title: Nonparametric estimation of benchmark doses in environmental risk assessment.
abstract: An important statistical objective in environmental risk analysis is estimation of minimum exposure levels, called benchmark doses (BMDs), that 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 benchmark doses, based on an isotonic regression method for dose-response estimation with quantal-response data (Bhattacharya and Kong, 2007). 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.
authors.affiliation: Program in Statistics, University of Arizona, Tucson, AZ, 85721 USA ; Department of Mathematics, University of Arizona, Tucson, AZ, 85721 USA.
authors.forename: Walter W
authors.initials: WW
authors.lastname: Piegorsch
authors.forename: Hui
authors.initials: H
authors.lastname: Xiong
authors.forename: Rabi N
authors.initials: RN
authors.lastname: Bhattacharya
authors.forename: Lizhen
authors.initials: L
authors.lastname: Lin
keywords: Benchmark analysis; bootstrap confidence limits; dose-response analysis; isotonic regression; pool-adjacent-violators algorithm
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