Nonparametric estimation of benchmark doses in environmental risk assessment

Walter W. Piegorsch, Hui Xiong, Rabi N. Bhattacharya, Lizhen Lin

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


An important statistical objective in environmental risk analysis is estimation of minimum exposure levels, called benchmark doses (BMDs), which induce a pre-specified benchmark response in a dose-response experiment. In such settings, representations of the risk are traditionally based on a parametric dose-response model. It is a well-known concern, however, that if the chosen parametric form is misspecified, inaccurate and possibly unsafe low-dose inferences can result. We apply a nonparametric approach for calculating BMDs, based on an isotonic dose-response estimator for quantal-response data. We determine the large-sample properties of the estimator, develop bootstrap-based confidence limits on the BMDs, and explore the confidence limits' small-sample properties via a short simulation study. An example from cancer risk assessment illustrates the calculations.

Original languageEnglish (US)
Pages (from-to)717-728
Number of pages12
Issue number8
StatePublished - Dec 2012


  • Benchmark analysis
  • Bootstrap confidence limits
  • Dose-response analysis
  • Isotonic regression
  • Pool-adjacent-violators algorithm

ASJC Scopus subject areas

  • Statistics and Probability
  • Ecological Modeling


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