Statistical Modeling and Analysis of Similar Compound Interaction in Scientific Research

In many practical scientific studies, two-way analysis of variance (ANOVA) and linear response surface methods are used for determining whether two or more similar compounds (substances, agents, or drugs) interact synergistically, antagonistically or independently. These models are often found lacking both in the means to assess interaction and with sufficient power. Using ten judiciously chosen illustrations (spanning fields as diverse as aquatic and environmental toxicology, botany, entomology, oncology, pharmacology, and virology), this paper introduces, explores, quantifies, illustrates, interprets, and extends several cutting-edge nonlinear assessment models and methods for measuring and describing interaction. Developed and used here are the Finney and Separate Ray models and extensions, a new cut line approach useful for so-called web designs, and extensions to more than two substances. As noted in the provided examples, the Finney model and extensions have the advantage of characterizing nonlinear interaction in a single measure, whereas the Separate Ray model extension is required when nonlinear interaction requires more than a single parameter for interaction assessment. The interaction results of the ten illustrations—of which antagonism is observed in four examples, synergy in five examples, and mixed results in one example—are summarized below. A discussion is also provided of efficient experimental design strategies as an aid to the practitioner and their future scientific studies.