In studies of the effects of multiple drug or chemical combinations, one goal may be to detect and characterize the interactions between the agents. The techniques currently applied to this problem have limitations when the experiments involve more than 2 agents. Certain response-surface techniques require an unrealistic number of observations for studies involving a large number of agents. Current graphical methods are impossible to use in studies of 3 or more agents. In this research two statistical techniques are described that can be applied to studies with an unlimited number of agents. In the first approach, dose combinations are collected along rays or at fixed ratios. Using properties of this experimental design, an additive model is derived. Comparing the fitted dose-response curve along each ray to the curve predicted under additivity, synergistic and antagonistic interactions between the agents can be detected. Statistical testing procedures are given to determine if these are significant interactions, not due to random fluctuations in the data. Graphical techniques that enhance the interpretation of the results are described. The second approach developed in this research is a point-wise test which determines if the agents interact in an nonadditive manner. This test can be applied to each dose combination of interest. After applying a multiple comparison adjustment to the resulting p-values, departures from additivity can then be characterized. These approaches are likely to be more economical than current techniques, implying that a larger number of agents can be studied in combination for the same experimental effort.
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