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

Abstract

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship.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 model by maximizing the partial likelihood are no longer appropriate. Instead, we propose a two-stage approach. In the first stage the longitudinal CD4 count data are modeled using a repeated measures random components model. In the second stage methods for estimating the parameters in a Cox model when the data are assumed to be of this form are derived. We also considered methods to account for missing data patterns. These methods are applied to CD4 data from a randomized clinical trial of AIDS patients where half of the patients were randomized to receive Zidovudine (ZDV) and the other half were randomized to receive a placebo. Although a strong correlation between CD4 counts and survival is demonstrated, we also show that CD4 counts may not serve as a useful surrogate marker for assessing treatments for this population of patients.

An Evaluation of a Measure of the Proportion of the Treatment Effect Explained by a Surrogate Marker

“…In view of the poor properties of P (FGS) , we believe it would be unwise to give any strong interpretation of this value other than demonstrating that CD4 is not a perfect surrogate. We believe that other methods of investigating surrogate markers are likely to be more fruitful, for example, a graphical approach [16] or by meta-analysis [18].…”

“…The protocol stipulated that patients' CD4 values were to be measured at baseline, 8,16,32,48,64, and 80 weeks. There were 428 individuals in the placebo arm, 453 in the low-dose arm, and 456 in the high-dose arm.…”

“…We adopt a two-stage approach in which we first impute marker values, denoted by Ẑ i *, at the event times and then uses these to fit the Cox model. In the simulation study we consider four different approaches for imputing values of Z i *: using the true (but unobserved) values of Z* (denoted by TRUE), using the last observed value of Z (denoted by OBS), using the Tsiatis et al [16] method with a random intercept and Brownian motion model (denoted by BM), and using the method of fitting a straight line separately to each subject's set of Z values and using the interpolation from that [17] (denoted by IRL). Bycott and Taylor [14] give a more complete description and comparison of these methods for fitting a time-dependent Cox model.…”

Stochastic model for analysis of longitudinal data on aging and mortality

“…The first, "longitudinal," process is observed at respective times of measurement and the second, "survival," process generates (possibly censored) event times that depend on the observations of the longitudinal process. The frequently used approach for a univariate case assumes that the longitudinal data follow a linear mixed-effects model [13] and that the hazard depends both on the random effects and other time-independent covariates through a Cox proportional hazard relationship [14][15][16]. Xu and Zeger [17] extended the model using the generalized linear model for the longitudinal process to allow for continuous or discrete covariates.…”

Joint modelling of repeated measurements and event time: Application to performance traits and survival of lambs bred in sub-humid tropics

“…In particular, several models have been developed in the area of acquired immunodeficiency syndrome (AIDS) research [5,7,20,22,24] and in schizophrenia studies [9,25]. A detailed review of research work in joint modelling of times to an event and repeated measurements is given in the reference [23].…”