Donor Umbilical Cord Blood Transplant in Treating Patients With Hematologic Cancer

RATIONALE: Giving chemotherapy and total-body irradiation before a donor umbilical cord blood transplant helps stop the growth of cancer and abnormal cells and helps stop the patient's immune system from rejecting the donor's stem cells. When the stem cells from a related or unrelated donor, that do not exactly match the patient's blood, are infused into the patient they may help the patient's bone marrow to make stem cells, red blood cells, white blood cells, and platelets. PURPOSE: This clinical trial is studying how well donor umbilical cord blood transplant works in treating patients with hematologic cancer.

OBJECTIVES: Primary * Determine the engraftment potential of umbilical cord blood (UCB) in patients with hematological cancers. * Determine the safety of UCB transplantation in these patients. Secondary * Determine the rate of neutrophil and platelet recovery and the completeness of donor cell engraftment. * Determine the incidence and severity of acute and chronic graft-versus-host disease. * Determine the incidence of relapse in patients with malignant disease. * Determine the probabilities of survival and event-free survival (EFS) at 1 and 2 years after UCB transplantation. OUTLINE: Patients are stratified according to degree of HLA disparity (0-1 vs 2-3 disparities between donor and recipient), donor type (related vs unrelated), and the basis of cell dose (\< 2 vs ≥ 2 x 10\^7 nucleated cells/kg recipient body weight). Patients are assigned to 1 of 4 treatment groups according to disease\*. NOTE: \*Patients with acute lymphocytic leukemia (ALL), secondary acute myeloid leukemia (AML), severe combined immunodeficiency, familial erythrophagocytic lymphohistiocytosis (FEL)/viral-associated hemophagocytic syndrome (VAHS), inborn errors of metabolism, aplastic anemia, Fanconi's anemia, or Diamond-Blackfan anemia who have an unrelated umbilical cord blood donor may proceed directly to transplantation. * Preparative regimen: * Group 1 (patients with chronic myelogenous leukemia, AML, myelodysplastic syndromes, or ALL): Patients receive cyclophosphamide IV once daily on days -7 and -6. Patients then undergo total-body irradiation (TBI) twice daily on days -4 to -1. Patients undergoing unrelated allogeneic umbilical cord blood transplantation (UCBT) also receive methylprednisone IV and anti-thymocyte globulin (ATG) IV twice daily on days -2 and -1. * Group 2 (patients with infant leukemia): Patients receive busulfan orally or IV four times daily on days -9 to -6 and melphalan IV once daily on days -4 to -2. Patients undergoing unrelated allogeneic UCBT also receive methylprednisolone IV and ATG IV twice daily on days -2 and -1. * Group 3 (patients with inborn errors of metabolism): Patients receive busulfan orally or IV four times daily on days -9 to -6 and cyclophosphamide IV once daily on days -5 to -2. Patients undergoing unrelated allogeneic UCBT also receive methylprednisolone IV and ATG IV twice daily on days -2 and -1. * Group 4 (patients with aplastic anemia): Patients receive cyclophosphamide IV once daily on days -6 to -3 and ATG IV twice daily on days -5 and -3. Patients then undergo TBI once on day -2. * Allogeneic UCBT: Patients undergo UCBT on day 0. Patients with inborn errors of metabolism receive methylprednisolone IV before and after UCBT on day 0. * Graft-versus-host disease (GVHD) prophylaxis: Patients receive 1 of the following regimens: * Related donor UCBT: Patients receive cyclosporine IV over 2 hours or orally beginning on day -3 and continuing until day 60. * Unrelated donor UCBT and myeloablative preparative regimen: Patients receive cyclosporine orally or IV over 2 hours twice daily beginning on day -3 and continuing until day 180. Patients also receive methylprednisolone IV twice daily on days 5-19. * Unrelated donor UCBT and nonmyeloablative preparative regimen: Patients receive cyclosporine IV over 2 hours or orally twice daily beginning on day -3 and continuing until day 180. Patients also receive mycophenolate mofetil IV or orally beginning on day 5 and continuing until day 30 or 7 days after active GVHD is controlled. All patients receive filgrastim (G-CSF) IV beginning on day 1 and continuing until blood counts recover. Patients are followed periodically for 2 years. PROJECTED ACCRUAL: A total of 60 patients will be accrued for this study.