Simple designs and model-free tests for synergy

Current statistical designs for studying whether two or more agents in combination act synergistically nearly always require the study of several doses of many dose ratios. The analysis is usually based on an assumed parametric model of the dose-response surface. In this paper, for both quantal and quantitative response variables, sufficient conditions are given for establishing synergy at a dose of the combination without the need to specify the model. This enables the use of simple designs with few doses even when there is sparse knowledge of the dose-response curves of the individual agents. The Min test, used for testing whether an identified treatment is best, may be used for testing synergy. Power issues are discussed.