4'-Thio-araC (Thiarabine) in Advanced Hematologic Malignancies

The Study Drug: Thiarabine is designed to damage and destroy the DNA of cancer cells. This may cause the cells to die. Study Groups: If you are found to be eligible to take part in this study, you will be assigned to 1 of 2 study groups based on when you joined the study. The first set of 3 participants will be enrolled in Group 1, and the 2nd set of 3 participants will be enrolled in Group 2. The 3rd set of 3 participants will be enrolled in Group 1, then the 4th set of 3 participants in Group 2, and so on until all participants are enrolled. * Group 1 will receive thiarabine for 3 days in a row in each cycle. * Group 2 will receive thiarabine for 5 days a row in each cycle. Cycles in this study are 3-6 weeks long, depending on how you are doing. You may begin a new cycle when your blood cell counts have returned to an appropriate level. However, you may begin a new study cycle earlier than that if the disease gets worse or does not improve. The dose of thiarabine you receive will depend on when you joined this study. The first set of participants will receive the lowest dose level of thiarabine. Each new set will receive a higher dose of thiarabine than the set before it, if no intolerable side effects were seen. This will continue until the highest tolerable dose of thiarabine is found. Study Drug Administration: You will receive thiarabine by vein over about 1 hour (+/- 15 minutes) on Days 1-3 (Group 1) or Days 1-5 (Group 2) of each cycle. Study Visits: Blood (about 2 tablespoons) will be drawn for routine tests 1 or 2 times a week. If the disease responds well, the study doctor may decide these blood tests will occur less often. At every study visit, you will be asked about any drugs you may be taking and symptoms you may be having. You will have an ECG within 2 days before each cycle. At any time the doctor thinks it is needed, you will have a bone marrow aspiration to check the status of the disease. Length of Participation: You may continue taking the study drug for as long as the doctor thinks it is in your best interest. You will be taken off study early if intolerable side effects occur. You may be taken off study early if the disease gets worse. Follow-Up: At 30 days after your last study drug dose, you will be asked about any side effects you may be having. This may be done during a regular clinic visit or by phone call from the study doctor or staff. This is an investigational study. Thiarabine is not FDA approved or commercially available. It is currently being used for research purposes only. Up to 70 patients will take part in this study. All will be enrolled at MD Anderson.