A common concern when a policymaker draws causal inferences from and makes decisions based on observational data is that the measured covariates are insufficiently rich to account for all sources of confounding, i.e., the standard no confoundedness assumption fails to hold. The recently proposed proximal causal inference framework shows that proxy variables that abound in real-life scenarios can be leveraged to identify causal effects and therefore facilitate decision-making. Building upon this line of work, we propose a novel optimal individualized treatment regime based on so-called outcome and treatment confounding bridges. We then show that the value function of this new optimal treatment regime is superior to that of existing ones in the literature. Theoretical guarantees, including identification, superiority, excess value bound, and consistency of the estimated regime, are established. Furthermore, we demonstrate the proposed optimal regime via numerical experiments and a real data application.

翻译：当政策制定者基于观察数据进行因果推断并做出决策时，常见的担忧是测量到的协变量不足以充分解释所有混杂来源，即标准的无混杂假设不成立。最近提出的近端因果推断框架表明，现实场景中大量存在的代理变量可用于识别因果效应，从而促进决策。基于这一研究方向，我们提出了一种新型的最优个体化治疗方案，该方案基于所谓的结局混杂桥与治疗混杂桥。随后我们证明，该新最优治疗方案的价值函数优于文献中现有方案。文中建立了理论保证，包括识别性、优越性、超额价值界以及估计方案的一致性。最后，通过数值实验和实际数据应用，我们展示了所提出的最优方案。