Asymptotic results for maximum likelihood estimators in joint analysis of repeated measurements and survival time

Maximum likelihood estimation has been extensively used in the joint analysis of repeated measurements and survival time. However, there is a lack of theoretical justification of the asymptotic properties for the maximum likelihood estimators. This paper intends to fill this gap. Specifically, we prove the consistency of the maximum likelihood estimators and derive their asymptotic distributions. The maximum likelihood estimators are shown to be semiparametrically efficient.

[1]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[2]  J. Kalbfleisch,et al.  The Statistical Analysis of Failure Time Data , 1980 .

[3]  R. Prentice,et al.  Commentary on Andersen and Gill's "Cox's Regression Model for Counting Processes: A Large Sample Study" , 1982 .

[4]  S. Johansen.  An Extension of Cox's Regression Model , 1983 .

[5]  W. Rudin.  Real and complex analysis, 3rd ed. , 1987 .

[6]  Raymond J. Carroll,et al.  Estimation and comparison of changes in the presence of informative right censoring by modeling the censoring process , 1988 .

[7]  K. Bailey,et al.  Estimation and comparison of changes in the presence of informative right censoring: conditional linear model. , 1989, Biometrics.

[8]  Niels Keiding,et al.  Statistical Models Based on Counting Processes , 1993 .

[9]  P. Bickel.  Efficient and Adaptive Estimation for Semiparametric Models , 1993 .

[10]  K. Do,et al.  Efficient and Adaptive Estimation for Semiparametric Models. , 1994 .

[11]  M. Wulfsohn,et al.  Modeling the Relationship of Survival to Longitudinal Data Measured with Error. Applications to Survival and CD4 Counts in Patients with AIDS , 1995 .

[12]  P. Diggle.  Analysis of Longitudinal Data , 1995 .

[13]  Jon A. Wellner,et al.  Weak Convergence and Empirical Processes: With Applications to Statistics , 1996 .

[14]  James M. Robins,et al.  Coarsening at Random: Characterizations, Conjectures, Counter-Examples , 1997 .

[15]  N M Laird,et al.  Mixture models for the joint distribution of repeated measures and event times. , 1997, Statistics in medicine.

[16]  M. Wulfsohn,et al.  A joint model for survival and longitudinal data measured with error. , 1997, Biometrics.

[17]  Erik T. Parner,et al.  Asymptotic theory for the correlated gamma-frailty model , 1998 .

[18]  R. Little,et al.  Proportional hazards regression with missing covariates , 1999 .

[19]  R Henderson,et al.  Joint modelling of longitudinal measurements and event time data. , 2000, Biostatistics.

[20]  Susan A. Murphy,et al.  Rejoinder to discussion of ``On Profile Likelihood''. , 2000 .

[21]  Tim B. Swartz,et al.  Approximating Integrals Via Monte Carlo and Deterministic Methods , 2000 .

[22]  Yi Li,et al.  Covariate measurement errors in frailty models for clustered survival data , 2000 .

[23]  Scott L. Zeger,et al.  Latent Variable Model for Joint Analysis of Multiple Repeated Measures and Bivariate Event Times , 2001 .

[24]  Anastasios A. Tsiatis,et al.  A semiparametric estimator for the proportional hazards model with longitudinal covariates measured with error , 2001 .

[25]  S L Zeger,et al.  The Evaluation of Multiple Surrogate Endpoints , 2001, Biometrics.

[26]  S. Zeger,et al.  Joint analysis of longitudinal data comprising repeated measures and times to events , 2001 .

[27]  O. Borgan.  The Statistical Analysis of Failure Time Data (2nd Ed.). John D. Kalbfleisch and Ross L. Prentice , 2003 .

[28]  Laurence L. George,et al.  The Statistical Analysis of Failure Time Data , 2003, Technometrics.