How to interpret and choose a Bayesian spatial model and a Poisson regression model in the context of describing...

The statistical Bayesian approach is widely used in disease mapping and Poisson regression. Results differ depending on the underlying hypothesis. Our objective is to give a comprehensive presentation of the tools that can be used to interpret results and choose between the different hypotheses. Data from the Isere cancer registry (France) illustrate this presentation.

We consider, first, Bayesian models for disease mapping. Classic heterogeneity (Potthoff-Whithinghill statistic) and spatial autocorrelation tests (Moran statistic) of the SIRs, the DIC criteria of the different Bayesian models and finally the comparison of the empirical variance of the unstructured and structured heterogeneity components of the BYM model are considered. The last two criteria are considered for Bayesian Poisson regression including a covariate. Mapping the components of the BYM model with a covariate is also considered.

Four cancer sites (prostate, lung, colon-rectum and bladder) in men diagnosed during the 1998-2007 period are used to illustrate our presentation. We show that the different criteria used to interpret and to choose a model give coherent results.

A relevant interpretation of results is a necessary step in choosing the best-adapted Bayesian model. This choice is easy to make with criteria such as the DIC. The comparison of the empirical variance of the unstructured and structured heterogeneity components of the BYM model is also informative.