John Wiley & Sons, Ltd.

Criteria for deviation from predictions by the concentration addition model

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Loewe's additivity (concentration addition; CA) is a well‐known model for predicting the toxic effects of chemical mixtures under the additivity assumption of toxicity. However, from the perspective of chemical risk assessment/management, it is important to identify chemicals whose toxicities are additive when present concurrently, i.e., it should be established whether there are chemical mixtures to which the CA predictive model can be applied. The objective of this study was to develop criteria for judging test results that deviated from the predictions by the CA chemical mixture model. These criteria were based on the confidence interval (CI) of the CA model's prediction and on estimation of errors of the predicted concentration‐effect curves by toxicity tests after exposure to single chemicals. A log‐logit model with two parameters was assumed for the concentration‐effect curve of each individual chemical. These parameters were determined by the maximum‐likelihood method, and the criteria were defined using the variances and the covariance of the parameters. In addition, the criteria were applied to a toxicity test of a binary mixture of p‐n‐nonylphenol (p‐n‐NP) and p‐n‐octylphenol (p‐n‐OP) using the Japanese killifish, medaka (Oryzias latipes). Consequently, the CA model using CI was capable of predicting the test results at any level, and no reason for rejecting the CA was found. This article is protected by copyright. All rights reserved

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