Dose and Sample Size Determination for Multi-Drug Combination Studies

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 recent progress in statistical methods for assessing drug interaction, there is a lack of general methods for determining the doses comprising the combinations and the sample sizes to detect departures from additivity, especially in the case of more than two drugs. We propose a general method for dose and sample size determination for detecting departures from additivity of multiple drugs based on a semiparametric statistical model applicable to both in vivo and in vitro experiments. We show that selecting doses that comprise the combinations uniformly scattered in the experimental domain maximizes the minimum power of the F-test for detecting departures from additivity. In addition, the method applies to drugs whose relative potency is not constant. With both analytic proof and a simulation, we show the proposed design has optimal properties that are not shared by the classic designs such as the fixed ratio (ray) and the checkerboard designs. Furthermore, we show the method is dependent upon the shape of the single drug dose-response curve; therefore, different classes of drugs have to be dealt with separately. To our surprise, such an extension to multi-drug case with three or more drugs is far more difficult than it appears. Using the general methodology, we derive the dose selection and sample size specifically for a common class of drugs to derive the experimental design. We illustrate the method with the SAHA and Ara-C and Etoposide combination study.