Parametric Bayesian analysis of case-control data with imprecise exposure measurements

Case-control data with imprecise exposure measurements can be analyzed via Bayesian fitting of a retrospective discriminant analysis model. The parameters of interest are the regression coefficients in the prospective log-odds ratio for disease. Under a standard noninformative prior, the posterior means of these parameters are infinite. Posterior medians, however, perform reasonably relative to other estimators that adjust for covariate imprecision. The Bayesian inference can be implemented with direct posterior simulation, so the analysis is not complicated by convergence and dependence issues associated with Markov chain Monte Carlo methods.