Ruxolitinib for Patients With Low or Intermediate-1 Risk Myelodysplastic Syndrome (MDS)

Study Groups: If you are found to be eligible to take part in this study, you will be assigned to a study group based on when you join this study. Up to 4 groups of 3-6 participants will be enrolled in Part 1 of the study, and up to 7 participants will be enrolled in Part 2. If you are enrolled in Part 1, the dose of ruxolitinib you receive will depend on when you joined this study. The first group of participants will receive the lowest dose of ruxolitinib. The second group of participants will receive the lowest dose of ruxolitinib for 1 cycle and if no intolerable side effects are seen, the dose will increase to the next higher dose for Cycles 2 and beyond. The third group of participants will receive the higher dose taken by the second group for 1 cycle and if no intolerable side effects are seen, the dose will be increased for Cycles 2 and beyond. The fourth group of participants will take the higher dose taken by the third group for 1 cycle and if no intolerable side effects are seen, the dose will increase to the next higher dose for Cycles 2 and beyond. If you are enrolled in Part 2, you will receive ruxolitinib at the highest dose that was tolerated in Part 1. Study Drug Administration: Each cycle is 28 days. You will take ruxolitinib by mouth 2 times a day (about 12 hours apart), with or without food. Study Visits: One (1) time a week during Cycles 1 and 2 and then on Day 1 of Cycles 3 and beyond, blood (about 2-3 teaspoons) will be drawn for routine tests. On Day 28 of each cycle and Day 1 of Cycles 3 and beyond, this blood may also be used for cytogenetic testing if your doctor thinks it is needed. On Day 28 of Cycles 1 and 2 and then every 3 cycles, you will have a bone marrow aspiration to check the status of the disease and for cytogenetic testing, if your doctor thinks it is needed. On Day 28 of Cycle 1 and Day 1 of Cycles 3 and beyond, you will have a physical exam. If the doctor thinks it is needed, urine will be collected on Day 1 of each cycle for routine tests. Length of Dosing: You may continue taking the study drug for up to 2 years. You will no longer be able to take the study drug if the disease gets worse, if intolerable side effects occur, or if you are unable to follow study directions. Your participation on the study will be over after the end-of-dosing visit. End-of-Dosing Visit: After you are finished taking the study drug: * You will have a physical exam. * You will have a bone marrow aspiration to check the status of the disease. * Blood (about 2-3 teaspoons) will be drawn for routine tests. This blood may also be used for cytogenetic testing if your doctor thinks it is needed. Follow-up Visit: About 30 days after the End-of-Dosing visit, a member of the study team will contact you by phone. You will be asked how you are feeling and about any side effects you may be experiencing. This phone call should take 10-15 minutes. This is an investigational study. Ruxolitinib is FDA approved and commercially available for the treatment of myelofibrosis. Its use in this study is investigational. The study doctor can explain how ruxolitinib is designed to work. Up to 31 participants will be enrolled in this study. All will take part at MD Anderson.