Bayesian disease mapping using product partition models

Our objective is to develop a model to estimate the relative risk of disease in each area, Ai, i=1, ... , n, of a region and to identify areas of unusually high or low risk. We use a product partition model (PPM) in which we assume that the true relative risks can be partitioned into a number of components or sets of areas where the relative risks are equal. The PPM allows the data to weight those partitions likely to hold and inference about particular parameters may be made by first conditioning on the partition and then averaging over all partitions. We develop Markov chain Monte Carlo (MCMC) techniques to approximate the posterior distributions of the partitions and the parameters. We first test the method in a simulation study and then apply it to data for two separate groups of different types of cancer in the Mid-Western Health Board region in Ireland. The results are compared with those obtained using the standardized mortality ratio method, an empirical Bayes method, a spatial scan method and a nonparametric Bayesian method.