Unmeasured confounding is a threat to causal inference and gives rise to biased estimates. In this article, we consider the problem of individualized decision-making under partial identification. Firstly, we argue that when faced with unmeasured confounding, one should pursue individualized decision-making using partial identification in a comprehensive manner. We establish a formal link between individualized decision-making under partial identification and classical decision theory by considering a lower bound perspective of value/utility function. Secondly, building on this unified framework, we provide a novel minimax solution (i.e., a rule that minimizes the maximum regret for so-called opportunists) for individualized decision-making/policy assignment. Lastly, we provide an interesting paradox drawing on novel connections between two challenging domains, that is, individualized decision-making and unmeasured confounding. Although motivated by instrumental variable bounds, we emphasize that the general framework proposed in this article would in principle apply for a rich set of bounds that might be available under partial identification.
翻译:无法衡量的混乱是对因果关系推论的威胁,并引起偏颇的估计。在本条中,我们考虑的是个人化决策的局部识别问题。首先,我们主张,在面对非计量的混乱时,应当以全面的方式利用部分识别进行个人化决策。我们通过考虑价值/效用功能的较低约束性观点,在部分识别和传统决策理论之间建立了正式联系。第二,在这一统一框架的基础上,我们为个人化决策/政策任务提供了一个新的小型解决方案(即尽可能减少所谓机会主义者的最大遗憾的规则)。最后,我们提供了一个有趣的自相矛盾现象,利用两个挑战性领域之间的新联系,即,即,个体化决策和非计量性整合。虽然我们是出于工具变量的动机,但我们强调,本条提议的总框架原则上适用于部分识别下可能具备的多种约束。