New Statistical Learning Methods for Estimating Optimal Dynamic Treatment Regimes

Abstract

Dynamic treatment regimes (DTRs) are sequential decision rules for individual patients that can adapt over time to an evolving illness. The goal is to accommodate heterogeneity among patients and find the DTR which will produce the best long-term outcome if implemented. We introduce two new statistical learning methods for estimating the optimal DTR, termed backward outcome weighted learning (BOWL), and simultaneous outcome weighted learning (SOWL). These approaches convert individualized treatment selection into an either sequential or simultaneous classification problem, and can thus be applied by modifying existing machine learning techniques. The proposed methods are based on directly maximizing over all DTRs a nonparametric estimator of the expected long-term outcome; this is fundamentally different than regression-based methods, for example, Q-learning, which indirectly attempt such maximization and rely heavily on the correctness of postulated regression models.

 We prove that the resulting rules are consistent, and provide finite sample bounds for the errors using the estimated rules. Simulation results suggest the proposed methods produce superior DTRs compared with Q-learning especially in small samples. We illustrate the methods using data from a clinical trial for smoking cessation. Supplementary materials for this article are available online.

• Classification
• Personalized medicine
• Q-learning
• Reinforcement learning
• Risk bound
• Support vector machine

Additional information

Notes on contributors

Ying-Qi Zhao

Ying-Qi Zhao is Assistant Professor, Department of Biostatistics and Medical Informatics, University of Wisconsin-Madison, WI 53792 (E-mail: [email protected])

Donglin Zeng

Donglin Zeng is Professor, Department of Biostatistics, University of North Carolina at Chapel Hill, NC 27599 (E-mail: [email protected])

Eric B. Laber

Eric B. Laber is Assistant Professor, Department of Statistics, North Carolina State University, NC 27695 (E-mail: [email protected])

Michael R. Kosorok

Michael R. Kosorok is W. R. Kenan, Jr. Distinguished Professor and Chair, Department of Biostatistics, and Professor, Department of Statistics and Operations Research, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599 (E-mail: [email protected]).