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The international journal of biostatistics
01 31, 2018;14 (1):

Joint Models of Longitudinal and Time-to-Event Data with More Than One Event Time Outcome: A Review.

Graeme L Hickey, Pete Philipson, Andrea Jorgensen, Ruwanthi Kolamunnage-Dona
Author Information
  1. Graeme L Hickey: Department of Biostatistics,University of Liverpool, Waterhouse Building, 1-5 Brownlow Street, Liverpool, L69 3GL, UK.
  2. Pete Philipson: Department of Mathematics,Physics and Electrical Engineering, Northumbria University, Ellison Place, Newcastle upon Tyne, NE1 8ST, UK.
  3. Andrea Jorgensen: Department of Biostatistics,University of Liverpool, Waterhouse Building, 1-5 Brownlow Street, Liverpool, L69 3GL, UK.
  4. Ruwanthi Kolamunnage-Dona: Department of Biostatistics,University of Liverpool, Waterhouse Building, 1-5 Brownlow Street, Liverpool, L69 3GL, UK.
PMID: 29389664 DOI: 10.1515/ijb-2017-0047

Abstract

Methodological development and clinical application of joint models of longitudinal and time-to-event outcomes have grown substantially over the past two decades. However, much of this research has concentrated on a single longitudinal outcome and a single event time outcome. In clinical and public health research, patients who are followed up over time may often experience multiple, recurrent, or a succession of clinical events. Models that utilise such multivariate event time outcomes are quite valuable in clinical decision-making. We comprehensively review the literature for implementation of joint models involving more than a single event time per subject. We consider the distributional and modelling assumptions, including the association structure, estimation approaches, software implementations, and clinical applications. Research into this area is proving highly promising, but to-date remains in its infancy.

Keywords

Joint models longitudinal data multivariate data recurrent events time-to-event data

References

  1. Ibrahim JG, Chu H, Chen LM. Basic concepts and methods for joint models of longitudinal and survival data. J Clin Oncol. 2010;28:2796–801.
  2. Chen LM, Ibrahim JG, Chu H. Sample size and power determination in joint modeling of longitudinal and survival data. Stat Med. 2011;30:2295–309.
  3. Hogan JW, Laird NM. Increasing efficiency from censored survival data by using random effects to model longitudinal covariates. Stat Methods Med Res. 1998;7:28–48.
  4. Rizopoulos D, Hatfield LA, Carlin BP, Takkenberg JJM. Combining dynamic predictions from joint models for longitudinal and time-to-event data using Bayesian model averaging. J Am Stat Assoc. 2014;109:1385–97.
  5. Tsiatis AA, DeGruttola V, Wulfsohn MS. Modeling the relationship of survival to longitudinal data measured with error - applications to survival and CD4 counts in patients with AIDS. J Am Stat Assoc. 1995;90:27–37.
  6. Hogan JW, Laird NM. Model-based approaches to analysing incomplete longitudinal and failure time data. Stat Med. 1997;16:259–72.
  7. Tsiatis AA, Davidian M. Joint modeling of longitudinal and time-to-event data: an overview. Stat Sin. 2004;14:809–34.
  8. Diggle PJ, Sousa I, Chetwynd AG. Joint modelling of repeated measurements and time-to-event outcomes: the fourth Armitage lecture. Stat Med. 2008;27:2981–98.
  9. Sousa I. A review on joint modelling of longitudinal measurements and time-to-event. Revstat Stat J. 2011;9:57–81.
  10. Proust-Lima C, Sene M, Taylor JMG, Jacqmin-Gadda H. Joint latent class models for longitudinal and time-to-event data: a review. Stat Methods Med Res. 2012;23:74–90.
  11. Gould AL, Boye ME, Crowther MJ, Ibrahim JG, Quartey G, Micallef S, et . 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;34:2181–95.
  12. Hickey GL, Philipson P, Jorgensen A, Kolamunnage-Dona R. Joint modelling of time-to-event and multivariate longitudinal outcomes: recent developments and issues. BMC Med Res Methodol. 2016;16:1–15.
  13. Rizopoulos D, Ghosh P. A Bayesian semiparametric multivariate joint model for multiple longitudinal outcomes and a time-to-event. Stat Med. 2011;30:1366–80.
  14. Njagi EN, Molenberghs G, Rizopoulos D, Verbeke G, Kenward MG, Dendale P, et . A flexible joint modeling framework for longitudinal and time-to-event data with overdispersion. Stat Methods Med Res. 2013;0:1–16.
  15. Li N, Elashoff RM, Li G, Saver J. Joint modeling of longitudinal ordinal data and competing risks survival times and analysis of the NINDS rt-PA stroke trial. Stat Med. 2010;29:546–57.
  16. Huang X, Li G, Elashoff RM, Pan J. A general joint model for longitudinal measurements and competing risks survival data with heterogeneous random effects. Lifetime Data Anal. 2011;17:80–100.
  17. Gueorguieva R, Rosenheck R, Lin H. Joint modelling of longitudinal outcome and interval-censored competing risk dropout in a schizophrenia clinical trial. J R Stat Soc Ser A Stat Soc. 2012;175:417–33.
  18. Thiébaut R, Jacqmin-Gadda H, Babiker AG, Commenges D. Joint modelling of bivariate longitudinal data with informative dropout and left-censoring, with application to the evolution of CD4+ cell count and HIV RNA viral load in response to treatment of HIV infection. Stat Med. 2005;24:65–82.
  19. Albert PS, Shih JH. An approach for jointly modeling multivariate longitudinal measurements and discrete time-to-event data. Ann Appl Stat. 2010;4:1517–32.
  20. Williamson PR, Kolamunnage-Dona R, Philipson P, Marson AG. Joint modelling of longitudinal and competing risks data. Stat Med. 2008;27:6426–38.
  21. Crowther MJ, Abrams KR, Lambert PC. Flexible parametric joint modelling of longitudinal and survival data. Stat Med. 2012;31:4456–71.
  22. Brown ER, Ibrahim JG, DeGruttola V. A flexible B-spline model for multiple longitudinal biomarkers and survival. Biometrics. 2005;61:64–73.
  23. Luo S, Wang J. Bayesian hierarchical model for multiple repeated measures and survival data: an application to Parkinson’s disease. Stat Med. 2014;33:4279–91.
  24. Touloumi G, Pantazis N, Babiker AG, Walker SA, Katsarou O, Karafoulidou A, et . Differences in HIV RNA levels before the initiation of antiretroviral therapy among 1864 individuals with known HIV-1 seroconversion dates. Aids. 2004;18:1697–705.
  25. Musoro JZ, Geskus RB, Zwinderman AH. A joint model for repeated events of different types and multiple longitudinal outcomes with application to a follow-up study of patients after kidney transplant. Biometrical J. 2015;57:185–200.
  26. Ibrahim JG, M-H C, Sinha D. Bayesian methods for joint modeling of longitudinal and survival data with applications to cancer vaccine trials. Stat Sin. 2004;14:863–83.
  27. Crowther MJ, Abrams KR, Lambert PC. Joint modeling of longitudinal and survival data. Stata J. 2013;13:165–84.
  28. Guo X, Carlin BP. Separate and joint modeling of longitudinal and event time data using standard computer packages. Am Stat. 2004;58:16–24.
  29. Philipson P, Sousa I, Diggle PJ, Williamson PR, Kolamunnage-Dona R, Henderson R, Hickey GL. Package “joineR”. R Foundation for Statistical Computing. Version 1.2.2 2017.
  30. Rizopoulos D. The R package JMbayes for fitting joint models for longitudinal and time-to-event data using MCMC. J Stat Softw. 2016;72:1–45.
  31. Zhang D, Chen M-H, Ibrahim JG, Boye ME, Shen W. JMFit: a SAS macro for joint models of longitudinal and survival data. J Stat Softw. 2016;71.
  32. Rizopoulos D. JM: an R package for the joint modelling of longitudinal and time-to-event data. J Stat Softw. 2010;35:1–33.
  33. Proust-Lima C, Philipps V, Liquet B. Estimation of latent class linear mixed models: the new package lcmm. arXiv Prepr. 2015.
  34. Hickey GL, Philipson P, Jorgensen A, Kolamunnage-Dona R. joineRML: joint modelling of multivariate longitudinal data and time-to-event outcomes. Comprehensive R Archive Network; 2017.
  35. Hickey GL, Philipson P, Jorgensen A, Kolamunnage-Dona R. A comparison of different joint models for longitudinal and competing risks data: with application to an epilepsy drug randomised control trial. J R Stat Soc Ser A Stat Soc. DOI: 10.1111/rssa.12348 . [DOI: 10.1111/rssa.12348]
  36. Król A, Ferrer L, Pignon JP, Proust-Lima C, Ducreux M, Bouché O, et . Joint model for left-censored longitudinal data, recurrent events and terminal event: predictive abilities of tumor burden for cancer evolution with application to the FFCD 2000-05 trial. Biometrics. 2016;72:907–16.
  37. Verbeke G, Fieuws S, Molenberghs G, Davidian M. The analysis of multivariate longitudinal data: A review. Stat Methods Med Res. 2012;23:42–59.
  38. Rizopoulos D. Joint models for longitudinal and time-to-event data, with applications in R. Boca Raton, FL: Chapman & Hall/CRC; 2012.
  39. Tang AM, Tang NS. Semiparametric Bayesian inference on skew–normal joint modeling of multivariate longitudinal and survival data. Stat Med. 2015;34:824–43.
  40. Dantan E, Joly P, Dartigues J-F, Jacqmin-Gadda H. Joint model with latent state for longitudinal and multistate data. Biostatistics. 2012;12:723–36.
  41. Huang W, Zeger SL, Anthony JC, Garrett E. Latent variable model for joint analysis of multiple repeated measures and bivariate event times. J Am Stat Assoc. 2001;96:906–14.
  42. Chi YY, Ibrahim JG. Joint models for multivariate longitudinal and multivariate survival data. Biometrics. 2006;62:432–45.
  43. Zhu H, Ibrahim JG, Chi YY, Tang NS. Bayesian influence measures for joint models for longitudinal and survival data. Biometrics. 2012;68:954–64.
  44. Tang NS, Tang AM, Pan DD. Semiparametric Bayesian joint models of multivariate longitudinal and survival data. Comput Stat Data Anal. 2014;77:113–29.
  45. Li Y, He X, Wang H, Sun J. Regression analysis of longitudinal data with correlated censoring and observation times. Lifetime Data Anal. 2016;22:343–62.
  46. Sun L, Song X, Zhou J, Liu L. Joint analysis of longitudinal data with informative observation times and a dependent terminal event. J Am Stat Assoc. 2012;107:688–700.
  47. Henderson R, Diggle PJ, Dobson A. Joint modelling of longitudinal measurements and event time data. Biostatistics. 2000;1:465–80.
  48. Shen Y, Huang H, Guan Y. A conditional estimating equation approach for recurrent event data with additional longitudinal information. Stat Med. 2016.
  49. Zhang H, Ye Y, Diggle PJ, Shi J. Joint modeling of time series measures and recurrent events and analysis of the effects of air quality on respiratory symptoms. J Am Stat Assoc. 2008;103:48–60.
  50. Rouanet A, Joly P, Dartigues J-F, Proust-Lima C, Jacqmin-Gadda H. Joint latent class model for longitudinal data and interval-censored semi-competing events: application to dementia. Biometrics. 2016;72(4):1123–1135.
  51. Han J, Slate EH, Pena EA. Parametric latent class joint model for a longitudinal biomarker and recurrent events. Stat Med. 2007;26:5285–302.
  52. Pena EA, Hollander M. Models for recurrent events in reliability and survival analysis. In: Soyer R, Mazzuchi T, Singpurwalla N, editors. Mathematical reliability: an expository perspective. Dordrecht: Kluwer Academic Publishers; 2004.
  53. Lin H, Turnbull BW, McCulloch CE, Slate EH. Latent class models for joint analysis of longitudinal biomarker and event process data: application to longitudinal prostate-specific antigen readings and prostate cancer. J Am Stat Assoc. 2002;97:53–65.
  54. Efendi A, Molenberghs G, Njagi EN, Dendale P. A joint model for longitudinal continuous and time-to-event outcomes with direct marginal interpretation. Biometrical J. 2013;55:572–88.
  55. Li S. Joint modeling of recurrent event processes and intermittently observed time-varying binary covariate processes. Lifetime Data Anal. Springer US. 2016;22:145–60.
  56. Liu L, Huang X, O’Quigley J. Analysis of longitudinal data in the presence of informative observational times and a dependent terminal event, with application to medical cost data. Biometrics. 2008;64:950–58.
  57. Liu L, Huang X. 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. J R Stat Soc Ser C Appl Stat. 2009;58:65–81.
  58. Kim S, Zeng D, Chambless L, Li Y. Joint models of longitudinal data and recurrent events with informative terminal event. Stat Biosci. 2012;4:262–81.
  59. Li Y, He X, Wang H, Sun J. Joint analysis of longitudinal data and informative observation times with time-dependent random effects. In: Jin Z, Liu M, Luo X, editors. New developments in statistical modeling, inference and application. Switzerland: Springer International Publishing; 2016.
  60. Han M, Song X, Sun L. Joint modeling of longitudinal data with informative observation times and dropouts. Stat Sin. 2014;24:1487–504.
  61. Miao R, Chen X, Sun L. Analyzing longitudinal data with informative observation and terminal event times. Acta Math Appl Sin. 2016;32:1035–52.
  62. Putter H, Fiocco M, Geskus RB. Tutorial in biostatistics: competing risks and multi-state models. Stat Med. 2007;26:2389–430.
  63. Deslandes E, Chevret S. Assessing surrogacy from the joint modelling of multivariate longitudinal data and survival: application to clinical trial data on chronic lymphocytic leukaemia. Stat Med. 2007;26:5411–21.
  64. Hu B, Li L, Wang X, Greene T. Nonparametric multistate representations of survival and longitudinal data with measurement error. Stat Med. 2012;31:2303–17.
  65. Le Cessie S, De Vries EGE, Buijs C, Post WJ. Analyzing longitudinal data with patients in different disease states during follow-up and death as final state. Stat Med. 2009;28:3829–43.
  66. Ferrer L, Rondeau V, Dignam J, Pickles T, Jacqmin-Gadda H, Proust-Lima C. Joint modelling of longitudinal and multi-state processes: application to clinical progressions in prostate cancer. Stat Med. 2016.
  67. Wulfsohn MS, Tsiatis AA. A joint model for survival and longitudinal data measured with error. Biometrics. 1997;53:330–39.
  68. Molenberghs G, Verbeke G, Demétrio CGB. An extended random-effects approach to modeling repeated, overdispersed count data. Lifetime Data Anal. 2007;13:513–31.
  69. Heagerty PJ, Zeger SL. Marginalized multilevel models and likelihood inference. Stat Sci. 2000;15:1–26.
  70. 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.
  71. Gelfand AE, Sahu SK, Carlin BP. Efficient parameterizations for normal linear mixed models.
  72. Gelman A, Carlin JB, Stern HS, Dunson DB, Vehtari A, Rubin DB. Bayesian data analysis, 3rd ed. Boca Raton, FL: CRC Press; 2013.
  73. Król A, Mauguen A, Mazroui Y, Laurent A, Michiels S and Rondeau V. Tutorial in Joint Modeling and Prediction: A Statistical Software for Correlated Longitudinal Outcomes, Recurrent Events and a Terminal Event. Journal of Statistical Software; 2017: 81(3), 1–52.
  74. Sweeting MJ, Thompson SG. Joint modelling of longitudinal and time-to-event data with application to predicting abdominal aortic aneurysm growth and rupture. Biometrical J. 2011;53: 750–763. doi: 10.18637/jss.v081.i03 [DOI: 10.18637/jss.v081.i03]
  75. Wang P, Shen W, Boye ME. Joint modeling of longitudinal outcomes and survival using latent growth modeling approach in a mesothelioma trial. Heal Serv Outcomes Res Methodol. 2012;12:182–99.
  76. Molenberghs G, Verbeke G, Demétrio CGB, Vieira AMC. A family of generalized linear models for repeated measures with normal and conjugate random effects. Stat Sci. 2011;25:325–47.

Grants

  1. MR/M013227/1/Medical Research Council

MeSH Term

Data Interpretation, Statistical
Humans
Longitudinal Studies
Models, Statistical
Outcome Assessment, Health Care
Journal Article Research Support, Non-U.S. Gov't Review
Article has an altmetric score of 10

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