Definition and Interpretation of Separable Path-specific Effects With Multiple Ordered Mediators

Causal mediation analysis examines the mechanism by which exposure affects outcome via mediators. In contrast to single-mediator scenarios, the presence of multiple ordered mediators introduces complex pathways and corresponding path-specific effects, which are difficult to interpret due to the cross-world counterfactual definition. Path-specific effects also require convoluted and unverifiable assumptions for identification. This article proposes a framework of separable path-specific effects as an extension of the separable effect method to the case of multiple ordered mediators. Compared to the traditional approach, separable path-specific effects can be interpreted as the causal effects of several separated components on the outcome, facilitating a more intuitive understanding of underlying mechanisms. We elucidate the relationship between separable and traditional path-specific effects by demonstrating their equivalence under the individual-level isolation assumptions and identifying both effects under the finest fully randomized causally interpretable structured tree graph (FFRCISTG) model, which inherently makes individual-level isolation assumptions. Moreover, weakening the individual-level isolation assumptions to their population-level counterparts, separable path-specific effects remain identifiable under the FFRCISTG model. Under this causal model, the assumptions for identifying separable path-specific effects can be verified in future experiments, thereby addressing the problem of relying on unverifiable cross-world assumptions in the traditional method. We also discuss how this framework can detect violations of assumptions such as the presence of intermediate confounders and the misspecification of causal order among mediators. In summary, compared with the traditional path-specific effects method, the proposed separable method provides a more verifiable and interpretable approach for causal multiple mediation analysis.