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Equivalence of prospective and retrospective likelihood methods in case-control studies

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Case-control studies are typically described by a retrospective likelihood, which is based on the probability of exposure given the disease status. Nevertheless, analyzing case-control studies by prospective likelihood methods, which have the advantage of decreasing the dimension of the nuisance parameter involved, is the default approach undertaken by most practitioners. In this talk we address the equivalence of the prospective and retrospective analyses in both Bayesian and frequentist settings. From a Bayesian perspective we give prior density conditions for the corresponding posterior distributions of the log-odds ratio parameter resulting from the prospective and retrospective likelihoods to be identical. These conditions give Seaman and Richardson’s priors when it is required that the nuisance parameters are independent of one another. From a frequentist perspective we show the Cox-Reid modified profile likelihoods derived from the prospective and retrospective models yield the same log-odds estimator up to second order. We examine the equivalence of the two models at higher order via a simulation study: for the prospective analysis we use Bartlett correction, Skovgaard’s statistic and a new approach based on matching priors with approximate Bayesian inference, while for the retrospective analysis we use Bartlett correction.

This talk is part of the Statistics series.

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