Modeling Spatial Variation in Disease Risk: A Geostatistical Approach

A valuable public health practice is to examine disease incidence and mortality rates across geographic regions. The data available for the construction of disease maps are typically in the form of aggregate counts within sets of disjoint, politically defined areas, and the Poisson variation inherent in these counts can lead to extreme raw rates in small areas. Relative risks tend to be similar in neighboring areas, and a common approach is to use random-effects models that allow estimation of relative risk in an area to "borrow strength" from neighboring areas, thus producing more stable estimation. Often a Markov random field structure is assumed to model the spatial dependence due to unmeasured risk factors. Such models consider the distribution of the relative risk of an area conditional on its neighbors, although the neighborhood schemes are typically defined only very simplistically. For example, two areas may be viewed as neighbors if they share a common boundary, in which case the relative positions, sizes, and shapes of the areas are not taken into account. In this article we describe a new method in which the correlation structure is derived through consideration of an underlying continuous risk surface. Specifically, we model the log relative risk as a Gaussian random field, a modeling approach that has seen extensive use in the geostatistics literature. We approximate the distribution of the area-level relative risks to provide an analytically tractable form. This leads to more realistic correlation structures between neighboring areas, and allows estimation not only of individual area-level relative risks, but also of the continuous underlying relative risk function. We first explore and illustrate our methods with simulated data. We then analyze a set of data on colorectal cancer in the U.K. district of Birmingham. The aims of the analysis were to investigate the extent of spatial variability and to investigate the extent to which this variability was associated with an area-level measure of socioeconomic status.