Van Ryzin J, Rai K
Biometrics. 1987 Mar;43(1):95-105.
This paper introduces a dose-response model for toxic quantal response data based on hit theory applied to the dose unit as transformed by a nonlinear kinetic equation. When spontaneous background response is included in the model, the resulting dose-response model has four parameters. The maximum likelihood estimators and their large-sample properties are given. Likelihood ratio tests of interest are developed, including one for whether the model is one-hit in the transformed dose and one to check whether nonlinear kinetics is operative. The use of the model for low-dose extrapolation is presented. Finally, the procedures developed are illustrated on data from three animal carcinogenicity bioassays that show, respectively, concave, linear, and convex dose-response curves in the observed data.
本文基于命中理论，针对经非线性动力学方程变换后的剂量单位的毒性定量反应数据，介绍了一种剂量反应模型。当模型中包含自发背景反应时，所得的剂量反应模型有四个参数。给出了最大似然估计量及其大样本性质。开发了感兴趣的似然比检验，包括一个用于检验模型在变换剂量下是否为单命中的检验，以及一个用于检查非线性动力学是否起作用的检验。介绍了该模型在低剂量外推中的应用。最后，利用来自三项动物致癌性生物测定的数据对所开发的程序进行了说明，这些数据在观测数据中分别呈现出凹形、线性和凸形剂量反应曲线。
