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A Joint Model for Longitudinal Measurements and Survival Data in the Presence of Multiple Failure Types

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  • Robert M. Elashoff
  • Gang Li
  • Ning Li

Abstract

Summary In this article we study a joint model for longitudinal measurements and competing risks survival data. Our joint model provides a flexible approach to handle possible nonignorable missing data in the longitudinal measurements due to dropout. It is also an extension of previous joint models with a single failure type, offering a possible way to model informatively censored events as a competing risk. Our model consists of a linear mixed effects submodel for the longitudinal outcome and a proportional cause‐specific hazards frailty submodel (Prentice et al., 1978, Biometrics34, 541–554) for the competing risks survival data, linked together by some latent random effects. We propose to obtain the maximum likelihood estimates of the parameters by an expectation maximization (EM) algorithm and estimate their standard errors using a profile likelihood method. The developed method works well in our simulation studies and is applied to a clinical trial for the scleroderma lung disease.

Suggested Citation

  • Robert M. Elashoff & Gang Li & Ning Li, 2008. "A Joint Model for Longitudinal Measurements and Survival Data in the Presence of Multiple Failure Types," Biometrics, The International Biometric Society, vol. 64(3), pages 762-771, September.
    • Handle: RePEc:bla:biomet:v:64:y:2008:i:3:p:762-771
    DOI: 10.1111/j.1541-0420.2007.00952.x
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    1. Yi-Kuan Tseng & Fushing Hsieh & Jane-Ling Wang, 2005. "Joint modelling of accelerated failure time and longitudinal data," Biometrika, Biometrika Trust, vol. 92(3), pages 587-603, September.
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    5. Elizabeth R. Brown & Joseph G. Ibrahim, 2003. "A Bayesian Semiparametric Joint Hierarchical Model for Longitudinal and Survival Data," Biometrics, The International Biometric Society, vol. 59(2), pages 221-228, June.
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    Cited by:

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    7. An-Min Tang & Nian-Sheng Tang & Dalei Yu, 2023. "Bayesian semiparametric joint model of multivariate longitudinal and survival data with dependent censoring," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(4), pages 888-918, October.
    8. Tao Lu, 2017. "Bayesian inference on longitudinal-survival data with multiple features," Computational Statistics, Springer, vol. 32(3), pages 845-866, September.
    9. Graeme L. Hickey & Pete Philipson & Andrea Jorgensen & Ruwanthi Kolamunnage‐Dona, 2018. "A comparison of joint models for longitudinal and competing risks data, with application to an epilepsy drug randomized controlled trial," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 181(4), pages 1105-1123, October.
    10. Shanshan Li, 2016. "Joint modeling of recurrent event processes and intermittently observed time-varying binary covariate processes," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 22(1), pages 145-160, January.
    11. Yi, Fengting & Tang, Niansheng & Sun, Jianguo, 2020. "Regression analysis of interval-censored failure time data with time-dependent covariates," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    12. Karimi, M. & Rey, G. & Latouche, A., 2018. "A Joint modelling of socio-professional trajectories and cause-specific mortality," Computational Statistics & Data Analysis, Elsevier, vol. 119(C), pages 39-54.
    13. Jaeun Choi & Jianwen Cai & Donglin Zeng, 2017. "Penalized Likelihood Approach for Simultaneous Analysis of Survival Time and Binary Longitudinal Outcome," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 79(2), pages 190-216, November.
    14. Shahedul A. Khan & Nyla Basharat, 2022. "Accelerated failure time models for recurrent event data analysis and joint modeling," Computational Statistics, Springer, vol. 37(4), pages 1569-1597, September.
    15. Jaeun Choi & Donglin Zeng & Andrew F. Olshan & Jianwen Cai, 2018. "Joint modeling of survival time and longitudinal outcomes with flexible random effects," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 24(1), pages 126-152, January.
    16. Rizopoulos, Dimitris, 2012. "Fast fitting of joint models for longitudinal and event time data using a pseudo-adaptive Gaussian quadrature rule," Computational Statistics & Data Analysis, Elsevier, vol. 56(3), pages 491-501.
    17. Dilip C. Nath & Atanu Bhattacharjee, 2014. "Joint longitudinal and survival data modelling: an application in anti-diabetes drug therapeutic effect," Statistics in Transition new series, Główny Urząd Statystyczny (Polska), vol. 15(3), pages 437-452, June.
    18. Zhang, Cuihong & Ning, Jing & Cai, Jianwen & Squires, James E. & Belle, Steven H. & Li, Ruosha, 2024. "Dynamic risk score modeling for multiple longitudinal risk factors and survival," Computational Statistics & Data Analysis, Elsevier, vol. 189(C).

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