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. 1998 Dec;106(Suppl 6):1367–1371. doi: 10.1289/ehp.98106s61367

A nonlinear isobologram model with Box-Cox transformation to both sides for chemical mixtures.

D G Chen 1, J G Pounds 1
PMCID: PMC1533464  PMID: 9860894

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, 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.

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Selected References

These references are in PubMed. This may not be the complete list of references from this article.

  1. Barton C. N., Braunberg R. C., Friedman L. Nonlinear statistical models for the joint action of toxins. Biometrics. 1993 Mar;49(1):95–105. [PubMed] [Google Scholar]
  2. Berenbaum M. C. Criteria for analyzing interactions between biologically active agents. Adv Cancer Res. 1981;35:269–335. doi: 10.1016/s0065-230x(08)60912-4. [DOI] [PubMed] [Google Scholar]
  3. Berenbaum M. C. Synergy, additivism and antagonism in immunosuppression. A critical review. Clin Exp Immunol. 1977 Apr;28(1):1–18. [PMC free article] [PubMed] [Google Scholar]
  4. Berenbaum M. C. What is synergy? Pharmacol Rev. 1989 Jun;41(2):93–141. [PubMed] [Google Scholar]
  5. Jackson T. E. Comparison of a class of regression equations. Am J Physiol. 1984 Mar;246(3 Pt 2):R271–R276. doi: 10.1152/ajpregu.1984.246.3.R271. [DOI] [PubMed] [Google Scholar]
  6. Kaiser J. Synergy paper questioned at toxicology meeting. Science. 1997 Mar 28;275(5308):1879–1879. doi: 10.1126/science.275.5308.1879. [DOI] [PubMed] [Google Scholar]
  7. Mauderly J. L. Toxicological approaches to complex mixtures. Environ Health Perspect. 1993 Dec;101 (Suppl 4):155–165. doi: 10.1289/ehp.93101s4155. [DOI] [PMC free article] [PubMed] [Google Scholar]
  8. Ramamoorthy K., Wang F., Chen I. C., Safe S., Norris J. D., McDonnell D. P., Gaido K. W., Bocchinfuso W. P., Korach K. S. Potency of combined estrogenic pesticides. Science. 1997 Jan 17;275(5298):405–406. doi: 10.1126/science.275.5298.405. [DOI] [PubMed] [Google Scholar]
  9. Sexton K., Beck B. D., Bingham E., Brain J. D., DeMarini D. M., Hertzberg R. C., O'Flaherty E. J., Pounds J. G. Chemical mixtures from a public health perspective: the importance of research for informed decision making. Toxicology. 1995 Dec 28;105(2-3):429–441. doi: 10.1016/0300-483x(95)03240-g. [DOI] [PubMed] [Google Scholar]

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