Abstract
Longitudinal data often occur in follow-up studies, and in many situations, there may exist informative observation times and a dependent terminal event such as death that stops the follow-up. We propose a semiparametric mixed effect model with time-varying latent effects in the analysis of longitudinal data with informative observation times and a dependent terminal event. Estimating equation approaches are developed for parameter estimation, and asymptotic properties of the resulting estimators are established. The finite sample behavior of the proposed estimators is evaluated through simulation studies, and an application to a bladder cancer study is provided.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Cai N, Lu W, Zhang H. Time-varying latent effect model for longitudinal data with informative observation times. Biometrics, 2012, 68: 1093–1102
Davis C S. Statistical Methods for the Analysis of Repeated Measurements. New York: Springer, 2002
Diggle P J, Liang K Y, Zeger S L. The Analysis of Longitudinal Data. Oxford: Oxford University Press, 1994
Fan J, Li R. New estimation and model selection procedures for semiparametric modeling in longitudinal data analysis. J Amer Statist Assoc, 2004, 99: 710–723
Fang S, Zhang H, Sun L. Joint analysis of longitudinal data with additive mixed effect model for informative observation times. J Statist Plann Inference, 2016, 169: 43–55
Fitzmaurice G M, Laird N M, Ware J H. Applied Longitudinal Analysis. New York: John Wiley and Sons, 2004
Gill R D, Johansen S. A survey of product-integration with a view toward application in survival analysis. Ann Statist, 1990, 18: 1501–1555
He X, Tong X, Sun J. Semiparametric analysis of panel count data with correlated observation and follow-up times. Lifetime Data Anal, 2009, 15: 177–196
Huang C Y, Wang M C. Joint modeling and estimation for recurrent event processes and failure time data. J Amer Statist Assoc, 2004, 99: 1153–1165
Laird N M, Ware J H. Random-effects models for longitudinal data. Biometrics, 1982, 38: 963–974
Liang K Y, Zeger S L. Longitudinal data analysis using generalized linear models. Biometrika, 1986, 73: 13–22
Liang Y, Lu W, Ying Z. Joint modeling and analysis of longitudinal data with informative observation times. Biometrics, 2009, 65: 377–384
Lin D Y, Ying Z. Semiparametric and nonparametric regression analysis of longitudinal data. J Amer Statist Assoc, 2001, 96, 103–126
Lin H, Scharfstein D O, Rosenheck R A. Analysis of longitudinal data with irregular outcome-dependent follow-up. J Roy Statist Soc Ser B, 2004, 66: 791–813
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: 950–958
Liu L, Wolfe R A, Huang X. Shared frailty models for recurrent events and a terminal event. Biometrics, 2004, 60: 747–756
Liu L, Wolfe R A, Kalbfleisch J D. A shared random effects model for censored medical costs and mortality. Stat Med, 2007, 26: 139–155
Pollard D. Empirical Processes: Theory and Applications. Hayward: Institute of Mathematical Statistics, 1990
Ryu D, Sinha D, Mallick B, et al. Longitudinal studies with outcome-dependent follow-up: Models and Bayesian regression. J Amer Statist Assoc, 2007, 102: 952–961
Song X, Mu X, Sun L. Regression analysis of longitudinal data with time-dependent covariates and informative observation times. Scand J Statist, 2012, 39: 248–258
Sun J, Park D-H, Sun L, et al. Semiparametric regression analysis of longitudinal data with informative observation times. J Amer Statist Assoc, 2005, 100: 882–889
Sun J, Sun L, Liu D. Regression analysis of longitudinal data in the presence of informative observation and censoring times. J Amer Statist Assoc, 2007, 102: 1397–1406
Sun L, Song X, Zhou J, et al. Joint analysis of longitudinal data with informative observation times and a dependent terminal event. J Amer Statist Assoc, 2012, 107: 688–700
van der Vaart A W, Wellner J A. Weak Convergence and Empirical Processes. New York: Springer, 1996
Welsh A H, Lin X, Carroll R J. Marginal longitudinal nonparametric regression: Locality and efficiency of spline and kernel methods. J Amer Statist Assoc, 2002, 97: 482–493
Wu M C, Carroll R J. Estimation and comparison of changes in the presence of informative right censoring by modeling the censoring process. Biometrics, 1988, 44: 175–188
Ye Y, Kalbfleisch J D, Schaubel D E. Semiparametric analysis of correlated recurrent and terminal events. Biometrics, 2007, 63: 78–87
Zeger S L, Diggle P J. Semiparametric models for longitudinal data with application to CD4 cell numbers in HIV seroconverters. Biometrics, 1994, 50: 689–699
Zeng D, Lin D. Semiparametric transformation models with random effects for joint analysis of recurrent and terminal events. Biometrics, 2009, 65: 746–752
Zhao X, Tong X, Sun L. Joint analysis of longitudinal data with dependent observation times. Statist Sinica, 2012, 22: 317–336
Zhou J, Zhao X, Sun L. A new inference approach for joint models of longitudinal data with informative observation and censoring times. Statist Sinica, 2013, 23: 571–593
Author information
Authors and Affiliations
Corresponding author
Additional information
In memory of Professor Xiru Chen (1934–2005)
Rights and permissions
About this article
Cite this article
Pei, Y., Du, T. & Sun, L. Time-varying latent model for longitudinal data with informative observation and terminal event times. Sci. China Math. 59, 2393–2410 (2016). https://doi.org/10.1007/s11425-016-0112-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11425-016-0112-6
Keywords
- estimating equations
- informative observation times
- joint modeling
- longitudinal data
- terminal event
- time-varying effect