A Potential Outcomes Calculus for Identifying Conditional Path-Specific Effects

Understand

The do-calculus is a well-known deductive system for deriving connections between interventional and observed distributions, and has been proven complete for a number of important identifiability problems in causal inference.

• Nevertheless, as it is currently defined, the do-calculus is inapplicable to causal problems that involve complex nested counterfactuals which cannot be expressed in terms of the "do" operator.
• Such problems include analyses of path-specific effects and dynamic treatment regimes.
• In this paper we present the potential outcome calculus (po-calculus), a natural generalization of do-calculus for arbitrary potential outcomes.