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Motivated by analyzing a national data base of annual air pollution andcardiovascular disease mortality rate for 3100 counties in the U.S. (arealdata), we develop a novel statistical framework to automatically detectspatially varying region-wise associations between air pollution exposures andhealth outcomes. The automatic region-wise spatially varying coefficient modelconsists three parts: we first compute the similarity matrix between theexposure-health outcome associations of all spatial units, then segment thewhole map into a set of disjoint regions based on the adjacency matrix withconstraints that all spatial units within a region are contiguous and havesimilar association, and lastly estimate the region specific associationsbetween exposure and health outcome. We implement the framework by usingregression and spectral graph techniques. We develop goodness of fit criteriafor model assessment and model selection. The simulation study confirms thesatisfactory performance of our model. We further employ our method toinvestigate the association between airborne particulate matter smaller than2.5 microns (PM 2.5) and cardiovascular disease mortality. The resultssuccessfully identify regions with distinct associations between the mortalityrate and PM 2.5 that may provide insightful guidance for environmental healthresearch.

Automatic Region-wise Spatially Varying Coefficient Regression Model: an  Application to National Cardiovascular Disease Mortality and Air Pollution  Association Study