An Overview of Joint Modeling of Longitudinal and Time to Event Data

At the thirteenth annual American Conference on Pharmacometrics (ACoP13), I gave a presentation that was an introduction/overview of joint models of longitudinal and time to event data. The slides from the talk can be downloaded here: acop4b-overview

Since joint modeling is the basis of many models used for pharmacometric applications, the intent of these slides was to give some of the general concepts together with multiple references for someone to get started if they are interested in learning more about this class of joint models. Some of the content is taken from other presentations and I have tried to make sure the original source is cited in all cases.

The general structure of the slides is:

  1. What is Joint Modeling of longitudinal and time to event data
  2. How do we develop joint models.
  3. Stepwise versus simultaneous estimation
  4. Bayesian Joint Models
  5. Applications of Joint Models with directions to stan code
  6. Additional Resources

I added many resources for people to go look at and they are broadly categorized below.

Overviews of Joint Modeling

  1. Basic Concepts and Methods for Joint Models of Longitudinal and Survival Data. J Clin Oncol 28:2796-2801. https://doi.org/10.1200/JCO.2009.25.0654
  2. Mechanistic Joint Modeling for Longitudinal and Time-to-Event Data in Oncology Drug Development
    https://www.ascpt.org/Portals/28/docs/Annual%20Meetings/2018%20Annual%20Meeting/Presentations/March%2023%202018/ASCPT_Session_Opening_Slide.pdf?ver=2018-04-12-193028-757
  3. Modelling the association between biomarkers and clinical outcome: An introduction to nonlinear joint models. https://doi.org/10.1111/bcp.15200
  4. Joint modelling of time-to-event and multivariate longitudinal outcomes: recent developments and issues. BMC Med Res Methodol 16, 117 (2016). https://doi.org/10.1186/s12874-016-0212-5

Tutorials:
Some good tutorial type resources to get started with:

  1. Joint Modeling of Longitudinal and Time-to-Event Data with Applications in R
    Dimitris Rizopoulos, Department of Biostatistics, Erasmus University Medical Center
    Course Slides: https://www.drizopoulos.com/courses/EMC/ESP72.pdf
  2. Joint longitudinal and time-to-event models via Stan (stan_jm). Stancon 2018 talk by Sam Brilleman
    https://github.com/stan-dev/stancon_talks/blob/master/2018/Contributed-Talks/03_brilleman/notebook.pdf
    video of talk: https://youtu.be/8r-Ipt885FA
  3. A workflow for the joint modeling of longitudinal and event data in the development of therapeutics: Tools, statistical methods, and diagnostics
    Tutorial in CPT:PSP, Zhudenkov et at 2021. https://doi.org/10.1002/psp4.12763
  4. Joint modeling of survival and longitudinal non-survival data: current methods and issues. Report of the DIA Bayesian joint modeling working group.
    Stat Med. 2015;34(14):2181-95.  https://doi.org/10.1002/sim.6141
  5. Bayesian joint modelling of longitudinal and time to event data: a methodological review.
    Alsefri et al. BMC Medical Research Methodology (2020) 20:94 https://doi.org/10.1186/s12874-020-00976-2

Stan code is available for joint models:

Additional Interesting Journal articles:

  1. Joint modeling of survival and longitudinal non-survival data: current methods and issues. Report of the DIA Bayesian joint modeling working group. Stat Med. 2015;34(14):2181-95.  
    https://doi.org/10.1002/sim.6141
  2. 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. https://doi.org/10.1002/sim.6948
  3. A Two-Stage Joint Model for Nonlinear Longitudinal Response and a Time-to-Event with Application in Transplantation Studies. Journal of Probability and Statistics. 2012. https://doi.org/10.1155/2012/194194
  4. Joint modelling of time-to-event and multivariate longitudinal outcomes: recent developments and issues. BMC Med Res Methodol 16, 117 (2016).
    https://doi.org/10.1186/s12874-016-0212-5
  5. Modelling the association between biomarkers and clinical outcome: An introduction to nonlinear joint models.
    https://doi.org/10.1111/bcp.15200
  6. Liu F, Li Q. A Bayesian model for joint analysis of multivariate repeated measures and time to event data in crossover trials. Stat Methods Med Res. 2014;0:1–13. https://doi.org/10.1177/0962280213519594
  7. Krishnan SM, Friberg LE, Bruno R, Beyer U, Jin JY, Karlsson MO. Multistate model for pharmacometric analyses of overall survival in HER2- negative breast cancer patients treated with docetaxel. CPT Pharmacometrics Syst Pharmacol. 2021;10:1255– 1266. https://doi.org/10.1002/psp4.12693
  8. Putter H, Fiocco M, Gekus RB. Tutorial in biostatistics: Competing risk and multi-state models. Stat Med. 2007;26:2389- 2430. https://doi.org/10.1002/sim.2712
  9. Broët P, de la Rochefordière A, Scholl SM, et al. Analyzing prognostic factors in breast cancer using a multistate model. Breast Cancer Res Treat. 1999;54:83- 89. https://doi.org/10.1023/a:1006197524405