Bayesian Model Averaging for Toxicity Study Design and Benchmark Dose Estimation

A methodology is proposed for assessing the value of information (VOI) for collecting future information through experimental design and integrating prior information in bioassay studies. Bayesian methods are applied to fit alternative dose-response models using a posterior sampling simulation method (i.e. Markov Chain Monte Carlo (MCMC) algorithm) for parameter estimation, and Bayesian model averaging (BMA) is used to compare and combine the alternative models. Bayesian model averaged predictions for benchmark dose (BMD) are developed. Uncertainty reductions are measured in terms of reduced interval widths of predicted BMD values. The methodology is illustrated using two existing datasets for TCDD carcinogenicity (Kociba et al and NTP 1982), fitted with two alternative dose-response models (logistic and quantal-linear).;The posterior sampling and BMA results provide a basis for the subsequent Monte Carlo pre-posterior analysis that determines expected reductions in uncertainty achieved by adding a new study at a new dose level or designing toxicological animal bioassay experiments from scratch. The results suggest that (1) as more animals are tested there is less uncertainty in BMD estimates; (2) one relatively high dose is needed and other doses can then be appropriately spread over the resulting dose scale; (3) placing different numbers of animals in different dose groups has very limited influence on improving BMD estimation; (4) when the total number of animals is fixed, using more (but smaller) dose groups is a preferred strategy.;With the goal of reducing the uncertainty in BMD estimates, three different methods of combining historical data are examined and compared. Pooled data, which have more dose groups, are beneficial for reducing the uncertainty in BMD estimates, but this method might not be statistically or biologically plausible. Hierarchical model builds another level of distribution for model parameters to take the heterogeneity among different studies into account, but this reasonable manner can increase the uncertainty in both parameter and BMD estimates significantly if data are highly incompatible. Newly proposed "partially-borrow" power prior method successfully reduces uncertainty in BMD estimates as well as considers and controls between-study uncertainty through a scalar parameter w0. However, this method still might be data-dependent and comprehensive investigation for its feasibility in toxicological study is needed.