Bayesian Models for Spatially Correlated Disease and Exposure Data

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Abstract
The study of geographical patterns of disease has a long tradition in epidemiology and is useful for generating and refining aetiological hypotheses. Area-specific incidence/mortality rates or relative risks are estimated using count data on the number of cases of disease and the population at risk in each area within the study region. When the disease of interest is relatively rare and/or the geographical areas are small, the counts tend to be low and associated sampling variation is high. Such data also often exhibit spatial correlation, possibly due to the influence of unmeasured or unknown risk factors which themselves vary systematically in space. Analysis of such data presents a number of statistical problems which have recently been addressed using Bayesian hierarchical models with Markov random field (MRF) priors. These models extend naturally to allow inclusion of area-level covariates, thus facilitating geographical correlation studies. However, the sensitivity of these MRF models to the assumed form of the spatial covariance function, the choice of neighbourhood structure over which the Markov random field extends, and the specification of the hyperprior distributions, is poorly understood. In this paper, we address some of these issues by investigating the properties of a variety of MRF models applied to simulated data on cancer incidence in Scottish districts. We also address some of the convergence problems associated with the Markov chain Monte Carlo algorithms used to implement such MRF models, and discuss methods for model comparison and diagnostics in this context.

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