The overall purpose of this proposal is to address statistical issues related to and to develop statistical methods for the analysis of interval-censored data arising from AIDS studies. Such studies play an essential role in AIDS treatment development and evaluation, the understanding of AIDS epidemic and the process of health-related policy-making. Specifically, the proposal consists of three aims and they are 1) the analysis of interval-censored failure time data with independent censoring, 2) the analysis of interval-censored failure time data with dependent censoring, and 3) the analysis of interval-censored count or longitudinal data. The three types of data that will be discussed in the three aims commonly occur in AIDS studies such as AIDS clinical trials, the key component of the development and evaluation of AIDS treatments, and AIDS cohort follow-up studies, commonly used to obtain the knowledge about the process of AIDS disease and HIV and AIDS epidemics. For the type of data in aim 1, some methods have been proposed, but most of them are either lack rigorous studies or are complicated, while for the type of data in aim 2, there exists little research in the literature. Thus the main goal for aim 1 is to develop rigorous and practical methods and evaluate existing methods. For aim 2, our focus will be to develop statistical methods that can deal with both interval- and dependent censoring together and in the meantime can be easily implemented. The type of data in aim 3 becomes more and more common in AIDS studies since, for example, AIDS markers are now commonly used to define end points for AIDS clinical studies. For the analysis of them, we will consider situations where clinical visits or observation times of AIDS patients may or may not depend on response variables of interest (e.g., AIDS markers). When observation times are independent of the response variables, some methods have been proposed for regression analysis, but there is no nonparametric method specially developed for treatment comparison. Note that methods for regression analysis commonly require some distribution and/or model assumptions. Also no approach is available when observation times depend on the response variables. We will develop practical and rigorous methods that allow the dependence of observation times on the response variables for both treatment comparison and regression analysis.