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, the so-called wild bootstrap. For the latter, three sub-versions based on differing distributions of the underlying random multipliers are examined. 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 resampling methods are further applied to data on the long-term survival in patients with early-stage Hodgkin’s disease.

g 公式可用于估计治疗效果，同时考虑观察性研究中的混杂偏差。然而，对于可能受到竞争风险影响的事件时间终点，为因果风险差异构建有效的逐点置信区间和时间同步置信带是复杂的。一种方便的解决方案是通过重采样方法来近似相应随机过程的渐近分布。在本文中，我们考虑三种不同的重采样方法，即经典的非参数引导、配备重采样方法的影响函数以及基于鞅的引导版本，即所谓的狂野引导。对于后者，检查了基于底层随机乘数的不同分布的三个子版本。我们建立了一项模拟研究来比较不同技术的准确性，结果表明，如果样本量适中并且已经积累了有关感兴趣事件的足够数据，则通常应首选野生引导法。为了说明这一点，重采样方法进一步应用于早期霍奇金病患者的长期生存数据。