Methylprednisolone, Horse Anti-Thymocyte Globulin, Cyclosporine, Filgrastim, and/or Pegfilgrastim or Pegfilgrastim Biosimilar in Treating Patients With Aplastic Anemia or Low or Intermediate-Risk Myelodysplastic Syndrome

This phase II trial studies methylprednisolone, horse anti-thymocyte globulin, cyclosporine, filgrastim, and/or pegfilgrastim or pegfilgrastim biosimilar in treating patients with aplastic anemia or low or intermediate-risk myelodysplastic syndrome. Horse anti-thymocyte globulin is made from horse blood and targets immune cells known as T-lymphocytes. Since T-lymphocytes are believed to be involved in causing low blood counts in aplastic anemia and in some cases of myelodysplastic syndromes, killing these cells may help treat the disease. Methylprednisolone and cyclosporine work to suppress immune cells called lymphocytes. This may help to improve low blood counts in aplastic anemia and myelodysplastic syndromes. Filgrastim and pegfilgrastim are designed to cause white blood cells to grow. This may help to fight infections and help improve the white blood cell count. Giving methylprednisolone and horse anti-thymocyte globulin together with cyclosporine, filgrastim, and/or pegfilgrastim may be an effective treatment for patients with aplastic anemia or myelodysplastic syndrome.

Inclusion Criteria: 1. Patients with the diagnosis of MDS (Low, Int-1 by IPSS, or hypocellular) who are either previously treated or untreated are eligible for this trial. 2. Patients with the diagnosis of aplastic anemia who are either previously treated or untreated are eligible if they are not currently candidates for an allogeneic stem cell transplant. 3. Patients ages 18 years and older are eligible 4. Patients must have been off of cytotoxic, immunosuppressive (except steroids), or targeted therapy for at least 2 weeks prior to entering this study, and have recovered from the toxic effects of that therapy to grade 1 or less. 5. Adequate organ function as defined below: * liver function (bilirubin \< 2mg/dL, AST \