Retrospective-prospective symmetry for the Bayesian analysis of case-control studies

Statistics – Methodology

Scientific paper

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13 pages

Scientific paper

The seminal paper of Prentice & Pyke (1979) established that the maximum likelihood estimator for the odds-ratio of a case-control study is that of a logistic regression. In other words, the incorrect prospective model is equivalent to the correct retrospective model. We identify necessary and sufficient conditions for the corresponding result in a Bayesian analysis, that is, that the posterior distribution for the odds-ratio be the same under both the prospective and retrospective likelihoods. These conditions can be used to derive a parametric family of prior laws that can be used for such an analysis.

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