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

Ecological regression studies are widely used to examine relationships betw een disease rates for small geographical areas and exposure to environmenta l risk factors. The raw data for such studies, including disease cases, env ironmental pollution concentrations, and the reference population at risk, are typically measured at various levels of spatial aggregation but are acc umulated 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 attrib utes such as age, gender, and smoking habits must either be summarized to p rovide area-level covariate values or used to stratify the analysis. This a rticle presents a spatial regression analysis of the effect of traffic poll ution on respiratory disorders in children. The analysis features data meas ured at disparate, nonnested scales, including spatially varying covariates , latent spatially varying risk factors, and case-specific individual attri butes. 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 mode ls is based on simulated samples drawn from Bayesian posterior distribution s, using Markov chain Monte Carlo methods with data augmentation.