Bayesian Detection of Clusters and Discontinuities in Disease Maps. (REVISED, February 1999)

An interesting epidemiological problem is the analysis of
geographical variation in rates of disease incidence or mortality.
One goal of such an analysis is to detect clusters of elevated (or
lowered) risk in order to identify unknown risk factors regarding
the disease. We propose a nonparametric Bayesian approach for the
detection of such clusters based on Green's (1995) reversible jump
MCMC methodology. The prior model assumes 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,
discrete space. We illustrate our method through an analysis of
oral cavity cancer mortality rates in Germany and compare the
results with those obtained by the commonly used Bayesian disease
mapping method of Besag, York and Mollie (1991).