  Disease maps display the spatial pattern in disease risk, so that high-risk
clusters can be identified. The spatial structure in the risk map is typically
represented by a set of random effects, which are modelled with a conditional
autoregressive (CAR) prior. Such priors include a global spatial smoothing
parameter, whereas real risk surfaces are likely to include areas of smooth
evolution as well as discontinuities, the latter of which are known as risk
boundaries. Therefore, this paper proposes an extension to the class of CAR
priors, which can identify both areas of localised spatial smoothness and risk
boundaries. However, allowing for this localised smoothing requires large
numbers of correlation parameters to be estimated, which are unlikely to be
well identified from the data. To address this problem we propose eliciting an
informative prior about the locations of such boundaries, which can be combined
with the information from the data to provide more precise posterior inference.
We test our approach by simulation, before applying it to a study of the risk
of emergency admission to hospital in Greater Glasgow, Scotland.
