Piegorsch Walter W, Xiong Hui, Bhattacharya Rabi N, Lin Lizhen
Program in Statistics, University of Arizona, Tucson, AZ, 85721 USA ; Department of Mathematics, University of Arizona, Tucson, AZ, 85721 USA.
Environmetrics. 2012 Dec 1;23(8):717-728. doi: 10.1002/env.2175.
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.
环境风险分析中的一个重要统计目标是估计最低暴露水平，即所谓的基准剂量（BMDs），它在剂量反应实验中引发预先指定的基准反应。在这种情况下，风险的表示传统上基于参数剂量反应模型。然而，一个众所周知的问题是，如果所选的参数形式指定错误，可能会导致不准确且可能不安全的低剂量推断。我们应用一种非参数方法来计算基准剂量，该方法基于用于定量反应数据的剂量反应估计的等渗回归方法（Bhattacharya和Kong，2007年）。我们确定估计量的大样本性质，开发基于自助法的BMDs置信限，并通过简短的模拟研究探索置信限的小样本性质。癌症风险评估的一个例子说明了这些计算。
