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A Joint Modeling Approach for Longitudinal Data with Informative Observation Times and a Terminal Event

Author

Listed:
  • Lianqiang Qu

    () (Central China Normal University)

  • Liuquan Sun

    () (Chinese Academy of Sciences)

  • Xinyuan Song

    () (The Chinese University of Hong Kong)

Abstract

In this article, we propose a new joint modeling approach for the analysis of longitudinal data with informative observation times and a dependent terminal event. We specify a semiparametric mixed effects model for the longitudinal process, a proportional rate frailty model for the observation process, and a proportional hazards frailty model for the terminal event. The association among the three related processes is modeled via two latent variables. Estimating equation approaches are developed for parameter estimation, and the asymptotic properties of the proposed estimators are established. The finite sample performance of the proposed estimators is examined through simulation studies, and an application to a medical cost study of chronic heart failure patients is illustrated.

Suggested Citation

  • 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.
  • Handle: RePEc:spr:stabio:v:10:y:2018:i:3:d:10.1007_s12561-018-9221-8
    DOI: 10.1007/s12561-018-9221-8
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    References listed on IDEAS

    as
    1. Sun, Jianguo & Sun, Liuquan & Liu, Dandan, 2007. "Regression Analysis of Longitudinal Data in the Presence of Informative Observation and Censoring Times," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1397-1406, December.
    2. Haiqun Lin & Daniel O. Scharfstein & Robert A. Rosenheck, 2004. "Analysis of longitudinal data with irregular, outcome‐dependent follow‐up," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(3), pages 791-813, August.
    3. Xinyuan Song & Xiaoyun Mu & Liuquan Sun, 2012. "Regression Analysis of Longitudinal Data with Time-Dependent Covariates and Informative Observation Times," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 39(2), pages 248-258, June.
    4. 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.
    5. Sun, Jianguo & Park, Do-Hwan & Sun, Liuquan & Zhao, Xingqiu, 2005. "Semiparametric Regression Analysis of Longitudinal Data With Informative Observation Times," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 882-889, September.
    6. Liuquan Sun & Xinyuan Song & Jie Zhou & Lei Liu, 2012. "Joint Analysis of Longitudinal Data With Informative Observation Times and a Dependent Terminal Event," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(498), pages 688-700, June.
    7. Na Cai & Wenbin Lu & Hao Helen Zhang, 2012. "Time-Varying Latent Effect Model for Longitudinal Data with Informative Observation Times," Biometrics, The International Biometric Society, vol. 68(4), pages 1093-1102, December.
    8. Ryu, Duchwan & Sinha, Debajyoti & Mallick, Bani & Lipsitz, Stuart R. & Lipshultz, Steven E., 2007. "Longitudinal Studies With Outcome-Dependent Follow-up: Models and Bayesian Regression," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 952-961, September.
    9. Yining Ye & John D. Kalbfleisch & Douglas E. Schaubel, 2007. "Semiparametric Analysis of Correlated Recurrent and Terminal Events," Biometrics, The International Biometric Society, vol. 63(1), pages 78-87, March.
    10. Lei Liu & Xuelin Huang & John O'Quigley, 2008. "Analysis of Longitudinal Data in the Presence of Informative Observational Times and a Dependent Terminal Event, with Application to Medical Cost Data," Biometrics, The International Biometric Society, vol. 64(3), pages 950-958, September.
    11. D. Y. Lin & L. J. Wei & I. Yang & Z. Ying, 2000. "Semiparametric regression for the mean and rate functions of recurrent events," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 711-730.
    12. John D. Kalbfleisch & Douglas E. Schaubel & Yining Ye & Qi Gong, 2013. "An Estimating Function Approach to the Analysis of Recurrent and Terminal Events," Biometrics, The International Biometric Society, vol. 69(2), pages 366-374, June.
    13. Yu Liang & Wenbin Lu & Zhiliang Ying, 2009. "Joint Modeling and Analysis of Longitudinal Data with Informative Observation Times," Biometrics, The International Biometric Society, vol. 65(2), pages 377-384, June.
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