On the equivalence of posterior inference based on retrospective and prospective likelihoods

The paper develops a class of priors which leads to equivalent posterior inference for odds ratio parameters based on prospective and retrospective models for categorical response data. The results are applicable to both unmatched and matched case-control studies. The proposed method can accommodate multiple and possibly ordered disease status as well as any arbitrary link function and is not restricted to the conventional logit link. The results are applied to the analysis of an ongoing case-control study on colorectal cancer.