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.

Designs for order-of-addition experiments.

The order-of-addition experiment aims at determining the optimal order of adding components such that the response of interest is optimized. Order of addition has been widely involved in many areas, including bio-chemistry, food science, nutritional science, pharmaceutical science, etc. However, such an important study is rather primitive in statistical literature. In this paper, a thorough study on pair-wise ordering designs for order of addition is provided. The recursive relation between two successive full pair-wise ordering designs is developed. Based on this recursive relation, the full pair-wise ordering design can be obtained without evaluating all the orders of components. The value of the D-efficiency for the full pair-wise ordering model is then derived. It provides a benchmark for choosing the fractional pair-wise ordering designs. To overcome the unaffordability of the full pair-wise ordering design, a new class of minimal-point pair-wise ordering designs is proposed. A job scheduling problem as well as simulation studies are conducted to illustrate the performance of the pair-wise ordering designs for determining the optimal orders. It is shown that the proposed designs are very efficient in determining the optimal order of addition.