Functional approach of flexibly modelling generalized longitudinal data and survival time

Journal of Statistical Planning and Inference

Volumn 138, Issue 4, 2008, Pages 995-1009

  Yao, Fang ^a  

^a UNIVERSITY OF TORONTO   (Canada)

Author keywords

Cox regression; EM algorithm; Functional principal components; Generalized linear mixed effects model; Longitudinal data; Survival

Indexed keywords

EID: 37249060736     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jspi.2007.03.053     Document Type: Article

References (44)

1. Abrams, D.I., Goldman, A.I., Launer, C., Korvick, J.A., Neaton, J.D., Crane, L.R., Grodesky, M., Wakefield, S., Muth, K., Kornegay, S., C.D.J., Haris, A., Luskin-Hawk, R., Markowitz, N., Sampson, J.H., Thompson, M., Deyton, L., the Terry Beirn Community Programs for Clinical Research on AIDS, 1994. Comparative trial of didanosine and zalcitabine in patients with human immunodeficiency virus infection who are intolerant or have failed zidovudine therapy. New England J. Med. 330, 657-662.
2. Berkey C.S., and Kent R.L.J. Longitudinal principal components and non-linear regression models of early childhood growth. Ann. Human Biol. 10 (1983) 523-536
3. Besse P., and Ramsay J.O. Principal components analysis of sampled functions. Psychometrika 51 (1986) 285-311
4. Booth J.G., and Hobert J.P. Maximizing generalized linear mixed model likelihoods with an automated Monte Carlo EM algorithm. J. Roy. Statist. Soc. Ser. B 61 (1999) 265-285
5. Breslow N.E., and Clayton D.G. Approximate inference in generalized linear mixed models. J. Amer. Statist. Assoc. 88 (1993) 9-25
6. Breslow, N.E., Lin, X., 1995. Bias correction in generalized linear mixed models with a single component of dispersion. Biometrika 82, 81-91.
7. Bycott P., and Taylor J. A comparison of smoothing techniques for CD4 data measured with error in a time-dependent Cox proportional hazard model. Statist. Med. 17 (1998) 2061-2077
8. Castro P.E., Lawton W.H., and Sylvestre E.A. Principal modes of variation for processes with continuous sample curves. Technometrics 28 (1986) 329-337
9. Cox D.R. Regression models and lifetables (with discussion). J. Roy. Statist. Soc. Ser. B 34 (1972) 187-200
10. Cox D.R. Partial likelihood. Biometrika 34 (1975) 269-276
11. Dafni U.G., and Tsiatis A.A. Evaluating surrogate markers if clinical outcomes measured with error. Biometrics 54 (1998) 1445-1462
12. Diggle P., Hergerty P., Liang K.Y., and Zeger S. Analysis of Longitudinal Data (2002), Oxford University Press, Oxford
13. Faucett C.L., and Thomas D.C. Simultaneously modelling censored survival data and repeatedly measured covariates: a Gibbs sampling approach. Statist. Med. 15 (1996) 1663-1685
14. Faucett C.L., Schenker N., and Elashoff R.M. Analysis of censored survival data with intermittently observed time-dependent binary covariates. J. Amer. Statist. Assoc. 93 (1998) 427-437
15. Goldman A.I., Carlin B.P., Crane L.R., Launer C., Korvick J.A., Deyton L., and Abrams D.I. Response of CD 4 lymphocytes and clinical consequences to treatment using ddI in patients with advanced HIV infection. J. Acquir. Immune Defic. Syndr. Hum. Retrovirol. 11 (1996) 161-169
16. Goldstein H. Nonlinear multilevel models, with an application to discrete response data. Biometrika 78 (1991) 45-51
17. Guo X., and Carlin B.P. Separate and joint modelling of longitudinal and event time data using standard computer packages. Amer. Statist. 58 (2004) 1-9
18. Henderson R., Diggle P.J., and Dobson A. Joint modelling of longitudinal measurements and event time data. Biostatistics 4 (2000) 465-480
19. James G., Hastie T.G., and Sugar C.A. Principal component models for sparse functional data. Biometrika 87 (2000) 587-602
20. James L.F., Priebe C.E., and Marchette D.J. Consistent estimation of mixture complexity. Ann. Statist. 29 (2001) 1281-1296
21. Larsen K. The Cox proportional hazards model with a continuous latent variable measured by binary indicators. Biometrics 61 (2005) 1049-1055
22. Lin X., and Breslow N.E. Bias correction in generalized linear mixed models with multiple components of dispersion. J. Amer. Statist. Assoc. 91 (1996) 1007-1016
23. McCullagh P., and Nelder J.A. Generalized Linear Models. 2nd ed. (1989), Chapman and Hall, London
24. McCulloch C.E. Maximum likelihood variance components estimation for binary data. J. Amer. Statist. Assoc. 89 (1994) 330-335
25. McCulloch C.E. Maximum likelihood algorithm for generalized linear mixed models. J. Amer. Statist. Assoc. 92 (1997) 162-170
26. Molenberghs G., Kenward M.G., and Lesaffre E. The analysis of longitudinal ordinal data with nonrandom drop-out. Biometrika 84 (1997) 33-44
27. Prentice R. Covariate measurement errors and parameter estimates in a failure time regression model. Biometrika 69 (1982) 331-342
28. Raboud J., Reid N., Coates R.A., and Farewell V.T. Estimating risks of progressing to AIDS when covariates are measured with error. J. Roy. Statist. Soc. Ser. A 156 (1993) 396-406
29. Ramsay J.O., and Silverman B.W. Functional Data Analysis (1997), Springer, New York
30. Ramsay J.O., and Silverman B.W. Applied Functional Data Analysis: Methods and Case Studies (2002), Springer, New York
31. Rice J., and Silverman B.W. Estimating the mean and covariance structure nonparametrically when the data are curves. J. Roy. Statist. Soc. Ser. B 53 (1991) 233-243
32. Schall R. Estimation in generalized linear models with random effects. Biometrika 78 (1991) 719-727
33. Silverman B.W. Smoothed functional principal components analysis by choice of norm. Ann. Statist. 24 (1996) 1-24
34. Taylor J.M.G., Tan S.J., Detels R., and Giorgi J.V. Applications of computer simulation model of the natural history of CD4 T-cell number in HIV-infected individuals. AIDS 5 (1991) 159-167
35. Taylor J.M.G., Cumberland W.G., and Sy J.P. A stochastic model for analysis of longitudinal data. J. Amer. Statist. Assoc. 89 (1994) 727-776
36. Tsiatis A.A., and Davidian M. Joint modeling of longitudinal and time-to-event data: an overview. Statist. Sinica 14 (2004) 809-834
37. Tsiatis A.A., Degruttola V., and Wulfsohn M.S. Modelling the relationship of survival to longitudinal data measured with error. Applications to survival and CD4 counts in patients with AIDS. J. Amer. Statist. Assoc. 90 (1995) 27-37
38. Wang Y., and Taylor J.M.G. Jointly modelling longitudinal and event time data with application to acquired immunodeficiency syndrome. J. Amer. Statist. Assoc. 96 (2001) 895-905
39. Wolfinger R., and O'Connell M. Generalized linear mixed models: a pseudo-likelihood approach. J. Statist. Comput. Simulation 48 (1993) 233-243
40. Wulfsohn M.S., and Tsiatis A.A. A joint model for survival and longitudinal data measured with error. Biometrics 53 (1997) 330-339
41. Xu J., and Zeger S.L. Joint analysis of longitudinal data comprising repeated measures and times to event. Appl. Statist. 50 (2001) 375-387
42. Yao F., Müller H.G., Clifford A.J., Dueker S.R., Follett J., Lin Y., Buchholz B.A., and Vogel J.S. Shrinkage estimation for functional principal component scores with application to the population kinetics of plasma folate. Biometrics 59 (2003) 676-685
43. Yao F., Müller H.G., and Wang J.L. Functional data analysis for sparse longitudinal data. J. Amer. Statist. Assoc. 100 (2005) 577-590
44. Zeger S.L., and Karim M.R. Generalized linear models with random effects: a Gibbs sampling approach. J. Amer. Statist. Assoc. 86 (1991) 79-86