Shared component models for detecting joint and selective clustering of two diseases

The study of spatial variations in disease rates is a common
epidemiological approach used to describe geographical clustering
of disease and to generate hypotheses about the possible `causes'
which could explain apparent differences in risk. Recent
statistical and computational developments have led to the use of
realistically complex models to account for overdispersion and
spatial correlation. However, these developments have focused
almost exclusively on spatial modelling of a single disease. Many
diseases share common risk factors (smoking being an obvious
example) and if similar patterns of geographical variation of
related diseases can be identified, this may provide more
convincing evidence of real clustering in the underlying risk
surface. In this paper, we propose shared component models for the
joint spatial analysis of two diseases. The key idea is to identify
shared and disease-specific spatially-varying latent risk factors
by appropriate partitioning of the underlying risk surface for each
disease. The various components of this partition are modelled
simulataneously using nonparametric cluster models implemented via
reversible jump Markov chain Monte Carlo methods. We illustrate the
methodology through an analysis of oral and oesophageal cancer
mortality in the 544 districts of Germany, 1986-1990.