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A Comparison of Three Methods for Calculating Confidence Intervals for the Benchmark Dose

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  • Mirjam Moerbeek
  • Aldert H. Piersma
  • Wout Slob

Abstract

Various methods exist to calculate confidence intervals for the benchmark dose in risk analysis. This study compares the performance of three such methods in fitting nonlinear dose‐response models: the delta method, the likelihood‐ratio method, and the bootstrap method. A data set from a developmental toxicity test with continuous, ordinal, and quantal dose‐response data is used for the comparison of these methods. Nonlinear dose‐response models, with various shapes, were fitted to these data. The results indicate that a few thousand runs are generally needed to get stable confidence limits when using the bootstrap method. Further, the bootstrap and the likelihood‐ratio method were found to give fairly similar results. The delta method, however, resulted in some cases in different (usually narrower) intervals, and appears unreliable for nonlinear dose‐response models. Since the bootstrap method is more time consuming than the likelihood‐ratio method, the latter is more attractive for routine dose‐response analysis. In the context of a probabilistic risk assessment the bootstrap method has the advantage that it directly links to Monte Carlo analysis.

Suggested Citation

  • Mirjam Moerbeek & Aldert H. Piersma & Wout Slob, 2004. "A Comparison of Three Methods for Calculating Confidence Intervals for the Benchmark Dose," Risk Analysis, John Wiley & Sons, vol. 24(1), pages 31-40, February.
    • Handle: RePEc:wly:riskan:v:24:y:2004:i:1:p:31-40
    DOI: 10.1111/j.0272-4332.2004.00409.x
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    1. Yiliang Zhu & Tao Wang & Jenny Z.H. Jelsovsky, 2007. "Bootstrap Estimation of Benchmark Doses and Confidence Limits with Clustered Quantal Data," Risk Analysis, John Wiley & Sons, vol. 27(2), pages 447-465, April.
    2. Hilko Van Der Voet & Wout Slob, 2007. "Integration of Probabilistic Exposure Assessment and Probabilistic Hazard Characterization," Risk Analysis, John Wiley & Sons, vol. 27(2), pages 351-371, April.
    3. Walter W. Piegorsch & Hui Xiong & Rabi N. Bhattacharya & Lizhen Lin, 2014. "Benchmark Dose Analysis via Nonparametric Regression Modeling," Risk Analysis, John Wiley & Sons, vol. 34(1), pages 135-151, January.
    4. Esben Budtz‐Jørgensen & David Bellinger & Bruce Lanphear & Philippe Grandjean & on behalf of the International Pooled Lead Study Investigators, 2013. "An International Pooled Analysis for Obtaining a Benchmark Dose for Environmental Lead Exposure in Children," Risk Analysis, John Wiley & Sons, vol. 33(3), pages 450-461, March.
    5. Alfred K. Mbah & Ibrahim Hamisu & Eknath Naik & Hamisu M. Salihu, 2014. "Estimating Benchmark Exposure for Air Particulate Matter Using Latent Class Models," Risk Analysis, John Wiley & Sons, vol. 34(11), pages 2053-2062, November.
    6. 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.
    7. Walter W. Piegorsch & R. Webster West, 2005. "Benchmark Analysis: Shopping with Proper Confidence," Risk Analysis, John Wiley & Sons, vol. 25(4), pages 913-920, August.
    8. Dette, Holger & Pepelyshev, Andrey & Shpilev, Piter & Wong, Weng Kee, 2009. "Optimal designs for estimating critical effective dose under model uncertainty in a dose response study," Technical Reports 2009,07, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    9. Dette, Holger & Pepelyshev, Andrey & Wong, Weng Kee, 2008. "Optimal designs for dose finding experiments in toxicity studies," Technical Reports 2008,09, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    10. Daniela K. Nitcheva & Walter W. Piegorsch & R. Webster West & Ralph L. Kodell, 2005. "Multiplicity-Adjusted Inferences in Risk Assessment: Benchmark Analysis with Quantal Response Data," Biometrics, The International Biometric Society, vol. 61(1), pages 277-286, March.
    11. Dette, Holger & Pepelyshev, Andrey & Shpilev, Piter & Wong, Weng Kee, 2009. "Optimal designs for estimating critical effective dose under model uncertainty in a dose response study," Technical Reports 2009,09, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    12. Walter W. Piegorsch, 2010. "Translational benchmark risk analysis," Journal of Risk Research, Taylor & Francis Journals, vol. 13(5), pages 653-667, July.
    13. 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.
    14. Gupta, Ramesh C. & Wang, Na, 2009. "Estimation of extra risk and benchmark dose in dose–response models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(7), pages 2036-2050.
    15. Xiaowei Ren & Jielai Xia, 2019. "An algorithm for computing profile likelihood based pointwise confidence intervals for nonlinear dose-response models," PLOS ONE, Public Library of Science, vol. 14(1), pages 1-10, January.

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