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

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.

arXiv comment52 pages, 20 figures, 12 tables

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• Classifying Causal Structures: Ascertaining when Classical Correlations are Constrained by Inequalities
• Necessary and sufficient graphical conditions for optimal adjustment sets in causal graphical models with hidden variables
• Finding and Listing Front-door Adjustment Sets
• Confounder selection via iterative graph expansion
• Towards unique and unbiased causal effect estimation from data with hidden variables
• Local search for efficient causal effect estimation