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.
Department of Biostatistics, University of Washington, Seattle 98195.
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Raghunathan
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