Modeling the Relationship of Survival to Longitudinal Data Measured with Error. Applications to Survival and CD4 Counts in Patients with AIDS

Abstract A question that has received a great deal of attention in evaluating new treatments in acquired immune deficiency syndrome (AIDS) clinical trials is that of finding a good surrogate marker for clinical progression. The identification of such a marker may be useful in assessing the efficacy of new therapies in a shorter period. The number of CD4-lymphocyte counts has been proposed as such a potential marker for human immune virus (HIV) trials because of its observed correlation with clinical outcome. But to evaluate the role of CD4 counts as a potential surrogate marker, we must better understand the relationship of clinical outcome to an individual's CD4 count history over time. The Cox proportional hazards regression model is used to study the relationship between CD4 counts as a time-dependent covariate and survival. Because the CD4 counts are measured only periodically and with substantial measurement error and biological variation, standard methods for estimating the parameters in the Cox mod...

[1]  E. Kaplan,et al.  Nonparametric Estimation from Incomplete Observations , 1958 .

[2]  C. R. Rao,et al.  Linear Statistical Inference and its Applications , 1968 .

[3]  D. Cox.  Regression Models and Life-Tables , 1972 .

[4]  N. Breslow.  Covariance analysis of censored survival data. , 1974, Biometrics.

[5]  Calyampudi R. Rao,et al.  Linear Statistical Inference and Its Applications. , 1975 .

[6]  R. Gill,et al.  Cox's regression model for counting processes: a large sample study : (preprint) , 1982 .

[7]  A. Tsiatis.  A Large Sample Study of Cox's Regression Model , 1981 .

[8]  J. Ware,et al.  Random-effects models for longitudinal data. , 1982, Biometrics.

[9]  R. Prentice.  Covariate measurement errors and parameter estimation in a failure time regression model , 1982 .

[10]  H. Ramlau-Hansen.  Smoothing Counting Process Intensities by Means of Kernel Functions , 1983 .

[11]  Steven G. Self,et al.  Asymptotic Distribution Theory for Cox-Type Regression Models with General Relative Risk Form , 1983 .

[12]  K. Liang,et al.  Asymptotic Properties of Maximum Likelihood Estimators and Likelihood Ratio Tests under Nonstandard Conditions , 1987 .

[13]  D. Bates,et al.  Newton-Raphson and EM Algorithms for Linear Mixed-Effects Models for Repeated-Measures Data , 1988 .

[14]  R. Prentice.  Surrogate endpoints in clinical trials: definition and operational criteria. , 1989, Statistics in medicine.

[15]  Yudi Pawitan,et al.  Modeling a Marker of Disease Progression and Onset of Disease , 1992 .