  Numerous studies have examined the associations between long-term exposure to
fine particulate matter (PM2.5) and adverse health outcomes. Recently, many of
these studies have begun to employ high-resolution predicted PM2.5
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 PM2.5 on all-cause mortality among Medicare enrollees
in New England from 2000-2012.
