• Incidence of dose limiting toxicity [ Time Frame: Up to 42 days after first injection ]
  Will be defined as any of the events: grade 3 or 4 graft versus host disease (GVHD), secondary graft failure, disease relapse, development of post-transplant lymphoproliferative disorder, development of progressive multifocal leukoencephalopathy or grade 3-4 organ failure attributable to recombinant human interleukin-7 (CYT107) and death.
• Maximum tolerated dose [ Time Frame: Up to 42 days after first injection ]
  Bayesian model averaging-continual reassessment method will be applied to determine an optimal recommended dose of CYT107.

• Rate of viral infections [ Time Frame: Up to 3 years ]
  Will determine the rate of cytomegalovirus, Epstein-Barr virus, and BK viral infections in cord blood transplant patients who receive three doses of CYT107 following engraftment.
• Overall survival [ Time Frame: Up to 3 years ]
  Will be estimated using the method of Kaplan and Meier.
• Progression-free survival [ Time Frame: Up to 12 months from the start of therapy ]
  Will be estimated using the method of Kaplan and Meier.
• Cumulative incidence of GVHD [ Time Frame: Up to 3 years ]
• Cumulative incidence of relapse [ Time Frame: Up to 3 years ]
• T, natural killer (NK), and B cell populations [ Time Frame: Up to 3 years ]
  Effects of CYT107 on the recovery of T, NK, and B cell populations and their functions in vitro will be evaluated.
• CYT107 blood levels [ Time Frame: Prior to first CYT107 injection and 1, 3, 5, 7, 9, and 24 hours after first injection ]
  CYT107 blood levels will be submitted to a Model-independent pharmacokinetic analysis allowing to estimate time to maximum concentration, concentration maximum, half-life, clearance and area-under-the-curve.

PRIMARY OBJECTIVES:

I. To determine the safety and establish the maximum tolerated dose (MTD) and dose limiting toxicities (DLT) of recombinant interleukin-7 (interleukin 7 [IL-7, CYT107]).

SECONDARY OBJECTIVES:

I. To determine the rate of cytomegalovirus (CMV), Epstein-Barr virus (EBV) and BK viral infections in cord blood transplant (CBT) patients who receive three doses of IL-7 following engraftment.

II. To calculate the overall survival (OS), progression-free survival (PFS), and cumulative incidence of graft versus host disease (GVHD) and cumulative incidence of relapse.

III. To evaluate the effects of CYT107 on the recovery of T, natural killer (NK) and B cell populations and their functions in vitro; these data will be used to identify the optimal dose to move to a phase II trial.

IV. To obtain information about the pharmacokinetic (PK) profile of CYT107 by estimating time to maximum concentration (Tmax), concentration maximum (Cmax), half-life, clearance and area-under-the-curve (AUC).

OUTLINE: This is a dose-escalation study.

Within 60-180 days after CBT, patients receive recombinant interleukin-7 intramuscularly (IM) or subcutaneously (SC) once per week for 3 weeks.

After completion of study treatment, patients are followed for up to 3 years.

• Acute Myeloid Leukemia
• Chronic Myelogenous Leukemia, BCR-ABL1 Positive
• Cord Blood Transplant Recipient
• Myelodysplastic Syndrome
• Myeloproliferative Neoplasm

Inclusion Criteria:

• Patient post a cord blood transplant (CBT) with documented absolute neutrophil engraftment and no evidence of GVHD or no history of acute or chronic GVHD requiring systemic steroids
• Patients with documented engraftment but require granulocyte-colony stimulating factor (G-CSF) to treat myelosuppression induced by drugs used to treat or prevent infection are eligible
• Karnofsky performance status (KPS) > 60%
• Absence of dyspnea or hypoxia (< 90% of saturation by pulse oximetry on room air)
• Bilirubin =< 1.5 x upper limit of normal (ULN)
• Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase [SGOT]) and/or alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase [SGPT]) =< 2.5 x ULN
• Prothrombin time (PT)/partial prothrombin time (PTT) < 1.5 x ULN
• Calculated creatinine clearance > 60 mL/min/1.73 m^2
• Diagnosis of acute myeloid leukemia; myelodysplastic syndrome; chronic myeloid leukemia or myeloproliferative disease

Exclusion Criteria:

• Pregnant or nursing
• History of lymphoid malignancy (including Hodgkin disease, non-Hodgkin lymphoma, acute lymphoblastic leukemia and chronic lymphocytic leukemia) or acute biphenotypic leukemia
• History of Epstein-Barr virus (EBV) associated lymphoproliferation
• Active uncontrolled viral, bacterial or fungal infection
• Documented human immunodeficiency virus (HIV)-1 or -2, hepatitis B virus (HBV), or hepatitis C virus (HCV) infection at any time before or after transplant. (A positive hepatitis B serology indicative of a previous immunization is not an exclusion criteria)
• EBV viremia equal to or greater than 500 copies EBV deoxyribonucleic acid (DNA)/mL of blood by quantitative polymerase chain reaction (PCR)
• Positive cytomegalovirus (CMV) antigenemia
• History of autoimmune disease
• Receiving systemic corticosteroid therapy
• Receiving concurrent treatment with another investigational drug and/or biological agent
• Receiving anticoagulant therapy
• Uncontrolled hypertension
• Corrected QT (QTc) prolongation (QTc > 470 ms) or prior history of significant arrhythmia or electrocardiogram (ECG) abnormalities
• Active drug or alcohol use or dependence that, in the opinion of the investigator, would interfere with adherence to study requirements
• Any past or current psychiatric illness that, in the opinion of the investigator, would interfere with adherence to study requirements or the ability and willingness to give written informed consent