Optimal Treatment Assignment to Maximize Expected Outcome with Multiple Treatments

Abstract

When there is substantial heterogeneity of treatment effectiveness, it is crucial to identify individualized treatment assignment rules for comparative treatment selection. Traditional approaches directly model clinical outcome and define optimal treatment rule according to the interactions between treatment and covariates. This approach relies on the success of separating the main effects from the covariate-treatment interaction effects, which may not be easy. To overcome this shortcoming, a recent approach, called outcome weighted learning, focuses on building an optimal treatment rule by maximizing the expected clinical outcome related with differential treatments. However, there seems to be a lack of approaches to explicitly deal with three or more treatments. In this article, we propose an outcome weighted learning method that extends estimating individualized treatment rules to multi-treatment case by using a vector hinge loss as a target function. Consistency of the resulting estimator is shown in the article. We demonstrate the performance of our approach in simulation studies and in a real data analysis.

Multicategory Individualized Treatment Regime Using Outcome Weighted Learning

“…This loss is used by Lou et al . () for multicategory ITR. When , as plotted in the left panel of Figure .…”

“…Lou et al . () proposed an outcome weighted learning method using a vector hinge loss under the assumptions of positive response and known propensity score. In this article, we propose a general framework for multicategory ITR using outcome weighted learning.…”

Estimating individualized treatment rules with risk constraint

“…We select the age, race, married or living with partner, and the number of years having mammography in last 5 years to be the covariates, as recommended by Lou et al . (2018).…”

Resampling‐based confidence intervals for model‐free robust inference on optimal treatment regimes

“…Applications in medicine, public policy, internet marketing, and other scientific areas often require estimating an individualized treatment rule (or regime, policy) to maximize the potential benefit. Several successful methods have been developed for estimating an optimal treatment regime, including Q‐learning (Watkins and Dayan, 1992; Murphy, 2005b; Chakraborty et al ., 2010; Qian and Murphy, 2011; Song et al ., 2015), A‐learning (Robins et al ., 2000; Murphy, 2003, 2005a; Moodie and Richardson, 2010; Shi et al ., 2018), model‐free methods (Robins et al ., 2008; Orellana et al ., 2010; Zhang et al ., 2012; Zhao et al ., 2012, 2015; Athey and Wager, 2017; Linn et al ., 2017; Zhou et al ., 2017; Zhu et al ., 2017; Lou et al ., 2018; Qi et al ., 2018; Wang et al ., 2018), tree or list‐based methods (Laber and Zhao, 2015; Cui et al ., 2017; Zhu et al ., 2017; Zhang et al ., 2018), targeted learning ensembles approach (Díaz et al ., 2018), among others.…”

“…A substantial challenge in inference for lies in the nonsmoothness of the decision function. A popular approach is to replaces the 0‐1 loss by a computationally convenient surrogate loss such as the hinge loss (Zhao et al ., 2012; Zhou et al ., 2017; Lou et al ., 2018) or the logistic loss (Jiang et al ., 2019). However, existing theory (eg, Fisher consistency, generalization error bound) that justifies the use of the surrogate loss is usually derived when the form of the decision rule is unconstrained and approximated in a reproducible kernel Hilbert space.…”