Adjustment Criteria in Causal Diagrams: An Algorithmic Perspective

Abstract

Identifying and controlling bias is a key problem in empirical sciences. Causal diagram theory provides graphical criteria for deciding whether and how causal effects can be identified from observed (nonexperimental) data by covariate adjustment. Here we prove equivalences between existing as well as new criteria for adjustment and we provide a new simplified but still equivalent notion of d-separation. These lead to efficient algorithms for two important tasks in causal diagram analysis: (1) listing minimal covariate adjustments (with polynomial delay); and (2) identifying the subdiagram involved in biasing paths (in linear time). Our results improve upon existing exponential-time solutions for these problems, enabling users to assess the effects of covariate adjustment on diagrams with tens to hundreds of variables interactively in real time.

References in corpus (3)

• Bayes-Ball: The Rational Pastime (for Determining Irrelevance and Requisite Information in Belief Networks and Influence Diagrams)
• On the Validity of Covariate Adjustment for Estimating Causal Effects
• An Algorithm for Finding Minimum d-Separating Sets in Belief Networks

Cited by in corpus (9)

• A generalized back-door criterion
• Separators and Adjustment Sets in Causal Graphs: Complete Criteria and an Algorithmic Framework
• A Complete Generalized Adjustment Criterion
• Structural Intervention Distance (SID) for Evaluating Causal Graphs
• Efficient adjustment sets in causal graphical models with hidden variables
• Learning from Pairwise Marginal Independencies
• Practically Effective Adjustment Variable Selection in Causal Inference
• Finding and Listing Front-door Adjustment Sets
• How balance and sample size impact bias in the estimation of causal treatment effects: A simulation study