Sirolimus, Tacrolimus, and Antithymocyte Globulin in Preventing Graft-Versus-Host Disease in Patients With Hematologic Cancer Who Are Undergoing Donor Stem Cell Transplant

OBJECTIVES: Primary * To determine the incidence and severity of acute graft-versus-host disease (GVHD) after HLA-matched or -mismatched unrelated donor peripheral blood stem cell transplantation (PBSCT) in patients with hematologic malignancies treated with immunosuppressive therapy comprising sirolimus, tacrolimus, and anti-thymocyte globulin as GVHD prophylaxis. * To determine the safety of this regimen in these patients at 6 months after PBSCT. Secondary * To determine the time to engraftment (i.e., platelet and absolute neutrophil recovery) in patients treated with this regimen. * To determine the length of hospital stay of these patients within 100 days after PBSCT. * To determine the incidence of infections, including CMV and EBV reactivation and post-transplant lymphoproliferative disorders, in patients treated with this regimen. * To determine the incidence of thrombotic microangiopathy and veno-occlusive disease in patients treated with this regimen. * To determine the incidence of chronic GVHD in patients treated with this regimen. * To determine the overall and disease-free survival of these patients at 2 years after PBSCT. * To determine the Karnofsky performance status of these patients at baseline and at various time points after PBSCT. * To conduct immunocorrelative studies prior to and at various time points after PBSCT. OUTLINE: * Conditioning regimen: Patients receive 1 of 6 conditioning regimens (standard of care treatment) between days -9 and -3, based on diagnosis and the treating physician's preference regarding regimen intensity. * Regimen I: Patients receive fludarabine phosphate IV and busulfan IV. * Regimen II: Patients undergo total body irradiation (TBI) twice daily for 8 fractions and receive etoposide IV. * Regimen III: Patients undergo TBI once or twice daily for 11 fractions and receive cyclophosphamide IV. * Regimen IV: Patients undergo TBI and receive fludarabine phosphate IV and busulfan IV. * Regimen V: Patients receive carmustine IV, etoposide IV, cytarabine IV, and melphalan IV. Some patients also receive rituximab IV. * Regimen VI: Patients receive fludarabine phosphate IV and melphalan IV. Some patients also undergo TBI. * Allogeneic peripheral blood stem cell transplantation: Patients undergo filgrastim (G-CSF)-mobilized allogeneic peripheral blood stem cell transplantation on day 0. * Graft-versus-host disease prophylaxis (GVHD): Patients receive tacrolimus IV continuously over 24 hours or orally and sirolimus orally beginning on day -3 and continuing until day 30 or day 90, followed by a taper in the absence of GVHD. Patients also receive anti-thymocyte globulin IV over 4-8 hours on days -3 to -1. Blood samples are obtained at baseline and periodically during study for correlative biomarker studies. Samples are analyzed by T-cell immunophenotyping, absolute subset number quantification, and multi-parameter flow cytometry for evaluation of immune reconstitution, T-cell differentiation status, NK-cell recovery, allo-reactivity of donor T-cells after transplantation, and regulatory T-cell reconstitution. After completion of study therapy, patients are followed periodically for up to 2 years.