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

You may be eligible if

• 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