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Properties of Model‐Averaged BMDLs: A Study of Model Averaging in Dichotomous Response Risk Estimation

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  • Matthew W. Wheeler
  • A. John Bailer

Abstract

Model averaging (MA) has been proposed as a method of accounting for model uncertainty in benchmark dose (BMD) estimation. The technique has been used to average BMD dose estimates derived from dichotomous dose‐response experiments, microbial dose‐response experiments, as well as observational epidemiological studies. While MA is a promising tool for the risk assessor, a previous study suggested that the simple strategy of averaging individual models' BMD lower limits did not yield interval estimators that met nominal coverage levels in certain situations, and this performance was very sensitive to the underlying model space chosen. We present a different, more computationally intensive, approach in which the BMD is estimated using the average dose‐response model and the corresponding benchmark dose lower bound (BMDL) is computed by bootstrapping. This method is illustrated with TiO2 dose‐response rat lung cancer data, and then systematically studied through an extensive Monte Carlo simulation. The results of this study suggest that the MA‐BMD, estimated using this technique, performs better, in terms of bias and coverage, than the previous MA methodology. Further, the MA‐BMDL achieves nominal coverage in most cases, and is superior to picking the “best fitting model” when estimating the benchmark dose. Although these results show utility of MA for benchmark dose risk estimation, they continue to highlight the importance of choosing an adequate model space as well as proper model fit diagnostics.

Suggested Citation

  • Matthew W. Wheeler & A. John Bailer, 2007. "Properties of Model‐Averaged BMDLs: A Study of Model Averaging in Dichotomous Response Risk Estimation," Risk Analysis, John Wiley & Sons, vol. 27(3), pages 659-670, June.
    • Handle: RePEc:wly:riskan:v:27:y:2007:i:3:p:659-670
    DOI: 10.1111/j.1539-6924.2007.00920.x
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Hojin Moon & Hyun‐Joo Kim & James J. Chen & Ralph L. Kodell, 2005. "Model Averaging Using the Kullback Information Criterion in Estimating Effective Doses for Microbial Infection and Illness," Risk Analysis, John Wiley & Sons, vol. 25(5), pages 1147-1159, October.
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    1. Fereshteh Kalantari & Joakim Ringblom & Salomon Sand & Mattias Öberg, 2017. "Influence of Distribution of Animals between Dose Groups on Estimated Benchmark Dose and Animal Distress for Quantal Responses," Risk Analysis, John Wiley & Sons, vol. 37(9), pages 1716-1728, September.
    2. 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.
    3. 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.
    4. Steven B. Kim & Ralph L. Kodell & Hojin Moon, 2014. "A Diversity Index for Model Space Selection in the Estimation of Benchmark and Infectious Doses via Model Averaging," Risk Analysis, John Wiley & Sons, vol. 34(3), pages 453-464, March.
    5. Harriet Namata & Marc Aerts & Christel Faes & Peter Teunis, 2008. "Model Averaging in Microbial Risk Assessment Using Fractional Polynomials," Risk Analysis, John Wiley & Sons, vol. 28(4), pages 891-905, August.
    6. Nilabja Guha & Anindya Roy & Leonid Kopylev & John Fox & Maria Spassova & Paul White, 2013. "Nonparametric Bayesian Methods for Benchmark Dose Estimation," Risk Analysis, John Wiley & Sons, vol. 33(9), pages 1608-1619, September.
    7. 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.

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