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The wild bootstrap for multivariate Nelson–Aalen estimators

Author

Listed:
  • Tobias Bluhmki

    (Ulm University)

  • Dennis Dobler

    (Vrije Universiteit Amsterdam)

  • Jan Beyersmann

    (Ulm University)

  • Markus Pauly

    (Ulm University)

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.

Suggested Citation

  • Tobias Bluhmki & Dennis Dobler & Jan Beyersmann & Markus Pauly, 2019. "The wild bootstrap for multivariate Nelson–Aalen estimators," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(1), pages 97-127, January.
    • Handle: RePEc:spr:lifeda:v:25:y:2019:i:1:d:10.1007_s10985-018-9423-x
    DOI: 10.1007/s10985-018-9423-x
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    References listed on IDEAS

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    1. Thomas H. Scheike & Torben Martinussen, 2004. "On Estimation and Tests of Time‐Varying Effects in the Proportional Hazards Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(1), pages 51-62, March.
    2. Markus Pauly & Edgar Brunner & Frank Konietschke, 2015. "Asymptotic permutation tests in general factorial designs," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(2), pages 461-473, March.
    3. D. Y. Lin & L. J. Wei & I. Yang & Z. Ying, 2000. "Semiparametric regression for the mean and rate functions of recurrent events," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 711-730.
    4. Bajorunaite, Ruta & Klein, John P., 2007. "Two-sample tests of the equality of two cumulative incidence functions," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4269-4281, May.
    5. Ward Whitt, 1980. "Some Useful Functions for Functional Limit Theorems," Mathematics of Operations Research, INFORMS, vol. 5(1), pages 67-85, February.
    6. D. Dobler & J. Beyersmann & M. Pauly, 2017. "Non-strange weird resampling for complex survival data," Biometrika, Biometrika Trust, vol. 104(3), pages 699-711.
    7. Anna Dudek & Maciej Goćwin & Jacek Leśkow, 2008. "Simultaneous confidence bands for the integrated hazard function," Computational Statistics, Springer, vol. 23(1), pages 41-62, January.
    8. David V. Glidden, 2002. "Robust Inference for Event Probabilities with Non-Markov Event Data," Biometrics, The International Biometric Society, vol. 58(2), pages 361-368, June.
    9. Wei Chen & Dehui Wang & Yanfeng Li, 2015. "A class of tests of proportional hazards assumption for left-truncated and right-censored data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(11), pages 2307-2320, November.
    10. Jan Beyersmann & Susanna Di Termini & Markus Pauly, 2013. "Weak Convergence of the Wild Bootstrap for the Aalen–Johansen Estimator of the Cumulative Incidence Function of a Competing Risk," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(3), pages 387-402, September.
    11. Thomas H. Scheike & Mei-Jie Zhang, 2003. "Extensions and Applications of the Cox-Aalen Survival Model," Biometrics, The International Biometric Society, vol. 59(4), pages 1036-1045, December.
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    2. Nießl, Alexandra & Allignol, Arthur & Beyersmann, Jan & Mueller, Carina, 2023. "Statistical inference for state occupation and transition probabilities in non-Markov multi-state models subject to both random left-truncation and right-censoring," Econometrics and Statistics, Elsevier, vol. 25(C), pages 110-124.

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