Inverse probability of treatment weighting (IPTW) has been well applied in causal inference. For time-to-event outcomes, IPTW is performed by weighting the event counting process and at-risk process, resulting in a generalized Nelson--Aalen estimator for population-level hazards. In the presence of competing events, we adopt the counterfactual cumulative incidence of a primary event as the estimated. When the propensity score is estimated, we derive the influence function of the hazard estimator, and then establish the asymptotic property of the incidence estimator. We show that the uncertainty in the estimated propensity score contributes to an additional variation in the IPTW estimator of the cumulative incidence. However, through simulation and real-data application, we find that the additional variation is usually small.

翻译：治疗逆概率加权（IPTW）方法已在因果推断领域得到广泛应用。针对时间-事件结局数据，IPTW通过对事件计数过程与风险过程进行加权处理，从而推导出总体风险水平的广义Nelson--Aalen估计量。在存在竞争事件的情况下，我们采用主要事件的潜在反事实累积发生率作为估计目标。当倾向得分需要估计时，我们推导出风险估计量的影响函数，进而建立发生率估计量的渐近性质。研究表明，倾向得分估计的不确定性会导致累积发生率IPTW估计量的额外变异。然而，通过模拟研究与实际数据应用，我们发现这种额外变异通常较小。