Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
139 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Flexible joint models for multivariate longitudinal and time-to-event data using multivariate functional principal components (2311.06409v2)

Published 10 Nov 2023 in stat.ME

Abstract: The joint modeling of multiple longitudinal biomarkers together with a time-to-event outcome is a challenging modeling task of continued scientific interest. In particular, the computational complexity of high dimensional (generalized) mixed effects models often restricts the flexibility of shared parameter joint models, even when the subject-specific marker trajectories follow highly nonlinear courses. We propose a parsimonious multivariate functional principal components representation of the shared random effects. This allows better scalability, as the dimension of the random effects does not directly increase with the number of markers, only with the chosen number of principal component basis functions used in the approximation of the random effects. The functional principal component representation additionally allows to estimate highly flexible subject-specific random trajectories without parametric assumptions. The modeled trajectories can thus be distinctly different for each biomarker. We build on the framework of flexible Bayesian additive joint models implemented in the R-package 'bamlss', which also supports estimation of nonlinear covariate effects via Bayesian P-splines. The flexible yet parsimonious functional principal components basis used in the estimation of the joint model is first estimated in a preliminary step. We validate our approach in a simulation study and illustrate its advantages by analyzing a study on primary biliary cholangitis.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (62)
  1. E.-R. Andrinopoulou and D. Rizopoulos. Bayesian shrinkage approach for a joint model of longitudinal and survival outcomes assuming different association structures. Statistics in Medicine, 35(26):4813–4823, 2016.
  2. A generalized additive model approach to time-to-event analysis. Statistical Modelling, 18(3-4):299–321, 2018.
  3. Generating survival times to simulate cox proportional hazards models. Statistics in Medicine, 24(11):1713–1723, 2005.
  4. Measurement error in nonlinear models: a modern perspective. Chapman and Hall/CRC, 2006.
  5. Fast symmetric additive covariance smoothing. Computational Statistics & Data Analysis, 120:25–41, 2018.
  6. Simulating biologically plausible complex survival data. Statistics in Medicine, 32(23):4118–4134, 2013.
  7. Jointly modelling multiple transplant outcomes by a competing risk model via functional principal component analysis. Journal of Applied Statistics, 50(1):43–59, 2023.
  8. Simultaneously modelling censored survival data and repeatedly measured covariates: a gibbs sampling approach. Statistics in Medicine, 15(15):1663–1685, 1996.
  9. Counting processes and survival analysis, volume 625. John Wiley & Sons, 2013.
  10. Immune monitoring after pediatric liver transplantation–the prospective chilsfree cohort study. BMC Gastroenterology, 18:1–9, 2018.
  11. Corrected confidence bands for functional data using principal components. Biometrics, 69(1):41–51, 2013.
  12. rstanarm: Bayesian applied regression modeling via Stan. ”https://mc-stan.org/rstanarm”, 2020. R package version 2.21.1.
  13. Association of cereal, gluten, and dietary fiber intake with islet autoimmunity and type 1 diabetes. JAMA Pediatrics, 173(10):953–960, 2019.
  14. C. Happ and S. Greven. Multivariate functional principal component analysis for data observed on different (dimensional) domains. Journal of the American Statistical Association, 113(522):649–659, 2018.
  15. joinerml: a joint model and software package for time-to-event and multivariate longitudinal outcomes. BMC Medical Research Methodology, 18:1–14, 2018.
  16. Efficient use of longitudinal cd4 counts and viral load measures in survival analysis. Statistics in Medicine, 31(19):2086–2097, 2012.
  17. Dynamic prediction of disease processes based on recurrent history and functional principal component analysis of longitudinal biomarkers: Application for ovarian epithelial cancer. Statistics in Medicine, 40(8):2006–2023, 2021.
  18. K. Kang and X. Y. Song. Joint modeling of longitudinal imaging and survival data. Journal of Computational and Graphical Statistics, 32(2):402–412, 2023.
  19. Flexible bayesian additive joint models with an application to type 1 diabetes research. Biometrical Journal, 59(6):1144–1165, 2017.
  20. Nonlinear association structures in flexible bayesian additive joint models. Statistics in Medicine, 37(30):4771–4788, 2018.
  21. Flcrm: Functional linear cox regression model. Biometrics, 74(1):109–117, 2018.
  22. Joint model for survival and multivariate sparse functional data with application to a study of alzheimer’s disease. Biometrics, 78(2):435–447, 2022.
  23. K. Li and S. Luo. Functional joint model for longitudinal and time-to-event data: an application to alzheimer’s disease. Statistics in Medicine, 36(22):3560–3572, 2017.
  24. K. Li and S. Luo. Bayesian functional joint models for multivariate longitudinal and time-to-event data. Computational Statistics & Data Analysis, 129:14–29, 2019a.
  25. K. Li and S. Luo. Dynamic prediction of alzheimer’s disease progression using features of multiple longitudinal outcomes and time-to-event data. Statistics in Medicine, 38(24):4804–4818, 2019b.
  26. A flexible joint model for multiple longitudinal biomarkers and a time-to-event outcome: With applications to dynamic prediction using highly correlated biomarkers. Biometrical Journal, 63(8):1575–1586, 2021.
  27. Functional survival forests for multivariate longitudinal outcomes: Dynamic prediction of alzheimer’s disease progression. Statistical Methods in Medical Research, 30(1):99–111, 2021.
  28. Joint models with multiple longitudinal outcomes and a time-to-event outcome: a corrected two-stage approach. Statistics and Computing, 30:999–1014, 2020.
  29. Pairwise estimation of multivariate longitudinal outcomes in a bayesian setting with extensions to the joint model. Statistical Modelling, 21(1-2):115–136, 2021.
  30. J. Murray. Package ’gmvjoint’: Joint models of survival and multivariate longitudinal data. ”https://github.com/jamesmurray7/gmvjoint”, 2023.
  31. J. Murray and P. Philipson. A fast approximate em algorithm for joint models of survival and multivariate longitudinal data. Computational Statistics & Data Analysis, 170:107438, 2022.
  32. J. Murray and P. Philipson. Fast estimation for generalised multivariate joint models using an approximate em algorithm. Computational Statistics & Data Analysis, page 107819, 2023.
  33. Primary biliary cirrhosis: prediction of short-term survival based on repeated patient visits. Hepatology, 20(1):126–134, 1994.
  34. A hidden markov model for continuous longitudinal data with missing responses and dropout. Biometrical Journal, page 2200016, 2023.
  35. An overview of joint modeling of time-to-event and longitudinal outcomes. Annual Review of Statistics and Its Application, 6:223–240, 2019.
  36. Faster monte carlo estimation of joint models for time-to-event and multivariate longitudinal data. Computational Statistics & Data Analysis, 151:107010, 2020.
  37. Numerical Recipes: The Art of Scientific Computing. Cambridge University Press, New York, 3rd edition, 2007. ISBN 9780521884075.
  38. C. Proust-Lima and J. M. Taylor. Development and validation of a dynamic prognostic tool for prostate cancer recurrence using repeated measures of posttreatment psa: a joint modeling approach. Biostatistics, 10(3):535–549, 2009.
  39. Functional data analysis. Springer Science & Business Media, second edition, 2005.
  40. D. Rizopoulos. Joint models for longitudinal and time-to-event data: With applications in R. CRC press, 2012.
  41. D. Rizopoulos. The r package JMbayes for fitting joint models for longitudinal and time-to-event data using mcmc. Journal of Statistical Software, 72(7):1–46, 2016.
  42. JMbayes2: Extended joint models for longitudinal and time-to-event data. https://github.com/drizopoulos/JMbayes2, 2022. https://drizopoulos.github.io/JMbayes2/.
  43. JMbayes2: Extended joint models for longitudinal and time-to-event data. https://CRAN.R-project.org/package=JMbayes2, 2023. URL https://CRAN.R-project.org/package=JMbayes2. R package version 0.4-5.
  44. Fast and flexible inference for joint models of multivariate longitudinal and survival data using integrated nested laplace approximations. Biostatistics, page kxad019, 2023.
  45. Functional additive mixed models. Journal of Computational and Graphical Statistics, 24(2):477–501, 2015.
  46. A. A. Tsiatis and M. Davidian. Joint modeling of longitudinal and time-to-event data: an overview. Statistica Sinica, pages 809–834, 2004.
  47. J. Tu and J. Sun. Gaussian variational approximate inference for joint models of longitudinal biomarkers and a survival outcome. Statistics in Medicine, 42(3):316–330, 2023.
  48. Bamlss: Bayesian additive models for location, scale, and shape (and beyond). Journal of Computational and Graphical Statistics, 27(3):612–627, 2018.
  49. bamlss: A Lego toolbox for flexible Bayesian regression (and beyond). Journal of Statistical Software, 100(4):1–53, 2021.
  50. bamlss: Bayesian additive models for location, scale, and shape (and beyond). http://www.bamlss.org/, 2023. URL http://www.bamlss.org/. R package version 1.2-1.
  51. Multivariate functional additive mixed models. Statistical Modelling, 23(4):303–326, 2023.
  52. S. Wood. mgcv: Mixed GAM computation vehicle with automatic smoothness estimation. https://CRAN.R-project.org/package=mgcv, 2021. URL https://CRAN.R-project.org/package=mgcv. R package version 1.8-34.
  53. S. N. Wood. Generalized additive models: An introduction with R. CRC press, 2017.
  54. A joint model for survival and longitudinal data measured with error. Biometrics, pages 330–339, 1997.
  55. Dynamic prediction of disease progression for leukemia patients by functional principal component analysis of longitudinal expression levels of an oncogene. The Annals of Applied Statistics, 11(3):1649–1670, 2017.
  56. Functional principal components analysis on moving time windows of longitudinal data: dynamic prediction of times to event. Journal of the Royal Statistical Society Series C: Applied Statistics, 67(4):961–978, 2018.
  57. F. Yao. Functional principal component analysis for longitudinal and survival data. Statistica Sinica, 17(3):965–983, 2007.
  58. Functional data analysis for sparse longitudinal data. Journal of the American Statistical Association, 100(470):577–590, 2005.
  59. Joint modeling of longitudinal drug using pattern and time to first relapse in cocaine dependence treatment data. The Annals of Applied Statistics, 9(3):1621–1642, 2015.
  60. Bayesian inference and dynamic prediction of multivariate joint model with functional data: An application to alzheimer’s disease. Statistics in Medicine, 40(30):6855–6872, 2021.
  61. Multivariate functional mixed model with mri data: An application to alzheimer’s disease. Statistics in Medicine, 42(10):1492–1511, 2023a.
  62. Bayesian inference and dynamic prediction for multivariate longitudinal and survival data. The Annals of Applied Statistics, 17(3):2574–2595, 2023b.
Citations (1)
View on Semantic Scholar

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now
Github Logo Streamline Icon: https://streamlinehq.com

GitHub

  1. GitHub - alexvolkmann/MJMbamlss (2 stars)