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.

翻译：半竞争风险是指主要结局事件（如死亡）可能截断中间事件（如疾病复发），但反之则不成立的现象。在多状态模型框架下，主要事件被分解为直接结局事件和通过中间事件间接发生的结局事件。在此框架内，我们证明主要事件累积发生率的总体处理效应可分解为三个可分离的路径效应，分别对应人口层面状态间转移概率的处理效应。接下来，我们通过带有逆概率加权的广义Nelson-Aalen估计量，提出在假设处理条件下主要事件反事实累积发生率的估计方法，并推导这些估计量的一致性和渐近正态性。最后，我们提出基于对数秩统计量对这些可分离路径效应进行假设检验的程序。通过大量模拟研究，我们验证了新方法的有效性及其相较于现有方法的优越性能。为说明其潜在应用价值，我们将所提方法应用于比较不同类型异基因干细胞移植对移植后总生存期的影响。