Spatial Poisson Regression for Health and Exposure Data Measured at Disparate Resolutions Nicola G. BEST, Katja ICKSTADT and Robert L. WOLPERT 1 JASA Manuscript A98-156-R0 Revised March 27, 2000, 10:17 Ecological regression studies are widely used to examine relationships between dis- ease rates for small geographical areas and exposure to environmental risk factors. The raw data for such studies, including disease cases, environmental pollution con- centrations and the reference population at risk, are typically measured at a variety of 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, while individ- ual 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 paper presents a spatial regression analysis of the effect of traffic pollution on respiratory disorders in children. The analysis features data measured at disparate, non-nested 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. 1 Nicola G. Best is Lecturer in Biostatistics, Department of Epidemiology and Public Health, Imperial College School of Medicine, St Marys’ Campus, London W2 1PG, UK (email: n.best@ic.ac.uk); Katja Ickstadt is Postdoctoral Research Fellow, Department of Mathematics, Darmstadt University of Technology, 64289 Darmstadt, Germany (email: ickstadt@mathematik.tu-darmstadt.de); and Robert L. Wolpert is Professor, Institute of Statistics and Decision Sciences, Duke University, Box 90251, Durham, NC 27708-0251 (email: wolpert@stat.duke.edu). The authors acknowledge gratefully the support of the Deutsche Forschungsgemeinschaft, of US NSF grants DMS-9626829 and DMS-9707914, of a Wellcome Research Travel grant, andof UK Medical Research Council grant G9803841. The SAVIAH study was funded by a grant from the European Union Third Framework Environment Programme. The authors thank Paul Elliott, Jeremy Bullard, David Briggs, Sue Collins, and Jon Wakefield for providing data and sharing insight, and Dave Higdon and the editor, associate editor and three anonymous referees for helpful suggestions. 1