Dasatinib and Venetoclax in Treating Patients With Philadelphia Chromosome Positive or BCR-ABL1 Positive Early Chronic Phase Chronic Myelogenous Leukemia

This phase II trial studies how well dasatinib and venetoclax work in treating patients with Philadelphia chromosome positive or BCR-ABL1 positive early chronic phase chronic myelogenous leukemia. Dasatinib and venetoclax may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth.

PRIMARY OBJECTIVES: I. To estimate the proportion of patients with previously-untreated chronic phase chronic myeloid leukemia (CML) who achieve major molecular response by 12 months of treatment with dasatinib 50 mg orally daily (first 70 patients) and of dasatinib 50 mg daily in combination with venetoclax 200 mg daily starting after 3 months of dasatinib therapy (after protocol amendment). SECONDARY OBJECTIVES: I. To estimate the 12 months molecular response (MR)4.5 rate and the cumulative overall rate of MR4.5 (BCR-ABL transcripts \[IS\] =\< 0.01%). II. To estimate the proportion of patients with MR4.5 at 6-, 12-, 18-, 24-, and 36-months of therapy. III. To estimate the proportion of patients with sustained MR4.5 of 3 years and more. IV. To estimate the treatment-free remission rate, time to progression, and overall survival. V. To assess the safety of this combination. OUTLINE: Patients receive dasatinib orally (PO) once daily (QD) for 15 years in the absence of disease progression or unacceptable toxicity. After 3 months of dasatinib treatment, patients also receive venetoclax PO QD on days 1-14 of each month for 3 years in the absence of disease progression or unacceptable toxicity (patients enrolled prior to 4/1/2018 receive only dasatinib).