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Monotonic Bayesian Semiparametric Benchmark Dose Analysis

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  • Matthew Wheeler
  • A. John Bailer

Abstract

Quantitative risk assessment proceeds by first estimating a dose‐response model and then inverting this model to estimate the dose that corresponds to some prespecified level of response. The parametric form of the dose‐response model often plays a large role in determining this dose. Consequently, the choice of the proper model is a major source of uncertainty when estimating such endpoints. While methods exist that attempt to incorporate the uncertainty by forming an estimate based upon all models considered, such methods may fail when the true model is on the edge of the space of models considered and cannot be formed from a weighted sum of constituent models. We propose a semiparametric model for dose‐response data as well as deriving a dose estimate associated with a particular response. In this model formulation, the only restriction on the model form is that it is monotonic. We use this model to estimate the dose‐response curve from a long‐term cancer bioassay, as well as compare this to methods currently used to account for model uncertainty. A small simulation study is conducted showing that the method is superior to model averaging when estimating exposure that arises from a quantal‐linear dose‐response mechanism, and is similar to these methods when investigating nonlinear dose‐response patterns.

Suggested Citation

  • Matthew Wheeler & A. John Bailer, 2012. "Monotonic Bayesian Semiparametric Benchmark Dose Analysis," Risk Analysis, John Wiley & Sons, vol. 32(7), pages 1207-1218, July.
  • Handle: RePEc:wly:riskan:v:32:y:2012:i:7:p:1207-1218
    DOI: 10.1111/j.1539-6924.2011.01786.x
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    References listed on IDEAS

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    1. Brezger, Andreas & Steiner, Winfried J., 2008. "Monotonic Regression Based on Bayesian PSplines: An Application to Estimating Price Response Functions From Store-Level Scanner Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 90-104, January.
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    4. 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.
    5. Wheeler, Matthew W. & Bailer, A. John, 2008. "Model Averaging Software for Dichotomous Dose Response Risk Estimation," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 26(i05).
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    Cited by:

    1. 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.
    2. 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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