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A note on nonparametric quantile inference for competing risks and more complex multistate models

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  • Jan Beyersmann
  • Martin Schumacher

Abstract

Nonparametric quantile inference for competing risks has recently been studied by Peng & Fine (2007). Their key result establishes uniform consistency and weak convergence of the inverse of the Aalen--Johansen estimator of the cumulative incidence function, using the representation of the cumulative incidence estimator as a sum of independent and identically distributed random variables. The limit process is of a form similar to that of the standard survival result, but with the cause-specific hazard of interest replacing the all-causes hazard. We show that this fact is not a coincidence, but can be derived from a general Hadamard differentiation result. We discuss a simplified proof and extensions of the approach to more complex multistate models. As a further consequence, we find that the bootstrap works. Copyright 2008, Oxford University Press.

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  • Jan Beyersmann & Martin Schumacher, 2008. "A note on nonparametric quantile inference for competing risks and more complex multistate models," Biometrika, Biometrika Trust, vol. 95(4), pages 1006-1008.
    • Handle: RePEc:oup:biomet:v:95:y:2008:i:4:p:1006-1008
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    File URL: http://hdl.handle.net/10.1093/biomet/asn044
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    Cited by:

    1. Arthur Allignol & Martin Schumacher & Jan Beyersmann, 2011. "Estimating summary functionals in multistate models with an application to hospital infection data," Computational Statistics, Springer, vol. 26(2), pages 181-197, June.
    2. Julien Worms & Rym Worms, 2018. "Extreme value statistics for censored data with heavy tails under competing risks," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(7), pages 849-889, October.
    3. S. R. Haile & J.-H. Jeong & X. Chen & Y. Cheng, 2016. "A 3-parameter Gompertz distribution for survival data with competing risks, with an application to breast cancer data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(12), pages 2239-2253, September.

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