Spatial Poisson regression for health and exposure data measured at disparate resolutions

Ecological regression studies are widely used to examine relationships between disease rates for small geographical areas and exposure to environmental risk factors. The raw data for such studies, including disease cases, environmental pollution concentrations, and the reference population at risk, are typically measured at various levels of spatial aggregation but are accumulated to a common geographical scale to facilitate statistical analysis. In this traditional approach, heterogeneous exposure distributions within the aggregate areas may lead to biased inference, whereas individual attributes such as age, gender, and smoking habits must either be summarized to provide area-level covariate values or used to stratify the analysis. This article presents a spatial regression analysis of the effect of traffic pollution on respiratory disorders in children. The analysis features data measured at disparate, nonnested scales, including spatially varying covariates, latent spatially varying risk factors, and case-specific individual attributes. The problem of disparate discretizations is overcome by relating all spatially varying quantities to a continuous underlying random field model. Case-specific individual attributes are accommodated by treating cases as a marked point process. Inference in these hierarchical Poisson/gamma models is based on simulated samples drawn from Bayesian posterior distributions, using Markov chain Monte Carlo methods with data augmentation.