The use of mixture models for identifying high risks in disease mapping

Conventional approaches for estimating risks in disease mapping or mortalit y studies are based on Poisson inference. Frequently, overdispersion is pre sent and this extra variability is modelled by introducing random effects. In this paper we compare two computationally simple approaches for incorpor ating random effects: one based on a non-parametric mixture model assuming that the population arises from a discrete mixture of Poisson distributions , and the second using a Poisson-normal mixture model which allows for spat ial autocorrelation. The comparison is focused on how well each of these me thods identify the regions which have high risks. Such identification is im portant because policy makers may wish to target regions associated with su ch extreme risks for financial assistance while epidemiologists may wish to target such regions for further study. The Poisson-normal mixture model is presented from both a frequentist, or empirical Bayes, and a fully Bayesia n point of view. We compare results obtained with the parametric and non-pa rametric models specifically in terms of detecting extreme mortality risks, using infant mortality data of British Columbia, Canada, for the period 19 81-1985, breast cancer data from Sardinia, for the period 1983-1987, and Sc ottish lip cancer data for 1975-1980. However, we also investigate the perf ormance of these models in a simulation study. The key finding is that disc rete mixture models seem to be able to locate regions which experience high risks; normal mixture models also work well in this regard, and perform su bstantially better when spatial autocorrelation is present. Copyright (C) 2 001 John Wiley & Sons, Ltd.