Bayesian Hierarchical Analysis for Multiple Health Endpoints in a Toxicity Study

Abstract

Bayesian hierarchical models are built to fit multiple health endpoints from a doseresponse study of a chemical contaminant, 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 empirical models to fit blood hormone concentration and thyroid histopathology data for rats exposed to perchlorate in the 90-day study of Springborn Laboratories Inc. (1998), based upon a mechanistic model derived from 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 Bayesian model specification allows us to address additional questions that arise after the analysis.

Potential Uncertainty Reduction in Model‐Averaged Benchmark Dose Estimates Informed by an Additional Dose Study

“…Expected reductions in BMA BMD interval widths are then computed as the average of the values achieved for these across the simulated outcomes. Five principal steps are implemented in the procedure: ( 14 )…”

“…Expected reductions in BMA BMD interval widths are then computed as the average of the values achieved for these across the simulated outcomes. Five principal steps are implemented in the procedure: (14) (1) One of the two candidate models is sampled at random, according to the posterior weights previously determined. For example, for Kociba's study, the logistic model has a 4.3% chance of being selected for each sample and the quantal-linear model a 95.7% chance; (2) One pair of parameters for the selected model is chosen from the posterior chain simulated by the MCMC model fitting algorithm; (3) For the selected model we calculate the response rate p given the selected parameters and the proposed dose level, using either Equation (1) or (2), depending on the model;…”

“…Nonetheless, the analysis does provide useful insights into where additional dosage rates could have yielded better resolved estimates, and how big the associated uncertainty reductions could have been. This approach is similar to that taken by Choi et al ., ( 14 ) and serves as a first step toward a more comprehensive approach to experimental design in which existing studies are used to inform the design of new ones (and this is a focus of our ongoing research).…”

A Bayesian Approach to a Logistic Regression Model with Incomplete Information

“…The covariate T4 is available for every rat, but the response HT is available only as counts within each dose‐level group. As in the simulations, we could use the average method described in , as was done by Choi et al (2004). The use of the average for different dose groups might be a suitable choice as a predictor, but it lacks a statistical justification and ignores available information.…”

Hierarchical dose–response modeling for high‐throughput toxicity screening of environmental chemicals

“…Bayesian hierarchical models have been used in many fields where the data takes a natural hierarchical structure. Several in vivo or developmental toxicity studies have used Bayesian hierarchical models to improve estimates when measuring the response of multiple correlated endpoints tested with a single chemical (e.g., Faes et al., ; Choi et al., ) or used a multivariate model that assumes correlation in residuals for multiple health outcomes (Neelon and Dunson, ).…”