title: Criteria for deviation from predictions by the concentration addition model.
abstract: Loewe's additivity (concentration addition) 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 and/or management, it is important to identify chemicals whose toxicities are additive when present concurrently, that is, it should be established whether there are chemical mixtures to which the concentration addition predictive model can be applied. The objective of the present study was to develop criteria for judging test results that deviated from the predictions by the concentration addition chemical mixture model. These criteria were based on the confidence interval of the concentration addition 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 2 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 and p-n-octylphenol using the Japanese killifish, medaka (Oryzias latipes). Consequently, the concentration addition model using confidence interval was capable of predicting the test results at any level, and no reason for rejecting the concentration addition was found. Environ Toxicol Chem 2016;35:1806-1814. © 2015 SETAC.
authors.affiliation: Research Institute of Science for Safety and Sustainability, National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba, Ibaraki, Japan.
authors.forename: Jun-Ichi
authors.initials: J
authors.lastname: Takeshita
authors.affiliation: Chemicals Evaluation and Research Institute, Japan (CERI), Kurume, Fukuoka, Japan.
authors.forename: Masanori
authors.initials: M
authors.lastname: Seki
authors.affiliation: Research Institute of Science for Safety and Sustainability, National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba, Ibaraki, Japan.
authors.forename: Masashi
authors.initials: M
authors.lastname: Kamo
mesh_terms: D000818:Animals; D016013:Likelihood Functions; D016015:Logistic Models; D008962:Models, Theoretical; D009010:Monte Carlo Method; D009990:Oryzias / Q000254:growth & development / Q000378:metabolism; D010636:Phenols / Q000633:toxicity; D018570:Risk Assessment; D023382:Toxicity Tests, Acute; D014874:Water Pollutants, Chemical / Q000737:chemistry / Q000633:toxicity
chemical_list: D010636:Phenols; D014874:Water Pollutants, Chemical; C025256:nonylphenol; C080417:4-octylphenol
keywords: Chemical mixture effect; Concentration addition model; Confidence interval; Deviation mixture models; Statistical method