  The wild bootstrap is the resampling method of choice in survival analytic
applications. Theoretic justifications rely on the assumption of existing
intensity functions which is equivalent to an exclusion of ties among the event
times. However, such ties are omnipresent in practical studies. It turns out
that the wild bootstrap should only be applied in a modified manner that
corrects for altered limit variances and emerging dependencies. This again
ensures the asymptotic exactness of inferential procedures. An analogous
necessity is the use of the Greenwood-type variance estimator for Nelson-Aalen
estimators which is particularly preferred in tied data regimes. All theoretic
arguments are transferred to bootstrapping Aalen-Johansen estimators for
cumulative incidence functions in competing risks. An extensive simulation
study as well as an application to real competing risks data of male intensive
care unit patients suffering from pneumonia illustrate the practicability of
the proposed technique.
