A Complete Generalized Adjustment Criterion

TL;DR

This paper introduces a comprehensive criterion for covariate adjustment that is both necessary and sufficient across multiple classes of graphical causal models, unifying existing criteria.

Contribution

It presents a unified adjustment criterion applicable to DAGs, MAGs, CPDAGs, and PAGs, simplifying causal effect estimation from observational data.

Findings

The criterion is necessary and sufficient for four classes of graphical models.

It subsumes and unifies existing adjustment criteria.

The approach improves causal inference robustness across different model types.

Abstract

Covariate adjustment is a widely used approach to estimate total causal effects from observational data. Several graphical criteria have been developed in recent years to identify valid covariates for adjustment from graphical causal models. These criteria can handle multiple causes, latent confounding, or partial knowledge of the causal structure; however, their diversity is confusing and some of them are only sufficient, but not necessary. In this paper, we present a criterion that is necessary and sufficient for four different classes of graphical causal models: directed acyclic graphs (DAGs), maximum ancestral graphs (MAGs), completed partially directed acyclic graphs (CPDAGs), and partial ancestral graphs (PAGs). Our criterion subsumes the existing ones and in this way unifies adjustment set construction for a large set of graph classes.