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The Kaplan-Meier Estimate for Dependent Failure Time Observations

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  • Ying, Z.
  • Wei, L. J.

Abstract

In some long term medical follow-up studies, a series of dependent and possibly censored failure times may be observed. Suppose that these failure times were generated from the same distribution function, and inferences about it are of our main interest. In this article, we show that under rather weak conditions for the dependence among the observations, the Kaplan-Meier estimator is still consistent and asymptotically normal. For a special dependent case in which highly stratified data are observed, a valid estimate for the limiting variance of the Kaplan-Meier estimate is also provided. Our proposal is illustrated with an examply.

Suggested Citation

  • Ying, Z. & Wei, L. J., 1994. "The Kaplan-Meier Estimate for Dependent Failure Time Observations," Journal of Multivariate Analysis, Elsevier, vol. 50(1), pages 17-29, July.
    • Handle: RePEc:eee:jmvana:v:50:y:1994:i:1:p:17-29
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    Cited by:

    1. Roussas, George G., 2000. "Asymptotic normality of the kernel estimate of a probability density function under association," Statistics & Probability Letters, Elsevier, vol. 50(1), pages 1-12, October.
    2. Yinxiao Huang & Stanislav Volgushev & Xiaofeng Shao, 2015. "On Self-Normalization For Censored Dependent Data," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(1), pages 109-124, January.
    3. R. Dhanya Nair & E. I. Abdul Sathar, 2024. "Nonparametric estimation of extropy based measures under right censoring," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 15(6), pages 2374-2382, June.
    4. Cai, Zongwu & Roussas, George G., 1998. "Kaplan-Meier Estimator under Association," Journal of Multivariate Analysis, Elsevier, vol. 67(2), pages 318-348, November.
    5. Emura, Takeshi & Kao, Fan-Hsuan & Michimae, Hirofumi, 2014. "An improved nonparametric estimator of sub-distribution function for bivariate competing risk models," Journal of Multivariate Analysis, Elsevier, vol. 132(C), pages 229-241.
    6. Nilanjan Chatterjee & Joanna Shih, 2001. "A Bivariate Cure-Mixture Approach for Modeling Familial Association in Diseases," Biometrics, The International Biometric Society, vol. 57(3), pages 779-786, September.
    7. Wei Pan & Thomas A. Louis, 2000. "A Linear Mixed-Effects Model for Multivariate Censored Data," Biometrics, The International Biometric Society, vol. 56(1), pages 160-166, March.
    8. Cai, Zongwu, 1998. "Asymptotic properties of Kaplan-Meier estimator for censored dependent data," Statistics & Probability Letters, Elsevier, vol. 37(4), pages 381-389, March.
    9. Chien-Lin Su & Russell J. Steele & Ian Shrier, 2021. "The semiparametric accelerated trend-renewal process for recurrent event data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 27(3), pages 357-387, July.
    10. 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.
    11. Guosheng Yin & Jianwen Cai, 2005. "Quantile Regression Models with Multivariate Failure Time Data," Biometrics, The International Biometric Society, vol. 61(1), pages 151-161, March.
    12. Taoufik Bouezmarni & Jeroen Rombouts, 2008. "Density and hazard rate estimation for censored and α-mixing data using gamma kernels," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(7), pages 627-643.
    13. Nour El Houda Rouabah & Nahima Nemouchi & Fatiha Messaci, 2019. "A rate of consistency for nonparametric estimators of the distribution function based on censored dependent data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(2), pages 259-280, June.
    14. Yi Wu & Wei Yu & Xuejun Wang, 2022. "Strong representations of the Kaplan–Meier estimator and hazard estimator with censored widely orthant dependent data," Computational Statistics, Springer, vol. 37(1), pages 383-402, March.

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