# Adjustment Criteria for Recovering Causal Effects from Missing Data

arXiv: https://arxiv.org/abs/1907.01654 · HTML: https://mlsanity.com/paper/1907.01654/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Jul 2019.

## Built on by (most cited first, 2 of 2)

- [On Testability and Goodness of Fit Tests in Missing Data Models](https://mlsanity.com/paper/2203.00132/) (2022)
- [Recursive Equations For Imputation Of Missing Not At Random Data With Sparse Pattern Support](https://mlsanity.com/paper/2507.16107/) (2025)

## Abstract (arXiv)

Confounding bias, missing data, and selection bias are three common obstacles to valid causal inference in the data sciences. Covariate adjustment is the most pervasive technique for recovering casual effects from confounding bias. In this paper, we introduce a covariate adjustment formulation for controlling confounding bias in the presence of missing-not-at-random data and develop a necessary and sufficient condition for recovering causal effects using the adjustment. We also introduce an adjustment formulation for controlling both confounding and selection biases in the presence of missing data and develop a necessary and sufficient condition for valid adjustment. Furthermore, we present an algorithm that lists all valid adjustment sets and an algorithm that finds a valid adjustment set containing the minimum number of variables, which are useful for researchers interested in selecting adjustment sets with desired properties.