Optimizing Two-Arm Clinical Trials for Personalized Medicine using Integer Programming and Heuristic Algorithms

Abstract

Subjects with complex diseases, such as malaria and leukemia, can have adverse reactions to the best-known treatments. The personalized medicine approach becomes beneficial because the subjects’ covariates are considered before a treatment assignment. Attractive statistical methods for personalized medicine determine the best treatment using the interaction between the treatments and the subject’s covariates. To estimate this interaction, we use a two-arm clinical trial in which one of two treatments is assigned to each subject in a pre-selected sample. In this article, we introduce a statistical criterion to evaluate two-arm clinical trials in terms of the interaction estimation for all potential subjects’ covariates, which can be quantitative or categorical. We develop theoretical results and two optimization algorithms to construct trials based on this criterion. Specifically, we introduce an integer programming algorithm that guarantees convergence to the optimal trial and a computationally efficient coordinate-exchange algorithm with a novel updating formula. Numerical experiments show the computational performance of our algorithms to construct two-arm trials for various simulated problems and an applied problem. Supplementary materials for this article are available online.