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

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?