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Experimental design and sample size determination for testing synergism in drug combination studies based on uniform measures.

Tan, M., Fang, H.B., Tian, G.L. and Houghton, P.J.

Statistics in Medicine, 22(13), 2091-2100 (2003).

In anticancer drug development, the combined use of two drugs is an important strategy to achieve greater therapeutic success. Often combination studies are performed in animal (mostly mice) models before clinical trials are conducted. These experiments on mice are costly, especially with combination studies. However, experimental designs and sample size derivations for the joint action of drugs are not currently available except for a few cases where strong model assumptions are made. For example, Abdelbasit and Plackett proposed an optimal design assuming that the dose-response relationship follows some specified linear models. Tallarida et al. derived a design by fixing the mixture ratio and used a t-test to detect the simple similar action. The issue is that in reality we usually do not have enough information on the joint action of the two compounds before experiment and to understand their joint action is exactly our study goal. In this paper, we first propose a novel non-parametric model that does not impose such strong assumptions on the joint action. We then propose an experimental design for the joint action using uniform measure in this non-parametric model. This design is optimal in the sense that it reduces the variability in modelling synergy while allocating the doses to minimize the number of experimental units and to extract maximum information on the joint action of the compounds. Based on this design, we propose a robust F-test to detect departures from the simple similar action of two compounds and a method to determine sample sizes that are economically feasible. We illustrate the method with a study of the joint action of two new anticancer agents: temozolomide and irinotecan.