Jointly Modeling Longitudinal and Event Time Data With Application to Acquired Immunodeficiency Syndrome

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Abstract
In many clinical and epidemiologic studies, periodically measured disease markers are used to monitor progression to the onset of disease. Motivated by 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 measurement error. A central component of the longitudinal model is an integrated Ornstein–Uhlenbeck stochastic process, which represents a family of covariance structures with a random effects model and Brownian motion as special cases. The regression model for the event time data is a proportional hazards model that includes the longitudinal marker as a time-dependent variable 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 study of HIV-infected men. The joint estimation approach allows the simultaneous estimation of the effect of baseline covariates on the progression of CD4 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 incorporate measurement error in CD4 counts into a hazard model.