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Monte Carlo methods for exploring sensitivity to distributional assumptions in a Bayesian analysis of a series of 2 x 2 tables.

T E Raghunathan
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Abstract

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.

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Bayes TheoremBinomial DistributionCase-Control StudiesChildFetusHumansModels, StatisticalMonte Carlo MethodPrecursor Cell Lymphoblastic Leukemia-LymphomaRadiographyRiskSampling StudiesSensitivity and SpecificityJournal ArticleResearch Support, U.S. Gov't, P.H.S.

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T E Raghunathan. 1994-08-15. Monte Carlo methods for exploring sensitivity to distributional assumptions in a Bayesian analysis of a series of 2 x 2 tables.. https://doi.org/10.1002/sim.4780131504

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