Bayesian detection of clusters and discontinuities in disease maps

An interesting epidemiological problem is the analysis of geographical vari ation in rates of disease incidence or mortality. One goal of such an analy sis is to detect clusters of elevated (or lowered) risk in order to identif y unknown risk factors regarding the disease. We propose a nonparametric Ba yesian approach for the detection of such clusters based on Green's (1995, Biometrika 82, 711-732) reversible jump MCMC methodology. The prior model a ssumes that geographical regions can be combined in clusters with constant relative risk within a cluster. The number of clusters, the location of the clusters, and the risk within each cluster is unknown. This specification can be seen as a change-point problem of variable dimension in irregular, d iscrete space. We illustrate our method through an analysis of oral cavity cancer mortality rates in Germany and compare the results with those obtain ed by the commonly used Bayesian disease mapping method of Besag, York, and Mollie (1991, Annals of the Institute of Statistical Mathematics, 43, 1-59 ).