Statistics and Its Interface

Volume 14 (2021)

Number 4

Multi-drug combination designs with experiments in silico

Pages: 373 – 388



Huang Hengzhen (College of Mathematics and Statistics, Guangxi Normal University, Guilin, China)


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.


computer experiments, dose-response surface, optimal design, prediction, uniform design

This work was completed at Georgetown University where the author was a post-doctoral research fellow. The author’s research was supported in part by the National Natural Science Foundation of China (Grant Nos. 11701109, 11801331 and 11861017) and Guangxi Nature Science Foundation (Grant Nos. 2018JJB110027 and 2018AD19235).

Received 9 February 2020

Accepted 13 December 2020

Published 8 July 2021