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Journal of Probability and Statistics
Volume 2012, Article ID 194194, 18 pages
http://dx.doi.org/10.1155/2012/194194
Research Article

A Two-Stage Joint Model for Nonlinear Longitudinal Response and a Time-to-Event with Application in Transplantation Studies

1Department of Biostatistics, Erasmus University Medical Center, P.O. Box 2040, 3000 CA Rotterdam, The Netherlands
2I-Biostat, Catholic University of Leuven, B-3000 Leuven, Belgium

Received 7 July 2011; Revised 27 October 2011; Accepted 6 November 2011

Academic Editor: Grace Y. Yi

Copyright © 2012 Magdalena Murawska et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. J. D. Kalbfleisch and R. L. Prentice, The Statistical Analysis of Failure Time Data, Wiley Series in Probability and Statistics, John Wiley & Sons, Hoboken, NJ, USA, Second edition, 2002. View at Zentralblatt MATH
  2. C. L. Faucett and D. C. Thomas, “Simultaneously modelling censored survival data and repeatedly measured covariates: a Gibbs sampling approach,” Statistics in Medicine, vol. 15, no. 15, pp. 1663–1685, 1996. View at Publisher · View at Google Scholar
  3. M. S. Wulfsohn and A. A. Tsiatis, “A joint model for survival and longitudinal data measured with error,” Biometrics. Journal of the International Biometric Society, vol. 53, no. 1, pp. 330–339, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. R. L. Prentice, “Covariate measurement errors and parameter estimation in a failure time regression model,” Biometrika, vol. 69, no. 2, pp. 331–342, 1982. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. A. Tsiatis, V. DeGruttola, and M. Wulfsohn, “Modeling the relationship of survival to longitudinal data measured with error: applications to survival and CD4 counts in patients with AIDS,” Journal of the American Statistical Association, vol. 90, pp. 27–37, 1995. View at Google Scholar
  6. P. S. Albert and J. H. Shih, “On estimating the relationship between longitudinal measurments and time-to-event data using a simple two-stage procedure,” Biometrics, vol. 66, pp. 983–991, 2009. View at Google Scholar
  7. D. Rizopoulos, G. Verbeke, and E. Lesaffre, “Fully exponential Laplace approximations for the joint modelling of survival and longitudinal data,” Journal of the Royal Statistical Society B, vol. 71, no. 3, pp. 637–654, 2009. View at Publisher · View at Google Scholar
  8. R. Henderson, P. Diggle, and A. Dobson, “Joint modelling of longitudinal measurements and event time data,” Biostatistics, vol. 4, pp. 465–480, 2000. View at Google Scholar
  9. V. DeGruttola and X. Tu, “Modeling progression of CD4 lymphocyte count and its relationship to survival time,” Biometrics, vol. 50, pp. 1003–1014, 1994. View at Google Scholar
  10. S. Self and Y. Pawitan, “Modeling a marker of disease progression and onset of disease,” in AIDS Epidemiology: Methodological Issues, N. P. Jewell, K. Dietz, and V.T. Farewell, Eds., Birkhauser, Boston, Mass, USA, 1992. View at Google Scholar
  11. A. A. Tsiatis and M. Davidian, “A semiparametric estimator for the proportional hazards model with longitudinal covariates measured with error,” Biometrika, vol. 88, no. 2, pp. 447–458, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. J. Xu and S. L. Zeger, “Joint analysis of longitudinal data comprising repeated measures and times to events,” Journal of the Royal Statistical Society C, vol. 50, no. 3, pp. 375–387, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. Y. Wang and J. M. G. Taylor, “Jointly modeling longitudinal and event time data with application to acquired immunodeficiency syndrome,” Journal of the American Statistical Association, vol. 96, no. 455, pp. 895–905, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. J. G. Ibrahim, M.-H. Chen, and D. Sinha, “Bayesian methods for joint modeling of longitudinal and survival data with applications to cancer vaccine trials,” Statistica Sinica, vol. 14, no. 3, pp. 863–883, 2004. View at Google Scholar · View at Zentralblatt MATH
  15. E. R. Brown and J. G. Ibrahim, “A Bayesian semiparametric joint hierarchical model for longitudinal and survival data,” Biometrics, vol. 59, no. 2, pp. 221–228, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. L. Wu, X. J. Hu, and H. Wu, “Joint inference for nonlinear mixed-effects models and time to event at the presence of missing data,” Biostatistics, vol. 9, pp. 308–320, 2008. View at Google Scholar
  17. C. Hu and M. E. Sale, “A joint model for nonlinear longitudinal data with informative dropout,” Journal of Pharmacokinetics and Pharmacodynamics, vol. 30, no. 1, pp. 83–103, 2003. View at Publisher · View at Google Scholar
  18. N. A. Kaciroti, T. E. Raghunathan, M. A. Schork, and N. M. Clark, “A Bayesian model for longitudinal count data with non-ignorable dropout,” Journal of the Royal Statistical Society C, vol. 57, no. 5, pp. 521–534, 2008. View at Publisher · View at Google Scholar · View at PubMed
  19. P. K. Andersen and R. D. Gill, “Cox's regression model for counting processes: a large sample study,” The Annals of Statistics, vol. 10, no. 4, pp. 1100–1120, 1982. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  20. D. Clayton, “Bayesian analysis of frailty models,” Tech. Rep., Medical Research Council Biostatistics Unit., Cambridge, UK, 1994. View at Google Scholar
  21. J. D. Kalbfleisch, “Non-parametric Bayesian analysis of survival time data,” Journal of the Royal Statistical Society B, vol. 40, no. 2, pp. 214–221, 1978. View at Google Scholar · View at Zentralblatt MATH
  22. K. Patra and D. K. Dey, “A general class of change point and change curve modeling for life time data,” Annals of the Institute of Statistical Mathematics, vol. 54, no. 3, pp. 517–530, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  23. J. Casellas, “Bayesian inference in a piecewise Weibull proportional hazards model with unknown change points,” Journal of Animal Breeding and Genetics, vol. 124, no. 4, pp. 176–184, 2007. View at Publisher · View at Google Scholar · View at PubMed
  24. B. P. Carlin and T. A. Louis, Bayes and Empirical Bayes Methods for Data Analysis, Chapman & Hall, New York, NY, USA, 2000.
  25. G. O. Roberts, A. Gelman, and W. R. Gilks, “Weak convergence and optimal scaling of random walk Metropolis algorithms,” The Annals of Applied Probability, vol. 7, no. 1, pp. 110–120, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  26. G. Verbeke and G. Molenberghs, Linear mixed models for longitudinal data, Springer Series in Statistics, Springer, New York, NY, USA, 2000.
  27. K. P. Nelson, S. R. Lipsitz, G. M. Fitzmaurice, J. Ibrahim, M. Parzen, and R. Strawderman, “Using the probability integral transformation for non-normal random effects in non-linear mixed models,” Journal of Computational and Graphical Statistics, vol. 15: 3957, 2004. View at Google Scholar
  28. L. Liu and Z. Yu, “A likelihood reformulation method in non-normal random effects models,” Statistics in Medicine, vol. 27, no. 16, pp. 3105–3124, 2008. View at Publisher · View at Google Scholar · View at PubMed
  29. M. Davidian and D. M. Giltinan, Nonlinear Models for Repeated Measurment Data, Chapman and Hall, New York, NY, USA, 1998.