# A Discontinuity Adjustment for Subdistribution Function Confidence Bands Applied to Right-Censored Competing Risks Data (with Erratum)

## TL;DR

This paper proposes a modified wild bootstrap method and variance estimator for more accurate confidence bands in survival analysis with tied event times, especially in competing risks data.

## Contribution

It introduces a discontinuity adjustment technique for bootstrap and variance estimation, improving inference accuracy in tied survival data.

## Key findings

- Enhanced bootstrap method with discontinuity adjustment improves coverage accuracy.
- Simulation studies demonstrate better finite-sample performance.
- Application to ICU pneumonia data confirms practical utility.

## Abstract

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.