How to use statistics to claim antagonism and synergism from binary mixture experiments.

We review statistical approaches applicable for the analysis of data from binary mixture experiments, which are commonly used in pesticide science for evaluating antagonistic or synergistic effects. Specifically, two different situations are reviewed, one where every pesticide is only available at a single dose level and a mixture simply combines these doses, and one where the pesticides and their mixture are used at increasing doses. The former corresponds to using factorial designs whereas the latter corresponds to fixed-ratio designs. We consider dose addition and independent action as references for lack of antagonistic and synergistic effects. Data from factorial designs should be analyzed using two-way analysis of variance models whereas data from fixed-ratio designs should be analyzed using non-linear dose-response analysis. In most cases, independent action seems the more natural choice for factorial designs. In contrast, dose addition is more appropriate for fixed-ratio designs although dose addition is not equally compatible with all types of dose-response data. Fixed-ratio designs should be preferred as they allow validation of the assumed dose-response relationship and, consequently, provide much stronger claims about antagonistic and synergistic effects than factorial designs. Finally, it should be noted that, in any case, simple ways of summarizing pesticide mixture effects may come at the price of more or less restrictive modeling assumptions.