Bayesian Methods for Modeling Cumulative Exposure to Extensive Environmental Health Hazards

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.