Locally adaptive spatial smoothing using conditional autoregressive models

Conditional autoregressive (CAR) models are commonly used to capture spatial correlation in areal unit data, and are typically specified as a prior distribution for a set of random effects, as part of a hierarchical Bayesian model. The spatial correlation structure induced by these models is determined by geographical adjacency, so that two areas have correlated random effects if they share a common border. However, this correlation structure is too simplistic for real data, which are instead likely to include sub-regions of strong correlation as well as locations at which the response exhibits a step-change. Therefore this paper proposes an extension to CAR priors, which can capture such localised spatial correlation. The proposed approach takes the form of an iterative algorithm, which sequentially updates the spatial correlation structure in the data as well as estimating the remaining model parameters. The efficacy of the approach is assessed by simulation, and its utility is illustrated in a disease mapping context, using data on respiratory disease risk in Greater Glasgow, Scotland.

Boundary detection in disease mapping studies

In disease mapping, the aim is to estimate the spatial pattern in disease risk over an extended geographical region, so that areas with elevated risks can be identified. A Bayesian hierarchical approach is typically used to produce such maps, which models the risk surface with a set of spatially smooth random effects. However, in complex urban settings there are likely to be boundaries in the risk surface, which separate populations that are geographically adjacent but have very different risk profiles. Therefore this paper proposes an approach for detecting such risk boundaries, and tests its effectiveness by simulation. Finally, the model is applied to lung cancer incidence data in Greater Glasgow, Scotland, between 2001 and 2005.