DOI QR코드

DOI QR Code

Joint HGLM approach for repeated measures and survival data

  • Ha, Il Do (Department of Statistics, Pukyong National University)
  • Received : 2016.06.17
  • Accepted : 2016.07.18
  • Published : 2016.07.31

Abstract

In clinical studies, different types of outcomes (e.g. repeated measures data and time-to-event data) for the same subject tend to be observed, and these data can be correlated. For example, a response variable of interest can be measured repeatedly over time on the same subject and at the same time, an event time representing a terminating event is also obtained. Joint modelling using a shared random effect is useful for analyzing these data. Inferences based on marginal likelihood may involve the evaluation of analytically intractable integrations over the random-effect distributions. In this paper we propose a joint HGLM approach for analyzing such outcomes using the HGLM (hierarchical generalized linear model) method based on h-likelihood (i.e. hierarchical likelihood), which avoids these integration itself. The proposed method has been demonstrated using various numerical studies.

Keywords

References

  1. Breslow, N. E. (1972). Discussion of professor Cox's paper. Journal of the Royal Statistical Society B, 34, 216-217.
  2. Christian, N. J., Ha, I. D. and Jeong, J. (2016). Hierarchical likelihood inference on clustered competing risks data. Statistics in Medicine, 35, 251-267. https://doi.org/10.1002/sim.6628
  3. Cox, D. R. (1972). Regression models and life tables (with Discussion). Journal of the Royal Statistical Society B, 74, 187-220.
  4. Elashoff, R. M., Li, G. and Li, N. (2008). A joint model for longitudinal measurements and survival data in the presence of multiple failure types. Biometrics, 64, 762-771. https://doi.org/10.1111/j.1541-0420.2007.00952.x
  5. Guo, X. and Carlin, B. P. (2004). Separate and joint modeling of longitudinal and event time data using standard computer packages. American Statistician, 58, 16-24. https://doi.org/10.1198/0003130042854
  6. Ha, I. D. and Cho, G.-H. (2012). H-likelihood approach for variable selection in gamma frailty models. Journal of the Korean Data & Information Science Society, 23, 199-207. https://doi.org/10.7465/jkdi.2012.23.1.199
  7. Ha, I. D. and Cho, G.-H. (2015). Variable selection in Poisson HGLMs using h-likelihood. Journal of the Korean Data & Information Science Society, 26, 1513-1521. https://doi.org/10.7465/jkdi.2015.26.6.1513
  8. Ha, I. D., Lee, Y. and Song, J. K. (2001). Hierarchical likelihood approach for frailty models. Biometrika, 88, 233-243. https://doi.org/10.1093/biomet/88.1.233
  9. Ha, I. D. and Lee, Y. (2003). Estimating frailty models via Poisson hierarchical generalized linear models. Journal of Computational and Graphical Statistics, 12, 663-681. https://doi.org/10.1198/1061860032256
  10. Ha, I. D. and Noh, M. (2013). A visualizing method for investigating individual frailties using frailtyHL R-package. Journal of the Korean Data & Information Science Society, 24, 931-940. https://doi.org/10.7465/jkdi.2013.24.4.931
  11. Ha, I.D., Park, T. and Lee, Y. (2003). Joint modelling of repeated measures and survival time data. Bio-metrical Journal, 45, 647-658.
  12. Henderson, R., Diggle, P. and Dobson, A. (2000). Joint modelling of longitudinal measurements and event time data. Biostatistics, 1, 465-480. https://doi.org/10.1093/biostatistics/1.4.465
  13. Lee, Y. and Nelder, J. A. (1996). Hierarchical generalized linear models (with discussion). Journal of the Royal Statistical Society B, 58, 619-678.
  14. Lee, Y., Nelder, J. A. and Pawitan, Y. (2006). Generalised Linear Models with Random Effects: Unified Analysis via h-Likelihood, Chapman and Hall, London.
  15. Paik, M. C., Lee, Y. and Ha, I. D. (2015). Frequentist inference on random effects based on summarizability. Statistica Sinica, 25, 1107-1132.
  16. Ripatti, S. and Palmgren, J. (2000). Estimation of multivariate frailty models using penalized partial like-lihood. Biometrics, 56, 1016-1022. https://doi.org/10.1111/j.0006-341X.2000.01016.x
  17. Rizopoulos, D. (2012). Joint models for longitudinal and time-to-event data with applications in R, Chap-man and Hall, London.