Wang Lan, Zhou Yu, Song Rui, Sherwood Ben
School of Statistics, University of Minnesota, Minneapolis, MN 55455.
Department of Statistics, North Carolina State University, Raleigh, NC 27695.
J Am Stat Assoc. 2018;113(523):1243-1254. doi: 10.1080/01621459.2017.1330204. Epub 2018 Jun 8.
Finding the optimal treatment regime (or a series of sequential treatment regimes) based on individual characteristics has important applications in areas such as precision medicine, government policies and active labor market interventions. In the current literature, the optimal treatment regime is usually defined as the one that maximizes the average benefit in the potential population. This paper studies a general framework for estimating the quantile-optimal treatment regime, which is of importance in many real-world applications. Given a collection of treatment regimes, we consider robust estimation of the quantile-optimal treatment regime, which does not require the analyst to specify an outcome regression model. We propose an alternative formulation of the estimator as a solution of an optimization problem with an estimated nuisance parameter. This novel representation allows us to investigate the asymptotic theory of the estimated optimal treatment regime using empirical process techniques. We derive theory involving a nonstandard convergence rate and a non-normal limiting distribution. The same nonstandard convergence rate would also occur if the mean optimality criterion is applied, but this has not been studied. Thus, our results fill an important theoretical gap for a general class of policy search methods in the literature. The paper investigates both static and dynamic treatment regimes. In addition, doubly robust estimation and alternative optimality criterion such as that based on Gini's mean difference or weighted quantiles are investigated. Numerical simulations demonstrate the performance of the proposed estimator. A data example from a trial in HIV+ patients is used to illustrate the application.
基于个体特征寻找最优治疗方案（或一系列序贯治疗方案）在精准医学、政府政策和积极的劳动力市场干预等领域有着重要应用。在当前文献中，最优治疗方案通常被定义为能使潜在人群的平均获益最大化的方案。本文研究了一个用于估计分位数最优治疗方案的通用框架，这在许多实际应用中都很重要。给定一组治疗方案，我们考虑对分位数最优治疗方案进行稳健估计，这不需要分析师指定结果回归模型。我们提出将估计量作为一个带有估计干扰参数的优化问题的解的另一种表述。这种新颖的表示使我们能够使用经验过程技术研究估计的最优治疗方案的渐近理论。我们推导了涉及非标准收敛速度和非正态极限分布的理论。如果应用均值最优准则，也会出现相同的非标准收敛速度，但尚未对此进行研究。因此，我们的结果填补了文献中一类通用政策搜索方法的重要理论空白。本文研究了静态和动态治疗方案。此外，还研究了双重稳健估计以及基于基尼平均差或加权分位数等替代最优准则。数值模拟展示了所提出估计量的性能。使用来自HIV+患者试验的数据示例来说明其应用。
