In survival contexts, substantial literature exists on estimating optimal treatment regimes, where treatments are assigned based on personal characteristics for the purpose of maximizing the survival probability. These methods assume that a set of covariates is sufficient to deconfound the treatment-outcome relationship. Nevertheless, the assumption can be limiting in observational studies or randomized trials in which noncompliance occurs. Thus, we advance a novel approach for estimating the optimal treatment regime when certain confounders are not observable and a binary instrumental variable is available. Specifically, via a binary instrumental variable, we propose two semiparametric estimators for the optimal treatment regime, one of which possesses the desirable property of double robustness, by maximizing Kaplan-Meier-like estimators within a pre-defined class of regimes. Because the Kaplan-Meier-like estimators are jagged, we incorporate kernel smoothing methods to enhance their performance. Under appropriate regularity conditions, the asymptotic properties are rigorously established. Furthermore, the finite sample performance is assessed through simulation studies. We exemplify our method using data from the National Cancer Institute's (NCI) prostate, lung, colorectal, and ovarian cancer screening trial.

翻译：在生存分析背景下，现有大量文献探讨如何估计最优治疗策略，即根据个体特征分配治疗方案以最大化生存概率。这些方法假设存在一组协变量足以消除治疗-结局关系中的混杂效应。然而，在观察性研究或存在非依从性的随机试验中，该假设可能具有局限性。为此，我们提出一种新方法，用于在存在不可观测混杂因素且可获取二值工具变量时估计最优治疗策略。具体而言，通过二值工具变量，我们提出了两种半参数估计量：其一是通过最大化预定义策略类内的类Kaplan-Meier估计量实现，其中一种估计量具有双重稳健性的理想性质。由于类Kaplan-Meier估计量呈锯齿状，我们引入核平滑方法以提升其性能。在适当正则条件下，严格建立了渐近性质。此外，通过模拟研究评估了有限样本表现。我们利用美国国家癌症研究所（NCI）的前列腺癌、肺癌、结直肠癌和卵巢癌筛查试验数据对方法进行了实例验证。