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Jointly modeling time-to-event and longitudinal data: a Bayesian approach

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  • Yangxin Huang
  • X. Hu
  • Getachew Dagne

Abstract

This article explores Bayesian joint models of event times and longitudinal measures with an attempt to overcome departures from normality of the longitudinal response, measurement errors, and shortages of confidence in specifying a parametric time-to-event model. We allow the longitudinal response to have a skew distribution in the presence of measurement errors, and assume the time-to-event variable to have a nonparametric prior distribution. Posterior distributions of the parameters are attained simultaneously for inference based on Bayesian approach. An example from a recent AIDS clinical trial illustrates the methodology by jointly modeling the viral dynamics and the time to decrease in CD4/CD8 ratio in the presence of CD4 counts with measurement errors to compare potential models with various scenarios and different distribution specifications. The analysis outcome indicates that the time-varying CD4 covariate is closely related to the first-phase viral decay rate, but the time to CD4/CD8 decrease is not highly associated with either the two viral decay rates or the CD4 changing rate over time. These findings may provide some quantitative guidance to better understand the relationship of the virological and immunological responses to antiretroviral treatments. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Yangxin Huang & X. Hu & Getachew Dagne, 2014. "Jointly modeling time-to-event and longitudinal data: a Bayesian approach," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 23(1), pages 95-121, March.
    • Handle: RePEc:spr:stmapp:v:23:y:2014:i:1:p:95-121
    DOI: 10.1007/s10260-013-0242-7
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    References listed on IDEAS

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    1. Philip Hougaard, 1999. "Fundamentals of Survival Data," Biometrics, The International Biometric Society, vol. 55(1), pages 13-22, March.
    2. Wei Liu & Lang Wu, 2007. "Simultaneous Inference for Semiparametric Nonlinear Mixed-Effects Models with Covariate Measurement Errors and Missing Responses," Biometrics, The International Biometric Society, vol. 63(2), pages 342-350, June.
    3. 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.
    4. Yangxin Huang & Dacheng Liu & Hulin Wu, 2006. "Hierarchical Bayesian Methods for Estimation of Parameters in a Longitudinal HIV Dynamic System," Biometrics, The International Biometric Society, vol. 62(2), pages 413-423, June.
    5. Arellano-Valle, Reinaldo B. & Genton, Marc G., 2005. "On fundamental skew distributions," Journal of Multivariate Analysis, Elsevier, vol. 96(1), pages 93-116, September.
    6. Hulin Wu & A. Adam Ding, 1999. "Population HIV-1 Dynamics In Vivo: Applicable Models and Inferential Tools for Virological Data from AIDS Clinical Trials," Biometrics, The International Biometric Society, vol. 55(2), pages 410-418, June.
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    8. 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.
    9. 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.
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    Cited by:

    1. Rui Martins, 2022. "A flexible link for joint modelling longitudinal and survival data accounting for individual longitudinal heterogeneity," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(1), pages 41-61, March.
    2. Hongbin Zhang & Lang Wu, 2018. "A non‐linear model for censored and mismeasured time varying covariates in survival models, with applications in human immunodeficiency virus and acquired immune deficiency syndrome studies," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 67(5), pages 1437-1450, November.

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