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

Thomas A. Gerds (), Jan Beyersmann, Liis Starkopf, Sandra Frank, Mark J. van der Laan and Martin Schumacher
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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

Chapter Chapter 2 in From Statistics to Mathematical Finance, 2017, pp 25-41 from Springer

Abstract: 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.

Keywords: Efficient influence function; Estimation of functionals; Inverse of the probability of censoring weighted; Survival regression analysis; Multi-state model (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-50986-0_2

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DOI: 10.1007/978-3-319-50986-0_2

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