Analysing clinical trials data using WinBUGS:
The results below show the results of 22 clinical trials involving heart attack patients. The patients in each trial were allocated to either receive beta-blockers (Treated) or not receive beta-blockers (Control). There are a large number of factors that can be different between the trials. For example, there may be differences in the exact dose of beta-blockers, in the regularity of check-ups by doctors, or in the characteristics of patients taking part in the trials. Therefore, the trials can be considered similar rather than exactly the same.
a) Write down an appropriate Bayesian hierarchical model for the number of deaths in the Control groups of the studies and discuss its assumptions. Write WinBUGS code to fit the model. Check the convergence and mixing of the chains and report your results. What do you conclude about differences in death rates in the Control groups in these studies?
b) The purpose of these studies is to decide whether there is a lower rate of deaths in the Treated group than the Control group. Write down and discuss an appropriate hierarchical model for both the Control and Treated patients.