Skip to main content
Springer Nature Link
Log in

Bayesian inference on partially linear mixed-effects joint models for longitudinal data with multiple features

  • Original Paper
  • Published:
Computational Statistics Aims and scope Submit manuscript

Abstract

The relationship between viral load and CD4 cell count is one of the interesting questions in AIDS research. Statistical models are powerful tools for clarifying this important problem. Partially linear mixed-effects (PLME) model which accounts for the unknown function of time effect is one of the important models for this purpose. Meanwhile, the mixed-effects modeling approach is suitable for the longitudinal data analysis. However, the complex process of data collection in clinical trials has made it impossible to rely on one particular model to address the issues. Asymmetric distribution, measurement error and left censoring are features commonly arisen in longitudinal studies. It is crucial to take into account these features in the modeling process to achieve reliable estimation and valid conclusion. In this article, we establish a joint model that accounts for all these features in the framework of PLME models. A Bayesian inferential procedure is proposed to estimate parameters in the joint model. A real data example is analyzed to demonstrate the proposed modeling approach for inference and the results are reported by comparing various scenarios-based models.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  • Arellano-Valle R, Genton M (2005) On fundamental skew distributions. J Multivar Anal 96:93–116

    Article  MathSciNet  MATH  Google Scholar 

  • Azzalini A, Capitanio A (2003) Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t-distribution. J R Stat Soc Series B 65:367–389

    Article  MathSciNet  MATH  Google Scholar 

  • Azzalini A, Genton M (2008) Robust likelihood methods based on the skew-t and related distributions. Int Stat Rev 76:106–129

    Article  MATH  Google Scholar 

  • Carroll R, Ruppert D, Stefanski L, Crainiceanu C (2006) Measurement error in nonlinear models: a modern perspective. Chapman and Hall, London

    Book  MATH  Google Scholar 

  • Gelman A, Rubin D (1992) Inference from iterative simulation using multiple sequences. Stat Sci 7:457–511

    Article  Google Scholar 

  • Gelman A, Carlin J, Stern H, Rubin D (2003) Bayesian data analysis. Chapman and Hall, London

    MATH  Google Scholar 

  • Hammer SM, Vaida F, Bennett KK, Holohan MK, Sheiner L, Eron JJ, Wheat LJ, Mitsuyasu RT, Gulick RM, Valentine FT, Aberg JA, Rogers MD, Karol CN, Saah AJ, Lewis RH, Bessen LJ, Brosgart C, DeGruttola V, Mellors JW (2002) AIDS clinical trials group 398 study team. Dual vs single protease inhibitor therapy following antiretroviral treatment failure: a randomized trial. JAMA 288:169–180

    Article  Google Scholar 

  • Härdle W, Liang H, Gao J (2000) Partially linear models. Springer Physica-Verlag, Heidelberg

    Book  MATH  Google Scholar 

  • Ho H, Lin T (2010) Robust linear mixed models using the skew-t distribution with application to schizophrenia data. Biom J 52:449–469

    Article  MathSciNet  MATH  Google Scholar 

  • Huang Y, Dagne G (2011) A Bayesian approach to joint mixed-effects models with a skew-normal distribution and measurement errors in covariates. Biometrics 67:260–269

    Article  MathSciNet  MATH  Google Scholar 

  • Huang Y, Dagne G (2012) Bayesian semiparametric nonlinear mixed-effects joint models for data with skewness, missing responses and measurement errors in covariates. Biometrics 68:943–953

    Article  MathSciNet  MATH  Google Scholar 

  • Huang Y, Dagne G, Wu L (2011) Bayesian inference on joint models of HIV dynamics for time-to-event and longitudinal data with skewness and covariate measurement errors. Stat Med 30:2930–2946

    Article  MathSciNet  Google Scholar 

  • Huang Y, Dagne G, Wu L (2012) Mixed-effects joint models with skew-normal distribution for HIV dynamic response with missing and mismeasured time-varying covariate. Int J Biostat 8(1):34

    Article  MathSciNet  Google Scholar 

  • Jara A, Quintana F, Martin E (2008) Linear mixed models with skew-elliptical distributions: a Bayesian approach. Comput Stat Data Anal 52:5033–5045

    Article  MathSciNet  MATH  Google Scholar 

  • Lachos V, Bandyopadhyay D, Dey D (2011) Linear and nonlinear mixed-effects models for censored HIV viral loads using normal/independent distributions. Biometrics 67:1594–1604

    Article  MathSciNet  MATH  Google Scholar 

  • Liang H, Ren H (2005) Generalized partially linear measurement error models. J Comput Graph Stat 14:237–250

    Article  MathSciNet  Google Scholar 

  • Liang H, Wang S, Robins J, Carroll R (2004) Estimation in partially linear models with missing covariates. J Am Stat Assoc 99:357–367

    Article  MathSciNet  MATH  Google Scholar 

  • Liu W, Wu L (2007) Simultaneous inference for semiparametric nonlinear mixed-effects models withco variate measurement errors and missing responses. Biometrics 63:342–350

    Article  MathSciNet  MATH  Google Scholar 

  • Lunn D, Thomas A, Best N, Spiegelhalter D (2000) WinBUGS-a Bayesian modelling framework: concepts, structure, an extensibility. Stat Comput 10:325–337

    Article  Google Scholar 

  • Sahu S, Dey D, Branco M (2003) A new class of multivariate skew distributions with applications to Bayesian regression models. Can J Stat 31:129–150

    Article  MathSciNet  MATH  Google Scholar 

  • Speckman P (1988) Kernel smoothing in partial linear models. J R Stat Soc Series B 50:413–436

    MathSciNet  MATH  Google Scholar 

  • Spiegelhalter D, Best N, Carlin B, Van der Linde A (2002) Bayesian measures of model complexity and fit. J R Stat Soc Series B 64:583–639

    Article  MathSciNet  MATH  Google Scholar 

  • Wu L (2002) A joint model for nonlinear mixed-effects models with censoring and covariates measured with error. J Am Stat Assoc 97:955–964

    Article  MATH  Google Scholar 

Download references

Acknowledgments

The authors gratefully acknowledge the Editor, Associate Editor and two anonymous referees for their insightful comments and detailed suggestions that led to a marked improvement of the article.

Author information

Authors and Affiliations

  1. Department of Epidemiology and Biostatistics, College of Public Health, University of South Florida, Tampa, FL, 33612, USA

    Yangxin Huang

  2. Department of Epidemiology and Biostatistics, State University of New York, Albany, NY, 12144, USA

    Tao Lu

Authors
  1. Yangxin Huang
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Tao Lu
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Yangxin Huang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Huang, Y., Lu, T. Bayesian inference on partially linear mixed-effects joint models for longitudinal data with multiple features. Comput Stat 32, 179–196 (2017). https://doi.org/10.1007/s00180-016-0671-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00180-016-0671-5

Keywords