The wild bootstrap for multivariate Nelson–Aalen estimators

Tobias Bluhmki; Dennis Dobler; Jan Beyersmann; Markus Pauly

doi:10.1007/s10985-018-9423-x

The wild bootstrap for multivariate Nelson–Aalen estimators

Tobias Bluhmki, Dennis Dobler^*, Jan Beyersmann, Markus Pauly

^*Corresponding author for this work

Mathematics

Research output: Contribution to Journal › Article › Academic › peer-review

Abstract

We rigorously extend the widely used wild bootstrap resampling technique to the multivariate Nelson–Aalen estimator under Aalen’s multiplicative intensity model. Aalen’s model covers general Markovian multistate models including competing risks subject to independent left-truncation and right-censoring. This leads to various statistical applications such as asymptotically valid confidence bands or tests for equivalence and proportional hazards. This is exemplified in a data analysis examining the impact of ventilation on the duration of intensive care unit stay. The finite sample properties of the new procedures are investigated in a simulation study.

Original language	English
Pages (from-to)	97-127
Number of pages	31
Journal	Lifetime data analysis
Volume	25
Issue number	1
Early online date	6 Mar 2018
DOIs	https://doi.org/10.1007/s10985-018-9423-x
Publication status	Published - 15 Jan 2019

Keywords

Conditional central limit theorem
Counting process
Equivalence test
Kolmogorov–Smirnov test
Proportional hazards
Survival analysis
Weak convergence

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10.1007/s10985-018-9423-x

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6323102

Cite this

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title = "The wild bootstrap for multivariate Nelson–Aalen estimators",

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AU - Dobler, Dennis

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AU - Pauly, Markus

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N2 - We rigorously extend the widely used wild bootstrap resampling technique to the multivariate Nelson–Aalen estimator under Aalen’s multiplicative intensity model. Aalen’s model covers general Markovian multistate models including competing risks subject to independent left-truncation and right-censoring. This leads to various statistical applications such as asymptotically valid confidence bands or tests for equivalence and proportional hazards. This is exemplified in a data analysis examining the impact of ventilation on the duration of intensive care unit stay. The finite sample properties of the new procedures are investigated in a simulation study.

AB - We rigorously extend the widely used wild bootstrap resampling technique to the multivariate Nelson–Aalen estimator under Aalen’s multiplicative intensity model. Aalen’s model covers general Markovian multistate models including competing risks subject to independent left-truncation and right-censoring. This leads to various statistical applications such as asymptotically valid confidence bands or tests for equivalence and proportional hazards. This is exemplified in a data analysis examining the impact of ventilation on the duration of intensive care unit stay. The finite sample properties of the new procedures are investigated in a simulation study.

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KW - Counting process

KW - Equivalence test

KW - Kolmogorov–Smirnov test

KW - Proportional hazards

KW - Survival analysis

KW - Weak convergence

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The wild bootstrap for multivariate Nelson–Aalen estimators

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