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Longitudinal Poisson modeling: an application for CD4 counting in HIV-infected patients

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  • Emilio Augusto Coelho-Barros
  • Jorge Alberto Achcar
  • Josmar Mazucheli

Abstract

In this paper, we present different “frailty” models to analyze longitudinal data in the presence of covariates. These models incorporate the extra-Poisson variability and the possible correlation among the repeated counting data for each individual. Assuming a CD4 counting data set in HIV-infected patients, we develop a hierarchical Bayesian analysis considering the different proposed models and using Markov Chain Monte Carlo methods. We also discuss some Bayesian discrimination aspects for the choice of the best model.

Suggested Citation

  • Emilio Augusto Coelho-Barros & Jorge Alberto Achcar & Josmar Mazucheli, 2010. "Longitudinal Poisson modeling: an application for CD4 counting in HIV-infected patients," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(5), pages 865-880.
  • Handle: RePEc:taf:japsta:v:37:y:2010:i:5:p:865-880
    DOI: 10.1080/02664760902914466
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    References listed on IDEAS

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    1. Robin Henderson, 2003. "A serially correlated gamma frailty model for longitudinal count data," Biometrika, Biometrika Trust, vol. 90(2), pages 355-366, June.
    2. Dunson, David B., 2003. "Dynamic Latent Trait Models for Multidimensional Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 555-563, January.
    3. R. Crouchley & R. B. Davies, 1999. "A comparison of population average and random‐effect models for the analysis of longitudinal count data with base‐line information," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 162(3), pages 331-347.
    4. Chib, Siddhartha & Greenberg, Edward & Winkelmann, Rainer, 1998. "Posterior simulation and Bayes factors in panel count data models," Journal of Econometrics, Elsevier, vol. 86(1), pages 33-54, June.
    5. 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.
    6. Irini Moustaki & Martin Knott, 2000. "Generalized latent trait models," Psychometrika, Springer;The Psychometric Society, vol. 65(3), pages 391-411, September.
    7. Mary Dupuis Sammel & Louise M. Ryan & Julie M. Legler, 1997. "Latent Variable Models for Mixed Discrete and Continuous Outcomes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(3), pages 667-678.
    8. J. Polzehl & V. G. Spokoiny, 2000. "Adaptive weights smoothing with applications to image restoration," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 335-354.
    9. David B. Dunson & Donna D. Baird, 2002. "A Proportional Hazards Model for Incidence and Induced Remission of Disease," Biometrics, The International Biometric Society, vol. 58(1), pages 71-78, March.
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    Cited by:

    1. Fernanda B. Rizzato & Roseli A. Leandro & Clarice G.B. Demétrio & Geert Molenberghs, 2016. "A Bayesian approach to analyse overdispersed longitudinal count data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(11), pages 2085-2109, August.

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