There is a fast-growing literature on estimating optimal treatment regimes based on randomized trials or observational studies under a key identifying condition of no unmeasured confounding. Because confounding by unmeasured factors cannot generally be ruled out with certainty in observational studies or randomized trials subject to noncompliance, we propose a general instrumental variable approach to learning optimal treatment regimes under endogeneity. Specifically, we establish identification of both value function $E[Y_{\mathcal{D}(L)}]$ for a given regime $\mathcal{D}$ and optimal regimes $\text{argmax}_{\mathcal{D}} E[Y_{\mathcal{D}(L)}]$ with the aid of a binary instrumental variable, when no unmeasured confounding fails to hold. We also construct novel multiply robust classification-based estimators. Furthermore, we propose to identify and estimate optimal treatment regimes among those who would comply to the assigned treatment under a standard monotonicity assumption. In this latter case, we establish the somewhat surprising result that complier optimal regimes can be consistently estimated without directly collecting compliance information and therefore without the complier average treatment effect itself being identified. Our approach is illustrated via extensive simulation studies and a data application on the effect of child rearing on labor participation.

中文翻译：

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内生性下最佳治疗方案的半参数工具变量方法

在没有不可测量的混杂因素的关键识别条件下，基于随机试验或观察性研究来估计最佳治疗方案的文献正在快速增长。由于在观察性研究或不合规的随机试验中，通常不能确定地排除未测量因素造成的混杂，因此我们提出了一种通用工具变量方法来学习内生性下的最佳治疗方案。具体来说，我们为给定机制 $\mathcal{D}$ 和最优机制 $\text{argmax}_{\mathcal{ 建立价值函数 $E[Y_{\mathcal{D}(L)}]$ 的识别D}} E[Y_{\mathcal{D}(L)}]$ 借助二元工具变量，当没有不可测量的混杂不成立时。我们还构建了新颖的基于多重鲁棒分类的估计器。此外，我们建议在标准单调性假设下识别和估计那些愿意遵守指定治疗的人的最佳治疗方案。在后一种情况下，我们得出了有点令人惊讶的结果，即可以一致地估计编译者最佳方案，而无需直接收集依从性信息，因此无需识别编译者平均治疗效果本身。我们的方法通过广泛的模拟研究和关于育儿对劳动参与的影响的数据应用来说明。