Department of Statistics, North Carolina State University, Raleigh, North Carolina.
Department of Mathematics, University of Arizona, Tucson, Arizona.
Stat Med. 2019 May 20;38(11):2059-2073. doi: 10.1002/sim.8102. Epub 2019 Feb 11.
Because different patients may respond quite differently to the same drug or treatment, there is an increasing interest in discovering individualized treatment rules. In particular, there is an emerging need to find optimal individualized treatment rules, which would lead to the "best" clinical outcome. In this paper, we propose a new class of loss functions and estimators based on robust regression to estimate the optimal individualized treatment rules. Compared to existing estimation methods in the literature, the new estimators are novel and advantageous in the following aspects. First, they are robust against skewed, heterogeneous, heavy-tailed errors or outliers in data. Second, they are robust against a misspecification of the baseline function. Third, under some general situations, the new estimator coupled with the pinball loss approximately maximizes the outcome's conditional quantile instead of the conditional mean, which leads to a more robust optimal individualized treatment rule than the traditional mean-based estimators. Consistency and asymptotic normality of the proposed estimators are established. Their empirical performance is demonstrated via extensive simulation studies and an analysis of an AIDS data set.
由于不同的患者对同一药物或治疗可能会有截然不同的反应，因此人们越来越感兴趣于发现个体化的治疗规则。特别是，人们越来越需要找到最佳的个体化治疗规则，这将带来“最佳”的临床效果。在本文中，我们提出了一类新的基于稳健回归的损失函数和估计器，用于估计最优的个体化治疗规则。与文献中的现有估计方法相比，新的估计器在以下几个方面具有新颖性和优势。首先，它们对数据中的偏态、异质性、重尾误差或异常值具有稳健性。其次，它们对基线函数的误设定具有稳健性。第三，在某些一般情况下，新的估计器与弹球损失相结合，近似最大化了结果的条件分位数，而不是条件均值，这比传统的基于均值的估计器产生了更稳健的最优个体化治疗规则。我们建立了所提出的估计器的一致性和渐近正态性。通过广泛的模拟研究和对艾滋病数据集的分析，展示了它们的经验性能。
