Estimating a Causal Exposure Response Function with a Continuous Error-Prone Exposure: A Study of Fine Particulate Matter and All-Cause Mortality

Abstract

Numerous studies have examined the associations between long-term exposure to fine particulate matter (PM_2.5) and adverse health outcomes. Recently, many of these studies have begun to employ high-resolution predicted PM_2.5 concentrations, which are subject to measurement error. Previous approaches for exposure measurement error correction have either been applied in non-causal settings or have only considered a categorical exposure. Moreover, most procedures have failed to account for uncertainty induced by error correction when fitting an exposure-response function (ERF). To remedy these deficiencies, we develop a multiple imputation framework that combines regression calibration and Bayesian techniques to estimate a causal ERF. We demonstrate how the output of the measurement error correction steps can be seamlessly integrated into a Bayesian additive regression trees (BART) estimator of the causal ERF. We also demonstrate how locally-weighted smoothing of the posterior samples from BART can be used to create a more accurate ERF estimate. Our proposed approach also properly propagates the exposure measurement error uncertainty to yield accurate standard error estimates. We assess the robustness of our proposed approach in an extensive simulation study. We then apply our methodology to estimate the effects of PM_2.5 on all-cause mortality among Medicare enrollees in New England from 2000-2012.

Figure 1:

ZIP-code and monitor locations (green dots) appearing across New-England in 2010. The heat map describes the difference between the posterior mean $L^{-1}{\sum }_{l=1}^L{A}_i^{(l)}$ and ${\tilde{Z}}_i$ in 2010. ZIP-codes with a grey fill had either missing exposure data or missing outcome data in 2010.

Figure 2:

An illustration about the nested structure of the data accompanying the relationship between the true ZIP-code, the true grid level, and the EPE grid measurements.

Figure 3:

ERF estimates averaged over 500 simulated iterations when n = 800 and M = 4000 and correct model specifications. When classical error is present then ω² = 2, when prediction error is present then τ² = 1. The BART approach to multiple imputation uses a BART outcome model while the GLM implementation uses a log-linear outcome model. The bar plot overlaying the ERF estimates represents the root mean squared errors for the corresponding methods.

Figure 4:

ERF estimate of PM_2.5 on all-cause mortality in New England between 2000–2012 amongst Medicare recipients under three different approaches to measurement error correction. The grey ribbon represents the 95% confidence interval computed from our multiple imputation approach. The histogram underlying the curves corresponds with the empirical distribution of the EPEs.