Monte carlo methods for exloring sensitivity to distributional assumptions in a bayesian analysis of a series of 2 × 2 tables

This paper develops Monte Carlo methods for a Bayesian analysis of a series of 2 x 2 tables under a variety of distributional assumptions. I assume that the data in each table were generated from a pair of binomial distributions and the logarithm of odds of a favourable response follows a bivariate distribution with means that are linear functions of covariates and an arbitrary covariance matrix. I use Gibbs and importance sampling methods to obtain various characteristics of the posterior distribution of the quantities of interest. I apply the method to analyse the data from a population case-control study. Given the size of the population at risk I also derive the posterior distribution of the risk difference defined as the difference in the probabilities of disease development in the exposed and unexposed groups.