Separators and Adjustment Sets in Causal Graphs: Complete Criteria and an Algorithmic Framework
This work provides efficient tools for causal inference researchers to determine when and how covariate adjustment can be used, extending existing solutions for graphical models.
The paper tackles the problem of identifying causal effects from non-experimental data using covariate adjustment, presenting an algorithmic framework for testing and constructing m-separators in ancestral graphs, and proves criteria to characterize all adjustment sets, including minimal ones, for multivariate exposures and outcomes with latent confounding.
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.