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Gamma frailty transformation models for multivariate survival times

Author

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  • Donglin Zeng
  • Qingxia Chen
  • Joseph G. Ibrahim

Abstract

We propose a class of transformation models for multivariate failure times. The class of transformation models generalize the usual gamma frailty model and yields a marginally linear transformation model for each failure time. Nonparametric maximum likelihood estimation is used for inference. The maximum likelihood estimators for the regression coefficients are shown to be consistent and asymptotically normal, and their asymptotic variances attain the semiparametric efficiency bound. Simulation studies show that the proposed estimation procedure provides asymptotically efficient estimates and yields good inferential properties for small sample sizes. The method is illustrated using data from a cardiovascular study. Copyright 2009, Oxford University Press.

Suggested Citation

  • Donglin Zeng & Qingxia Chen & Joseph G. Ibrahim, 2009. "Gamma frailty transformation models for multivariate survival times," Biometrika, Biometrika Trust, vol. 96(2), pages 277-291.
    • Handle: RePEc:oup:biomet:v:96:y:2009:i:2:p:277-291
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    File URL: http://hdl.handle.net/10.1093/biomet/asp008
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    Citations

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    Cited by:

    1. Liuquan Sun & Shuwei Li & Lianming Wang & Xinyuan Song & Xuemei Sui, 2022. "Simultaneous variable selection in regression analysis of multivariate interval‐censored data," Biometrics, The International Biometric Society, vol. 78(4), pages 1402-1413, December.
    2. He, W., 2014. "Analysis of multivariate survival data with Clayton regression models under conditional and marginal formulations," Computational Statistics & Data Analysis, Elsevier, vol. 74(C), pages 52-63.
    3. Mário Castro & Ming-Hui Chen & Joseph G. Ibrahim & John P. Klein, 2014. "Bayesian Transformation Models for Multivariate Survival Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(1), pages 187-199, March.
    4. Lianqiang Qu & Liuquan Sun & Xinyuan Song, 2018. "A Joint Modeling Approach for Longitudinal Data with Informative Observation Times and a Terminal Event," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 10(3), pages 609-633, December.
    5. Xifen Huang & Jinfeng Xu & Yunpeng Zhou, 2022. "Profile and Non-Profile MM Modeling of Cluster Failure Time and Analysis of ADNI Data," Mathematics, MDPI, vol. 10(4), pages 1-21, February.
    6. 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.
    7. Ruosha Li & Yu Cheng & Qingxia Chen & Jason Fine, 2017. "Quantile association for bivariate survival data," Biometrics, The International Biometric Society, vol. 73(2), pages 506-516, June.
    8. Qingning Zhou & Tao Hu & Jianguo Sun, 2017. "A Sieve Semiparametric Maximum Likelihood Approach for Regression Analysis of Bivariate Interval-Censored Failure Time Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 664-672, April.
    9. Zhongwen Zhang & Xiaoguang Wang & Yingwei Peng, 2022. "An additive hazards frailty model with semi-varying coefficients," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 28(1), pages 116-138, January.
    10. Xianghua Lu & Tian Lu & Chong (Alex) Wang & Ruofan Wu, 2021. "Can Social Notifications Help to Mitigate Payment Delinquency in Online Peer‐to‐Peer Lending?," Production and Operations Management, Production and Operations Management Society, vol. 30(8), pages 2564-2585, August.

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