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An adaptive nonparametric method in benchmark analysis for bioassay and environmental studies

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  • Bhattacharya, Rabi
  • Lin, Lizhen

Abstract

We present a novel nonparametric method for bioassay and benchmark analysis in risk assessment, which averages isotonic MLEs based on disjoint subgroups of dosages. The asymptotic theory for the methodology is derived, showing that the MISEs (mean integrated squared error) of the estimates of both the dose-response curve F and its inverse F-1 achieve the optimal rate O(N-4/5). Also, we compute the asymptotic distribution of the estimate of the effective dosage [zeta]p=F-1(p) which is shown to have an optimally small asymptotic variance.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:23-24:p:1947-1953
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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.
    2. G. W. Cran, 1980. "Amalgamation of Means in the Case of Simple Ordering," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 29(2), pages 209-211, June.
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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. 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.
    3. Bhattacharya, Rabi & Lin, Lizhen, 2013. "Recent progress in the nonparametric estimation of monotone curves—With applications to bioassay and environmental risk assessment," Computational Statistics & Data Analysis, Elsevier, vol. 63(C), pages 63-80.
    4. 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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