In observational studies with time-to-event outcomes, the g-formula can be used to estimate a treatment effect in the presence of confounding factors. However, the asymptotic distribution of the corresponding stochastic process is complicated and thus not suitable for deriving confidence intervals or time-simultaneous confidence bands for the average treatment effect. A common remedy are resampling-based approximations, with Efron's nonparametric bootstrap being the standard tool in practice. We investigate the large sample properties of three different resampling approaches and prove their asymptotic validity in a setting with time-to-event data subject to competing risks.

翻译：在具有事件发生时间结局的观察性研究中，g公式可用于在存在混杂因素时估计处理效应。然而，相应随机过程的渐近分布较为复杂，因此不适用于构建平均处理效应的置信区间或时点同时置信带。常用的解决方法是基于重抽样的近似方法，其中Efron非参数自助法在实践中是标准工具。我们研究了三种不同重抽样方法的大样本性质，并在存在竞争风险的事件发生时间数据情境下证明了它们的渐近有效性。