Mixture effects of chemicals: The difficulty to choose appropriate mathematical models for appropriate conclusions

Many different approaches have been proposed to evaluate and predict mixture effects. From a regulatory perspective, several guidance documents have been recently published and provide a strategy for mixture risk assessment based on valuable frameworks to investigate potential synergistic effects. However, some methodological aspects, e.g. for considering mathematical models, are not sufficiently defined. Therefore, the aim of this study was to examine the usefulness of five main mathematical models for mixture effect interpretation: theoretical additivity (TA), concentration addition (CA), independent action (IA), Chou-Talalay (CT), and a benchmark dose approach (BMD) were tested using a fictional data set depicting scenarios of additivity, synergism and antagonism. The synergism and antagonism scenarios were split in x-axis and y-axis synergism/antagonism, meaning a shift of the curve on x-axis or y-axis. The BMD approach was the only model which showed a perfect correspondence for dose addition. Regarding synergism and antagonism, all approaches correspond well for the x-axis synergism and antagonism with only few exceptions. In contrast, some limitations were observed in the particular scenarios of y-axis synergism and antagonism. Therefore our results show that each model has advantages and disadvantages, and that therefore no single model appears the best one for all kinds of application. We would recommend instead the parallel use of different models to increase confidence in the result of mixture effect evaluation.