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

Abstract

Subjects with complex and serious diseases, such as malaria and leukemia, can have adverse reactions to the best-known treatments. The personalized medicine approach becomes beneficial because the subjects’ characteristics or 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 demonstrate the computational performance of our algorithms to construct two-arm clinical trials for various problems. As an application, we show that our algorithms can redesign a two-arm Scleroderma clinical trial with a smaller variance of the interaction estimate than the implemented trial for a test set of subjects.

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Alan Roberto Vazquez
Research Professor

Data scientist working on the development of cost-effective experimental plans using modern optimization techniques