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Semi-competing risks refer to the phenomenon where a primary event (such asmortality) can ``censor'' an intermediate event (such as relapse of a disease),but not vice versa. Under the multi-state model, the primary event consists oftwo specific types: the direct outcome event and an indirect outcome eventdeveloped from intermediate events. Within this framework, we show that thetotal treatment effect on the cumulative incidence of the primary event can bedecomposed into three separable pathway effects, capturing treatment effects onpopulation-level transition rates between states. We next propose twoestimators for the counterfactual cumulative incidences of the primary eventunder hypothetical treatment components. One estimator is given by thegeneralized Nelson--Aalen estimator with inverse probability weighting undercovariates isolation, and the other is given based on the efficient influencefunction. The asymptotic normality of these estimators is established. Thefirst estimator only involves a propensity score model and avoid modeling thecause-specific hazards. The second estimator has robustness against themisspecification of submodels. As an illustration of its potential usefulness,the proposed method is applied to compare effects of different allogeneic stemcell transplantation types on overall survival after transplantation.

Separable pathway effects of semi-competing risks using multi-state models