Selective inference in disease mapping

The main goal of Disease Mapping is to investigate the geographical distribution of the risk of diseases. Spatially-structured priors were considered in all the proposed models in the literature to estimate relative risk surfaces. Selective inference on area-specific relative risks received little attention in the literature. We refer to selection and estimation of relative risks of areas at unusual (higher and/or lower) risk. Previous use of cross-validation posterior predictive distributions to detect outlying observation misses to address the selection effect in inference. In this work we review this issue in the context of hierarchical Bayesian models and we take advantage of a real example on the distribution of Lung cancer in Tuscany.