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In observational studies, when a total causal effect of interest is notidentified, the set of all possible effects can be reported instead. Thistypically occurs when the underlying causal DAG is only known up to a Markovequivalence class, or a refinement thereof due to background knowledge. Assuch, the class of possible causal DAGs is represented by a maximally orientedpartially directed acyclic graph (MPDAG), which contains both directed andundirected edges. We characterize the minimal additional edge orientationsrequired to identify a given total effect. A recursive algorithm is thendeveloped to enumerate subclasses of DAGs, such that the total effect in eachsubclass is identified as a distinct functional of the observed distribution.This resolves an issue with existing methods, which often report possible totaleffects with duplicates, namely those that are numerically distinct due tosampling variability but are in fact causally identical.

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