#### Abstract

PLEASE NOTE THAT AN UPDATED VERSION OF THIS RESEARCH IS AVAILABLE AS WORKING PAPER 350 IN THE UNIVERSITY OF WASHINGTON BIOSTATISTICS WORKING PAPER SERIES (http://www.bepress.com/uwbiostat/paper350).

In environmental epidemiology and related problems in environmental statistics, it is typically not practical to directly measure the exposure for each subject. Environmental monitoring is employed with a statistical model to assign exposures to individuals. The result is a form of exposure misspecification that can result in complicated errors in the health effect estimates if the exposure is naively treated as known. The exposure error is neither “classical” nor “Berkson”, so standard regression calibration methods do not apply. We decompose the health effect estimation error into three components. First, the standard errors are too small if the exposure field is correlated, independent of variability in estimating the exposure field parameters. Second, the standard errors are too small because they do not account for variability in estimating the exposure field parameters. Third, there is a bias from using approximate exposure field parameters in place of the unobserved true ones. We outline a three-stage correction procedure to account separately for each of these errors. A key insight is that we can account for the second part of the error (sampling variability in estimating the exposure) by averaging over simulations from the part of the posterior exposure surface that is informative for the outcome. This amounts to averaging over samples of the posterior exposure model parameters, a procedure that we call “parameter simulation”. One implication is that it is preferable to use a parametric correlation model (e.g., kriging) rather than a semi-parametric approximation. While the latter approach has been found to be effective in estimating mean exposure fields, it does not provide the needed decomposition of the posterior into informative and non-informative components. We illustrate the properties of our corrected estimators in a simulation study and present an example from environmental statistics. The focus of this paper is on linear health effect models with uncorrelated outcomes, but extensions to generalized linear models and correlated outcomes are possible.

#### Disciplines

Statistical Methodology | Statistical Theory

#### Suggested Citation

Szpiro, Adam A.; Sheppard, Lianne; and Lumley, Thomas, "Accounting for Errors from Predicting Exposures in Environmental Epidemiology and Environmental Statistics" (June 2008). *UW Biostatistics Working Paper Series.* Working Paper 330.

https://biostats.bepress.com/uwbiostat/paper330