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Biostatistics. 2016 Apr;17(2):377-89. doi: 10.1093/biostatistics/kxv048. Epub 2015 Nov 29.

Spatial measurement error and correction by spatial SIMEX in linear regression models when using predicted air pollution exposures.

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Institute for Mathematics Applied to Geosciences, National Center for Atmospheric Research, Boulder, CO USA and Department of Biostatistics, Harvard School of Public Health, Boston, MA, USA
Department of Statistics, Texas A & M University, College Station, TX, USA.
Department of Biostatistics, Harvard School of Public Health, Boston, MA, USA.


Spatial modeling of air pollution exposures is widespread in air pollution epidemiology research as a way to improve exposure assessment. However, there are key sources of exposure model uncertainty when air pollution is modeled, including estimation error and model misspecification. We examine the use of predicted air pollution levels in linear health effect models under a measurement error framework. For the prediction of air pollution exposures, we consider a universal Kriging framework, which may include land-use regression terms in the mean function and a spatial covariance structure for the residuals. We derive the bias induced by estimation error and by model misspecification in the exposure model, and we find that a misspecified exposure model can induce asymptotic bias in the effect estimate of air pollution on health. We propose a new spatial simulation extrapolation (SIMEX) procedure, and we demonstrate that the procedure has good performance in correcting this asymptotic bias. We illustrate spatial SIMEX in a study of air pollution and birthweight in Massachusetts.


Air pollution; Birthweight; Environmental epidemiology; Kriging; Model uncertainty; Spatial model

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