Jointly modeling longitudinal and event time data with application to acquired immunodeficiency syndrome

In many clinical and epidemiologic studies, periodically measured disease m arkers are used to monitor progression to the onset of disease. Motivated b y a study of CD4 counts in men infected with human immunodeficiency virus ( HIV) at risk for acquired immunodeficiency syndrome (AIDS), we developed a joint model for analysis of both longitudinal and event time data. We use a longitudinal model for continuous data that incorporates a mean structure dependent on covariates, a random intercept, a stochastic process, and meas urement error. A central component of the longitudinal model is an integrat ed Ornstein-Uhlenbeek stochastic process, which represents a family of cova riance structures with a random effects model and Brownian motion as specia l cases. The regression model for the event time data is a proportional haz ards model that includes the longitudinal marker as a time-dependent variab le and other covariates. A Markov chain Monte Carlo algorithm was developed for fitting the joint model. The joint modeling approach is evaluated and compared with the approach of separate modeling through simulation studies, and it is applied to CD4 counts and AIDS event time data from a cohort stu dy of HIV-infected men. The joint estimation approach allows the simultaneo us estimation of the effect of baseline covariates on the progression of CD 4 counts and the effect of the current CD4 count and baseline covariates on the hazard of AIDS. The joint modeling approach also gives a way to incorp orate measurement error in CD4 counts into a hazard model.