The goal of this research is to develop new statistical methods for analyzing, interpreting, and designing clinical trials for patients with Acquired Immune Deficiency Syndrome (AIDS). Methods will be developed to model the relationship of longitudinally measured biological variables such as CD4 counts to clinical outcome such as death or time to AIDS. In particular, we will develop methods that will account for the bias that occurs when the variables are missing over time in a non-random fashion as well as being measured with error. The primary purpose of this research is to study whether biological variables could be identified that may be used as early surrogates of clinical outcome. We shall develop tests of hypotheses and parameter estimates for censored survival data that are more efficient by incorporating auxiliary time dependent prognostic variables to recover information that is lost due to censoring. We shall develop a comprehensive approach for monitoring AIDS clinical trials whose primary endpoint is time to event using group sequential boundaries. In particular, we shall show how to apply these methods to arbitrary parametric models as well as some nonparametric models.