A Bayesian Hierarchical method for fitting multiple health endpoints in a toxicity study

Bayesian hierarchical models are built to fit multiple health endpoints from a dose-response study of a toxic chemical, perchlorate. Perchlorate exposure results in iodine uptake inhibition in the thyroid, with health effects manifested by changes in blood hormone concentrations and histopathological effects on the thyroid. We propose linked empirical models to fit blood hormone concentration and thyroid histopathology data for rats exposed to perchlorate in the 90-day study of Springborn Laboratory Inc. (1998), based upon the assumed toxicological relationships between dose and the various endpoints. All of the models are fit in a Bayesian framework, and predictions about each endpoint in response to dose are simulated based on the posterior predictive distribution. A hierarchical model tries to exploit possible similarities between different combinations of sex and exposure duration, and it allows us to produce more stable estimates of dose-response curves. We also illustrate how the hierarchical model allows us to address additional questions that arise after the analysis.