Semiparametric Bayesian analysis of matched case-control studies with missing exposure

This article considers Bayesian analysis of matched case-control problems when one of the covariates is partially missing. Within the likelihood context, the standard approach to this problem is to posit a fully parametric model among the controls for the partially missing covariate as a function of the covariates in the model and the variables making up the strata. Sometimes the strata effects are ignored at this stage. Our approach differs not only in that it is Bayesian, but, far more importantly, in the manner in which it treats the strata effects. We assume a Dirichlet process prior with a normal base measure for the stratum effects and estimate all of the parameters in a Bayesian framework. Three matched case-control examples and a simulation study are considered to illustrate our methods and the computing scheme. KEY WORDS: Case-control studies; Conditional inference; Dirichlet process; Endometrial cancer; Equine epidemiology; Exponential family; Low birth weight study; Matching; Metropolis-Hastings; Missing data; Retrospective studies.