Motivated by environmental health research on air pollution, we address the challenge of uncertainty quantification for causal exposure-response functions. A causal exposure-response function (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 higher order 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 PM 2.5 on all cause mortality among Medicare enrollees in the United States.
翻译:在对空气污染进行环境卫生研究的推动下,我们应对因果接触-反应功能的不确定性量化挑战。因果接触-反应功能(CERF)描述了持续变化的接触(或处理)及其对结果的因果关系之间的关系。我们建议采用新的巴伊西亚方法,以高斯进程模型为基础来估计中央应急循环基金。我们用通用预测分数(GPS)将GP的共差(内核)功能进行假称,以模拟因果匹配。选择匹配功能的调试参数是为了优化共差平衡。我们的方法是以高计算效率实现中央应急循环基金自动的不确定性评估,通过对中央应急循环基金更高订单衍生物的推论,从而能够发现变化点,并产生预期的因果估计设计和分析阶段的分离。我们提供了理论结果,表明我们的巴伊西亚GP框架和因果推断传统方法之间的对应关系,以估计持续接触的因果关系。我们采用了520 711 ZIP代码水平观测方法,以估计美国长期接触PPM 2.5的所有原因死亡率的因果关系。