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

Authors

  • Kan Shao,

    Corresponding author
      Kan Shao, Civil and Environmental Engineering, Porter Hall 119, Frew St., Pittsburgh, PA 15213, USA; tel: 412-589-9765; fax: 412-268-7813; kshao@cmu.edu
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    • Civil and Environmental Engineering, Carnegie Mellon University, Pittsburgh, PA, USA.

    • Engineering and Public Policy, Carnegie Mellon University, Pittsburgh, PA, USA.

  • Mitchell J. Small

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    • Civil and Environmental Engineering, Carnegie Mellon University, Pittsburgh, PA, USA.


Kan Shao, Civil and Environmental Engineering, Porter Hall 119, Frew St., Pittsburgh, PA 15213, USA; tel: 412-589-9765; fax: 412-268-7813; kshao@cmu.edu

Abstract

A methodology is presented for assessing the information value of an additional dosage experiment in existing bioassay studies. The analysis demonstrates the potential reduction in the uncertainty of toxicity metrics derived from expanded studies, providing insights for future studies. Bayesian methods are used to fit alternative dose-response models using Markov chain Monte Carlo (MCMC) simulation for parameter estimation and Bayesian model averaging (BMA) is used to compare and combine the alternative models. BMA predictions for benchmark dose (BMD) are developed, with uncertainty in these predictions used to derive the lower bound BMDL. The MCMC and BMA results provide a basis for a subsequent Monte Carlo analysis that backcasts the dosage where an additional test group would have been most beneficial in reducing the uncertainty in the BMD prediction, along with the magnitude of the expected uncertainty reduction. Uncertainty reductions are measured in terms of reduced interval widths of predicted BMD values and increases in BMDL values that occur as a result of this reduced uncertainty. The methodology is illustrated using two existing data sets for TCDD carcinogenicity, fitted with two alternative dose-response models (logistic and quantal-linear). The example shows that an additional dose at a relatively high value would have been most effective for reducing the uncertainty in BMA BMD estimates, with predicted reductions in the widths of uncertainty intervals of approximately 30%, and expected increases in BMDL values of 5–10%. The results demonstrate that dose selection for studies that subsequently inform dose-response models can benefit from consideration of how these models will be fit, combined, and interpreted.

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