Testing the Addition of Ruxolitinib to the Usual Treatment (Tyrosine Kinase Inhibitors) for Chronic Myeloid Leukemia

Inclusion Criteria: * Patients must have a diagnosis of chronic phase chronic myeloid leukemia without any history of progression to accelerated or blast phase CML; no new bone marrow aspiration and biopsy is needed to prove diagnosis prior to randomization; however, documentation stating the patient is in chronic phase is required * Patients must have detectable BCR-ABL transcripts measured by reverse transcriptase (RT)-PCR at a clinical laboratory improvement act (CLIA)-approved laboratory and reported on the international scale (IS) with a value of \> 0.0032% IS and =\< 1.0% IS within 21 days prior to randomization; the RT-PCR assay must have the sensitivity to detect a 4.5 log reduction in BCR-ABL transcripts from 100% IS (0.0032% IS or lower) * Patients must have been receiving TKI treatment for CML for at least 12 months prior to randomization. Hydroxyurea prior to initiation of TKI is allowed. * Patients must be currently receiving treatment with bosutinib (within the allowable dose range of 200-500 mg daily), nilotinib (within the allowable dose range of 150-400 mg BID or a cumulative daily dose of 300-800 mg), dasatinib (within the allowable dose range of 40-140 mg daily), or imatinib (within the allowable dose range of 300-400 mg daily); they must have received their current TKI for a minimum of 6 months prior to randomization and must be expected to remain on the same TKI for the next 12 months * Patient must not have a history of resistance to any prior TKI drug;…