4. [6 marks] (a) [3 marks] Use Bayes' rule to prove that the case-control based and cohort study based odds ratio expressions are equivalent. PIE + (D+]/(1 - P[E + [D+]) P[D + |E+]/(1 -P[D + [E+]) PIE + (D-]/(1 - PIE + (D-]) P[D + |E-1/(1 -P[D + |E-]) (b) The western collaborative group study (WCGS) was a large prospective cohort study designed to investigate the factors associated with the risk of incident coronary heart disease (CHD). We will consider multiple logistic regression models fit to the data from 3154 study participants 4. i. [1 mark] One potentially important predictor of CHD risk is age at entry. Con- sider the simple logistic regression model presented in Table 2. The response is an indicator of the development of CHD (1=CHD, 0= no CHD) and the primary exposure or variable of interest is age (a continuous variable measured years). A set of potential confounders are also included in the model: cholesterol (mg/dL), BMI (kg/m-), systolic blood pressure (mmHg), and smoking (1= smokes cigarettes, 0=nonsmoker). Give a precise written interpretation of the regression parameter for the age term. ii. [2 marks] Using the model in Table 2 find the predicted probability of developing CHD for a 60-year-old smoker with cholesterol, SBP, and BMI values of 250 mg/dL, 150 mmlg, and 20, respectively