Causal mediation analysis with multiple mediators (causal multi-mediation analysis) is critical in understanding why an intervention works, especially in medical research. Deriving the path-specific effects (PSEs) of exposure on the outcome through a certain set of mediators can detail the causal mechanism of interest. However, the existing models of causal multi-mediation analysis are usually restricted to partial decomposition, which can only evaluate the cumulative effect of several paths. Moreover, the general form of PSEs for an arbitrary number of mediators has not been proposed. In this study, we provide a generalized definition of PSE for partial decomposition (partPSE) and for complete decomposition, which are extended to the survival outcome. We apply the interventional analogues of PSE (iPSE) for complete decomposition to address the difficulty of non-identifiability. Based on Aalen’s additive hazards model and Cox’s proportional hazards model, we derive the generalized analytic forms and illustrate asymptotic property for both iPSEs and partPSEs for survival outcome. The simulation is conducted to evaluate the performance of estimation in several scenarios. We apply the new methodology to investigate the mechanism of methylation signals on mortality mediated through the expression of three nested genes among lung cancer patients.



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