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Model Selection and Estimation with Quantal‐Response Data in Benchmark Risk Assessment

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  • Edsel A. Peña
  • Wensong Wu
  • Walter Piegorsch
  • Ronald W. West
  • LingLing An

Abstract

This article describes several approaches for estimating the benchmark dose (BMD) in a risk assessment study with quantal dose‐response data and when there are competing model classes for the dose‐response function. Strategies involving a two‐step approach, a model‐averaging approach, a focused‐inference approach, and a nonparametric approach based on a PAVA‐based estimator of the dose‐response function are described and compared. Attention is raised to the perils involved in data “double‐dipping” and the need to adjust for the model‐selection stage in the estimation procedure. Simulation results are presented comparing the performance of five model selectors and eight BMD estimators. An illustration using a real quantal‐response data set from a carcinogenecity study is provided.

Suggested Citation

  • Edsel A. Peña & Wensong Wu & Walter Piegorsch & Ronald W. West & LingLing An, 2017. "Model Selection and Estimation with Quantal‐Response Data in Benchmark Risk Assessment," Risk Analysis, John Wiley & Sons, vol. 37(4), pages 716-732, April.
    • Handle: RePEc:wly:riskan:v:37:y:2017:i:4:p:716-732
    DOI: 10.1111/risa.12644
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    References listed on IDEAS

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    1. Zellner, Arnold & Rossi, Peter E., 1984. "Bayesian analysis of dichotomous quantal response models," Journal of Econometrics, Elsevier, vol. 25(3), pages 365-393, July.
    2. A. John Bailer & Robert B. Noble & Matthew W. Wheeler, 2005. "Model Uncertainty and Risk Estimation for Experimental Studies of Quantal Responses," Risk Analysis, John Wiley & Sons, vol. 25(2), pages 291-299, April.
    3. Lelys Bravo Guenni & Susan J. Simmons & Walter W. Piegorsch & Hui Xiong & Rabi N. Bhattacharya & Lizhen Lin, 2012. "Nonparametric estimation of benchmark doses in environmental risk assessment," Environmetrics, John Wiley & Sons, Ltd., vol. 23(8), pages 717-728, December.
    4. Lelys Bravo Guenni & Susan J. Simmons & R. Webster West & Walter W. Piegorsch & Edsel A. Peña & Lingling An & Wensong Wu & Alissa A. Wickens & Hui Xiong & Wenhai Chen, 2012. "The impact of model uncertainty on benchmark dose estimation," Environmetrics, John Wiley & Sons, Ltd., vol. 23(8), pages 706-716, December.
    5. Christel Faes & Marc Aerts & Helena Geys & Geert Molenberghs, 2007. "Model Averaging Using Fractional Polynomials to Estimate a Safe Level of Exposure," Risk Analysis, John Wiley & Sons, vol. 27(1), pages 111-123, February.
    6. Morales, Knashawn H. & Ibrahim, Joseph G. & Chen, Chien-Jen & Ryan, Louise M., 2006. "Bayesian Model Averaging With Applications to Benchmark Dose Estimation for Arsenic in Drinking Water," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 9-17, March.
    7. Claeskens,Gerda & Hjort,Nils Lid, 2008. "Model Selection and Model Averaging," Cambridge Books, Cambridge University Press, number 9780521852258, October.
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    Cited by:

    1. Signe M. Jensen & Felix M. Kluxen & Christian Ritz, 2019. "A Review of Recent Advances in Benchmark Dose Methodology," Risk Analysis, John Wiley & Sons, vol. 39(10), pages 2295-2315, October.
    2. Maria A. Sans‐Fuentes & Walter W. Piegorsch, 2021. "Benchmark dose risk analysis with mixed‐factor quantal data in environmental risk assessment," Environmetrics, John Wiley & Sons, Ltd., vol. 32(5), August.

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