Study of Venetoclax Plus DA-EPOCH-R for the Treatment of Aggressive B-Cell Lymphomas

Inclusion criteria: * Adults age 18-80 years * Histologically confirmed, biopsy-proven diagnosis of DLBCL, BCLu, HGBCL, or TiNHL. Richter's transformation from Chronic Lymphocytic Leukemia (CLL) is not eligible. * Subjects with DLBCL, BCLu, HGBCL NOS, or HGBCL with translocations of MYC and BCL2 and/or BCL6, must have had no prior chemotherapy for lymphoma. Steroids for palliation prior to enrollment are allowed. * Subjects with TiNHL are eligible if they have received no prior cytotoxic chemotherapy for lymphoma. Steroids, rituximab, and external beam radiation therapy as prior therapy for indolent lymphoma is allowed. * Ann Arbor stage II-IV disease (Stage I primary mediastinal B-cell lymphoma will also be eligible) * Ability to provide signed Informed Consent Form * Ability and willingness to comply with the requirements of the study protocol * Measureable disease (defined as at least 1.5 cm in diameter). * Adequate organ and bone marrow function: * Absolute neutrophil count (ANC) at least 1,000/mm3 * Platelet count at least 100,000/mm3. * Total bilirubin at most1.5 x the upper limit of the normal range (ULN), except Gilbert's disease * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) at most 3 x ULN. * Calculated creatinine clearance at least 30 mL/min. Exclusion criteria: * Known hypersensitivity to any of the study drugs * History of other malignancy that could affect compliance with the protocol or interpretation of results * Patients with a history of curatively treated basal or squamous cell carcinoma of the skin or in situ carcinoma of the cervix are generally eligible. Patients with a malignancy that has been treated, but not with curative intent, will also be excluded, unless the malignancy has been in remission without treatment for at least 2 years prior to enrollment. * Known CNS involvement at diagnosis * Richter's transformation from CLL * Evidence of other clinically significant uncontrolled condition(s) including, but not limited to, uncontrolled systemic infection (viral, bacterial, or fungal) * Major surgery within 3 weeks prior to the start of study treatment * Infection with human immunodeficiency virus (HIV) * Women who are pregnant or lactating * Female patients who are not surgically sterile or postmenopausal (for at least 1 year) must practice at least one of the following methods of birth control throughout the duration of study participation and for at least 3 months after study treatment: * Total abstinence from sexual intercourse * A vasectomized partner * Hormonal contraceptives (oral, parenteral, vaginal ring, or transdermal) that started at least 3 months prior to study drug administration * Double-barrier method (condom plus diaphragm or cervical cup with spermicidal contraceptive sponge, jellies, or cream) * Non-vasectomized male patients must comply with at least one of the following methods of birth control throughout the duration of study participation and for at least 3 months after study treatment: * A partner who is surgically sterile or postmenopausal (for at least 1 year) or who is taking hormonal contraceptives (oral, parenteral, vaginal ring, or transdermal) for at least 3 months prior to study drug administration * Total abstinence from sexual intercourse * Double-barrier method (condom plus diaphragm or cervical cup with spermicidal, contraceptive sponge, jellies, or cream) * Malabsorption syndrome or other condition that precludes enteral route of administration * Known allergy to both xanthine oxidase inhibitors and rasburicase * Subjects with positive HBV core antibody or surface antigen are eligible as long as they have an undetectable HBV DNA PCR, and receive concurrent antiviral therapy with entecavir, tenofovir, or lamivudine, and continued for a minimum of 6 months after completion of therapy. * Active hepatitis C (defined as a positive HCV viral load) * Chronic use of moderate or strong CYP3A4 modulators (inhibitor or inducer) or any other prohibited medications. A washout period of 7 days is required prior to venetoclax dosing if a prohibited medication is discontinued. * Chronic use of a P-gp inhibitor, or a P-gp substrate with a narrow therapeutic index. A washout period of 7 days is required prior to venetoclax dosing if a prohibited medication is discontinued.