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

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  • Kan Shao
  • Jeffrey S. Gift

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.

Suggested Citation

  • Kan Shao & Jeffrey S. Gift, 2014. "Model Uncertainty and Bayesian Model Averaged Benchmark Dose Estimation for Continuous Data," Risk Analysis, John Wiley & Sons, vol. 34(1), pages 101-120, January.
    • Handle: RePEc:wly:riskan:v:34:y:2014:i:1:p:101-120
    DOI: 10.1111/risa.12078
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    References listed on IDEAS

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    Cited by:

    1. Matthew W. Wheeler & Jose Cortiñas Abrahantes & Marc Aerts & Jeffery S. Gift & Jerry Allen Davis, 2022. "Continuous model averaging for benchmark dose analysis: Averaging over distributional forms," Environmetrics, John Wiley & Sons, Ltd., vol. 33(5), August.
    2. Jin‐Hua Chen & Chun‐Shu Chen & Meng‐Fan Huang & Hung‐Chih Lin, 2016. "Estimating the Probability of Rare Events Occurring Using a Local Model Averaging," Risk Analysis, John Wiley & Sons, vol. 36(10), pages 1855-1870, October.
    3. Marc Aerts & Matthew W. Wheeler & José Cortiñas Abrahantes, 2020. "An extended and unified modeling framework for benchmark dose estimation for both continuous and binary data," Environmetrics, John Wiley & Sons, Ltd., vol. 31(7), November.
    4. Kan Shao & Bruce C. Allen & Matthew W. Wheeler, 2017. "Bayesian Hierarchical Structure for Quantifying Population Variability to Inform Probabilistic Health Risk Assessments," Risk Analysis, John Wiley & Sons, vol. 37(10), pages 1865-1878, October.
    5. Signe M. Jensen & Christian Ritz, 2015. "Simultaneous Inference for Model Averaging of Derived Parameters," Risk Analysis, John Wiley & Sons, vol. 35(1), pages 68-76, January.

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