Bayesian Modelling of Inseparable Space-Time Variation in Disease Risk

This paper proposes a unified framework for a Bayesian analysis of
incidence or mortality data in space and time. We introduce four
different types of prior distributions for space $\times$ time
interaction in extension of a model with only main effects. Each
type implies a certain degree of prior dependence for the
interaction parameters, and corresponds to the product of one of
the two spatial with one of the two temporal main effects. The
methodology is illustrated by an analysis of Ohio lung cancer data
1968-88 via Markov chain Monte Carlo simulation. We compare the fit
and the complexity of several models with different types of
interaction by means of quantities related to the posterior
deviance. Our results confirm an epidemiological hypothesis about
the temporal development of the association between urbanization
and risk factors for cancer.