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 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.