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 limited in observational studies or randomized trials in which non-adherence occurs. Thus, we propose 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 by maximizing Kaplan-Meier-like estimators within a pre-defined class of regimes, one of which possesses the desirable property of double robustness. 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. Finally, we exemplify our method using data from the National Cancer Institute's (NCI) prostate, lung, colorectal, and ovarian cancer screening trial.

翻译：在生存资料的分析中，已有大量关于估计最优治疗方案的研究文献，这类方案根据个体特征分配治疗方式以最大化生存概率。现有方法假设存在一组协变量足以消除治疗-结局间的混杂效应。然而在观察性研究或存在非依从性的随机试验中，该假设可能受限。为此，我们提出一种当部分混杂因素不可观测且存在二元工具变量时的最优治疗方案估计新方法。具体而言，通过二元工具变量，我们在预定义方案类中最大化类Kaplan-Meier估计量，构建了两种半参数最优治疗方案估计量，其中一种具有双稳健性。针对类Kaplan-Meier估计量存在的锯齿现象，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。最后，运用美国国家癌症研究所（NCI）的前列腺癌、肺癌、结直肠癌及卵巢癌筛查试验数据展示了该方法的应用。