Skip to main content
SpringerLink
Log in

Joint Modeling of Longitudinal and Time-to-Event Data: Challenges and Future Directions

  • Chapter
  • First Online:
Advances in Theoretical and Applied Statistics

Part of the book series: Studies in Theoretical and Applied Statistics ((STASSPSS))

Abstract

In longitudinal studies measurements are often collected on different types of outcomes for each subject. These may include several longitudinally measured responses (such as blood values relevant to the medical condition under study) and the time at which an event of particular interest occurs (e.g., death, development of a disease or dropout from the study). These outcomes are often separately analyzed; however, in many instances, a joint modeling approach is either required or may produce a better insight into the mechanisms that underlie the phenomenon under study. In this chapter we provide a general overview of the joint modeling framework, discuss its main features, and we refer to future directions.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Brown, E., Ibrahim, J.: A Bayesian semiparametric joint hierarchical model for longitudinal and survival data. Biometrics 59, 221–228 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  2. Brown, E., Ibrahim, J., DeGruttola, V.: A flexible b-spline model for multiple longitudinal biomarkers and survival. Biometrics 61, 64–73 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  3. Chi, Y.Y., Ibrahim, J.: Joint models for multivariate longitudinal and multivariate survival data. Biometrics 62, 432–445 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  4. Ding, J., Wang, J.L.: Modeling longitudinal data with nonparametric multiplicative random effects jointly with survival data. Biometrics 64, 546–556 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  5. Elashoff, R., Li, G., Li, N.: A joint model for longitudinal measurements and survival data in the presence of multiple failure types. Biometrics 64, 762–771 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  6. Faucett, C., Schenker, N., Elashoff, R.: Analysis of censored survival data with intermittently observed time-dependent binary covariates. J. Am. Stat. Assoc. 93, 427–437 (1998)

    Article  MATH  Google Scholar 

  7. Follmann, D., Wu, M.: An approximate generalized linear model with random effects for informative missing data. Biometrics 51, 151–168 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  8. Henderson, R., Diggle, P., Dobson, A.: Joint modelling of longitudinal measurements and event time data. Biostatistics 1, 465–480 (2000)

    Article  MATH  Google Scholar 

  9. Hsieh, F., Tseng, Y.K., Wang, J.L.: Joint modeling of survival and longitudinal data: likelihood approach revisited. Biometrics 62, 1037–1043 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  10. Kalbfleisch, J., Prentice, R.: The Statistical Analysis of Failure Time Data, 2nd edn. Wiley, New York (2002)

    Book  MATH  Google Scholar 

  11. Lange, K.: Optimization. Springer, New York (2004)

    Book  MATH  Google Scholar 

  12. Little, R., Rubin, D.: Statistical Analysis with Missing Data, 2nd edn. Wiley, New York (2002)

    MATH  Google Scholar 

  13. Murtaugh, P., Dickson, E., Van Dam, G., Malincho, M., Grambsch, P., Langworthy, A., Gips, C.: Primary biliary cirrhosis: prediction of short-term survival based on repeated patient visits. Hepatology 20, 126–134 (1994)

    Article  Google Scholar 

  14. Nobre, J., Singer, J.: Residuals analysis for linear mixed models. Biomet. J. 6, 863–875 (2007)

    Article  MathSciNet  Google Scholar 

  15. Proust-Lima, C., Joly, P., Dartigues, J.F., Jacqmin-Gadda, H.: Joint modelling of multivariate longitudinal outcomes and a time-to-event: a nonlinear latent class approach. Comput. Stat. Data Anal. 53, 1142–1154 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  16. Rizopoulos, D.: JM: an R package for the joint modelling of longitudinal and time-to-event data. J. Stat. Software 35(9), 1–33 (2010)

    Google Scholar 

  17. Rizopoulos, D., Ghosh, P.: A Bayesian semiparametric multivariate joint model for multiple longitudinal outcomes and a time-to-event. Stat. Med. 30, 1366–1380 (2011)

    Article  MathSciNet  Google Scholar 

  18. Rizopoulos, D., Verbeke, G., Lesaffre, E.: Fully exponential laplace approximations for the joint modelling of survival and longitudinal data. J. Roy. Stat. Soc. Ser. B 71, 637–654 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  19. Rizopoulos, D., Verbeke, G., Molenberghs, G.: Shared parameter models under random effects misspecification. Biometrika 95, 63–74 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  20. Rizopoulos, D., Verbeke, G., Molenberghs, G.: Multiple-imputation-based residuals and diagnostic plots for joint models of longitudinal and survival outcomes. Biometrics 66, 20–29 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  21. Rubin, D.: Inference and missing dat. Biometrika 63, 581–592 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  22. Song, X., Davidian, M., Tsiatis, A.: A semiparametric likelihood approach to joint modeling of longitudinal and time-to-event data. Biometrics 58, 742–753 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  23. Therneau, T., Grambsch, P.: Modeling Survival Data: Extending the Cox Model. Springer, New York (2000)

    Google Scholar 

  24. Tsiatis, A., Davidian, M.: A semiparametric estimator for the proportional hazards model with longitudinal covariates measured with error. Biometrika 88, 447–458 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  25. Tsiatis, A., Davidian, M.: Joint modeling of longitudinal and time-to-event data: an overview. Statistica Sinica 14, 809–834 (2004)

    MathSciNet  MATH  Google Scholar 

  26. Verbeke, G., Molenberghs, G.: Linear Mixed Models for Longitudinal Data. Springer, New York (2000)

    MATH  Google Scholar 

  27. Wang, Y., Taylor, J.: Jointly modeling longitudinal and event time data with application to acquired immunodeficiency syndrome. J. Am. Stat. Assoc. 96, 895–905 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  28. Wu, M., Bailey, K.: Analysing changes in the presence of informative right censoring caused by death and withdrawal. Stat. Med. 7, 337–346 (1988)

    Article  Google Scholar 

  29. Wu, M., Carroll, R.: Estimation and comparison of changes in the presence of informative right censoring by modeling the censoring process. Biometrics 44, 175–188 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  30. Wulfsohn, M., Tsiatis, A.: A joint model for survival and longitudinal data measured with error. Biometrics 53, 330–339 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  31. Xu, J., Zeger, S.: Joint analysis of longitudinal data comprising repeated measures and times to events. Appl. Stat. 50, 375–387 (2001)

    MathSciNet  MATH  Google Scholar 

  32. Yu, M., Law, N., Taylor, J., Sandler, H.: Joint longitudinal-survival-cure models and their application to prostate cancer. Statistica Sinica 14, 835–832 (2004)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Biostatistics, Erasmus University Medical Center, 2040, 3000 CA, Rotterdam, the Netherlands

    Dimitris Rizopoulos

Authors
  1. Dimitris Rizopoulos
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dimitris Rizopoulos .

Editor information

Editors and Affiliations

  1. Department of Statistics, University of Trieste, P.le Europa 1, Trieste, 34127, Italy

    Nicola Torelli

  2. Department of Statistics, University of Padua, Via Cesare Battisti 241, Padova, 35121, Italy

    Fortunato Pesarin

  3. Université Paris Descartes, rue des Saints-Pères 45, Paris, 75270, France

    Avner Bar-Hen

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Rizopoulos, D. (2013). Joint Modeling of Longitudinal and Time-to-Event Data: Challenges and Future Directions. In: Torelli, N., Pesarin, F., Bar-Hen, A. (eds) Advances in Theoretical and Applied Statistics. Studies in Theoretical and Applied Statistics(). Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35588-2_19

Download citation

Publish with us

Policies and ethics

Search

Navigation