Modelling risks in disease mapping.

In this article, we propose a strategy of analysis of mortality data with the aim of providing a guideline for epidemiologists and public health researchers to choose a reasonable model for estimating mortality (or incidence) risks. Maps displaying the crude mortality rates or ratios are usually misleading because of the instability of the estimators in low populated areas. As an alternative, many smoothing methods have been presented in the literature based on Poisson inference. They account for the extra-Poisson variation (overdispersion), frequently present in the homogeneous Poisson model, by incorporating random effects. Here, we recommend to test for the potential sources of extra-Poisson variation because, depending on them, the models which fit better the data may be different. Overdispersion can be mainly due to spatial autocorrelation, unstructured heterogeneity or to a combination of these two, and also, when studying very rare diseases, it can be due to an excess of zeros in the data. In this article, different situations the analyst may encounter are detailed and appropriate procedures for each case are presented. The alternative models are illustrated using mortality data provided by the Statistical Institute of Navarra, Spain.