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A shared parameter model of longitudinal measurements and survival time with heterogeneous random-effects distribution


  • Taban Baghfalaki
  • Mojtaba Ganjali
  • Geert Verbeke


Typical joint modeling of longitudinal measurements and time to event data assumes that two models share a common set of random effects with a normal distribution assumption. But, sometimes the underlying population that the sample is extracted from is a heterogeneous population and detecting homogeneous subsamples of it is an important scientific question. In this paper, a finite mixture of normal distributions for the shared random effects is proposed for considering the heterogeneity in the population. For detecting whether the unobserved heterogeneity exits or not, we use a simple graphical exploratory diagnostic tool proposed by Verbeke and Molenberghs [34] to assess whether the traditional normality assumption for the random effects in the mixed model is adequate. In the joint modeling setting, in the case of evidence against normality (homogeneity), a finite mixture of normals is used for the shared random-effects distribution. A Bayesian MCMC procedure is developed for parameter estimation and inference. The methodology is illustrated using some simulation studies. Also, the proposed approach is used for analyzing a real HIV data set, using the heterogeneous joint model for this data set, the individuals are classified into two groups: a group with high risk and a group with moderate risk.

Suggested Citation

  • Taban Baghfalaki & Mojtaba Ganjali & Geert Verbeke, 2017. "A shared parameter model of longitudinal measurements and survival time with heterogeneous random-effects distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(15), pages 2813-2836, November.
  • Handle: RePEc:taf:japsta:v:44:y:2017:i:15:p:2813-2836
    DOI: 10.1080/02664763.2016.1266309

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    References listed on IDEAS

    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.
    2. Chen, Ming-Hui & Ibrahim, Joseph G. & Sinha, Debajyoti, 2004. "A new joint model for longitudinal and survival data with a cure fraction," Journal of Multivariate Analysis, Elsevier, vol. 91(1), pages 18-34, October.
    3. 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.
    4. 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.
    5. Lang Wu & Wei Liu & Grace Y. Yi & Yangxin Huang, 2012. "Analysis of Longitudinal and Survival Data: Joint Modeling, Inference Methods, and Issues," Journal of Probability and Statistics, Hindawi, vol. 2012, pages 1-17, December.
    6. Rizopoulos, Dimitris, 2010. "JM: An R Package for the Joint Modelling of Longitudinal and Time-to-Event Data," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 35(i09).
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    Blog mentions

    As found by, the blog aggregator for Economics research:
    1. Method of the month: Shared parameter models
      by Sam Watson in The Academic Health Economists' Blog on 2018-07-26 06:00:40

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