Chen D G, Pounds J G
Pacific Biological Station, Department of Fisheries and Oceans, Nanaimo, British Columbia, Canada.
Environ Health Perspect. 1998 Dec;106 Suppl 6(Suppl 6):1367-71. doi: 10.1289/ehp.98106s61367.
The linear logistical isobologram is a commonly used and powerful graphical and statistical tool for analyzing the combined effects of simple chemical mixtures. In this paper a nonlinear isobologram model is proposed to analyze the joint action of chemical mixtures for quantitative dose-response relationships. This nonlinear isobologram model incorporates two additional new parameters, Ymin and Ymax, to facilitate analysis of response data that are not constrained between 0 and 1, where parameters Ymin and Ymax represent the minimal and the maximal observed toxic response. This nonlinear isobologram model for binary mixtures can be expressed as [formula: see text] In addition, a Box-Cox transformation to both sides is introduced to improve the goodness of fit and to provide a more robust model for achieving homogeneity and normality of the residuals. Finally, a confidence band is proposed for selected isobols, e.g., the median effective dose, to facilitate graphical and statistical analysis of the isobologram. The versatility of this approach is demonstrated using published data describing the toxicity of the binary mixtures of citrinin and ochratoxin as well as a new experimental data from our laboratory for mixtures of mercury and cadmium.
线性对数等效线图是一种常用且强大的图形和统计工具，用于分析简单化学混合物的联合效应。本文提出了一种非线性等效线图模型，用于分析化学混合物的联合作用以建立定量剂量-反应关系。该非线性等效线图模型纳入了另外两个新参数Ymin和Ymax，以方便分析不受0到1之间限制的反应数据，其中参数Ymin和Ymax分别代表观察到的最小和最大毒性反应。二元混合物的这种非线性等效线图模型可表示为[公式：见原文]。此外，对两边进行Box-Cox变换以提高拟合优度，并提供一个更稳健的模型来实现残差的同质性和正态性。最后，为选定的等效线（例如半数有效剂量）提出了一个置信带，以方便对等效线图进行图形和统计分析。使用已发表的描述桔青霉素和赭曲霉毒素二元混合物毒性的数据以及我们实验室关于汞和镉混合物的新实验数据，证明了该方法的通用性。
