Umbilical Cord Blood Stem Cell Transplant in Treating Patients With Hematologic Cancer or Other Disease

DISEASE CHARACTERISTICS:

• Histologically confirmed diagnosis of 1 of the following:
• Acute myeloid leukemia meeting the following criteria:
• M0-M7 histologic subtypes by French-American-British classification
• Previously treated disease
• Meets 1 of the following criteria:
• Persistent disease as evidenced by 5-30% persistent blasts in bone marrow after induction or salvage therapy
• In second or subsequent complete remission (CR)
• In first CR with 1 of the following high-risk features:
• Philadelphia chromosome present
• Noncore-binding factor type of chromosomal abnormalities
• Myelodysplastic syndromes with 1 of the following International Prognostic Scoring System (IPSS) scores:
• Intermediate-1
• Intermediate-2
• High-risk score with transfusion dependence
• Chronic myelogenous leukemia meeting 1 of the following criteria:
• In accelerated or blastic phase
• Failed prior imatinib mesylate therapy
• Acute lymphoblastic leukemia meeting 1 of the following criteria:
• In first CR with any of the following high-risk features:
• Philadelphia chromosome present
• Translocation t(4;11) present
• WBC > 30,000/mm³ (adult patients)
• More than 4 weeks from initiation of treatment was required to achieve CR (adult patients)
• DNA index of near haploid (N=23 chromosomes) (pediatric patients)
• In second or subsequent CR
• Persistent disease as evidenced by 5-20% persistent blasts in bone marrow after induction or salvage therapy
• Hodgkin's or non-Hodgkin's lymphoma meeting the following criteria:
• Recurrent or refractory disease
• Tumor ≤ 5 cm in diameter
• Myeloma or plasma cell neoplasm meeting 1 of the following staging criteria:
• Stage III at presentation
• Stage I-II at presentation
• Not responding OR progressed after first-line therapy
• Chronic lymphocytic leukemia or Waldenstrom's macroglobulinemia with refractory or progressive disease after first-line therapy
• No 5-6/6 HLA-matched related or 7-8/8 HLA-matched unrelated marrow or peripheral blood stem cell donor available
• No single 4-6/6 HLA-A, -B, or -DRB1-matched umbilical cord blood unit ≥ 3.5 x 10^7 nucleated cells/kg available

PATIENT CHARACTERISTICS:

• ECOG performance status (PS) 0-2 OR Karnofsky or Lansky PS 70-100%
• Not pregnant
• Fertile patients must use effective contraception prior to and during study participation
• HIV negative
• Bilirubin < 3.0 mg/dL
• AST and ALT ≤ 3 times upper limit of normal
• Creatinine < 2.0 mg/dL OR creatinine clearance > 50 mL/min
• Cardiac ejection fraction > 50% by echocardiogram OR shortening fraction > 27%
• No uncontrolled symptomatic congestive heart failure
• No unstable angina pectoris
• No cardiac arrhythmia
• FEV_1 > 50% of normal
• Forced vital capacity > 50% of normal
• DLCO normal
• Oxygen saturation > 92% on room air (for patients < 5 years of age)
• No history of allergic reactions attributed to compounds of similar chemical or biological composition to busulfan and fludarabine phosphate
• No ongoing or active infection
• No psychiatric illness or social situation that would preclude study compliance
• No other uncontrolled illness

PRIOR CONCURRENT THERAPY:

• See Disease Characteristics
• At least 4 weeks since prior and no concurrent surgery
• At least 4 weeks since prior and no other concurrent investigational or commercial agents or therapies for the malignancy, including chemotherapy, biologic therapy, or radiotherapy