Bayesian analysis of case-control studies with categorical covariates

In a case-control study, subjects are chosen according to disease status and then their exposure is determined. Thus the appropriate likelihood is thèretrospective' likelihood, i.e. likelihood of exposure given disease. For the classical (frequentist) analysis, thèprospective' likelihood, i.e. 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, however, is not so simple. Yet the Bayesian framework for case-control studies ooers exi-ble possibilities of hierarchical modelling needed in many contexts. We review the Bayesian approaches to analysis of case-control studies developed so far, approaches which are limited, either for structural or computational reasons, to the analysis of a study with a single binary exposure or two continuous exposure variables, and we show how to extend these approaches to the situation of a study with any number of categorical or ordinal exposure variables and identify suitable priors. It is then shown how the resulting models may be tted using Markov chain Monte Carlo methods, and a small illustration on genotype data is given.