Simultaneous Modelling of Survival and Longitudinal Data with an Application to Repeated Quality of Life Measures

In biomedical studies, interest often focuses on the relationship between patient’s characteristics or some risk factors and both quality of life and survival time of subjects under study. In this paper, we propose a simultaneous modelling of both quality of life and survival time using the observed covariates. Moreover, random effects are introduced into the simultaneous models to account for dependence between quality of life and survival time due to unobserved factors. EM algorithms are used to derive the point estimates for the parameters in the proposed model and profile likelihood function is used to estimate their variances. The asymptotic properties are established for our proposed estimators. Finally, simulation studies are conducted to examine the finite-sample properties of the proposed estimators and a liver transplantation data set is analyzed to illustrate our approaches.

[1]  J. Robins,et al.  Semiparametric regression estimation in the presence of dependent censoring , 1995 .

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

[3]  J. Robins,et al.  Estimation of Regression Coefficients When Some Regressors are not Always Observed , 1994 .

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

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

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

[7]  P. Diggle,et al.  Analysis of Longitudinal Data , 2003 .

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

[9]  A A Tsiatis,et al.  Efficient Estimation of the Distribution of Quality‐Adjusted Survival Time , 1999, Biometrics.

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

[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]  James M. Robins,et al.  Semiparametric Regression for Repeated Outcomes With Nonignorable Nonresponse , 1998 .

[13]  M. Davidian,et al.  Estimating the parameters in the Cox model when covariate variables are measured with error. , 1998, Biometrics.

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

[15]  A. W. van der Vaart,et al.  On Profile Likelihood , 2000 .

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

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

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

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