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A Semiparametric Bayesian Joint Modelling of Skewed Longitudinal and Competing Risks Failure Time Data: With Application to Chronic Kidney Disease

Author

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  • Melkamu Molla Ferede

    (Pan African University Institute for Basic Sciences, Technology and Innovation (PAUSTI), Nairobi 62000-00200, Kenya
    Department of Statistics, University of Gondar, Gondar 196, Ethiopia)

  • Samuel Mwalili

    (Department of Statistics and Actuarial Sciences, Jomo Kenyatta University of Agriculture and Technology (JKUAT), Nairobi 62000-00200, Kenya)

  • Getachew Dagne

    (Department of Epidemiology and Biostatistics, College of Public Health, University of South Florida, 13201 Bruce B. Downs, Tampa, FL 33612, USA)

  • Simon Karanja

    (School of Public Health, Jomo Kenyatta University of Agriculture and Technology (JKUAT), Nairobi 62000-00200, Kenya)

  • Workagegnehu Hailu

    (Department of Internal Medicine, College of Medicine and Health Sciences, University of Gondar, Gondar 196, Ethiopia)

  • Mahmoud El-Morshedy

    (Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia
    Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt)

  • Afrah Al-Bossly

    (Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj 11942, Saudi Arabia)

Abstract

In clinical and epidemiological studies, when the time-to-event(s) and the longitudinal outcomes are associated, modelling them separately may give biased estimates. A joint modelling approach is required to obtain unbiased results and to evaluate their association. In the joint model, a subject may be exposed to more than one type of failure event (competing risks). Considering the competing event as an independent censoring of the time-to-event process may underestimate the true survival probability and give biased results. Within the joint model, longitudinal outcomes may have nonlinear (irregular) trajectories over time and exhibit skewness with heavy tails. Accordingly, fully parametric mixed-effect models may not be flexible enough to model this type of complex longitudinal data. In addition, assuming a Gaussian distribution for model errors may be too restrictive to adequately represent within-individual variations and may lack robustness against deviation from distributional assumptions. To simultaneously overcome these issues, in this paper, we presented semiparametric joint models for competing risks failure time and skewed-longitudinal data by using a smoothing spline approach and a multivariate skew-t distribution. We also considered different parameterization approaches in the formulation of joint models and used a Bayesian approach to make the statistical inference. We illustrated the proposed methods by analyzing real data on a chronic kidney disease. To evaluate the performance of the methods, we also carried out simulation studies. The results of both the application and simulation studies revealed that the joint modelling approach proposed in this study performed well when the semiparametric, random-effects parameterization, and skew-t distribution specifications were taken into account.

Suggested Citation

  • Melkamu Molla Ferede & Samuel Mwalili & Getachew Dagne & Simon Karanja & Workagegnehu Hailu & Mahmoud El-Morshedy & Afrah Al-Bossly, 2022. "A Semiparametric Bayesian Joint Modelling of Skewed Longitudinal and Competing Risks Failure Time Data: With Application to Chronic Kidney Disease," Mathematics, MDPI, vol. 10(24), pages 1-21, December.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:24:p:4816-:d:1007275
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    References listed on IDEAS

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    1. 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.
    2. Xiao Song & Marie Davidian & Anastasios A. Tsiatis, 2002. "A Semiparametric Likelihood Approach to Joint Modeling of Longitudinal and Time-to-Event Data," Biometrics, The International Biometric Society, vol. 58(4), pages 742-753, December.
    3. Jeevanantham Rajeswaran & Eugene H Blackstone & John Barnard, 2018. "Joint Modeling of Multivariate Longitudinal Data and Competing Risks Using Multiphase Sub-models," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 10(3), pages 651-685, December.
    4. 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.
    5. Tang, Nian-Sheng & Tang, An-Min & Pan, Dong-Dong, 2014. "Semiparametric Bayesian joint models of multivariate longitudinal and survival data," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 113-129.
    6. Josua Mwanyekange & Samuel Mwalili & Oscar Ngesa, 2018. "Bayesian Inference in a Joint Model for Longitudinal and Time to Event Data with Gompertz Baseline Hazards," Modern Applied Science, Canadian Center of Science and Education, vol. 12(9), pages 159-159, September.
    7. Ali Azarbar & Yu Wang & Saralees Nadarajah, 2021. "Simultaneous Bayesian modeling of longitudinal and survival data in breast cancer patients," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 50(2), pages 400-414, January.
    8. L. Wu & W. Liu & X. J. Hu, 2010. "Joint Inference on HIV Viral Dynamics and Immune Suppression in Presence of Measurement Errors," Biometrics, The International Biometric Society, vol. 66(2), pages 327-335, June.
    9. T. Baghfalaki & M. Ganjali & D. Berridge, 2014. "Joint modeling of multivariate longitudinal mixed measurements and time to event data using a Bayesian approach," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(9), pages 1934-1955, September.
    10. Yangxin Huang & Getachew Dagne, 2011. "A Bayesian Approach to Joint Mixed-Effects Models with a Skew-Normal Distribution and Measurement Errors in Covariates," Biometrics, The International Biometric Society, vol. 67(1), pages 260-269, March.
    11. J. T. Gaskins & M. J. Daniels & B. H. Marcus, 2016. "Bayesian Methods for Nonignorable Dropout in Joint Models in Smoking Cessation Studies," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1454-1465, October.
    12. Wei Yang & Dawei Xie & Qiang Pan & Harold I. Feldman & Wensheng Guo, 2017. "Joint Modeling of Repeated Measures and Competing Failure Events in a Study of Chronic Kidney Disease," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 9(2), pages 504-524, December.
    13. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    14. Adelchi Azzalini & Antonella Capitanio, 2003. "Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t‐distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 367-389, May.
    15. Lei Liu & Xuelin Huang, 2009. "Joint analysis of correlated repeated measures and recurrent events processes in the presence of death, with application to a study on acquired immune deficiency syndrome," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 58(1), pages 65-81, February.
    16. R.B. Arellano-Valle & H. Bolfarine & V.H. Lachos, 2007. "Bayesian Inference for Skew-normal Linear Mixed Models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 34(6), pages 663-682.
    17. Kiranmoy Das, 2016. "A semiparametric Bayesian approach for joint modeling of longitudinal trait and event time," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(15), pages 2850-2865, November.
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