Model Uncertainty and Bayesian Model Averaged Benchmark Dose Estimation for Continuous Data

Abstract

The benchmark dose (BMD) approach has gained acceptance as a valuable risk assessment tool, but risk assessors still face significant challenges associated with selecting an appropriate BMD/BMDL estimate from the results of a set of acceptable dose-response models. Current approaches do not explicitly address model uncertainty, and there is an existing need to more fully inform health risk assessors in this regard. In this study, a Bayesian model averaging (BMA) BMD estimation method taking model uncertainty into account is proposed as an alternative to current BMD estimation approaches for continuous data. Using the "hybrid" method proposed by Crump, two strategies of BMA, including both "maximum likelihood estimation based" and "Markov Chain Monte Carlo based" methods, are first applied as a demonstration to calculate model averaged BMD estimates from real continuous dose-response data. The outcomes from the example data sets examined suggest that the BMA BMD estimates have higher reliability than the estimates from the individual models with highest posterior weight in terms of higher BMDL and smaller 90th percentile intervals. In addition, a simulation study is performed to evaluate the accuracy of the BMA BMD estimator. The results from the simulation study recommend that the BMA BMD estimates have smaller bias than the BMDs selected using other criteria. To further validate the BMA method, some technical issues, including the selection of models and the use of bootstrap methods for BMDL derivation, need further investigation over a more extensive, representative set of dose-response data.

NTP Research Report on National Toxicology Program Approach to Genomic Dose-Response Modeling

“…In such cases, the feature will not be considered in the gene-set analysis described below. Note: The US EPA is currently working on methods for model averaging that will obviate the need to select a best-fit model 25 . NTP plans to evaluate model averaging for use in genomic dose-response analysis once the US EPA establishes it as a viable alternative to the best model selection approach.…”

Benchmark Dose Calculation for Ordered Categorical Responses

“…Therefore, derivation of the BMD tends to be standardized, and model uncertainty may not be a major issue. To develop a model uncertainty technique for ordered categorical data, existing methods for the dichotomous (22,23) and continuous (24) data may be extended, and a similar Bayesian model averaging (25) procedure may be employed.…”

Bayesian Hierarchical Structure for Quantifying Population Variability to Inform Probabilistic Health Risk Assessments

“…Bayesian methods have been widely applied in dose-response modeling research. (11)(12)(13) In this study, we propose to characterize the interpopulation variability through the background risk (i.e., relative risk at background exposure) and response sensitivity (i.e., response rate), which corresponds to placing a hierarchical structure over parameters "a" (risk at background exposure) and "b" (a responsesensitivity-equivalent parameter) in Equation (4). The first level of the hierarchy represents the studyspecific estimate and the next level of the hierarchy is a distribution characterizing these parameters.…”