When inference is desired regarding some attribute of a particular geographic region, it often happens that data are not directly available for that region. However, it may be that data are available over the same general area, but reported according to a different set of regional boundaries. Recently, powerful computer programs called geographic information systems (GIS's) have enabled the simultaneous display of such "misaligned" data sets, but these systems address only the descriptive needs of the user, leaving the inferential goal unmet. In this paper we describe a hierarchical Bayes approach, implemented via Markov chain Monte Carlo methods, which provides a natural solution to this problem through its ability to sensibly combine information from several sources of data and available prior information. After presenting a simple idealized example to illustrate the method, we apply it to a data set on leukemia rates in Tompkins County, New York, wherein we use census tract-level covariate information to interpolate disease counts given only aggregate (block group-level) summaries. We display our results graphically using both statistical ( S-plus) and GIS (ArcInfo) software packages. The approach emerges as flexible, accurate, and suggestive of promising related methods for spatial smoothing of underlying relative risks.

This is joint work with Andrew S. Mugglin.

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