A Discontinuity Adjustment for Subdistribution Function Confidence Bands Applied to Right-Censored Competing Risks Data

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Abstract

The wild bootstrap is the resampling method of choice in survival analytic applications. Theoretic justifications typically 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.

Original languageEnglish
Pages (from-to)3673-3702
Number of pages30
JournalElectronic Journal of Statistics
Volume11
Issue number2
DOIs
Publication statusPublished - 2017
Externally publishedYes

Keywords

  • Aalen-Johansen estimator
  • Counting process
  • Discontinuous cumulative hazard functions
  • Discontinuous cumulative incidence functions
  • Greenwood-type variance estimator
  • Nelson-Aalen estimator
  • Survival analysis
  • Tied event times
  • Wild bootstrap

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