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Pseudo Self‐Consistent Estimation of a Copula Model with Informative Censoring

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  • HONGYU JIANG
  • JASON P. FINE
  • MICHAEL R. KOSOROK
  • RICK CHAPPELL

Abstract

. We consider the case where a terminal event censors a non‐terminal event, but not vice versa. When the events are dependent, estimation of the distribution of the non‐terminal event is a competing risks problem, while estimation of the distribution of the terminal event is not. The dependence structure of the event times is formulated with the gamma frailty copula on the upper wedge, with the marginal distributions unspecified. With a consistent estimator of the association parameter, pseudo self‐consistency equations are derived and adapted to the semiparametric model. Existence, uniform consistency and weak convergence of the new estimator for the marginal distribution of the non‐terminal event is established using theories of empirical processes, U‐statistics and Z‐estimation. The potential practical utility of the methodology is illustrated with simulated and real data sets.

Suggested Citation

  • Hongyu Jiang & Jason P. Fine & Michael R. Kosorok & Rick Chappell, 2005. "Pseudo Self‐Consistent Estimation of a Copula Model with Informative Censoring," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 32(1), pages 1-20, March.
    • Handle: RePEc:bla:scjsta:v:32:y:2005:i:1:p:1-20
    DOI: 10.1111/j.1467-9469.2005.00412.x
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    Cited by:

    1. Fei Jiang & Sebastien Haneuse, 2017. "A Semi-parametric Transformation Frailty Model for Semi-competing Risks Survival Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(1), pages 112-129, March.
    2. Dongdong Li & X. Joan Hu & Mary L. McBride & John J. Spinelli, 2020. "Multiple event times in the presence of informative censoring: modeling and analysis by copulas," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(3), pages 573-602, July.
    3. Menggang Yu & Constantin T. Yiannoutsos, 2015. "Marginal and Conditional Distribution Estimation from Double-sampled Semi-competing Risks Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(1), pages 87-103, March.
    4. Renke Zhou & Hong Zhu & Melissa Bondy & Jing Ning, 2016. "Semiparametric model for semi-competing risks data with application to breast cancer study," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 22(3), pages 456-471, July.
    5. Lajmi Lakhal & Louis-Paul Rivest & Belkacem Abdous, 2008. "Estimating Survival and Association in a Semicompeting Risks Model," Biometrics, The International Biometric Society, vol. 64(1), pages 180-188, March.
    6. Hsieh, Jin-Jian & Hsu, Chia-Hao, 2018. "Estimation of the survival function with redistribution algorithm under semi-competing risks data," Statistics & Probability Letters, Elsevier, vol. 132(C), pages 1-6.
    7. Heuchenne, Cedric & Laurent, Stephane & Legrand, Catherine & Van Keilegom, Ingrid, 2011. "Likelihood based inference for semi-competing risks," LIDAM Discussion Papers ISBA 2011022, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    8. N. Davarzani & L. Golparvar & A. Parsian & R. Peeters, 2017. "Estimation on dependent right censoring scheme in an ordinary bivariate geometric distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(8), pages 1369-1384, June.

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