Deng Yuhao, Wang Rui
Department of Biostatistics, School of Public Health, University of Michigan, Ann Arbor, MI, USA.
Department of Biostatistics, School of Public Health, University of Washington, Seattle, WA, USA.
Stat Med. 2025 May;44(10-12):e70085. doi: 10.1002/sim.70085.
Inverse probability of treatment weighting (IPW) has been well applied in causal inference to estimate population-level estimands from observational studies. For time-to-event outcomes, the failure time distribution can be estimated by estimating the cumulative hazard in the presence of random right censoring. IPW can be performed by weighting the event counting process and at-risk process by the inverse treatment probability, resulting in an adjusted Nelson-Aalen estimator for the population-level counterfactual cumulative incidence function. We consider the adjusted Nelson-Aalen estimator with an estimated propensity score in the competing risks setting. When the estimated propensity score is regular and asymptotically linear, we derive the influence functions for the counterfactual cumulative hazard and cumulative incidence. Then we establish the asymptotic properties for the estimators. We show that the uncertainty in the estimated propensity score contributes to an additional variation in the estimators. However, through simulation and real-data application, we find that such an additional variation is usually small.
治疗权重逆概率（IPW）已在因果推断中得到很好的应用，用于从观察性研究中估计总体水平的估计量。对于生存时间结局，在存在随机右删失的情况下，可以通过估计累积风险来估计失效时间分布。IPW可以通过用治疗概率的倒数对事件计数过程和风险过程进行加权来实现，从而得到总体水平反事实累积发病率函数的调整后的纳尔逊-奥尔森估计量。我们考虑在竞争风险设定下使用估计的倾向得分的调整后的纳尔逊-奥尔森估计量。当估计的倾向得分是正则且渐近线性时，我们推导反事实累积风险和累积发病率的影响函数。然后我们建立估计量的渐近性质。我们表明，估计的倾向得分中的不确定性会导致估计量出现额外的变异。然而，通过模拟和实际数据应用，我们发现这种额外的变异通常很小。
