The current body of research on developing optimal treatment strategies often places emphasis on intention-to-treat analyses, which fail to take into account the compliance behavior of individuals. Methods based on instrumental variables have been developed to determine optimal treatment strategies in the presence of endogeneity. However, these existing methods are not applicable when there are two active treatment options and the average causal effects of the treatments cannot be identified using a binary instrument. In order to address this limitation, we present a procedure that can identify an optimal treatment strategy and the corresponding value function as a function of a vector of sensitivity parameters. Additionally, we derive the canonical gradient of the target parameter and propose a multiply robust classification-based estimator for the optimal treatment strategy. Through simulations, we demonstrate the practical need for and usefulness of our proposed method. We apply our method to a randomized trial on Adaptive Treatment for Alcohol and Cocaine Dependence.

翻译：当前关于制定最优治疗策略的研究往往侧重于意图治疗分析，这类分析未考虑个体的依从行为。基于工具变量的方法已被开发用于在内生性存在的情况下确定最优治疗策略。然而，当存在两种积极治疗方案且无法通过二元工具变量识别治疗的平均因果效应时，这些现有方法并不适用。为解决这一局限性，我们提出了一种方法，该方法能够识别出最优治疗策略及相应的值函数，并将其表示为敏感性参数向量的函数。此外，我们推导了目标参数的正则梯度，并提出了基于多重稳健分类的最优治疗策略估计量。通过模拟验证，我们证明了所提出方法的实际必要性和有效性。我们将该方法应用于一项关于酒精和可卡因依赖自适应治疗的随机试验中。