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Frailty modelling approaches for semi-competing risks data

Author

Listed:
  • Il Do Ha

    (Pukyong National University)

  • Liming Xiang

    (Nanyang Technological University)

  • Mengjiao Peng

    (Nanyang Technological University)

  • Jong-Hyeon Jeong

    (University of Pittsburgh)

  • Youngjo Lee

    (Seoul National University)

Abstract

In the semi-competing risks situation where only a terminal event censors a non-terminal event, observed event times can be correlated. Recently, frailty models with an arbitrary baseline hazard have been studied for the analysis of such semi-competing risks data. However, their maximum likelihood estimator can be substantially biased in the finite samples. In this paper, we propose effective modifications to reduce such bias using the hierarchical likelihood. We also investigate the relationship between marginal and hierarchical likelihood approaches. Simulation results are provided to validate performance of the proposed method. The proposed method is illustrated through analysis of semi-competing risks data from a breast cancer study.

Suggested Citation

  • Il Do Ha & Liming Xiang & Mengjiao Peng & Jong-Hyeon Jeong & Youngjo Lee, 2020. "Frailty modelling approaches for semi-competing risks data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(1), pages 109-133, January.
    • Handle: RePEc:spr:lifeda:v:26:y:2020:i:1:d:10.1007_s10985-019-09464-2
    DOI: 10.1007/s10985-019-09464-2
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    References listed on IDEAS

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    1. Il Do Ha & Maengseok Noh & Youngjo Lee, 2010. "Bias Reduction of Likelihood Estimators in Semiparametric Frailty Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(2), pages 307-320, June.
    2. Ha, Il Do & Sylvester, Richard & Legrand, Catherine & MacKenzie, Gilbert, 2011. "Frailty modelling for survival data from multi-centre clinical trials," LIDAM Reprints ISBA 2011060, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. Samuli Ripatti & Juni Palmgren, 2000. "Estimation of Multivariate Frailty Models Using Penalized Partial Likelihood," Biometrics, The International Biometric Society, vol. 56(4), pages 1016-1022, December.
    4. Georg Heinze & Michael Schemper, 2001. "A Solution to the Problem of Monotone Likelihood in Cox Regression," Biometrics, The International Biometric Society, vol. 57(1), pages 114-119, March.
    5. Jinfeng Xu & John D. Kalbfleisch & Beechoo Tai, 2010. "Statistical Analysis of Illness–Death Processes and Semicompeting Risks Data," Biometrics, The International Biometric Society, vol. 66(3), pages 716-725, September.
    6. Kyu Ha Lee & Sebastien Haneuse & Deborah Schrag & Francesca Dominici, 2015. "Bayesian semiparametric analysis of semicompeting risks data: investigating hospital readmission after a pancreatic cancer diagnosis," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 64(2), pages 253-273, February.
    7. Noh, Maengseok & Lee, Youngjo, 2007. "REML estimation for binary data in GLMMs," Journal of Multivariate Analysis, Elsevier, vol. 98(5), pages 896-915, May.
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