Hierarchical Modeling of Spatio - temporally Misaligned

Bayes and empirical Bayes methods have proven eeective in smoothing crude maps of disease risk, eliminating the instability of estimates in low-population areas while maintaining overall geographic trends and patterns. Recent work applies these methods to the analysis of areal data which are spatially misaligned, i.e., involving variables (typically counts or rates) which are aggregated over diiering sets of regional boundaries. In this paper we extend this hierarchical modeling approach to the spatio-temporal case, so that misalignment can arise either within a given timepoint, or across timepoints (as when the regional boundaries themselves evolve over time). Implemented using Markov chain Monte Carlo computing methods, our approach sensibly combines the relevant data sources and imposes the necessary constraints over the misaligned regional grids. We illustrate the method through an analysis of the dataset that motivated the method, which relates traac density to pediatric asthma hospitalizations in San Diego County, California. We compare two diierent measures of the traac covariate (neither of which is aligned with the zip code-level asthma data), mapping the resulting tted risk estimates in the Geographic Information System (GIS) ARC/INFO. Results in both cases are consistent with those of several previous authors who have investigated the traac-asthma link.