A hierarchical Bayesian approach to multiple testing in disease mapping

We propose a Bayesian approach to multiple testing in disease mapping. This study was motivated by a real example regarding the mortality rate for lung cancer, males, in the Tuscan region (Italy). The data are relative to the period 1995-1999 for 287 municipalities. We develop a tri-level hierarchical Bayesian model to estimate for each area the posterior classification probability that is the posterior probability that the municipality belongs to the set of non-divergent areas. We show also the connections of our model with the false discovery rate approach. Posterior classification probabilities are used to explore areas at divergent risk from the reference while controlling for multiple testing. We consider both the Poisson-Gamma and the Besag, York and Mollie model to account for extra Poisson variability in our Bayesian formulation. Posterior inference on classification probabilities is highly dependent on the choice of the prior. We perform a sensitivity analysis and suggest how to rely on subject-specific information to derive informative a priori distributions. Hierarchical Bayesian models provide a sensible way to model classification probabilities in the context of disease mapping.