A Bayesian analysis for spatial processes with application to disease mapping

In epidemiology, maps of disease rates and disease risk provide a spatial p erspective for researching disease aetiology. For rare diseases or when the population base is small, the rate and risk estimates may be unstable. We propose using a Bayesian analysis based on the conditional autoregressive ( CAR) process that will spatially smooth disease rates or risk estimates by allowing each site to 'borrow strength' from its neighbours. Covariates may be included in the model in such a way as to establish a possible associat ion between risk factors and disease incidence. Bayesian inferences are imp lemented from a direct resampling scheme where large samples are generated from the various posterior distributions. The methodology is demonstrated w ith a simulation that assesses the effect of sample size and the model para meters on inferences for the parameters. Our approach is also used to spati ally smooth district lip cancer rates in Scotland using the CAR model with a covariate that allows for exposure to sunlight. Copyright (C) 2000 John W iley & Sons, Ltd.