A significant challenge in air pollution epidemiology is that we cannot directly measure exposures for study subjects.  In cohort studies, ambient concentrations at subject locations can be predicted from measured data at different monitoring locations by means of a “land-use” regression model with spatial smoothing.  This presents statistical challenges related to optimally selecting the prediction model and to accounting for the resulting exposure measurement error when estimating health effects. 

 Although measurement error from using predicted exposures is neither Berkson nor classical, it can be decomposed into Berkson-like and classical-like components.  The Berkson-like component accounts for smoothing from the exposure model.  It is similar to Berkson error in that (for suitable models) it introduces little or no bias, but unlike Berkson error a correction is needed for valid standard error estimates.  The classical-like component results from uncertainty in estimating the exposure model parameters.  It is similar to classical measurement error in that it can introduce bias and inflate standard errors, but unlike classical measurement error the bias tends to be asymptotically small compared to the added variability.  For a correctly specified exposure model, parametric bootstrap and joint likelihood-based corrections are valid.  We propose computationally efficient approximations to the parametric bootstrap in this setting.  In the case of a misspecified exposure model, we propose to combine model-robust asymptotic bias calculations with non-parametric bootstrap resampling.

 Finally, we show in a simulation study and with asymptotic calculations that selecting an exposure model to optimize prediction accuracy does not necessarily lead to optimal health effect inference (in terms of bias or efficiency).  We propose an approach to selecting between exposure models with the goal of optimizing health effect inference, rather than the intermediate objective of accurate exposure prediction.

 We illustrate our methods using simulations and data from the MESA Air study of air pollution and cardiovascular disease.