A Bayesian hierarchical approach for combining case-control and prospective studies

Motivated by the absolute risk predictions required in medical decision mak ing and patient counseling, we propose an approach for the combined analysi s of case-control and prospective studies of disease risk factors. The appr oach is hierarchical to account for parameter heterogeneity among studies a nd among sampling units of the same study. It is based on modeling the retr ospective distribution of the covariates given the disease outcome, a strat egy that greatly simplifies both the combination of prospective and retrosp ective studies and the computation of Bayesian predictions in the hierarchi cal case-control context. Retrospective modeling differentiates our approac h from most current strategies for inference on risk factors, which are bas ed on the assumption of a specific prospective model. To ensure modeling fl exibility, we propose using a mixture model for the retrospective distribut ions of the covariates. This leads to a general nonlinear regression family for the implied prospective likelihood. After introducing and motivating o ur proposal, we present simple results that highlight its relationship with existing approaches, develop Markov chain Monte Carlo methods for inferenc e and prediction, and present an illustration using ovarian cancer data.