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Nonparametric benchmark analysis in risk assessment: a comparative study by simulation and data analysis

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Abstract

We consider the finite sample performance of a new nonparametric method for bioassay and benchmark analysis in risk assessment, which averages isotonic MLEs based on disjoint subgroups of dosages, and whose asymptotic behavior is essentially optimal (Bhattacharya and Lin, Stat Probab Lett 80:1947–1953, 2010). It is compared with three other methods, including the leading kernel-based method, called DNP, due to Dette et al. (J Am Stat Assoc 100:503–510, 2005) and Dette and Scheder (J Stat Comput Simul 80(5):527–544, 2010). In simulation studies, the present method, termed NAM, outperforms the DNP in the majority of cases considered, although both methods generally do well. In small samples, NAM and DNP both outperform the MLE.

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Acknowledgements

The authors are indebted to Professor P.K. Sen for his suggestions, and wish to thank the referee for helpful comments and for pointing out to us the use of the Robbins–Monroe approximation procedure for binary quantal response.

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Authors and Affiliations

  1. Department of Mathematics, The University of Arizona, Tucson, AZ, 85721, USA

    Rabi Bhattacharya & Lizhen Lin

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  1. Rabi Bhattacharya
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  2. Lizhen Lin
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Correspondence to Rabi Bhattacharya.

Additional information

Research supported by NIH grant R21-ES016791 and NSF grant DMS 0806011.

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Bhattacharya, R., Lin, L. Nonparametric benchmark analysis in risk assessment: a comparative study by simulation and data analysis. Sankhya B 73, 144–163 (2011). https://doi.org/10.1007/s13571-011-0019-7

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  • DOI: https://doi.org/10.1007/s13571-011-0019-7

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