A review of independent action compared to concentration addition as reference models for mixtures of compounds with different molecular target sites

Abstract

From a theoretical point of view, it has often been argued that the model of independent action (IA) is the most correct reference model to use for predicting the joint effect of mixtures of chemicals with different molecular target sites. The theory of IA, however, relies on a number of assumptions that are rarely fulfilled in practice. It has even been argued that, theoretically, the concentration addition (CA) model could be just as correct. In the present study, we tested the accuracy of both IA and CA in describing binary dose-response surfaces of chemicals with different molecular targets using statistical software. We compared the two models to determine which best describes data for 158 data sets. The data sets represented 98 different mixtures of, primarily, pesticides and pharmaceuticals tested on one or several of seven test systems containing one of the following: Vibrio fischeri, activated sludge microorganisms, Daphnia magna, Pseudokirchneriella subcapitata, Lemna minor, Tripleurospermum inodorum, or Stellaria media. The analyses showed that approximately 20% of the mixtures were adequately predicted only by IA, 10% were adequately predicted only by CA, and both models could predict the outcome of another 20% of the experiment. Half of the experiments could not be correctly described with either of the two models. When quantifying the maximal difference between modeled synergy or antagonism and the reference model predictions at a 50% effect concentration, neither of the models proved significantly better than the other. Thus, neither model can be selected over the other on the basis of accuracy alone.