This randomized phase III trial compares topical or ablative treatment with active monitoring in preventing anal cancer in patients with human immunodeficiency virus (HIV) and high-grade squamous intraepithelial lesions (HSIL). Anal HSIL is tissue in the anal canal that has been damaged by infection with human papillomavirus (HPV) and is at risk for turning into anal cancer. It is not yet known if treating HSIL is more effective than active monitoring in preventing patients from developing anal cancer.