Stem Cell Clinical Trials - Sirolimus/Tacrolimus Versus Tacrolimus/Methotrexate for Preventing Graft-Versus-Host Disease (GVHD) National Heart, Lung, and Blood Institute (NHLBI);Blood and Marrow Transplant Clinical Trials Network ;National Cancer Institute (NCI) The study is designed as a phase III, randomized, open label, multicenter, prospective, comparative trial of sirolimus and tacrolimus versus tacrolimus and methotrexate as graft-versus-host disease (GVHD) prophylaxis after human leukocyte antigen (HLA)-matched, related, peripheral blood stem cell transplantation in individuals with hematologic cancer. Participants will be stratified by transplant center and will be randomly assigned to the sirolimus/tacrolimus or tacrolimus/methotrexate arms at a 1:1 ratio.