Multi-Armed Angle-Based Direct Learning for Estimating Optimal Individualized Treatment Rules With Various Outcomes

Estimating an optimal individualized treatment rule (ITR) based on patients’ information is an important problem in precision medicine. An optimal ITR is a decision function that optimizes patients’ expected clinical outcomes. Many existing methods in the literature are designed for binary treatment settings with the interest of a continuous outcome. Much less work has been done on estimating optimal ITRs in multiple treatment settings with good interpretations. In this article, we propose angle-based direct learning (AD-learning) to efficiently estimate optimal ITRs with multiple treatments. Our proposed method can be applied to various types of outcomes, such as continuous, survival, or binary outcomes. Moreover, it has an interesting geometric interpretation on the effect of different treatments for each individual patient, which can help doctors and patients make better decisions. Finite sample error bounds have been established to provide a theoretical guarantee for AD-learning. Finally, we demonstrate the superior performance of our method via an extensive simulation study and real data applications. Supplementary materials for this article are available online.