Design and modeling for drug combination experiments with order effects

Combinations of drugs are now ubiquitous in treating complex diseases such as cancer and HIV due to their potential for enhanced efficacy and reduced side effects. The traditional combination experiments of drugs focus primarily on the dose effects of the constituent drugs. However, with the doses of drugs remaining unchanged, different sequences of drug administration may also affect the efficacy endpoint. Such drug effects shall be called as order effects. The common order-effect linear models are usually inadequate for analyzing combination experiments due to the nonlinear relationships and complex interactions among drugs. In this article, we propose a random field model for order-effect modeling. This model is flexible, allowing nonlinearities, and interaction effects to be incorporated with a small number of model parameters. Moreover, we propose a subtle experimental design that will collect good quality data for modeling the order effects of drugs with a reasonable run size. A real-data analysis and simulation studies are given to demonstrate that the proposed design and model are effective in predicting the optimal drug sequences in administration.