Azacitidine Plus Nivolumab Following Reduced-intensity Allogeneic PBSC Transplantation for Patients With AML and High-risk Myelodysplasia

Inclusion Criteria: * Written informed consent and HIPAA authorization for release of personal health information. NOTE: HIPAA authorization may be included in the informed consent or obtained separately. Patients must be capable of understanding the investigational nature, potential risks and benefits of the study and provide valid informed consent. * Age ≥ 60 years at the time of consent who are deemed candidates (by their transplant physician) for reduced-intensity allogeneic PBSC transplantation. A recent randomized trial in patients aged 18-65 years demonstrated that myeloablative conditioning regimens are associated with improved overall survival in AML (largely due to a reduction in the risk of relapse), but resulted in equivalent survival in patients with MDS.4 However, it is acknowledged that some AML patients between 55-65 years may not tolerate myeloablative regimens due to associated comorbidities. Physicians should take the risks of the disease versus the patient's comorbidities in deciding on the appropriate preparative regimen in a given patient. * Patients aged 18-59 years at the time of consent who are judged not to be candidates for myeloablative allogeneic PBSC transplantation by the transplant physician. * Karnofsky performance status (KPS) ≥ 70% * Patients must have any of the following hematological malignancies at the time of transplantation: * Acute myeloid leukemia (AML) in first (CR1) or subsequent complete remission (CR2, CR3 or beyond), as defined by less than 5% blasts in the bone marrow and peripheral blood. * Myelodysplastic disorder (MDS) of high or very high-risk according to the revised International Prognostic Scoring System (IPSS-R).1 * Patients with MDS should have the bone marrow and the peripheral blood blast percentage reduced to \<10% within at least 45 days of transplantation. * The type of cytoreduction therapy used is at the discretion of the treating physician and may include use of hypomethylating drugs but not immune checkpoint inhibitors. * Therapy-related MDS (regardless of IPSS score) * Patients must receive a reduced-intensity conditioning (RIC) regimen as defined operationally by the National Marrow Donor Program and CIBMTR. RIC regimens are defined as those containing: * ≤ 500 cGy total-body irradiation (TBI) * ≤9 mg/kg total busulfan dose (PO or IV) * ≤140 mg/m2 total melphalan dose * ≤10 mg/kg total thiotepa dose * Usually includes a purine analogue (fludarabine, cladribine, or pentostatin). * Use of fludarabine and cyclophosphamide (up to 200 mg/kg total dose) is also considered RIC.99 * Patients must have received GVHD prophylaxis with any of the regimens below. Accepted regimens are: * Calcineurin inhibitor (tacrolimus or cyclosporine A) plus methotrexate * Calcineurin inhibitor plus mycophenolate mofetil * Calcineurin inhibitor plus sirolimus * Post-transplant cyclophosphamide (PtCy) (in combination with calcineurin inhibitor or sirolimus, plus mycophenolate mofetil) * Patients receiving the above regimens should be beginning to taper immunosuppression drugs between days +100 to +120 (in the absence of acute GVHD) with the goal of discontinuing immunosuppression by approximately day +180 as tolerated and according to institutional standards. * Stem cell source must be mobilized peripheral blood (i.e., PBSC) and not bone marrow or cord blood. * Allogeneic grafts from 6/6 HLA-matched siblings or from 10/10 HLA allele matched volunteer unrelated donors (matched for at least HLA-A, B, C and DRB1 and DQB1 by high resolution typing) are included. * Are in complete remission defined as having \<5% blasts in the bone marrow with normal karyotype and no extramedullary disease. This should be documented on a bone marrow biopsy performed within 14 days before study registration. * Absolute neutrophil count (ANC) \>1.5x109/l * Platelet count \>100x109/l (with no platelet transfusions in past 7 days) * Serum creatinine \<2.0 mg/dl * Serum bilirubin \< 2 x upper limit of normal * AST and ALT \<2.5 x upper limit of normal * Non-pregnant and non-nursing. * Women are considered of childbearing potential (WOCBP) unless they are surgically sterile (have undergone a hysterectomy, bilateral tubal ligation, or bilateral oophorectomy) or are post-menopausal. Menopause is defined clinically as 12 months of amenorrhea in a woman over 45 in the absence of other biological or physiological causes. * Women of childbearing potential must be willing to abstain from heterosexual activity or use an effective method of contraception from the time of informed consent until 5 months after the last dose of study drug. * Men who are sexually active with WOCBP must use any contraceptive method with a failure rate of less than 1% per year. Men receiving study drug and who are sexually active with WOCBP will be instructed to adhere to contraception from the first dose of study drug until 7 months after the last dose of study drug. Exclusion Criteria: * Use of a myeloablative preparative regimen * Active central nervous system (CNS) leukemia. Patients with prior CNS leukemia that is now in remission are eligible. * Prior allogeneic or autologous stem cell transplantation before current transplant * Use of bone marrow or cord blood as stem cell source * History of acute GvHD of any grade * Use of systemic corticosteroids within 28 days prior to registration (except for use as replacement for adrenal insufficiency). * Uncontrolled bacterial, viral or fungal infection at time of registration (defined as currently taking medication and progression or persistence of clinical symptoms). Patients with prior infection (e.g., fungal infection) that is resolved but need continuing prophylaxis can be included. * HIV infection or disease at time of transplant. Patients with immune dysfunction are at a significantly higher risk of infection from intensive immunosuppressive therapies. Infectious disease testing will be performed according to local practice. * Known additional malignancy that is active and/or progressive requiring treatment; exceptions include basal cell or squamous cell skin cancer, in situ cervical or bladder cancer, or other cancer for which the subject has been disease-free for at least three (3) years. * Patients who have received a live/attenuated vaccine within 30 days of first expected treatment with nivolumab. However, it is recommended that patients who have received an allogeneic transplant should not receive live/attenuated vaccines within two years after allogeneic transplantation.