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Primary Submission Category: Missing Data and Self-Censoring

Causal Inference Under Self-Censoring Treatment and Outcome

Authors: Jacob M. Chen, Daniel Malinsky, Rohit Bhattacharya,

Presenting Author: Jacob M. Chen*

“Self-censoring” is a type of missingness-not-at-random (MNAR) phenomenon that poses a particularly difficult obstacle to valid inference. If treatment and/or outcome directly determine their own missingness, this may lead to severely biased estimates for the causal effect. The possibility of unmeasured confounding in conjunction with self-censoring also complicates identifying a valid set of covariates to adjust for. Shadow variables, proposed by Miao et al. (2015), are auxiliary variables that can be used to overcome self-censoring if certain conditions are met. However, these conditions are difficult to verify: that (i) the proposed shadow variable is associated with the censored variable and (ii) it does not directly affect the missingness of the censored variable. Here, we extend prior work in covariate selection to account for both self-censoring and unmeasured confounding. We propose a two-stage test; the first stage confirms dependence between a pre-treatment variable and the missingness indicator of the outcome after conditioning on some subset of observed covariates, and the second stage confirms independence between the same variables while additionally conditioning on the treatment. We prove that if the test passes, then the pre-treatment variable is indeed a valid shadow variable while the observed covariates are a valid backdoor adjustment set. Using this information, we propose an inverse probability weight-based estimator for the causal effect of interest.