Bayesian Modeling for Exposure Response Curve via Gaussian Processes: Causal Effects of Exposure to Air Pollution on Health Outcomes

Motivated by environmental health research on air pollution, we address the challenge of estimation and uncertainty quantification of causal exposure-response function (CERF). The CERF describes the relationship between a continuously varying exposure (or treatment) and its causal effect on a outcome. We propose a new Bayesian approach that relies on a Gaussian process (GP) model to estimate the CERF. We parametrize the covariance (kernel) function of the GP to mimic matching via a Generalized Propensity Score (GPS). The tuning parameters of the matching function are chosen to optimize covariate balance. Our approach achieves automatic uncertainty evaluation of the CERF with high computational efficiency, enables change point detection through inference on derivatives of the CERF, and yields the desired separation of design and analysis phases for causal estimation. We provide theoretical results showing the correspondence between our Bayesian GP framework and traditional approaches in causal inference for estimating causal effects of a continuous exposure. We apply the methods to 520,711 ZIP-code-level observations to estimate the causal effect of long-term exposures to PM2.5 on all-cause mortality among Medicare enrollees in the United States.