In the acquired immunodeficiency syndrome (AIDS) studies, some statistical problems are rather unique (cf., J.R. Anderson, 1989. Biometric Bulletin. Feb. Issue). New methods are needed to address these particular issues. Here, we propose to study five important statistical problems arising in AIDS trials. The results from this research should be quite useful in developing and analyzing AIDS studies. These problems are: a) Drug combinations for Phase I and Phase II studies; b) Analysis of repeated virologic measurements; c) Analysis of repeated ordered categorical response data: d) The adaptive randomization designs for clinical trials; and e) The robust inference for Cox's proportional hazards model.