Measuring the impact of an environmental point source exposure on the risk of disease, like cancer or childhood asthma, is well-developed. Modeling how an environmental health hazard that is extensive in space, like a wastewater canal, impacts disease risk is not. We propose a novel Bayesian generative semiparametric model for characterizing the cumulative spatial exposure to an environmental health hazard that is not well-represented by a single point in space. The model couples a dose-response model with a log-Gaussian Cox process integrated against a distance kernel with an unknown length-scale. We show that this model is a well-defined Bayesian inverse model, namely that the posterior exists under a Gaussian process prior for the log-intensity of exposure, and that a simple integral approximation adequately controls the computational error. We quantify the finite-sample properties and the computational tractability of the discretization scheme in a simulation study. Finally, we apply the model to survey data on household risk of childhood diarrheal illness from exposure to a system of wastewater canals in Mezquital Valley, Mexico.

翻译：测量环境点源暴露对疾病（如癌症或儿童哮喘）风险的影响已有成熟方法。然而，对于空间上广泛分布的环境健康危害（如废水运河）如何影响疾病风险的建模研究尚不充分。本文提出了一种新颖的贝叶斯生成半参数模型，用于表征无法用单一空间点充分表征的环境健康危害的累积空间暴露。该模型将剂量-反应模型与对数高斯考克斯过程相结合，后者通过具有未知长度尺度的距离核进行积分。我们证明该模型是一个定义良好的贝叶斯逆模型，即在暴露对数强度的高斯过程先验下后验分布存在，且简单的积分近似足以控制计算误差。通过模拟研究，我们量化了离散化方案的有限样本性质与计算可行性。最后，我们将该模型应用于墨西哥梅斯基塔尔河谷地区废水运河系统暴露导致的家庭儿童腹泻疾病风险的调查数据。