  Semi-competing risks refer to the phenomenon where a primary outcome event
(such as mortality) can truncate an intermediate event (such as relapse of a
disease), but not vice versa. Under the multi-state model, the primary event is
decomposed to a direct outcome event and an indirect outcome event through
intermediate events. Within this framework, we show that the total treatment
effect on the cumulative incidence of the primary event can be decomposed into
three separable pathway effects, corresponding to treatment effects on
population-level transition rates between states. We next propose estimators
for the counterfactual cumulative incidences of the primary event under
hypothetical treatments by generalized Nelson-Aalen estimators with inverse
probability weighting, and then derive the consistency and asymptotic normality
of these estimators. Finally, we propose hypothesis testing procedures on these
separable pathway effects based on logrank statistics. We have conducted
extensive simulation studies to demonstrate the validity and superior
performance of our new method compared with existing methods. As an
illustration of its potential usefulness, the proposed method is applied to
compare effects of different allogeneic stem cell transplantation types on
overall survival after transplantation.
