Preclinical experiment on multi-drug combination has an increasingly important role in (especially cancer) drug development because of the need to reduce development time and costs. Despite of recent progresses in statistical methods for assessing drug interaction, there is a lack of general method for experimental design for such studies. We propose a general method for determining the doses comprising the combinations and the sample sizes to detect departures from additivity especially in the

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... case of more than two drugs in a semi-parametric statistical model. We utilize the uniform scattered points in the experimental domain to determine the doses comprising the combinations and calculate the sample size so that the power to detect departure from additivity is maximized. To our surprise, such an extension to multi-drug is far more difficult than what it appears when there are three or more drugs involved. Using the general methodology, we derive the combinations and sample size specifically for a common class of drugs to derive the experimental design. In addition, we illustrate the method with the SAHA and Ara-C and Etoposide combination studies.