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Ding G. Chen¹ and Joel G. Pounds²

¹Pacific Biological Station, Department of Fisheries and Oceans, Nanaimo, British Columbia, Canada;
²Institute of Chemical Toxicology, Wayne State University, Detroit, Michigan

Abstract

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, y_min and y_max, to facilitate analysis of response data that are not constrained between 0 and 1, where parameters y_min and y_max represent the minimal and the maximal observed toxic response. This nonlinear isobologram model for binary mixtures can be expressed as:

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. -- Environ Health Perspect 106(Suppl 6) :1367-1371 (1998) .

http://ehpnet1.niehs.nih.gov/docs/1998/Suppl-6/1367-1371chen/abstract.html

Key words: chemical mixtures, dose-response modeling, maximum likelihood estimation, risk assessment, toxicology