Causal Inference with Unmeasured Confounding from Nonignorable Missing Outcomes

• Main Author: Zheng, Renzhong
• Format: Journal Article
• Language: English
• Published: 11-05-2023
• Subjects: Statistics - Methodology
• DOI: 10.48550/arxiv.2305.07226

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.