Hierarchical Modeling of Arsenic Concentrations at Entry Points in US Public Drinking Water Supplies

A Bayesian hierarchical model is built to describe arsenic concentrations in treated water from sources of public drinking water systems. The model allows us to decompose the total variability in arsenic concentration into three components: between-system, between-source (within system) and within-source variabilities. Predictions about what percentage of a state's systems and sources affected by the various proposed maximum contaminant level (MCL) regulations are simulated based on the posterior predictive distribution. We investigate the potential impact of the between-source variability on this percentage by comparing predictions based on the full model and based on the reduced model which eliminates the between-source variability. Other issues addressed in the modeling are the possibility that the arsenic concentration in source water is changing over time and the possibility that changes in measurement methods and their detection limits cause a change in the precision and accuracy of the measurement methods. The analysis is conducted based on data from four states: California, Illinois, New Mexico and Utah.