Multi-drug combination designs with experiments in silico

It has become evident to medical and statistical scientists treating complex diseases that satisfactory efficacy is more likely to be achieved by using combinations of drugs. Experimental design for drug combination in pre-clinical studies is an important stage to move new combination therapies rapidly into clinical trials. The existing design methods for pre-clinical studies are primarily applied to combination experiments with two or three combined drugs. However, as the research of systems biology advancing it is becoming more desire to consider combinations with multiple drugs. In this paper, we propose efficient experimental designs for multi-drug combination studies. The aim of the proposed design is to establish a good quality and high dimensional dose-response model which provides a basis for future developments on statistical analysis for complex multi-drug dose-finding problems. By borrowing the strength of experiments in silico, it turns out that the uniform design measure is the optimal design with respect to model prediction accuracy. Methods for sample size determination and how to construct uniform designs are given. Since the proposed uniform designs are constructed in regular dose regions, they are convenient to be applied to multi-drug combination experiments. The usefulness of the proposed design is illustrated by simulations and an application with multiple combined drugs.