  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.
