Bayesian analysis of case-control studies with categorical covariates

In a case-control study the appropriate likelihood is the 'retrospective' l ikelihood, i.e. the likelihood of exposure given disease. For the classical frequentist analysis, the 'prospective' likelihood, i.e. the likelihood of disease given exposure, and the retrospective likelihood produce the same odds-ratio estimators for exposure, and so logistic regression may be used for both. The Bayesian analysis is not so simple, but the Bayesian framewor k for case-control studies offers flexible possibilities for the hierarchic al modelling that is needed in many contexts. We review the Bayesian approa ches to the analysis of case-control studies developed so far, show how to extend these approaches to the situation of a study with any number of cate gorical or discretised continuous exposure variables, and identifying suita ble priors. We then show how the resulting models may be fitted using Marko v chain Monte Carlo methods, and provide an illustration based on genotype data.