Please see the attached assignment for questions. Any calculations should show work for how the answer was derived.
[Document title] Assignment Instructions: Solve the questions below using short answer responses and algebra. 1. In a 5-year cohort study conducted in Fulton County, Georgia, involving seniors 70 years of age or older, one research question concerned evaluating the relationship of social support network on risk of mortality. A logistic regression model was fit to describe the relationship between social support network and odds of death. Consider the following variables: DEATH: coded 0 for no death and 1 for death SSN (social support network): coded ordinally 0 (weak), 1, 2, 3, 4, 5 (strong) AGE: continuous variable SEX: coded 0 for female and 1 for male COMORB: coded 0 for no serious comorbidities and 1 for ≥ 1comorbidities 1A. State the general form of the expression for the logistic regression model that contains all of the covariates. = B0 + β1 death + β2SSN + β3age + β4sex + β5Comorb 1B. State the expression for the logistic model that includes an interaction term for the variables SSN and SEX. 1C. Using the expression from part 1A, state the expression for the odds ratio comparing a person with SSN=5 compared to SSN=2, adjusting for AGE, SEX, and COMORB. 1D. State the null hypothesis for the interaction term in part 1B. 1E. Assume we reject the null hypothesis in part 1D. Using the expression from part 1B, state the expressions for the odds ratios comparing a person with SSN=4 to a person with SSN=2. 2. An epidemiologist is interested in studying the association between early life exposures to antibiotics and risk of diabetes mellitus in adulthood. Consider the following model: Ln = β0 + β 1(Antibiotic) Let D be a binary variable for adult onset type 2 diabetes (coded 1 for diabetes and 0 for no diabetes). Let Antibiotic be a binary variable for early childhood exposure to antibiotics (coded 1 for antibiotic use between 0-3 years old, and 0 for no antibiotic use in the first 3 years of life). The following is SAS output from the model fit with logistic regression: Parameter DF Estimate Standard Error Intercept (Bo) 1 -1.0517 0.1150 Antibiotic (B1) 1 0.6283 0.1681 2A. Use the logistic model results to recreate the 2X2 table below. Show your calculations. Antibiotic Use No Antibiotic Use Diabetes No Diabetes 278 672 2B. Calculate the odds ratio and 95% confidence interval. Show your calculations. Interpret the results in one sentence. 3. A cohort study was conducted to determine the association between frequent consumption of artificially sweetened beverages (diet soda) and 10-year risk of hypertension. The exposure was defined dichotomously as >36oz of artificially sweetened soda per week in the past six months and was measured by self-reported questionnaire. Patients were enrolled and followed for 10 years at which time all participants were screened for hypertension. Below is data from the cohort study >36 oz diet soda ≤ 36 oz diet soda Hypertensive 16 103 Normal blood pressure 128 844 3A. Calculate and interpret the crude odds ratio. 3B. After the study ended, it was discovered those with two risk alleles (compared to those with 1 or 0 risk alleles) in the THIRSTY gene were more likely to have hypertension and predisposed to drink copious quantities of diet soda. At the time of the study inception, the investigators failed to realize that there was likely confounding in their cohort resulting from the single nucleotide polymorphisms in the gene THIRSTY. You decide to perform a sensitivity analysis to assess the impact of the unmeasured confounder THIRSTY. Assume the following: Prevalence of two risk alleles in those with > 36 oz diet soda: 11.9% Prevalence of two risk alleles in those with ≤ 36 oz diet soda exposure was: 6.6% The risk odds ratio of hypertension by comparing levels of THIRSTY was: 2.0 Using information on the prevalence of the confounder (THIRSTY gene), calculate the odds ratio for the relationship between THIRSTY gene and diet soda consumption. 3C. Using sensitivity analysis calculations for unmeasured confounding, calculate the THIRSTY gene adjusted odds ratio for the relationship between diet soda exposure and hypertension based on the prevalence and odds ratio listed in part 3B. 3D. Choose two other levels of prevalence of the risk alleles (for those with and without high exposure to soda) and another odds ratio for the relationship between the unmeasured confounder with hypertension. Calculate the THIRSTY gene adjusted odds ratio again. 3E. Use the results from 3D and 3C and compare to the results in 2A. What do you conclude about the role of unmeasured confounding due to the THIRSTY gene? 4. This problem is an extension of the biologic interaction in class exercise from Nov 11/13. Table 3. 1-year risk of death (percentage) among patients with extra pulmonary TB HIV + HIV - Alcohol abuse + 20.2 8.7 No alcohol abuse 11.4 3.8 Table 4. Odds ratio for death compared to those with no alcohol and HIV- among patients with extra pulmonary TB HIV + HIV - Alcohol abuse + 6.43 2.41 No alcohol abuse 3.25 1.00 Table 5. 1-year odds of death among patients with extra pulmonary TB HIV + HIV - Alcohol abuse + No alcohol abuse Formula 1. Biologic Interaction Risk = RiskAB – RiskA – RiskB + RiskU Formula 2. Biologic Interaction Independence = (RRA-1) + (RRB-1) = (RRAB-1) 4A. Using the risk of death among the exposure categories (Table 3), calculate the odds of death for each of the 4 categories. Fill in Table 5 above. Using the formulas for Biologic Interaction, calculate the proportion of risk/odds in the jointly exposed (HIV and Alcohol Abuse) due to biologic interaction three ways (4B, 4C, 4D). Use formula 1 for 4C and formula 2 for 4D but substitute odds for risk. 4B. Using risk 4C. Using odds 4D. Using odds ratios 4E. How does the calculation in part 4C compare to part 4D? 5. For parts 5A through 5E, refer to the article “Low-level mercury exposure and risk of asthma in school-age children” by Kim et al, Epidemiology 2015 SEP (PMID: 26154023) 5A. What is the study’s hypothesis? 5B. What are the study’s primary exposure and outcome? How were each measured? 5C. In one sentence, explain the study’s main findings? 5D. In three sentences, explain the type of sensitivity analyses that were performed and what additional information (if any) the sensitivity analyses provided beyond the primary analysis? 5E. What additional sensitivity analysis would you suggest? Explain your answer. 6. Write a final exam question focused on logistic regression models, meta-analyses, or sensitivity analyses. The exam question must be calculation based. Also include a solution to the question. 7. Consider the following causal diagram (assume it is correct): The study exposure (E) is job-site assignment, which influences worker decisions of when to leave work (L). Unmeasured health conditions (U) also influence decisions of when to leave work and are also causally related to mortality (D). If the interest is in estimating the causal association between E and D, then which of the following is true. Explain. a) You should control for L b) You should not control for L c) It makes no difference whether of not you control for L. 1