A statistical method for judging synergism: application to an endocrine disruptor animal experiment

This article proposes a statistical method for judging whether or not the combined action of chemicals is synergistic, being focused on the case in which two or more endocrine disruptors are made to act simultaneously. After defining synergism, the synergistic relation of two chemicals is formulated for a higher response than that expected under an exchangeable relation between them. Using this formulation as a basis, we then rationalize the triangular design for an animal experiment in which all dose settings are controlled within a triangle domain that prescribes the sum of doses of simultaneously applied chemicals less than a certain level. In addition, a statistical test is proposed for judging the synergism among chemicals used in animal experiments, i.e. the test evaluates the discrepancy between the observed mean response from simultaneous administration groups of chemicals and an estimated response under the null hypothesis of zero interaction based on data from single administration groups. Finally, test performance is examined using a simulation study and a case study-the rodent uterotrophic assay. The simulation study revealed that the test is not superior in power to the standard analysis of variance test based on a linear model with interaction term, yet robust in the sense that type I errors under variance heterogeneity were better controlled using Welch correction than the analysis of variance test. The application of the proposed statistical test to an animal experiment is considered acceptable based on results.