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

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.