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Nonparametric estimation of the multivariate survivor function: the multivariate Kaplan–Meier estimator

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  • Ross L. Prentice

    (Fred Hutchinson Cancer Research Center)

  • Shanshan Zhao

    (National Institute of Environmental Health Sciences)

Abstract

The Dabrowska (Ann Stat 16:1475–1489, 1988) product integral representation of the multivariate survivor function is extended, leading to a nonparametric survivor function estimator for an arbitrary number of failure time variates that has a simple recursive formula for its calculation. Empirical process methods are used to sketch proofs for this estimator’s strong consistency and weak convergence properties. Summary measures of pairwise and higher-order dependencies are also defined and nonparametrically estimated. Simulation evaluation is given for the special case of three failure time variates.

Suggested Citation

  • Ross L. Prentice & Shanshan Zhao, 2018. "Nonparametric estimation of the multivariate survivor function: the multivariate Kaplan–Meier estimator," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 24(1), pages 3-27, January.
    • Handle: RePEc:spr:lifeda:v:24:y:2018:i:1:d:10.1007_s10985-016-9383-y
    DOI: 10.1007/s10985-016-9383-y
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    References listed on IDEAS

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    1. R. L. Prentice, 2014. "Self-consistent nonparametric maximum likelihood estimator of the bivariate survivor function," Biometrika, Biometrika Trust, vol. 101(3), pages 505-518.
    2. R. L. Prentice, 2016. "Higher dimensional Clayton–Oakes models for multivariate failure time data," Biometrika, Biometrika Trust, vol. 103(1), pages 231-236.
    3. J. Fan & R. L. Prentice & L. Hsu, 2000. "A class of weighted dependence measures for bivariate failure time data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(1), pages 181-190.
    4. Michael G. Akritas & Ingrid Van Keilegom, 2003. "Estimation of bivariate and marginal distributions with censored data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 457-471, May.
    5. Yi Li & Ross L. Prentice & Xihong Lin, 2008. "Semiparametric maximum likelihood estimation in normal transformation models for bivariate survival data," Biometrika, Biometrika Trust, vol. 95(4), pages 947-960.
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    Cited by:

    1. Douglas E. Schaubel & Bin Nan, 2018. "Special issue dedicated to Jack Kalbfleisch," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 24(1), pages 1-2, January.
    2. Bernard Rosner & Camden Bay & Robert J. Glynn & Gui-shuang Ying & Maureen G. Maguire & Mei-Ling Ting Lee, 2023. "Estimation and testing for clustered interval-censored bivariate survival data with application using the semi-parametric version of the Clayton–Oakes model," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(4), pages 854-887, October.

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