Observational studies are the primary source of data for causal inference, but it is challenging when existing unmeasured confounding. Missing data problems are also common in observational studies. How to obtain the causal effects from the nonignorable missing data with unmeasured confounding is a challenge. In this paper, we consider that how to obtain complier average causal effect with unmeasured confounding from the nonignorable missing outcomes. We propose an auxiliary variable which plays two roles simultaneously, the one is the shadow variable for identification and the other is the instrumental variable for inference. We also illustrate some difference between some missing outcomes mechanisms in the previous work and the shadow variable assumption. We give a causal diagram to illustrate this description. Under such a setting, we present a general condition for nonparametric identification of the full data law from the nonignorable missing outcomes with this auxiliary variable. For inference, firstly, we recover the mean value of the outcome based on the generalized method of moments. Secondly, we propose an estimator to adjust for the unmeasured confounding to obtain complier average causal effect. We also establish the asymptotic results of the estimated parameters. We evaluate its performance via simulations and apply it to a real-life dataset about a political analysis.

翻译：观察性研究是因果推断的主要数据来源，但当存在未测量混杂时具有挑战性。缺失数据问题在观察性研究中同样普遍。如何在未测量混杂存在的情况下，从不可忽略缺失数据中获得因果效应是一个难题。本文考虑如何从存在未测量混杂的不可忽略缺失结局数据中获取依从者平均因果效应。我们提出一个辅助变量，该变量同时发挥两个作用：其一是用于识别的阴影变量，其二是用于推断的工具变量。我们还阐述了先前研究中某些缺失结局机制与阴影变量假设之间的差异，并给出因果示意图加以说明。在此设定下，我们提出了利用该辅助变量从不可忽略缺失结局中识别完整数据分布的非参数化充分条件。在推断方面，我们首先基于广义矩方法恢复结局变量的均值；其次，提出一种校正未测量混杂的估计量以获取依从者平均因果效应。同时建立了参数估计的渐近性质，并通过模拟实验和一项政治分析的真实数据集验证了其性能。