Estimating individualized treatment rules for treatments with hierarchical structure

Yiwei Fan ,Yufeng Liu,Haoda Fu,Junwei Zhao ,Xiaoling Lü

doi:10.1214/21-ejs1948

Abstract

Precision medicine is an increasingly important area of research. Due to the heterogeneity of individual characteristics, patients may respond differently to treatments. One of the most important goals for precision medicine is to develop individualized treatment rules (ITRs) involving patients’ characteristics directly. As an interesting topic in clinical research, many statistical methods have been developed in recent years to find optimal ITRs. For binary treatments, outcome weighted learning (OWL) was proposed to find a decision function of patient characteristics maximizing the expected clinical outcome. Treatments with hierarchical structure are commonly seen in practice. In hierarchical scenarios, how to estimate ITRs is still unclear. We propose a new framework named hierarchical outcome-weighted angle-based learning (HOAL) to estimate ITRs for treatments with hierarchical structure. Statistical properties including Fisher consistency and convergence rates of the proposed method are presented. Simulations and an application to a type 2 diabetes study under linear and nonlinear learning show the highly competitive performance of our proposed procedure in both numerical accuracy and computational efficiency.

Highlights

Precision medicine is an increasingly important area of research
There is a large body of literature in developing individualized treatment rules (ITRs), by first learning a regression model of outcomes using covariates and assigning the treatment with the best estimated outcome for a patient given covariates based on this regression model [18, 24]
Zhao et al [37] developed outcome weighted learning (OWL) by treating the ITR problem as a weighted classification problem, where misclassification errors are weighted by clinical outcomes

Summary

Introduction

Precision medicine is an increasingly important area of research. Due to the heterogeneity of individual characteristics, patients may respond differently to treatments. As an interesting topic in clinical research, many statistical methods have been developed in recent years to find optimal ITRs. For binary treatments, outcome weighted learning (OWL) was proposed to find a decision function of patient characteristics maximizing the expected clinical outcome. We propose a new framework named hierarchical outcome-weighted angle-based learning (HOAL) to estimate ITRs for treatments with hierarchical structure. The 0–1 loss function in Qian and Murphy [23] is replaced by a surrogate hinge loss, and the corresponding optimization problem becomes feasible This approach presented an important idea to use statistical machine learning tools to directly estimate ITRs by maximizing clinical outcomes. We propose a statistical learning framework to deal with ITR estimation in hierarchical treatment scenarios. We assume each node has at most one parent, where the hierarchy is called a tree structure, and each node either is a leaf or has at least two children

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