The importance of disease markers in understanding the progression of acquired immune deficiency syndrome (AIDS) and devising treatment strategies is well recognized. This issue is usually addressed using cross-sectional data analysis, which tends to ignore the longitudinal data collected on the individuals. Available longitudinal data for nontransfusion-related AIDS raise some technical challenges to standard longitudinal analyses due to left and right censoring as well as left truncation. We describe a likelihood method to model the disease markers as a function of time by modeling the joint distribution of the markers, the time of infection, and the time to AIDS. We address the problems of censoring and truncation using standard survival analysis techniques. We also consider the prediction of time to AIDS given a series of disease marker measurements. An illustrative example, using data from the Toronto AIDS cohort study, is given. In particular, the analysis shows that the slope of the decline in T4 cell count measurements or T4/T8 ratio is associated with the time to AIDS. We compare the prediction of the time to AIDS for an individual with or without a series of T4/T8 measurements and with a known or unknown infection time.