Learning Individualized Treatment Rules with Many Treatments: A Supervised Clustering Approach Using Adaptive Fusion

Learning an optimal Individualized Treatment Rule (ITR) is a very important problem in precision medicine. This paper is concerned with the challenge when the number of treatment arms is large, and some groups of treatments in the large treatment space may work similarly for the patients. Motivated by the recent development of supervised clustering, we propose a novel adaptive fusion based method to cluster the treatments with similar treatment effects together and estimate the optimal ITR simultaneously through a single convex optimization. The problem is formulated as balancing \textit{loss}$+$\textit{penalty} terms with a tuning parameter, which allows the entire solution path of the treatment clustering process to be clearly visualized hierarchically. For computation, we propose an efficient algorithm based on accelerated proximal gradient and further conduct a novel group-lasso based algorithm for variable selection to boost the performance. Moreover, we demonstrate the theoretical guarantee of recovering the underlying true clustering structure of the treatments for our method. Finally, we demonstrate the superior performance of our method via both simulations and a real data application on cancer treatment, which may assist the decision making process for doctors.