Non-Myeloablative Conditioning for Unrelated Donor Umbilical Cord Blood Transplant

OBJECTIVES: Primary * Determine the one- and two-year survival of patients with hematologic malignancies treated with a nonmyeloablative conditioning regimen comprising fludarabine, cyclophosphamide, and total-body irradiation followed by umbilical cord blood transplantation and post-transplant immunosuppression comprising sirolimus and mycophenolate mofetil. Secondary * Determine the six-month nonrelapse mortality of patients treated with this regimen. * Determine the presence of chimerism in patients treated with this regimen at days 21, 60, 100, 180, and 365. * Determine the incidence of neutrophil engraftment by day 42 in patients treated with this regimen. * Determine the incidence of platelet engraftment by six months in patients treated with this regimen. * Determine the incidence of grade II-IV and grade III-IV acute graft-versus-host disease (GVHD) at day 100 in patients treated with this regimen. * Determine the incidence of chronic GVHD at one year in patients treated with this regimen. * Determine the probability of overall survival within one or two years in patients treated with this regimen. * Determine the probability of progression-free survival within one or two years in patients treated with this regimen. * Determine the incidence of relapse or disease progression within one or two years in patients treated with this regimen. OUTLINE: This is a nonrandomized study. Patients are stratified into five disease groups: 1. acute myeloid leukemia, myelodysplastic syndromes, chronic myelogenous leukemia \[CML\] in first chronic phase and second chronic phase \[CP2\] after myeloid blast crisis; 2. acute lymphoblastic leukemia, Burkitt's lymphoma, CML CP2 post lymphoid blast crisis, 3. large-cell B and T-cell lymphoma, mantle cell lymphoma; 4. chronic lymphocytic leukemia/small lymphocytic lymphoma, prolymphocytic leukemia, marginal zone B-cell lymphoma, follicular lymphoma; 5. Hodgkin's lymphoma and multiple myeloma. * Nonmyeloablative conditioning: Patients receive fludarabine intravenously on days -6 to -2 and cyclophosphamide IV on day -6. Patients who did not undergo prior autologous transplant or who received ≤ 1 course of prior multiagent chemotherapy or no severely immunosuppressive therapy in the past 3 months also receive anti-thymocyte globulin IV on days -6 to -4. All patients also undergo total-body irradiation on day -1. * Umbilical cord blood transplant: Patients undergo umbilical cord blood transplantation on day 0. * Post-transplant immunosuppression: Sirolimus will be administered starting at day -3 with 8mg-12mg mg oral loading dose followed by single dose 4 mg/day with a target serum concentration of 3 to 12 mg/mL. Levels are to be monitored 3 times/week in the first 2 weeks, weekly until day +60, and as clinically indicated until day +100 post-transplantation. In the absence of acute GVHD sirolimus may be tapered starting at day +100 and eliminated by day +180 post-transplantation. Patients also receive mycophenolate mofetil IV on days -3 to 5 and then orally on days 6-30. After completion of study treatment, patients are followed periodically for 5 years. PROJECTED ACCRUAL: A total of 320 patients will be accrued for this study.