Homoharringtonine With Oral Gleevec in Chronic, Accelerated and Blast Phase Chronic Myeloid Leukemia (CML)

Inclusion Criteria: * Male or female patients 16 years or older * Philadelphia chromosome (Ph) positive chronic myelogenous leukemia (CML) in either chronic, accelerated or blast phase * Patients with chronic phase CML will be either refractory (failed to achieve hematologic or cytogenetic response) or resistant (responded initially but subsequently lost hematologic or cytogenetic response) to prior imatinib mesylate therapy. Failure to achieve cytogenetic response is defined as follows: no cytogenetic response after 3 months of therapy with imatinib mesylate, no major cytogenetic response at 12 months of therapy, loss of complete cytogenetic response documented twice, or loss of major cytogenetic response at least once. * Patients with accelerated or blast phase may be newly diagnosed and previously untreated or if previously treated with imatinib mesylate, will be refractory or resistant to this agent or have failed to achieve at least a complete hematologic or cytogenetic response to treatment, as previously defined. * Patients in accelerated phase will meet one or more of the following criteria: greater than or equal to 15% through less than 30% blasts in peripheral blood or bone marrow, greater than or equal to 30% blasts + promyelocytes in peripheral blood or bone marrow, greater than or equal to 20% basophils in peripheral blood, platelet count less than 100\*10\^9/L unrelated to therapy or clonal evolution. * CML in blast phase will be defined as greater than or equal to 30% blasts in the bone marrow or presence of extramedullary disease * Patients must have completed all previous anti-leukemic therapy for at least 2 weeks, except as noted, and have fully recovered from side effects of a previous therapy, unless disease progression necessitates early therapy. Patients may receive leukapheresis, hydroxyurea and anagrelide for up to 24 hours prior to start of study treatment. Patients receiving imatinib mesylate may continue to receive it uninterrupted, except for a 3-day window at treatment cycle 1. * Bilirubin less than or equal to 2 times the upper limit of normal (ULN); alanine aminotransferase (ALT) less than or equal to 3 times ULN; creatinine less than or equal to 1.5 times ULN * Eastern Cooperative Oncology Group (ECOG) performance status 0 - 2 * Be able to comply with the requirements of the entire study * Be able and willing to provide written informed consent prior to any study related procedure * Patients and their partners must use an effective contraceptive during the study dosing period. The following are considered effective contraceptives: oral contraceptive pill, condom, diaphragm plus spermicide, abstinence, patient or partner surgically sterile, patient or partner more than 2 years post-menopausal, or injectable or implantable agent/device. Exclusion Criteria: * New York Heart Association (NYHA) Class III or IV heart disease, active ischemia or any other uncontrolled cardiac condition such as angina pectoris, clinically significant cardiac arrhythmia and requiring therapy, uncontrolled hypertension or congestive heart failure * Myocardial infarction in the previous 12 weeks * Other intercurrent illness which would preclude study conduct and assessment, including but not limited to another active malignancy, uncontrolled and active infection, positive human immunodeficiency virus (HIV) or human T-cell lymphotropic virus (HTLV) I/II status * Pregnant or lactating * Any medical or psychiatric condition which may compromise the ability to give written informed consent or to comply with the study protocol