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Environ Toxicol Chem. 2017 Jan;36(1):265-275. doi: 10.1002/etc.3503. Epub 2016 Jul 26.

Generalized concentration addition approach for predicting mixture toxicity.

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Center for Health and Environmental Risk Research, National Institute for Environmental Studies, Tsukuba, Ibaraki, Japan.
Sophia University, Graduate School of Global Environmental Studies, Chiyoda, Tokyo, Japan.


A new mathematical model for analyzing data and predicting the effect of mixtures of toxic substances is presented as a generalized form of the concentration addition model. The proposed method, the generalized concentration addition (GCA) model, can be applied to mixtures with arbitrary strengths of interactions (synergistic or antagonistic). It requires mixture effect data for least 1 exposure concentration of the mixture in which fractions of all components and concentration-response functions for each component are known. The GCA model evaluates the interaction between components by introducing a novel response function, which is independent of the response functions for each individual components, to describe the effect of addition between different components. The GCA method was applied to published mixture toxicity data, and it was found to fit the mixture effect better than both the concentration addition model and the independent action model, the implication being that the proposed approach is widely applicable. Environ Toxicol Chem 2017;36:265-275.


Compound effect; Concentration addition; Mixture effect; Mixture model; Mixture toxicology

[Indexed for MEDLINE]

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