Measurement error in two-stage analyses, with application to air pollution epidemiology

TL;DR

This paper develops a robust analytical framework to address complex measurement errors in two-stage environmental health studies, ensuring valid inference even when the first-stage exposure model is misspecified.

Contribution

It introduces a methodology that corrects finite-sample bias and estimates standard errors accurately, improving inference in two-stage exposure-health effect analyses.

Findings

Method effectively corrects bias in simulations.

Framework guarantees consistency under certain model conditions.

Application to air pollution data demonstrates practical utility.

Abstract

Public health researchers often estimate health effects of exposures (e.g., pollution, diet, lifestyle) that cannot be directly measured for study subjects. A common strategy in environmental epidemiology is to use a first-stage (exposure) model to estimate the exposure based on covariates and/or spatio-temporal proximity and to use predictions from the exposure model as the covariate of interest in the second-stage (health) model. This induces a complex form of measurement error. We propose an analytical framework and methodology that is robust to misspecification of the first-stage model and provides valid inference for the second-stage model parameter of interest. We decompose the measurement error into components analogous to classical and Berkson error and characterize properties of the estimator in the second-stage model if the first-stage model predictions are plugged in without correction. Specifically, we derive conditions for compatibility between the first- and second-stage models that guarantee consistency (and have direct and important real-world design implications), and we derive an asymptotic estimate of finite-sample bias when the compatibility conditions are satisfied. We propose a methodology that (1) corrects for finite-sample bias and (2) correctly estimates standard errors. We demonstrate the utility of our methodology in simulations and an example from air pollution epidemiology.