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Nonparametric Benchmark Dose Estimation with Continuous Dose-Response Data

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  • Lizhen Lin
  • Walter W. Piegorsch
  • Rabi Bhattacharya

Abstract

type="main" xml:id="sjos12132-abs-0001"> We propose a new method for risk-analytic benchmark dose (BMD) estimation in a dose-response setting when the responses are measured on a continuous scale. For each dose level d, the observation X(d) is assumed to follow a normal distribution: N ( μ ( d ) , σ 2 ) . No specific parametric form is imposed upon the mean μ(d), however. Instead, nonparametric maximum likelihood estimates of μ(d) and σ are obtained under a monotonicity constraint on μ(d). For purposes of quantitative risk assessment, a ‘hybrid’ form of risk function is defined for any dose d as R(d) = P[X(d) > c], where c > 0 is a constant independent of d. The BMD is then determined by inverting the additional risk functionR A (d) = R(d) − R(0) at some specified value of benchmark response. Asymptotic theory for the point estimators is derived, and a finite-sample study is conducted, using both real and simulated data. When a large number of doses are available, we propose an adaptive grouping method for estimating the BMD, which is shown to have optimal mean integrated squared error under appropriate designs.

Suggested Citation

  • Lizhen Lin & Walter W. Piegorsch & Rabi Bhattacharya, 2015. "Nonparametric Benchmark Dose Estimation with Continuous Dose-Response Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(3), pages 713-731, September.
    • Handle: RePEc:bla:scjsta:v:42:y:2015:i:3:p:713-731
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    File URL: http://hdl.handle.net/10.1111/sjos.12132
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    References listed on IDEAS

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    1. Dette, Holger & Neumeyer, Natalie & Pilz, Kay F., 2005. "A Note on Nonparametric Estimation of the Effective Dose in Quantal Bioassay," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 503-510, June.
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    6. Bhattacharya, Rabi & Lin, Lizhen, 2010. "An adaptive nonparametric method in benchmark analysis for bioassay and environmental studies," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1947-1953, December.
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    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.

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