  Semi-competing risks refer to the phenomenon that the terminal event (such as
death) can censor the non-terminal event (such as disease progression) but not
vice versa. The treatment effect on the terminal event can be delivered either
directly following the treatment or indirectly through the non-terminal event.
We consider two strategies to decompose the total effect into a direct effect
and an indirect effect under the framework of mediation analysis in completely
randomized experiments by adjusting the prevalence and hazard of non-terminal
events, respectively. They require slightly different assumptions on
cross-world quantities to achieve identifiability. We establish asymptotic
properties for the estimated counterfactual cumulative incidences and
decomposed treatment effects. We illustrate the subtle difference between these
two decompositions through simulation studies and two real-data applications.
