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The wild bootstrap for multivariate Nelson-Aalen estimators.

Tobias Bluhmki1, Dennis Dobler2, Jan Beyersmann1

  • 1Institute of Statistics, Ulm University, Helmholtzstrasse 20, 89081, Ulm, Germany.

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Summary
This summary is machine-generated.

This study extends the wild bootstrap resampling technique for the multivariate Nelson-Aalen estimator. This advancement enables statistically valid confidence bands and tests for complex survival data, including competing risks.

Keywords:
Conditional central limit theoremCounting processEquivalence testKolmogorov–Smirnov testProportional hazardsSurvival analysisWeak convergence

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Area of Science:

  • Survival analysis
  • Biostatistics
  • Statistical modeling

Background:

  • The multivariate Nelson-Aalen estimator is crucial for analyzing complex survival data.
  • Aalen's multiplicative intensity model accommodates multistate models with competing risks, left-truncation, and right-censoring.
  • Existing resampling techniques may have limitations in these complex scenarios.

Purpose of the Study:

  • To extend the wild bootstrap resampling technique to the multivariate Nelson-Aalen estimator.
  • To develop statistically valid methods for confidence bands and hypothesis testing in multistate models.
  • To address challenges posed by competing risks, left-truncation, and right-censoring.

Main Methods:

  • Rigorous extension of the wild bootstrap resampling technique.
  • Application within Aalen's multiplicative intensity model framework.
  • Simulation studies to evaluate finite sample properties.
  • Data analysis of intensive care unit stay duration.

Main Results:

  • The proposed wild bootstrap method provides asymptotically valid confidence bands.
  • The technique facilitates statistically sound tests for equivalence and proportional hazards.
  • Demonstrated utility in a real-world data analysis concerning ICU stay.

Conclusions:

  • The extended wild bootstrap is a valuable tool for multivariate survival analysis.
  • Enables robust statistical inference in the presence of competing risks and censoring.
  • Offers practical applications in medical research and other fields.