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The Kaplan-Meier Integral in the Presence of Covariates: A Review

In: From Statistics to Mathematical Finance

Author

Listed:
  • Thomas A. Gerds

    (University of Copenhagen, Section of Biostatistics)

  • Jan Beyersmann

    (University of Ulm, Institute of Statistics)

  • Liis Starkopf

    (University of Copenhagen, Section of Biostatistics)

  • Sandra Frank

    (University of Ulm, Institute of Statistics)

  • Mark J. van der Laan

    (University of California, Division of Biostatistics, School of Public Health)

  • Martin Schumacher

    (University of Freiburg, Institute for Medical Biometry and Statistics)

Abstract

In a series of papers, Winfried Stute introduced and studied the Kaplan-Meier integral as an estimator of parameters of the joint distribution of survival times and covariates based on right censored survival times. We present a review of this work and show that his estimator has an inverse probability of censoring weighting (IPCW) representation. We further investigate large sample bias and efficiency. As a central application in a biostatistical context, Kaplan-Meier integrals are used to estimate transition probabilities in a non-Markov illness-death model. We extend already existing approaches by introducing a novel estimator that also works in the presence of additional left truncation. This application illustrates that Winfried Stute’s work can successfully be used to develop inferential statistical methods in complex survival models.

Suggested Citation

  • Thomas A. Gerds & Jan Beyersmann & Liis Starkopf & Sandra Frank & Mark J. van der Laan & Martin Schumacher, 2017. "The Kaplan-Meier Integral in the Presence of Covariates: A Review," Springer Books, in: Dietmar Ferger & Wenceslao González Manteiga & Thorsten Schmidt & Jane-Ling Wang (ed.), From Statistics to Mathematical Finance, chapter 0, pages 25-41, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-50986-0_2
    DOI: 10.1007/978-3-319-50986-0_2
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