.3.1,](#page-400-3) the population proportion of children who would experience virologic failure after treatment with...	{ "Header 1": "8.5 Outcome-based sampling: case-control studies", "Header 3": "8.5.3 Estimates of association in case-control studies", "token_count": 444, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
In a study like the PPHN case-control study, the natural population parameter of interest would be the relative risk of PPHN for infants exposed to an SSRI during after week 20 of gestation compared to those who were not exposed. However, in the design of this study, participating mothers were sampled and grouped accor...	{ "Header 1": "8.5 Outcome-based sampling: case-control studies", "Header 3": "P (virologic failure\|treatment with nevirapine) <sup>P</sup> (virologic failure\|treatment with lopinarvir) .", "token_count": 1160, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
Two-way tables are often used to summarize data from medical research studies, and entire texts have been written about methods of analysis for these tables. This chapter covers only the most basic of those methods. Until recently, Fisher's exact test could only be calculated for 2×2 tables with small cell counts. Re...	{ "Header 1": "8.6 Notes", "token_count": 734, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
[8.8](#page-457-7) Legalization of marijuana, Part I. The General Social Survey asked 1,578 US residents: "Do you think the use of marijuana should be made legal, or not?" 61% of the respondents said it should be made legal.[29](#page-422-0) - (a) Is 61% a sample statistic or a population parameter? Explain. - (b...	{ "Header 1": "8.7 Exercises", "Header 3": "8.7. EXERCISES 423", "token_count": 1801, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
[8.17](#page-458-6) Social experiment, Part I. A "social experiment" conducted by a TV program questioned what people do when they see a very obviously bruised woman getting picked on by her boyfriend. On two different occasions at the same restaurant, the same couple was depicted. In one scenario the woman was dre...	{ "Header 1": "8.7 Exercises", "Header 3": "8.7.2 Inference for the difference of two proportions", "token_count": 1798, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
[8.24](#page-459-3) Prenatal vitamins and Autism. Researchers studying the link between prenatal vitamin use and autism surveyed the mothers of a random sample of children aged 24 - 60 months with autism and conducted another separate random sample for children with typical development. The table below shows the nu...	{ "Header 1": "8.7 Exercises", "Header 3": "8.7. EXERCISES 427", "token_count": 1054, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
[8.31](#page-459-10) PREVEND, Part IV. In the PREVEND data, researchers measured various features of study participants, including data on statin use and highest level of education attained. A two-way table of education level and statin use is shown below. \| \| Primary \| LowerSec \| UpperSec \| Univ \| Sum \| ...	{ "Header 1": "8.7 Exercises", "Header 3": "8.7. EXERCISES 429", "token_count": 1915, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
The National Health Care Anti-Fraud Association estimates that approximately \$68 billion is lost to health care fraud each year. Often when fraud is suspected, an audit of randomly selected billings is conducted. The selected claims are reviewed by experts and each claim is classified as allowed or not allowed. The cl...	{ "Header 1": "8.7 Exercises", "Header 3": "8.7. EXERCISES 429", "token_count": 1304, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
[1.1](#page-74-3) (a) Treatment: 10/43 = 0.23 → 23%. (b) Control: 2/46 = 0.04 → 4%. (c) A higher percentage of patients in the treatment group were pain free 24 hours after receiving acupuncture. (d) It is possible that the observed difference between the two group percentages is due to chance. **[1.3](...	{ "Header 1": "End of chapter exercise solutions", "Header 3": "1 Introduction to data", "token_count": 2019, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
2.1 (a) False. These are independent trials. (b) False. There are red face cards. (c) True. A card cannot be both a face card and an ace. 2.3 (a) $\frac{1}{4}$ . Solution 1: A colorblind male has genotype $X^-Y$ . He must have inherited $X^-$ from his mother (probability of $\frac{1}{2}$ ) and Y ...	{ "Header 1": "End of chapter exercise solutions", "Header 3": "2 Probability", "token_count": 2014, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
2.21 Mumps is the most likely disease state, since $P(B_3\|A) = 0.563$ , $P(B_1\|A) = 0.023$ , and $P(B_2\|A) = .415$ . $P(B_i\|A) = \frac{P(A\|B_i)P(B_i)}{P(A)}$ . $P(A) = P(A \text{ and } B_1) + P(A \text{ and } B_2) + P(A \text{ and } B_3) = P(A\|B_1)P(B_1) + P(A\|B_2)P(B_2) + P(A\|B_3)P(B_3)$ . 2.23 (a) Le...	{ "Header 1": "End of chapter exercise solutions", "Header 3": "2 Probability", "token_count": 1964, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
$$P(D_1\|M_2, R) = \frac{P(M_2 \cap D_1 \cap R)}{P(M_2 \cap R)} = \frac{0.045}{(0.10)(0.60)} = 0.75$$ $$P(D_2\|M_2, R) = \frac{P(M_2 \cap D_2 \cap R)}{P(M_2 \cap R)} = \frac{0.012}{(0.10)(0.60)} = 0.20$$ Back to the original question ... $$P(M_2 \cap D^C \cap R) = P(D^C \| M_2, R) P(M_2 \| R) P(R)$$ $$= \frac{P(D^C \|...	{ "Header 1": "End of chapter exercise solutions", "Header 3": "2 Probability", "token_count": 1179, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
[3.1](#page-184-1) (a) 13. (b) No, these 27 students are not a random sample from the university's student population. For example, it might be argued that the proportion of smokers among students who go to the gym at 9 am on a Saturday morning would be lower than the proportion of smokers in the university as a wh...	{ "Header 1": "End of chapter exercise solutions", "Header 3": "3 Distributions of random variables", "token_count": 2017, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
![](_page_442_Figure_17.jpeg) (b) P ercV R = 0.9007 ≈ 90%, P ercQR = 0.6990 ≈ 70%. 100% − 90% = 10% did better than her on VR, and 100% − 70% = 30% did better than her on QR. (c) 159. (d) 147. [3.25](#page-189-0) (a) 0.115. (b) The coldest 10% of days are colder than 70.59◦F. **[3.27](#page-189-1)...	{ "Header 1": "End of chapter exercise solutions", "Header 3": "3 Distributions of random variables", "token_count": 1477, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
P (X = 4) = 0.09435. (c) P (X ≤ 2) = 0.663. (d) 0.09437, from the binomial distribution. With a large sample size, sampling with replacement is highly unlikely to result in any particular individual being sampled again. In this case, the hypergeometric and binomial distributions will produce equal proba...	{ "Header 1": "End of chapter exercise solutions", "Header 3": "3 Distributions of random variables", "token_count": 1596, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
4.1 (a) $\overline{x} = 0.6052$ . (b) s = 0.0131. (c) $Z_{0.63} = \frac{0.63 - 0.6052}{0.0131} = 1.893$ . No, this level of BGC is within 2 SD of the mean. (d) The standard error of the sample mean is given by $\frac{s}{\sqrt{n}} = \frac{0.0131}{\sqrt{70}} = 0.00157$ . 4.3 (a) This is the sampling di...	{ "Header 1": "End of chapter exercise solutions", "Header 3": "4 Foundations for inference", "token_count": 2028, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
There is sufficient evidence to reject the null hypothesis and conclude that the mean birthweight of babies from inner-city teaching hospitals is lower than 3,260 grams. 4.21 (a) $H_0$ : Anti-depressants do not help symptoms of fibromyalgia. $H_A$ : Anti- depressants do treat symptoms of fibromyalgia. (b) Concl...	{ "Header 1": "End of chapter exercise solutions", "Header 3": "4 Foundations for inference", "token_count": 309, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
5.1 (a) df = 6 - 1 = 5, $t_5^{\star} = 2.02$ (column with two tails of 0.10, row with df = 5). (b) df = 21 - 1 = 20, $t_{20}^{\star} = 2.53$ (column with two tails of 0.02, row with df = 20). (c) df = 28, $t_{28}^{\star} = 2.05$ . (d) df = 11, $t_{11}^{\star} = 3.11$ . 5.3 On a z-distribution, the cut...	{ "Header 1": "End of chapter exercise solutions", "Header 3": "5 Inference for numerical data", "token_count": 2021, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
<sup>H</sup><sup>A</sup> : <sup>µ</sup>dif f , 0. Independence: random sample from less than 10% of population. Sample size of at least 30. The skew of the differences is, at worst, slight. Z = 2.72 → p-value = 0.0066. Since p-value < 0.05, reject H0. The data provide strong evidence that the average IQ s...	{ "Header 1": "End of chapter exercise solutions", "Header 3": "5 Inference for numerical data", "token_count": 2041, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
Furthermore, the data indicate patients in the distracted eating (treatment) group consume more food than patients in the control group. [5.35](#page-283-1) Let <sup>µ</sup>dif f <sup>=</sup> <sup>µ</sup>pre <sup>−</sup>µpost. <sup>H</sup><sup>0</sup> : <sup>µ</sup>dif f = 0: Treatment has no effect. *<...	{ "Header 1": "End of chapter exercise solutions", "Header 3": "5 Inference for numerical data", "token_count": 1659, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
[6.1](#page-316-1) (a) Strong relationship, but a straight line would not fit the data. (b) Strong relationship, and a linear fit would be reasonable. (c) Weak relationship, and trying a linear fit would be reasonable. (d) Moderate relationship, but a straight line would not fit the data. (e) Strong relationship, a...	{ "Header 1": "End of chapter exercise solutions", "Header 3": "6 Simple linear regression", "token_count": 1315, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
where the explanatory variable is a binary variable taking on value 1 if the diamond is 1 carat. [6.23](#page-325-1) (a) The relationship is positive, moderate-to-strong, and linear. There are a few outliers but no points that appear to be influential. (b) weight <sup>=</sup> <sup>−</sup>105.0113 + 1.<sup...	{ "Header 1": "End of chapter exercise solutions", "Header 3": "6 Simple linear regression", "token_count": 746, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
(h) No, a 95% confidence interval for $\beta_1$ would not be expected to contain the null value 0, since the p-value is less than 0.05. 6.27 (a) The point estimate and standard error are $b_1 = 0.9112$ and SE = 0.0259. We can compute a T-score: T = (0.9112 - 1)/0.0259 = -3.43. Using df = 168, the p-value ...	{ "Header 1": "End of chapter exercise solutions", "Header 3": "6 Simple linear regression", "token_count": 1096, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
7.1 Although the use of statins appeared to be associated with lower RFFT score when no adjustment was made for possible confounders, statin use is not significantly associated with RFFT score in a model that adjusts for age. After adjusting for age, the estimated difference in mean RFFT score between statin users ...	{ "Header 1": "End of chapter exercise solutions", "Header 3": "7 Multiple linear regression", "token_count": 2002, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
[7.19](#page-380-0) (a) post <sup>d</sup> <sup>=</sup> <sup>−</sup>17.58+1.28(pre)+67.75(neutral)+64.42(therapeutic)−0.99(pre×neutral)−1.01(pre×therapeutic) (b) The coefficient for pre is the predicted increase in post score associated with a 1 unit increase in pre-score for individual...	{ "Header 1": "End of chapter exercise solutions", "Header 3": "7 Multiple linear regression", "token_count": 1479, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
[8.1](#page-420-3) (a) False. Doesn't satisfy success-failure condition. (b) True. The success-failure condition is not satisfied. In most samples we would expect pˆ to be close to 0.08, the true population proportion. While pˆ can be much above 0.08, it is bound below by 0, suggesting it would take on a right ...	{ "Header 1": "End of chapter exercise solutions", "Header 3": "8 Inference for categorical data", "token_count": 2021, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
[8.19](#page-424-4) (a) Standard error: $$SE = \sqrt{\frac{0.79(1 - 0.79)}{347} + \frac{0.55(1 - 0.55)}{617}} = 0.03$$ Using z ? = 1.96, we get: $$0.79 - 0.55 \pm 1.96 \times 0.03 \rightarrow (0.181, 0.299)$$ We are 95% confident that the proportion of Democrats who support the plan is 18.1% to 29.9% ...	{ "Header 1": "End of chapter exercise solutions", "Header 3": "8 Inference for categorical data", "token_count": 1405, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
\| \| Mosqu \| \| \| \| \| \| \|------------\|-------\|--------\|-----\|--\|--\|--\| \| \| No \| No Yes \| \| \| \| \| \| Malaria \| 30 \| 22 \| 52 \| \| \| \| \| No Malaria \| 70 \| 78 \| 148 \| \| \| \| \| Total \| 100 \| 100 \| 200 \| \| \| \| (b) Expected number of infected chil...	{ "Header 1": "End of chapter exercise solutions", "Header 3": "8.35 (a) One possible $2 \\times 2$ contingency table:", "token_count": 2041, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
(c) The easiest way of calculating the OR for the table is the cross-product of the diagonal elements of the table: [(10)(4000)]/ [(2000)(7)] = 2.86. Using the definition, it can be calculated as: $$\hat{OR} = \frac{\frac{\hat{P}(\text{CNS}\|\text{Usage})}{1-\hat{P}(\text{CNS}\|\text{Usage})}}{\frac{\hat{P}(\text...	{ "Header 1": "End of chapter exercise solutions", "Header 3": "8.35 (a) One possible $2 \\times 2$ contingency table:", "token_count": 453, "source_pdf": "datasets/websources/Med_v1/med_textbook/biostat.pdf" }
\| Definition of Epidemiology<br> \| 1-2 \| \|-----------------------------------------\|------\| \| Historical Evolution of Epidemiology \| 1-7 \| \| Uses \| 1-12 \| \| Core Epidemiologic Functions<br> \| 1-15 \| \| The Epidemiologic Approach \| 1-21 \| \| Descriptive ...	{ "Header 1": "Major Sections", "token_count": 346, "source_pdf": "datasets/websources/Med_v1/med_textbook/cdc_6914_DS1.pdf" }
Epidemiology is a scientific discipline with sound methods of scientific inquiry at its foundation. Epidemiology is data-driven and relies on a systematic and unbiased approach to the collection, analysis, and interpretation of data. Basic epidemiologic methods tend to rely on careful observation and use of valid compa...	{ "Header 1": "Definition of Epidemiology", "Header 2": "Study", "token_count": 262, "source_pdf": "datasets/websources/Med_v1/med_textbook/cdc_6914_DS1.pdf" }
Epidemiology is concerned with the frequency and pattern of health events in a population: > Frequency refers not only to the number of health events such as the number of cases of meningitis or diabetes in a population, but also to the relationship of that number to the size of the population. The result...	{ "Header 1": "Definition of Epidemiology", "Header 2": "Distribution", "token_count": 220, "source_pdf": "datasets/websources/Med_v1/med_textbook/cdc_6914_DS1.pdf" }
In the mid-1800s, an anesthesiologist named John Snow was conducting a series of investigations in London that warrant his being considered the "father of field epidemiology." Twenty years before the development of the microscope, Snow conducted studies of cholera outbreaks both to discover the cause of disease and to ...	{ "Header 1": "Historical Evolution of Epidemiology", "Header 2": "1854", "token_count": 1698, "source_pdf": "datasets/websources/Med_v1/med_textbook/cdc_6914_DS1.pdf" }
In the mid- and late-1800s, epidemiological methods began to be applied in the investigation of disease occurrence. At that time. most investigators focused on acute infectious diseases. In the 1930s and 1940s, epidemiologists extended their methods to noninfectious diseases. The period since World War II has seen an e...	{ "Header 1": "Historical Evolution of Epidemiology", "Header 2": "19th and 20<sup>th</sup> centuries", "token_count": 447, "source_pdf": "datasets/websources/Med_v1/med_textbook/cdc_6914_DS1.pdf" }
When investigating a disease outbreak, epidemiologists rely on health-care providers and laboratorians to establish the proper diagnosis of individual patients. But epidemiologists also contribute to physicians' understanding of the clinical picture and natural history of disease. For example, in late 1989, a physician...	{ "Header 1": "Historical Evolution of Epidemiology", "Header 2": "Making individual decisions", "Header 3": "Completing the clinical picture", "token_count": 230, "source_pdf": "datasets/websources/Med_v1/med_textbook/cdc_6914_DS1.pdf" }
Public health surveillance is the ongoing, systematic collection, analysis, interpretation, and dissemination of health data to help guide public health decision making and action. Surveillance is equivalent to monitoring the pulse of the community. The purpose of public health surveillance, which is sometimes called "...	{ "Header 1": "Core Epidemiologic Functions", "Header 2": "Public health surveillance", "token_count": 476, "source_pdf": "datasets/websources/Med_v1/med_textbook/cdc_6914_DS1.pdf" }
As noted above, surveillance provides information for action. One of the first actions that results from a surveillance case report or report of a cluster is investigation by the public health department. The investigation may be as limited as a phone call to the healthcare provider to confirm or clarify the circumstan...	{ "Header 1": "Core Epidemiologic Functions", "Header 2": "Public health surveillance", "Header 3": "Field investigation", "token_count": 505, "source_pdf": "datasets/websources/Med_v1/med_textbook/cdc_6914_DS1.pdf" }
Surveillance and field investigations are usually sufficient to identify causes, modes of transmission, and appropriate control and prevention measures. But sometimes analytic studies employing more rigorous methods are needed. Often the methods are used in combination — with surveillance and field investigations provi...	{ "Header 1": "Core Epidemiologic Functions", "Header 2": "Analytic studies", "token_count": 496, "source_pdf": "datasets/websources/Med_v1/med_textbook/cdc_6914_DS1.pdf" }
Epidemiologists, who are accustomed to using systematic and quantitative approaches, have come to play an important role in evaluation of public health services and other activities. Evaluation is the process of determining, as systematically and objectively as possible, the relevance, effectiveness, efficiency, and im...	{ "Header 1": "Core Epidemiologic Functions", "Header 2": "Evaluation", "token_count": 247, "source_pdf": "datasets/websources/Med_v1/med_textbook/cdc_6914_DS1.pdf" }
As with all scientific endeavors, the practice of epidemiology relies on a systematic approach. In very simple terms, the epidemiologist: - Counts cases or health events, and describes them in terms of time, place, and person; - Divides the number of cases by an appropriate denominator to calculate rates; and...	{ "Header 1": "The Epidemiologic Approach", "token_count": 272, "source_pdf": "datasets/websources/Med_v1/med_textbook/cdc_6914_DS1.pdf" }
Before counting cases, the epidemiologist must decide what to count, that is, what to call a case. For that, the epidemiologist uses a case definition. A case definition is a set of standard criteria for classifying whether a person has a particular disease, syndrome, or other health condition. Some case definition...	{ "Header 1": "The Epidemiologic Approach", "Header 3": "Defining a case", "token_count": 439, "source_pdf": "datasets/websources/Med_v1/med_textbook/cdc_6914_DS1.pdf" }
Clinically compatible illness with L. monocytogenes isolated - From a normally sterile site - In a resident of Winston-Salem, North Carolina - With onset between October 24, 2000 and January 4, 2001 Source: MacDonald P, Boggs J, Whitwam R, Beatty M, Hunter S, MacCormack N, et al. Listeria-associated birth complicat...	{ "Header 1": "The Epidemiologic Approach", "Header 3": "Case definition", "token_count": 239, "source_pdf": "datasets/websources/Med_v1/med_textbook/cdc_6914_DS1.pdf" }
Suspected: Any febrile illness accompanied by rash Probable: A case that meets the clinical case definition, has noncontributory or no serologic or virologic testing, and is not epidemiologically linked to a confirmed case Confirmed: A case that is laboratory confirmed or that meets the clinical case definition and...	{ "Header 1": "The Epidemiologic Approach", "Header 2": "Criteria in case definitions", "Header 3": "Case classification", "token_count": 526, "source_pdf": "datasets/websources/Med_v1/med_textbook/cdc_6914_DS1.pdf" }