A STOCHASTIC-MODEL FOR THE ANALYSIS OF BIVARIATE LONGITUDINAL AIDS DATA

We present a model for multivariate repeated measures that incorporate s random effects, correlated stochastic processes, and measurement err ors. The model is a multivariate generalization of the model for univa riate longitudinal data given by Taylor, Cumberland, and Sy (1994, Jou rnal of the American Statistical Association 89, 727-736). The stochas tic process used in this paper is the multivariate integrated Ornstein -Uhlenbeck (OU) process, which includes Brownian motion and a random e ffects model as special limiting cases. This process is an underlying continuous-time autoregressive order [AR(1)] process for the derivativ es of the multivariate observations. The model allows unequally spaced observations and missing values for some of the variables. We analyze CD4 T-cell and beta-2-microglobulin measurements of the seroconverter s at multiple time points from the Los Angeles section of the Multicen ter AIDS Cohort Study. The model allows us to investigate the relation ship between CD4 and beta-2-microglobulin through the correlations bet ween their random effects and their serial correlation. The data sugge st that CD4 and beta-2-microglobulin follow a bivariate Brownian motio n process. The fit of the model implies that an increase in beta-2-mic roglobulin is associated with a decrease in future CD4 but not vice ve rsa, agreeing with immunologic postulates about the relationship betwe en these two variables.