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RATIONALE: Umbilical cord blood transplantation may be able to replace immune cells that were destroyed by chemotherapy or radiation therapy. PURPOSE: This phase II trial is studying how well umbilical cord blood works as a source of stem cells in treating patients with types of cancer as well as other diseases. OBJECTIVES: Primary * Determine the impact of the use of umbilical cord blood as a source of hematopoietic stem cells for children with life-threatening oncologic, hematologic, or genetic/metabolic disorders in need of a stem cell transplant. * Compare the incidence of graft-versus-host disease in patients receiving cord blood transplants in this study with historical data for unrelated donor stem cell transplants. * Compare the incidence of engraftment in patients receiving cord blood transplants in this study with historical data for unrelated donor stem cell transplants. OUTLINE: * Preparative therapy: Patients are treated on 1 of 4 preparative therapy regimens. * Regimen A: Patients undergo total body irradiation (TBI) two times daily on days -7 to -4. Patients receive cyclophosphamide IV over 30-60 minutes on days -3 and -2 and anti-thymocyte globulin (ATG) IV over at least 6 hours on days -3 to -1. * Regimen B (patients who do not receive TBI): Patients receive oral busulfan 4 times daily on days -8 to -5, and ATG IV over at least 6 hours and melphalan IV over 15-20 minutes on days -4 to -2. * Regimen C (patients with Fanconi's anemia and related disorders): Patients undergo TBI on day -6. Patients receive ATG IV over at least 6 hours and methylprednisolone IV on days -5 to -1 and fludarabine IV over 30 minutes and cyclophosphamide IV over 30-60 minutes on days -5 to -2. * Regimen D: Patients receive oral or IV busulfan 4 times daily on days -9 to -5, ATG IV over at least 6 hours on days -5 to -3, and cyclophosphamide IV over 30-60 minutes on days -5 to -2. * Cord blood transplant: All patients undergo umbilical cord blood transplantation on day 0. * Graft-versus-host disease prophylaxis: Patients receive oral or IV cyclosporine twice daily beginning on day -1. Patients also receive methylprednisolone IV twice daily beginning on day 5 and continuing until at least day 28. PROJECTED ACCRUAL: A total of 25 patients will be accrued for this study.
DISEASE CHARACTERISTICS: * Diagnosis of malignant or non-malignant disease, including but not limited to any of the following: * Acute myeloid leukemia or acute lymphoblastic leukemia (ALL) with resistant disease beyond first clinical remission (CR) * ALL in first CR at high-risk because of 1 of the following factors: * Hypoploidy * Pseudodiploidy with translocations t(9;22), t(4;11), or t(8;14) * Elevated WBC at diagnosis as follows: * \> 100,000/mm\^3 for patients 6-12 months of age * \> 50,000/mm\^3 for patients 10-20 years of age * \> 20,000/mm\^3 for patients 21 years of age * Burkitt's lymphoma/leukemia * Chronic myelogenous leukemia in first chronic phase or beyond * Juvenile myelomonocytic leukemia * Advanced stage or relapsed lymphoma * Advanced stage or relapsed solid tumors, including any of the following: * Neuroblastoma * Ewing's sarcoma * Rhabdomyosarcoma * Myelodysplastic syndromes, excluding patients with grade 3 or 4 myelofibrosis * Familial erythrophagocytic histiocytosis * Histiocytosis unresponsive to medical management * Inborn errors of metabolism * Langerhans cell histiocytosis unresponsive to medical management * Immune deficiencies, including: * Severe combined immune deficiency * Wiskott-Aldrich * Hemoglobinopathies, including sickle cell disease and thalassemia * Severe aplastic anemia * Fanconi's anemia * Metabolic storage diseases * Unrelated cord blood donor must be HLA-identical OR may be mismatched for 1, 2, or 3 HLA-loci (A, B, DR) * No other existing HLA-identical related donor available at the time of transplantation PATIENT CHARACTERISTICS: Age * 21 and under Performance status * Not specified Life expectancy * Not specified Hematopoietic * See Disease Characteristics Hepatic * Not specified Renal * Not specified PRIOR CONCURRENT THERAPY: Biologic therapy * Not specified Chemotherapy * Not specified Endocrine therapy * Not specified Radiotherapy * Not specified Surgery * Not specified
are designated in this study