A common concern when a policy-maker draws causal inferences and makes decisions from 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 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-inducing and treatment-inducing 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, and excess value bound of the estimated regime, are established. Moreover, we demonstrate the proposed optimal regime via numerical experiments and a real data application.

翻译：当决策者从观察数据中得出因果关系推论并作出决定时,一个共同的关切是,测量到的共变体不够丰富,无法说明所有混乱来源,即标准、没有根据的假设不能成立。最近提议的准因果推论框架表明,可以利用代理变数来查明因果关系,从而便利决策。在这项工作的基础上,我们提议以所谓的结果产生和治疗造成混淆的桥梁为基础,建立一个新的最佳个人化处理制度。然后,我们表明,这一新的最佳处理制度的价值作用高于文献中的现有制度。确立了理论保证,包括确定估计制度的特征、优越性和超额价值。此外,我们通过数字实验和真实的数据应用,展示了拟议的最佳制度。