Abstract

Many clinical studies generate a dataset having longitudinal repeated biomarker measurement data and time to an event data, which often depend on each other. In such studies, characteristics of the pattern of a biomarker change, and the association between the primary survival endpoint and features of the longitudinal profiles are commonly of interest. Often separate analyses using a mixed effects model for the longitudinal outcome and a survival model for the time to event outcome are performed. However, separate models are overly simplified because they do not consider the association between two components of such data and so produce misleading conclusions. An alternative approach is two-stage modeling which allows a separate biomarker pathway for each patient but the parameter estimates are still biased. Joint modeling is the most sophisticated complex approach but enables the repeated biomarker measurements and survival processes to be modelled while accounting for the interrelationship between the two processes. We demonstrate the use of joint modeling in analysis of an HIV dataset with CD4+ count measurements and survival time. In the joint model, we combine a linear Gaussian random effects sub-model for the repeated CD4+ count measurements and Cox or Weibull survival sub-model, linked through their shared dependence on the latent variable. Our study showed that the hazard rate of death depended on the longitudinal progression of CD4+ counts, i.e., a patient's baseline CD4+ count and the rate of change in CD4+ counts significantly impact on his or her survival time.

Keywords: Joint model, random effects model, survival model, longitudinal data, event time data, HIV