Spatial Measurement Error in Two-Stage Regression, with Application to Air Pollution Epidemiology

• Activity Number: 52
• Type: Invited
• Date/Time: Sunday, July 29, 2012 : 4:00 PM to 5:50 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Christopher J Paciorek*+ and Adam A Szpiro
• Companies: University of California at Berkeley and University of Washington
• Keywords: measurement error ; spatial statistics ; air pollution ; epidemiology ; nonparametric bootstrap

Abstract

In environmental epidemiology, the health effect of an exposure is often estimated by using predictions from a first stage exposure model as an explanatory variable in the second stage health analysis. The uncertainty about the true exposure produces measurement error in the second stage model, with a complicated dependence structure induced by the first stage model. We propose a new probabilistic framework to analyze the effects of measurement error in two-stage settings with a spatial context. We treat the spatial locations as random and the unknown exposure surface as deterministic and arbitrary, providing an approach that is robust to exposure model misspecification. We decompose the measurement error into Berkson-like and classical-like components and analyze the bias and variance induced by the different components. We develop an asymptotic estimator for the bias produced by variability in the first stage regression coefficients. Finally, we suggest a design-based nonparametric bootstrap to estimate the full uncertainty in the second stage analysis. We illustrate the ideas in analyzing long-term health effects of air pollution.