Motivated by environmental policy questions, we address the challenges of estimation, change point detection, and uncertainty quantification of a causal exposure-response function (CERF). Under a potential outcome framework, the CERF describes the relationship between a continuously varying exposure (or treatment) and its causal effect on an outcome. We propose a new Bayesian approach that relies on a Gaussian process (GP) model to estimate the CERF nonparametrically. To achieve the desired separation of design and analysis phases, we parametrize the covariance (kernel) function of the GP to mimic matching via a Generalized Propensity Score (GPS). The hyper-parameters as well as the form of the kernel function of the GP are chosen to optimize covariate balance. Our approach achieves automatic uncertainty evaluation of the CERF with high computational efficiency, and enables change point detection through inference on derivatives of the CERF. 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, ozone, and NO2 on all-cause mortality among Medicare enrollees in the US. A computationally efficient implementation of the proposed GP models is provided in the GPCERF R package, which is available on CRAN.

翻译：受环境政策问题驱动，我们解决了因果暴露反应函数（CERF）在估计、变点检测和不确定性量化方面的挑战。在潜在结果框架下，CERF描述了连续变化的暴露（或处理）与其对结果因果效应之间的关系。我们提出了一种新的贝叶斯方法，该方法依赖高斯过程（GP）模型非参数地估计CERF。为了实现设计和分析阶段的理想分离，我们将GP的协方差（核）函数参数化，以通过广义倾向性评分（GPS）模拟匹配。GP的超参数以及核函数形式被选择用于优化协变量平衡。我们的方法以高计算效率实现了CERF的自动不确定性评估，并通过CERF的导数推断实现变点检测。我们提供了理论结果，展示了我们的贝叶斯GP框架与传统因果推断方法在估计连续暴露因果效应之间的对应关系。我们将该方法应用于520,711个ZIP码级别的观测数据，以估计美国医疗保险参保者中长期暴露于PM2.5、臭氧和NO2对全因死亡率的因果效应。所提出的GP模型的计算高效实现已提供于GPCERF R包中，该包可在CRAN上获取。