Cord Blood With T-Cell Depleted Haplo-identical Peripheral Blood Stem Cell Transplantation for Hematological Malignancies

Inclusion Criteria: Note: protocol eligible patients according to the criteria outlined below will then be divided according to age, diagnosis, performance status, organ function, prior transplantation, hematopoietic cell transplant comorbidity index (HCT-CI)23, and CB TNC dose into those who are at standard risk (Arm A) or high risk (Arm B) for early post-transplant death for the purposes of applying stopping rules and outcome analysis. Age: o 2 - 70 years. Diagnosis of severe aplastic anemia: eligibility to be discussed with PI and Service Chief. Such patients will be assessed in Arm B. Diagnosis of high risk hematological malignancy: Any acute leukemia in first complete remission (CR) considered at high risk for relapse, or second or third CR, or relapse/refractory less than 10% blasts in bone marrow, or aplasia post-therapy. This includes de novo acute leukemia or acute leukemia that is therapy related or arising from an antecedent hematologic disorder including myelodysplasia (MDS), chronic myeloid leukemia (CML) or other myeloproliferative disorder. * Juvenile myelomonocytic leukemia (JMML) in CR, or relapse with less than 10% bone marrow blasts. * CML with tyrosine kinase inhibitor failure in chronic or accelerated phase or evolved to acute leukemia. * MDS or other myeloproliferative disorder with life-threatening cytopenia(s), and/or red blood cell or platelet transfusion dependence, or patients with aplasia, or patients with excess blasts less than 10% blasts in the bone marrow at work-up. * Aggressive lymphoma: patients in CR1 with disease at high risk of relapse or CR2-3. * Indolent lymphoma or chronic lymphocytic leukemia (CLL): any disease status provided any transformed component is in CR. * Hodgkin's lymphoma that is primary refractory or relapsed not suitable for other therapy and in PR or CR or small volume stable disease. Performance status: * Karnofsky score ≥ 70 or Lansky score ≥ 70. • Organ function: * Resting left ventricular ejection fraction (LVEF) ≥ 50%. * Spirometry (FEV1 and FVC) \& corrected DLCO ≥ 50% predicted. In small children use history and physical and CT scan to determine pulmonary status. * Total bilirubin ≤ to 1.5 mg/dl (unless benign congenital elevated bilirubin); ALT ≤ 3 x upper limit of normal (ULN). * Calculated creatinine (calc. creat.) clearance ≥ to 60 ml/min. * Albumin ≥ 3.0. Graft: o Cryopreserved dose will be ≥ 1.5 x 10\^7 TNC/kilogram in each unit for double unit CB grafts. This will be the CB graft for the majority of patients. In select patients with access to CB units that have high TNC (\> 5.0 x 10\^7/kg), and are from good quality CB banks a single unit could be considered with a back-up CB unit on standby. * In select patients who have a very poor search and only have one suitable CB unit available, this unit could be given as a single unit. This unit must have a TNC ≥ 2.0 x 10\^7 TNC/kilogram and a CD34+ cell dose ≥ 1.5 x 10\^5 CD34+/kilogram. * Haploidentical donors who are 5/10 or better but not HLA-identical will be used as outlined in section 6.4. Assignment of conditioning intensity (high dose vs reduced intensity) will be based on patient disease status, age, extent of prior therapy, organ function and presence of significant comorbidities as outlined in Section 9.2. For the purposes of analysis (not assignment of preparative regimen), patients will be assigned to Arms A and B as summarized below according to their risk of early post-transplant death. Eligible patients who fulfill all of the following criteria will be assigned to risk Arm A: Age 2-49 years Diagnosis Any acute leukemia in CR1 - CR2 (includes therapy-related and arising from MDS or myeloproliferative disease). JMML in CR. CML with TKI failure \& \< 5% blasts. MDS with \< 5% blasts at work-up. Lymphoma (including CLL) CR1-2. Performance Status Karnofsky ≥ 80; Lansky ≥ 80 Organ Function Resting LVEF ≥ to 60% Spirometry (FEV1 and FVC) \& corrected DLCO ≥ 80% predicted. Total bilirubin normal; ALT normal-1.4 x ULN. Calc. creat. clearance ≥ 70 ml/min. Prior HSC Transplant No HCT-CI score\^23 0-2 Pre-thaw TNC Dose Each unit ≥ to 2.0 x 10\^7/kg Eligible patients who meet any of the following criteria will be assigned to risk Arm B: Age 50-70 years Diagnosis Any acute leukemia in relapse/ refractory disease in BM or circulating blasts or CR3 or aplasia. JMML not in CR. MDS with aplasia or ≥ 5% blasts. Lymphoma (including CLL) with disease other than CR1-2. Severe myelofibrosis of the bone marrow Performance Status Karnofsky 70; Lansky 70 Organ Function LVEF 50-59%. Spirometry \& corrected DLCO 50-79% predicted. Total bilirubin 1.1-1.5 mg/dl; ALT 1.5-3 x ULN. Calc. creat. clearance 60-69 ml/min. Prior HSC Transplant Yes HCT-CI score23 3 or higher Pre-thaw TNC Dose Either or both units 1.5-1.9 x 10\^7/kg. Exclusion Criteria: * Active CNS leukemia. * Any acute leukemia (including prior myelodysplasia or CML blast crisis) with morphologic relapse or persistent disease ≥ 10% blasts in the BM, or doubling of the blasts in the blood in the 2 weeks preceding admission, or need for hydroxyurea in the 2 weeks prior to admission, or uncontrolled extra-medullary disease. * Two prior stem cell transplants of any kind. * One prior autologous stem cell transplant within the preceding 12 months. * One prior allogeneic stem cell transplant within the preceding 24 months. * Prior radiation therapy with 400 cGy or more of TBI. If 200 cGy of prior TBI then only 400 CGy of TBI on this protocol is permitted. * Uncontrolled viral, bacteria or fungal infection at time of study enrollment. * Sero-positive or NAT positive for HIV. * Females who are pregnant or breast feeding. * Patient or guardian unable to give informed consent or unable to comply with the treatment protocol including appropriate supportive care, follow-up, and research tests Cord Blood Grafts: Units will be selected based on the HLA-match to the patient and individual cell doses of the units according to current MSKCC unit selection criteria. HLA-testing will be done using molecular techniques. The standard cord blood graft for this protocol will consist of 2 units as a double unit graft although single units are permitted. Each unit will be at least 4 of 6 HLA-A, -B antigen and -DRB1 allele matched with the recipient. Each unit of a double unit graft will have a cryopreserved dose of at least 1.5 x 10\^7 TNC/recipient body weight (TNC/kg). In the occasional patient with a large well matched good quality single unit or the rare patient with only one unit of suitable match and dose characteristics the cord blood graft can consist of a single unit as described in section 6.1 . Haploidentical Donor Inclusion Criteria: A HLA-haploidentical related donor will be selected as available as per standard MSKCC Adult BMT guidelines. Mismatched family members who are matched at more than 5 of 10 HLA-loci are permitted. Factors to be taken into account when selecting a haplo-identical donor will include donor age, weight, health status and comorbidities, compliance, venous access, recipent donor specific HLA-antibody status, and NK cell alloreactivity. * The donor must meet criteria outlined in the FACT-approved SOP for "DONOR EVALUATION AND SELECTION FOR ALLOGENEIC TRANSPLANTATION" in the Blood and Marrow Transplant Program Manual, document E-1 (see attached, or link to URL:(https://one.mskcc.org/sites/pub/corp/bmt/Documents/D2\_SOP\_Donor%20Selection%20and%20Evaluation\_04\_2015.pdf) * The donor must have adequate peripheral venous catheter access for leukapheresis or must agree to placement of a central catheter. * The donor must be \>25 kg in weight. Haploidentical Donor Exclusion Criteria: Evidence of active infection (including active urinary tract infection, or upper respiratory tract infection) or evidence of viral hepatitis exposure on screening unless only HbsAb+ and HBV DNA negative. * Medical or physical reason which makes the donor unlikely to tolerate or cooperate with growth factor therapy and leukapheresis. * Factors which place the donor at increased risk for complications from leukapheresis or G-CSF therapy (e.g., active autoimmune disease, sickle cell trait, symptomatic coronary artery disease requiring therapy). * Pregnancy (positive serum or urine β-HCG) or breastfeeding. Women of childbearing age must avoid becoming pregnant while on the study.