Bayesian modelling of inseparable space‐time variation in disease risk

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Abstract
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 x 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 1968-1988 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.

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