The g-formula can be used to estimate the treatment effect while accounting for confounding bias in observational studies. With regard to time-to-event endpoints, possibly subject to competing risks, the construction of valid pointwise confidence intervals and time-simultaneous confidence bands for the causal risk difference is complicated, however. A convenient solution is to approximate the asymptotic distribution of the corresponding stochastic process by means of resampling approaches. In this paper, we consider three different resampling methods, namely the classical nonparametric bootstrap, the influence function equipped with a resampling approach as well as a martingale-based bootstrap version. We set up a simulation study to compare the accuracy of the different techniques, which reveals that the wild bootstrap should in general be preferred if the sample size is moderate and sufficient data on the event of interest have been accrued. For illustration, the three resampling methods are applied to data on the long-term survival in patients with early-stage Hodgkin's disease.

翻译：在观察性研究中，g公式可用于估计处理效应并校正混杂偏倚。然而，对于可能受竞争风险影响的时间-事件终点，构建因果风险差的有效逐点置信区间和时域同步置信带较为复杂。一个便捷的解决方案是利用重抽样方法逼近相应随机过程的渐近分布。本文考察了三种不同的重抽样方法，即经典非参数自助法、配备重抽样方法的影响函数方法以及基于鞅的自助法变体。我们通过模拟研究比较了不同技术的精确性，结果表明：当样本量适中且已积累足够的目标事件数据时，通常应优先选择野自助法。为直观展示，我们将三种重抽样方法应用于早期霍奇金病患者长期生存数据的分析。