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An Extension of the Model Free Test to Test Synergy in Multiple Drug Combinations

Interactions in a combination of drugs or chemicals are important in therapeutics, toxicology, environmental studies, and normal and abnormal physiology. It is important to be able to decide whether the observed effect of a combination is additive, synergistic or antagonistic. The traditional statistical approaches to the assessment of interactions of n drugs involve estimation of the (n + 1) dimensional response surface, the response surface method (RSM), or the estimation of n 2‐dimensional dose‐response curves, the marginal dose‐response curve method (MDRCM). Laska et al. (1994) proposed a unique approach to assessing synergy in two‐drug combinations that avoids the estimation of any dose‐response curve: their Model‐Free Test (MFT). This method enables the use of simple designs with only three dosages for two drugs: the combination dose of interest and a marginal dosage of each drug. The choice of the marginal dosages depends on the potency ratio of the two drugs at response e, ρ(e). Since ρ(e) is usually unknown, an estimate, r, is used instead. Laska et al. (1994) conclude that the power of the MFT depends heavily on the accuracy of the estimate r. We extend Laska's MFT to assess synergy in three or more drug combinations, and examine the effects of r, different combination dosages and different dose‐response functions on the power of the MFT. Additionally the power of the MFT is compared to the more traditional method, MDRCM. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)