The wild bootstrap is a popular resampling method in the context of time-to-event data analyses. Previous works established the large sample properties of it for applications to different estimators and test statistics. It can be used to justify the accuracy of inference procedures such as hypothesis tests or time-simultaneous confidence bands. This paper consists of two parts: in Part~I, a general framework is developed in which the large sample properties are established in a unified way by using martingale structures. The framework includes most of the well-known non- and semiparametric statistical methods in time-to-event analysis and parametric approaches. In Part II, the Fine-Gray proportional sub-hazards model exemplifies the theory for inference on cumulative incidence functions given the covariates. The model falls within the framework if the data are censoring-complete. A simulation study demonstrates the reliability of the method and an application to a data set about hospital-acquired infections illustrates the statistical procedure.

翻译：野生自助法是一种在时间至事件数据分析中广泛使用的重抽样方法。已有研究确立了该方法在不同估计量和检验统计量应用中的大样本性质，可验证假设检验或时间同步置信带等推断程序的准确性。本文分为两部分：第一部分建立了一个通用框架，通过利用鞅结构以统一方式确立大样本性质。该框架涵盖了时间至事件分析中大多数已知的非参数与半参数统计方法及参数方法。第二部分以Fine-Gray比例子风险模型为例，阐释了协变量条件下累积发生函数推断的理论。若数据满足删失完备性条件，该模型即纳入前述框架。模拟研究验证了方法的可靠性，对医院获得性感染数据的应用则展示了统计流程的实施。