The statistics of synergism.

Biological scientists often want to determine whether two agents or events, for example, extracellular stimuli and/or intracellular signaling pathways, act synergistically when eliciting a biological response. When setting out to study whether two experimental treatments act synergistically, most biologists design the correct experiment--they administer four treatment combinations consisting of (1) the first treatment alone, (2) the second treatment alone, (3) both treatments together, and (4) neither treatment (i.e. the control). Many biologists are less clear about the correct statistical approach to determining whether the data collected in such an experimental design support a conclusion regarding synergism, or lack thereof. The non-additivity of two experimental treatments that is central to the definition of synergism leads to an algebraic formulation corresponding to the statistical null hypothesis appropriate for testing whether or not there is synergism. The resulting complex contrast among the four treatment group means is identical to the interaction effect tested in a two-way analysis of variance (ANOVA). This should not be surprising, because synergism, by definition, occurs when two treatments interact, rather than act independently, to influence a biological response. Hence, in the most readily implemented approach, the correct statistical analysis of a question of synergism is based on testing the interaction effect in a two-way ANOVA. This review presents the rationale for this correct approach to analysing data when the question is of synergism, and applies this approach to a recent published example. In addition, a common incorrect approach to analysing data with regards to synergism is presented. Finally, several associated statistical issues with regard to correctly implementing a two-way ANOVA are discussed.