Table of Contents Author Guidelines Submit a Manuscript
BioMed Research International
Volume 2018, Article ID 7409284, 13 pages
https://doi.org/10.1155/2018/7409284
Research Article

A Proposed Approach for Joint Modeling of the Longitudinal and Time-To-Event Data in Heterogeneous Populations: An Application to HIV/AIDS’s Disease

Department of Biostatistics, School of Medicine, Shiraz University of Medical Sciences, Shiraz, Iran

Correspondence should be addressed to Seyyed Mohammad Taghi Ayatollahi; ri.ca.smus@mihalotaya

Received 13 July 2017; Revised 15 November 2017; Accepted 5 December 2017; Published 9 January 2018

Academic Editor: Momiao Xiong

Copyright © 2018 Narges Roustaei 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. Q. Chen, R. C. May, J. G. Ibrahim, H. Chu, and S. R. Cole, “Joint modeling of longitudinal and survival data with missing and left-censored time-varying covariates,” Statistics in Medicine, vol. 33, no. 26, pp. 4560–4576, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  2. J. Han, E. H. Slate, and E. A. Pena, “Parametric latent class joint model for a longitudinal biomarker and recurrent events,” Statistics in Medicine, vol. 26, no. 29, pp. 5285–5302, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  3. L. Liu and X. Huang, “Joint analysis of correlated repeated measures and recurrent events processes in the presence of death, with application to a study on acquired immune deficiency syndrome,” Journal of the Royal Statistical Society: Series C (Applied Statistics), vol. 58, no. 1, pp. 65–81, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. S. Li, “Joint modeling of recurrent event processes and intermittently observed time-varying binary covariate processes,” Lifetime Data Analysis, vol. 22, no. 1, pp. 145–160, 2016. View at Publisher · View at Google Scholar · View at Scopus
  5. C. Proust-Lima, M. Sene, J. M. Taylor, and H. Jacqmin-Gadda, “Joint latent class models for longitudinal and time-to-event data: a review,” Statistical Methods in Medical Research, vol. 23, no. 1, pp. 74–90, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  6. C. Brombin, C. Di Serio, and P. M. V. Rancoita, “Joint modeling of HIV data in multicenter observational studies: A comparison among different approaches,” Statistical Methods in Medical Research, vol. 25, no. 6, pp. 2472–2487, 2016. View at Publisher · View at Google Scholar · View at Scopus
  7. D. Rizopoulos, G. Verbeke, and G. Molenberghs, “Multiple-imputation-based residuals and diagnostic plots for joint models of longitudinal and survival outcomes,” Biometrics, vol. 66, no. 1, pp. 20–29, 2010. View at Publisher · View at Google Scholar · View at Scopus
  8. M. Sudell, R. Kolamunnage-Dona, and C. Tudur-Smith, “Joint models for longitudinal and time-to-event data: A review of reporting quality with a view to meta-analysis,” BMC Medical Research Methodology, vol. 16, no. 1, article no. 168, 2016. View at Publisher · View at Google Scholar · View at Scopus
  9. A. Chakrabortya and K. Dasb, “Inferences for joint modelling of repeated ordinal scores and time to event data,” Computational and Mathematical Methods in Medicine, vol. 11, no. 3, pp. 281–295, 2010. View at Publisher · View at Google Scholar · View at Scopus
  10. L. Wu, W. Liu, G. Y. Yi, and Y. Huang, “Analysis of longitudinal and survival data: Joint modeling, inference methods, and issues,” Journal of Probability and Statistics, Article ID 640153, 2012. View at Publisher · View at Google Scholar · View at Scopus
  11. X. Guo and B. P. Carlin, “Separate and joint modeling of longitudinal and event time data using standard computer packages,” The American Statistician, vol. 58, no. 1, pp. 16–24, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  12. J. G. Ibrahim, H. Chu, and L. M. Chen, “Basic concepts and methods for joint models of longitudinal and survival data,” Journal of Clinical Oncology, vol. 28, no. 16, pp. 2796–2801, 2010. View at Publisher · View at Google Scholar · View at Scopus
  13. Y. Liu, L. Liu, and J. Zhou, “Joint latent class model of survival and longitudinal data: An application to CPCRA study,” Computational Statistics & Data Analysis, vol. 91, pp. 40–50, 2015. View at Publisher · View at Google Scholar · View at Scopus
  14. H. J. Lim, P. Mondal, and S. Skinner, “Joint modeling of longitudinal and event time data: application to HIV study,” Journal of Medical Statistics and Informatics, vol. 1, no. 1, p. 1, 2013. View at Google Scholar
  15. M. J. Sweeting and S. G. Thompson, “Joint modelling of longitudinal and time-to-event data with application to predicting abdominal aortic aneurysm growth and rupture,” Biometrical Journal, vol. 53, no. 5, pp. 750–763, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. L. M. Chen, J. G. Ibrahim, and H. Chu, “Sample size and power determination in joint modeling of longitudinal and survival data,” Statistics in Medicine, vol. 30, no. 18, pp. 2295–2309, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. H. Lin, B. W. Turnbull, C. E. McCulloch, and E. H. Slate, “Latent class models for joint analysis of longitudinal biomarker and event process data: application to longitudinal prostate-specific antigen readings and prostate cancer,” Journal of the American Statistical Association, vol. 97, no. 457, pp. 53–65, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. D. Rizopoulos, Joint models for longitudinal and time-to-event data: With applications in R, CRC Press, Boca Raton, Fl, USA, 2012.
  19. H. Jacqmin-Gadda, C. Proust-Lima, J. M. G. Taylor, and D. Commenges, “Score test for conditional independence between longitudinal outcome and time to event given the classes in the joint latent class model,” Biometrics, vol. 66, no. 1, pp. 11–19, 2010. View at Publisher · View at Google Scholar · View at Scopus
  20. C. Proust-Lima and J. M. G. Taylor, “Development and validation of a dynamic prognostic tool for prostate cancer recurrence using repeated measures of posttreatment PSA: A joint modeling approach,” Biostatistics, vol. 10, no. 3, pp. 535–549, 2009. View at Publisher · View at Google Scholar · View at Scopus
  21. C. Proust-Lima and B. Liquet, “lcmm: an R package for estimation of latent class mixed models and joint latent class models,” in Proceedings of the The R User Conference, useR! 2011, University of Warwick, Coventry, UK, August, 2011.
  22. C. Proust-Lima, L. Letenneur, and H. Jacqmin-Gadda, “A nonlinear latent class model for joint analysis of mutivariate longitudinal data and a binary outcome,” Statistics in Medicine, vol. 26, no. 10, pp. 2229–2245, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  23. C. Proust-Lima, P. Joly, J.-F. Dartigues, and H. Jacqmin-Gadda, “Joint modelling of multivariate longitudinal outcomes and a time-to-event: A nonlinear latent class approach,” Computational Statistics & Data Analysis, vol. 53, no. 4, pp. 1142–1154, 2009. View at Publisher · View at Google Scholar · View at Scopus
  24. H. Lin, C. E. McCulloch, and R. A. Rosenheck, “Latent pattern mixture models for informative intermittent missing data in longitudinal studies,” Biometrics, vol. 60, no. 2, pp. 295–305, 2004. View at Publisher · View at Google Scholar · View at Scopus
  25. C. Proust-Lima, V. Philipps, and B. Liquet, “Estimation of extended mixed models using latent classes and latent processes: the R package lcmm,” Journal of Statistical Software, vol. 78, no. 2, pp. 1–56, 2017. View at Publisher · View at Google Scholar
  26. J. A. Hagenaars and A. L. McCutcheon, Applied Latent Class Analysis, Cambridge University Press, 2002.
  27. J. Petersen, K. Bandeen-Roche, E. Budtz-Jørgensen, and K. G. Larsen, “Predicting latent class scores for subsequent analysis,” Psychometrika, vol. 77, no. 2, pp. 244–262, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  28. P. C. Austin, “Generating survival times to simulate Cox proportional hazards models with time-varying covariates,” Statistics in Medicine, vol. 31, no. 29, pp. 3946–3958, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  29. R. Bender, T. Augustin, and M. Blettner, “Generating survival times to simulate Cox proportional hazards models,” Statistics in Medicine, vol. 24, no. 11, pp. 1713–1723, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  30. D. Rizopoulos, “Dynamic Predictions and Prospective Accuracy in Joint Models for Longitudinal and Time-to-Event Data,” Biometrics, vol. 67, no. 3, pp. 819–829, 2011. View at Publisher · View at Google Scholar · View at Scopus
  31. D. Gökengin, F. Doroudi, J. Tohme, B. Collins, and N. Madani, “HIV/AIDS: Trends in the Middle East and North Africa region,” International Journal of Infectious Diseases, vol. 44, pp. 66–73, 2016. View at Publisher · View at Google Scholar · View at Scopus
  32. WHO organization., “HIV/AIDS,” 2017, http://www.who.int/hiv/data/en.
  33. M. Farahani, V. Novitsky, R. Wang et al., “Prognostic value of HIV-1 RNA on CD4 trajectories and disease progression among antiretroviral-naive HIV-infected adults in Botswana: A joint modeling analysis,” AIDS Research and Human Retroviruses, vol. 32, no. 6, pp. 573–578, 2016. View at Publisher · View at Google Scholar · View at Scopus
  34. S. L. Brilleman, M. J. Crowther, M. T. May, M. Gompels, and K. R. Abrams, “Joint longitudinal hurdle and time-to-event models: an application related to viral load and duration of the first treatment regimen in patients with HIV initiating therapy,” Statistics in Medicine, vol. 35, no. 20, pp. 3583–3594, 2016. View at Publisher · View at Google Scholar · View at MathSciNet
  35. R. Song, H. I. Hall, T. A. Green, C. L. Szwarcwald, and N. Pantazis, “Using CD4 Data to Estimate HIV Incidence, Prevalence, and Percent of Undiagnosed Infections in the United States,” Journal of Acquired Immune Deficiency Syndromes, vol. 74, no. 1, pp. 3–9, 2017. View at Publisher · View at Google Scholar · View at Scopus
  36. D. I. Abrams, A. I. Goldman, C. Launer et al., “A comparative trial of didanosine or zalcitabine after treatment with zidovudine in patients with human immunodeficiency virus infection,” The New England Journal of Medicine, vol. 330, no. 10, pp. 657–662, 1994. View at Publisher · View at Google Scholar · View at Scopus
  37. R. M. Elashoff, G. Li, and N. Li, “An approach to joint analysis of longitudinal measurements and competing risks failure time data,” Statistics in Medicine, vol. 26, no. 14, pp. 2813–2835, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  38. R. Henderson, P. Diggle, and A. Dobson, “Joint modelling of longitudinal measurements and event time data,” Biostatistics, vol. 1, no. 4, pp. 465–480, 2000. View at Publisher · View at Google Scholar
  39. Ö. Asar, J. Ritchie, P. A. Kalra, and P. J. Diggle, “Joint modelling of repeated measurement and time-to-event data: An introductory tutorial,” International Journal of Epidemiology, vol. 44, no. 1, pp. 334–344, 2015. View at Publisher · View at Google Scholar · View at Scopus
  40. Y.-K. Tseng, F. Hsieh, and J.-L. Wang, “Joint modelling of accelerated failure time and longitudinal data,” Biometrika, vol. 92, no. 3, pp. 587–603, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus