# Adjustment Criteria for Recovering Causal Effects from Missing Data

## TL;DR

This paper develops new criteria and algorithms for covariate adjustment to recover causal effects in the presence of missing data, confounding, and selection biases, providing necessary and sufficient conditions for valid adjustment.

## Contribution

It introduces a covariate adjustment framework with necessary and sufficient conditions for handling missing-not-at-random data and biases, along with algorithms for selecting optimal adjustment sets.

## Key findings

- Established necessary and sufficient conditions for causal effect recovery with missing data.
- Developed algorithms to list all valid adjustment sets and find minimal adjustment sets.
- Enhanced causal inference methods for complex missing data scenarios.

## Abstract

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.