Intermittent Duvelisib Dosing in Treating Patients With Chronic Lymphocytic Leukemia or Small Lymphocytic Lymphoma

PRIMARY OBJECTIVE: I. To evaluate the efficacy of duvelisib (induction followed by maintenance \[intermittent dosing\]) in patients with relapsed or refractory chronic lymphocytic leukemia (CLL), as measured by the progression free survival (PFS). SECONDARY OBJECTIVES: I. To evaluate safety of duvelisib induction and maintenance (by intermittent dosing) in relapsed/refractory CLL. II. To evaluate clinical benefits to duvelisib treatment. EXPLORATORY OBJECTIVE: I. To evaluate T-cell populations in patients with CLL treated with duvelisib. OUTLINE: INDUCTION: Patients receive duvelisib orally (PO) twice daily (BID) on days 1-28. Cycles repeat every 28 days for 12 weeks in the absence of disease progression or unacceptable toxicity. MAINTENANCE: Patients receive duvelisib PO BID on days 1-2, 8-9, 15-16, and 22-23. Cycles repeat every 28 days in the absence of disease progression or unacceptable toxicity. After completion of study treatment, patients are followed up every 3 months for up to 12 months.