DuncanÂ Lee

Mapping the distribution of disease risk over a set of *n* contiguous small-areas is a common problem in spatial epidemiology, and the primary aim of such an analysis is to determine if there are areas that exhibit excess levels of risk. This spatial pattern in disease risk can be estimated using a Bayesian hierarchical model, where the observed number of disease cases in each small-area is regressed against covariate risk factors, after adjusting for the size and age structure of the population. However, the disease counts are often overdispersed with respect to the Poisson likelihood and display spatial autocorrelation, even after the effects of the covariates have been accounted for. These factors can be modelled by a convolution of spatial and non-spatial random effects, where the former are represented by a conditionally autoregressive (CAR) prior distribution. This prior represents spatial dependence via a binary *n* by *n* neighbourhood matrix *W*, where *w _{ij}* equals 1 if areas

This model assumes that all pairs of adjacent areas have similar risks of disease, even though in some locations communities with vastly different social characteristics are geographically adjacent. Therefore this paper extends the standard CAR model to reflect such a non-uniform spatial dependence structure. Thus our approach allows random effects in adjacent areas to be correlated or independent, depending on the areas' level of social, environmental or geographical similarity. This approach provides a more realistic description of the spatial correlation in small-area data, as well as allowing us to determine where spatial discontinuities in disease risk exist. We illustrate our methodology by mapping hospital admissions due to alcohol abuse in Greater Glasgow between 2001 to 2004, which is a rapidly growing public health problem in Scotland.

**Keywords:** Bayesian disease mapping; Boundary detection; Conditional autoregressive models

**Biography:** Duncan has been a lecturer in Statistics at the University of Glasgow for four years, after completing a PhD at the University of Bath. His broad research focus is on developing spatio-temporal models for use in environmental epidemiology. His particular interests are in estimating the effects of air pollution on human health, and developing models for Bayesian disease mapping.