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

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 \<3 x ULN) * kidney function (creatinine \< 2.5 x ULN ). 6. ECOG performance status of ≤ 2. 7. Women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation. Should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately. 8. A negative urine pregnancy test is required within 1 week for all women of childbearing potential prior to enrolling on this trial. 9. Patient must have the ability to understand the requirements of the study and signed informed consent. A signed informed consent by the patient or his legally authorized representative is required prior to their enrollment on the protocol. 10. Patients should have an indication for therapy for their disease such as transfusion dependence or morbidity associated with their cytopenia(s) such as bleeding, severe fatigue, or frequent/multiple infections (eg. neutropenia). Exclusion Criteria: 1. Pregnant women are excluded from this study. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with the study agents, breastfeeding should be discontinued if the mother is treated on this study. 2. Known HIV infection. 3. Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements. 4. Patient with documented hypersensitivity to any of the component medications.