### Abstract

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 language | English (US) |
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Pages (from-to) | 717-728 |

Number of pages | 12 |

Journal | Environmetrics |

Volume | 23 |

Issue number | 8 |

DOIs | |

State | Published - Dec 1 2012 |

### Keywords

- 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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## Cite this

*Environmetrics*,

*23*(8), 717-728. https://doi.org/10.1002/env.2175