Eltrombopag in Myelodysplastic Syndrome (MDS) Patients With Thrombocytopenia

Inclusion Criteria: * Confirmed diagnosis of MDS using the World Health Organization (WHO) classification or a diagnosis of WHO Myelodysplastic/ Myeloproliferative Neoplasm (MDS/MPN) or MDS refractory anemia with excess blast in transformation (RAEB-t) by French American British (FAB) classification (AML with 20-30% myeloblasts by WHO classification). * All prognostic risk groups according to the International Prognostic Scoring System (IPSS) and MD Anderson Risk Model * At least one prior HMTA treatment with either azacitidine or decitabine and subsequent loss of response to HMTA, progression while on HMTA, or no response to HMTA, defined as failure to achieve at least HI after 4 cycles of treatment * The mean of the two platelet counts taken within 1 month prior to dosing must be ≤50 x 10\^9/L. Platelets counts must reflect pre-transfusion trough results or be obtained no sooner than 1 week after platelet transfusion to assure stable baseline platelet count. The platelet count obtained should be outside the expected nadir of prior therapies. * Eastern Cooperative Oncology Group (ECOG) performance status 0-2 (Karnofsky \>60% * Adequate liver function, as evidenced by total serum bilirubin ≤ 1.5 times the upper limit of normal (patients with Gilbert's disease are eligible, provided intermittent indirect hyperbilirubinemia), aspartic transaminase (AST) or alanine transaminase (ALT) ≤ 3 times the upper limit of normal (ULN). * A serum creatinine concentration ≤ 2 x ULN * 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. * Ability to understand and the willingness to sign a written informed consent document. Exclusion Criteria: * Clinically significant bleeding within 4 weeks of screening defined as any grade 3 or grade 4 bleeding by WHO Bleeding Scale or any gastrointestinal (GI) bleeding or intracranial hemorrhage * Splenic enlargement extending \>8 cm below the left costal margin * Myelodysplastic syndrome with fibrosis (MF 3) * Received Anti-Thymocyte Globulin (ATG) within 6 months of screening * Received immunomodulating agents, histone deacetylase inhibitors, cyclosporine, or mycophenolate within 4 weeks of screening * History of treatment with eltrombopag, romiplostim or other thrombopoietin receptor (TPO-R) agonists * Concurrent use of granulocyte colony-stimulating factor (G-CSF) except for the short-term management of neutropenic infection. Stable doses of erythropoietin stimulating agents or corticosteroids that were being administered prior to screening are allowed. * Treatment with an investigational drug within 30 days or 5 half-lives (whichever is longer) preceding the first dose of study medication. * Pregnant or breast feeding * Current alcohol or drug abuse * Known Hepatitis B or Hepatitis C infection or liver cirrhosis * Uncontrolled current 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. * At eltrombopag dose levels 200 mg and above cohorts, participants with a QT corrected for heart rate (QTc) \> 480 msec at screening, if other drugs known to cause prolonged QT are stopped an EKG documenting QTc below 480 msec is required. * History of metastatic malignancy in the preceding 2 years * Known Human Immunodeficiency Virus (HIV) positive patients. These patients are excluded because they may have morphologic dysplasia which mimics MDS but is not true MDS Tand thrombocytopenia could be multifactorial secondary to HIV infection or to medications. * Receiving, or planning to receive, any of the medications listed in the Prohibited Medications section during conduct of the study. * East Asian patients (Chinese, Japanese, Taiwanese, and Korean ancestry) are excluded during stage I of the study (dose escalation phase) due to the different pharmacogenomics in this patient population.