An isobole-based statistical model and test for synergism/antagonism in binary mixture toxicity experiments

Abstract

Synergism and antagonism are often defined in relation to the model of Concentration Addition (CA). Hence, it is vital for the conclusion of mixture toxicity studies to be able to test whether an observed deviation from CA reflects a true deviation or whether it is simply due to random variation. In this paper we consider a non-linear regression model for the classical ray designs for binary mixture experiments. The model combines dose-response curves for each mixture in the experiment with an isobole model, describing possible deviations from CA. The method allows us to test whether the chosen isobole model is reasonable for the data and to test the hypothesis of CA. Furthermore, it provides us with a measure of the degree of synergism/antagonism. The method is flexible since both the dose-response relationships and the isobole model can be chosen arbitrarily. We demonstrate the use of the method on datasets where combinations of pesticides are tested on a floating plant, Lemna minor, and an algae, Pseudokirchneriella subcapitata. Furthermore, we conduct a simulation study in order to explore the power with which a specific deviation from CA can be distinguished in different test-systems.

Glyphosate-Resistant Kochia (Kochia scoparia) in Kansas: EPSPS Gene Copy Number in Relation to Resistance Levels

“…The dataset is analysed in Soerensen et al (2007). The concentration addition model can be entertained for this dataset.…”

An efficient methodology for quantification of synergy and antagonism in single electron transfer antioxidant assays

“…The importance of the assumptions of CA concerning both the degree of similarity of site of action and the similarity of slope has been debated since the introduction of the model (Cedergreen et al 2008;Hertzberg and MacDonell 2002;Jonker et al 2005;Sørensen et al 2007). The response to a mixed dose of two antioxidant agents (A 1 and A 2 ) in the absence of interactive effects (null interaction) can be postulated as the response of two fictitious "mixed" doses of the same agent, as described by (Murado and Prieto 2013a) as follows:…”

Mixture toxicity of three toxicants with similar and dissimilar modes of action to Daphnia magna

“…Mixture experiments were conducted following a fixed ratio design (Greco et al, 1995;Sørensen et al, 2007). The compounds were mixed in ratios corresponding to five effect ratios (0:100, 25:75, 50:50, 75:25 and 100:0%) for binary mixtures and a 33:33:33% effect ratio for the ternary mixture.…”

“…Concentration addition-and experimental EC 50 isoboles were fitted to all mixture toxicity data using the software package drc Sørensen et al (2007). This approach was chosen since it allows statistical comparison between the CA reference isobole and the isobole that fits the data best, and thus allows a determination of the deviation from CA.…”

“…A disadvantage with the standard isobole diagram described by Kortenkamp and Altenburger (1998) is that it is difficult to evaluate whether the isobole is statistically different from the additivity line. One way to overcome this problem is to apply an advanced isobole model to the data, which enables a statistical determination of whether the experimental isobole deviates from an additivity isobole (Sørensen et al, 2007). The model is based on Equation (1), in which the standard isobole equa-tion (Kortenkamp and Altenburger, 1998) is extended with an extra parameter (λ).…”