Monte Carlo methods for exploring sensitivity to distributional assumptions in a Bayesian analysis of a series of 2 x 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.
Raghunathan
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Department of Biostatistics, University of Washington, Seattle 98195.
D001499:Bayes Theorem; D016010:Binomial Distribution; D016022:Case-Control Studies; D002648:Child; D005333:Fetus / Q000528:radiation effects; D006801:Humans; D015233:Models, Statistical; D009010:Monte Carlo Method; D054198:Precursor Cell Lymphoblastic Leukemia-Lymphoma / Q000453:epidemiology; D011859:Radiography / Q000009:adverse effects; D012306:Risk; D012494:Sampling Studies; D012680:Sensitivity and Specificity