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 multiple 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.

Using copulas to enable causal inference from nonexperimental data: Tutorial and simulation studies.

“…Covariate adjustment approaches are effective when all relevant confounders are known to the researcher, or more precisely, when she has pinpointed a core subset of these that: (a) is sufficient for blocking or intercepting the influences of unobservables (Cheng et al, 2020; Cummiskey et al, 2020; Gultchin et al, 2020; van der Zander et al, 2019; Witte et al, 2020); and (b) can be reliably measured (Lockwood & McCaffrey, 2019; Sengewald et al, 2019). Intuitively, the preferred strategy would seem to be an “everything but the kitchen sink” approach, in which as many potential confounders as possible are measured and included in the model as covariates.…”

Invariant Ancestry Search

“…Instead, for IAS, we exploit the recent development of efficient algorithms for computing all minimal d-separators (for two given sets of nodes) in a given DAG (see, e.g., Tian et al, 1998;van der Zander et al, 2019). A set S is called a minimal d-separator of E and Y if it d-separates E and Y given S and no strict subset of S satisfies this property.…”

Causal Effect Identification from Multiple Incomplete Data Sources: A General Search-Based Approach

“…Algorithms implemented in causaleffect run in polynomial time and can outperform dosearch in their respective restricted problem settings especially with larger graphs. For a comprehensive performance comparison between causaleffect and various adjustment criteria, see (Van der Zander, Liśkiewicz, and Textor 2019).…”