Two-stage model-free tests of synergy in drug combinations

Laska et al. ( 1994 ) proposed a model-free method of detecting synergy in two drug combinations that requires no assumptions about the underlying dose-response curves of the drugs, just an estimate of the potency ratio of the two drugs. It was noted that the power of this method is highly dependent on the accuracy of the potency ratio estimated, with low power when the estimate is inaccurate. Additionally, the test used to detect synergy (the Min test) has been shown to be conservative in many practical applications, and non-monotonic alternative tests that have greater power have been proposed. We suggest a two-stage, non-monotonic alternative to the Laska et al. model-free test that is less dependent on the accuracy of potency ratio estimate and has greater power in many situations. We illustrate the method with an example of two chemotherapeutic agents.