Sankhya B

, 73:144 | Cite as

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



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.


Monotone dose-response curve estimation Effective dosage Nonparametric method Pool-adjacent-violators algorithm Mean integrated squared error Confidence interval Bootstrap 


  1. Ayer, M., H.D. Brunk, G.M. Ewing, W.T. Reid, and E. Silverman. 1955. An empirical distribution function for sampling with incomplete information. Annals of Mathematical Statistics 26:641–647.MathSciNetMATHCrossRefGoogle Scholar
  2. Barlow, R.E., D.J. Bartholomew, J.M. Bremner, and H.D. Brunk. 1972. Statistical inference under order restrictions: The theory and application of isotonic regression. London: Wiley.MATHGoogle Scholar
  3. Bhattacharya, R., and M. Kong. 2007. Consistency and asymptotic normality of the estimated effective dose in bioassay. Journal of Statistical Planning and Inference 137:643–658.MathSciNetMATHCrossRefGoogle Scholar
  4. Bhattacharya, R., and L. Lin. 2010. An adaptive nonparametric method in benchmark analysis for bioassay and environmental studies. Statistics & Probability Letters 80:1947–1953.MathSciNetMATHCrossRefGoogle Scholar
  5. Bliss, C.I. 1935. The calculations of dose-mortality curve (with an appendix by Fisher, R.A.). Annals of Applied Biology 22:134–167 (Table IV).CrossRefGoogle Scholar
  6. Cran, G.W. 1980. AS149 amalgamation of means in the case of simple ordering. Applied Statistics 29(2):209–211.MATHCrossRefGoogle Scholar
  7. Dette, H., and R. Scheder. 2010. A finite sample comparison of nonparametric estimates of the effective dose in quantal bioassay. Journal of Statistical Computation and Simulation 80(5):527–544.MATHCrossRefGoogle Scholar
  8. Dette, H., N. Neumeyer, and K.F. Pliz. 2005. A note on nonparametric estimation of the effective dose in quantal bioassay. Journal of the American Statistical Association 100:503–510.MathSciNetMATHCrossRefGoogle Scholar
  9. Efron, B., and R.J. Tibshirani. 1993. An introduction to the bootstrap. London: Chapman & Hall.MATHGoogle Scholar
  10. Eubank, R.L. 1999. Nonparametric regression and spline smoothing (2nd ed.). New York: Marcel Dekker.MATHGoogle Scholar
  11. Györfi, L., M. Kohler, A. Krzyźak, and H. Walk. 2002. A distribution-free theory of nonparametric regression. New York: Springer.MATHCrossRefGoogle Scholar
  12. Hall, P.G. 1992. The bootstrap and Edgeworth expansion. New York: Springer.Google Scholar
  13. Joseph, V.R. 2004. Efficient Robbins–Monro procedure for binary data. Biometrika 91:461–470.MathSciNetMATHCrossRefGoogle Scholar
  14. Lee, E.T. 1974. A computer program for linear logistic regression analysis. Computer Programs in Biomedicine 4:80–92.CrossRefGoogle Scholar
  15. Martin, J.T. 1942. The problem of the evaluation of rotenone-containing plants. VI. The toxicity of l-elliptone and of poisons applied jointly, with further observations on the rotenone equivalent method of assessing the toxicity of derris root. Annals of Applied Biology 30:293–300.CrossRefGoogle Scholar
  16. Morgan, B.J.T. 1992. Analysis of quantal response data. Monographs on statistics and applied probability (vol. 46). Chapman and Hall/CRC.Google Scholar
  17. Müller, H.G., and T. Schmitt. 1988. Kernel and probit estimation in quantal bioassay. Journal of the American Statisttical Association 83(403):750–759.MATHCrossRefGoogle Scholar
  18. Nitcheva, D.K., W.W. Piegorsch, and R.W. West. 2007. On use of the multistage dose-response model for assessing laboratory animal carcinogenicity. Regulatory Toxicology and Pharmacology 48:135–147.CrossRefGoogle Scholar
  19. Park, D., and S. Park. 2006. Parametric and nonparametric estimators of ED 100α. Journal of Statistical Computation and Simulation 76(8):661–672.MathSciNetMATHCrossRefGoogle Scholar
  20. Piegorsch, W.W., and A.J. Bailer. 2005. Analyzing environmental data. New York: Wiley.CrossRefGoogle Scholar
  21. Rice, J. 1984. Bandwidth choice for nonparametric regression. Annals of Statistics 12:1215–1230.MathSciNetMATHCrossRefGoogle Scholar
  22. Robbins, H., and S. Monroe. 1951. A stochastic approximation method. Annals of Mathematical Statistics 22(3):400–407.MathSciNetMATHCrossRefGoogle Scholar
  23. USEPA. 1997. Exposure factors handbook (Final report). U.S. Environmental Protection Agency, Washington, DC, EPA/600/P-95/002F a-c.Google Scholar
  24. Wetherill, G.B., and K.D. Glazebrook. 1986. Sequential methods in statistics. Monographs on statistics and applied probability. London: Chapman and Hall.Google Scholar

Copyright information

© Indian Statistical Institute 2011

Authors and Affiliations

  1. 1.Department of MathematicsThe University of ArizonaTucsonUSA

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