Minimal enumeration of all possible total effects in a Markov equivalence class

TL;DR

This paper introduces a recursive algorithm to efficiently enumerate all subclasses of causal graphs within a Markov equivalence class, identifying total effects without duplicates caused by sampling variability.

Contribution

It provides a minimal enumeration method for total effects in Markov equivalence classes, improving accuracy and efficiency over existing approaches.

Findings

Algorithm successfully enumerates subclasses with distinct total effects.

Reduces duplicates caused by sampling variability in effect estimation.

Enhances causal inference accuracy in observational studies.

Abstract

In observational studies, when a total causal effect of interest is not identified, the set of all possible effects can be reported instead. This typically occurs when the underlying causal DAG is only known up to a Markov equivalence class, or a refinement thereof due to background knowledge. As such, the class of possible causal DAGs is represented by a maximally oriented partially directed acyclic graph (MPDAG), which contains both directed and undirected edges. We characterize the minimal additional edge orientations required to identify a given total effect. A recursive algorithm is then developed to enumerate subclasses of DAGs, such that the total effect in each subclass is identified as a distinct functional of the observed distribution. This resolves an issue with existing methods, which often report possible total effects with duplicates, namely those that are numerically distinct due to sampling variability but are in fact causally identical.