Separators and Adjustment Sets in Causal Graphs: Complete Criteria and an Algorithmic Framework

TL;DR

This paper develops a comprehensive algorithmic framework for identifying covariate adjustment sets in causal graphs, extending existing methods to handle latent confounders and providing practical tools for causal effect estimation.

Contribution

It introduces efficient algorithms for testing, constructing, and enumerating adjustment sets in ancestral graphs, and establishes a reduction linking causal effect identification to m-separation.

Findings

Algorithms quantify the gap between covariate adjustment and do-calculus.

Constructive criteria characterize all adjustment sets, including minimal and minimum sets.

Empirical analysis demonstrates the effectiveness of the algorithms in various scenarios.

Abstract

Principled reasoning about the identifiability of causal effects from non-experimental data is an important application of graphical causal models. This paper focuses on effects that are identifiable by covariate adjustment, a commonly used estimation approach. We present an algorithmic framework for efficiently testing, constructing, and enumerating $m$-separators in ancestral graphs (AGs), a class of graphical causal models that can represent uncertainty about the presence of latent confounders. Furthermore, we prove a reduction from causal effect identification by covariate adjustment to $m$-separation in a subgraph for directed acyclic graphs (DAGs) and maximal ancestral graphs (MAGs). Jointly, these results yield constructive criteria that characterize all adjustment sets as well as all minimal and minimum adjustment sets for identification of a desired causal effect with multivariate exposures and outcomes in the presence of latent confounding. Our results extend several existing solutions for special cases of these problems. Our efficient algorithms allowed us to empirically quantify the identifiability gap between covariate adjustment and the do-calculus in random DAGs and MAGs, covering a wide range of scenarios. Implementations of our algorithms are provided in the R package dagitty.