# Causal inference with confounders missing not at random

arXiv: https://arxiv.org/abs/1702.03951 · HTML: https://mlsanity.com/paper/1702.03951/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Feb 2017.

## Built on by (most cited first, 7 of 7)

- [Eliciting Numerical Predictive Distributions of LLMs Without Autoregression](https://mlsanity.com/paper/2603.02913/) (2026)
- [Causal-StoNet: Causal Inference for High-Dimensional Complex Data](https://mlsanity.com/paper/2403.18994/) (2024)
- [A Unified Framework of Policy Learning for Contextual Bandit with Confounding Bias and Missing Observations](https://mlsanity.com/paper/2303.11187/) (2023)
- [Augmented transfer regression learning for completely missing covariates](https://mlsanity.com/paper/2605.04469/) (2026)
- [Bounds and Sensitivity Analysis of the Causal Effect Under Outcome-Independent MNAR Confounding](https://mlsanity.com/paper/2410.06726/) (2024)
- [Bayesian Counterfactual Prediction Models for HIV Care Retention with Incomplete Outcome and Covariate Information](https://mlsanity.com/paper/2410.22481/) (2024)
- [An Interdisciplinary and Cross-Task Review on Missing Data Imputation](https://mlsanity.com/paper/2511.01196/) (2025)

## Abstract (arXiv)

It is important to draw causal inference from observational studies, which, however, becomes challenging if the confounders have missing values. Generally, causal effects are not identifiable if the confounders are missing not at random. We propose a novel framework to nonparametrically identify causal effects with confounders subject to an outcome-independent missingness, that is, the missing data mechanism is independent of the outcome, given the treatment and possibly missing confounders. We then propose a nonparametric two-stage least squares estimator and a parametric estimator for causal effects.