Carfilzomib, Rituximab, and Combination Chemotherapy in Treating Patients With Diffuse Large B-Cell Lymphoma

Inclusion Criteria: * Patients must have histologically confirmed diffuse large B-cell lymphoma (DLBCL); patients with previously diagnosed indolent lymphoma (follicular lymphoma and marginal zone lymphoma but not small lymphocytic lymphoma) who have transformed to DLBCL are eligible only if they have not previously been treated for indolent lymphoma. For the Phase II study, patients must have non-GC DLBCL as determined by Hans Algorithm. * Patients must have radiographically measurable disease * Patients may have received brief (\<15 days) treatment with glucocorticoids and/or 1 cycle of chemotherapy such as R-CHOP \[or some component(s) thereof\] for the diagnosis of B-cell lymphoma provided they had all necessary staging tests performed prior to R-CHOP including CT and/or PET/CT scans, echocardiogram and bone marrow biopsy. Treatment must occur within 60 days prior to enrollment. * Eastern Cooperative Oncology Group (ECOG) performance status ≤ 2; performance status of 3 will be accepted if impairment is caused by DLBCL complications and improvement is expected once therapy is initiated * Hemoglobin ≥ 7.0 g/dl * Absolute neutrophil count ≥ 1,500/mcL * Platelet count ≥ 100,000/mcL * Total bilirubin within normal institutional limits unless due to Gilbert's disease * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\]) ≤ 2.5 X institutional upper limit of normal * Alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) ≤ 2.5 X institutional upper limit of normal * Creatinine clearance ≥ 45 mL/min calculated by Cockcroft-Gault * Adequate cardiac function left ventricular ejection fraction (LVEF) \> 50% as assessed by echocardiogram or MUGA (Multi Gated Acquisition Scan) * The effects of Carfilzomib on the developing human fetus are unknown. For this reason and because chemotherapeutic agents used in this study are known to be teratogenic, women of child-bearing potential and men must agree to use adequate contraception (double barrier method of birth control or abstinence) 2 weeks prior to initiation of treatment, for the duration of study participation and for 3 months after completing treatment. Should a woman become pregnant or suspect that she is pregnant while she or her partner is participating in this study, she should inform the treating physician immediately. Men must agree to refrain from sperm donation for at least 90 days after the last dose of carfilzomib. * Subjects must have the ability to understand and the willingness to sign a written informed consent document * International Prognostic Index must be documented: * ECOG performance status ≥ 2 (1 point) * Age ≥ 60 (1 point) * ≥ 2 extranodal sites (1 point) * Lactate dehydrogenase (LDH) \> upper limit of normal (1 point) * Ann Arbor stage III or IV (1 point) Exclusion Criteria: * Patients who have not recovered from adverse events due to agents administered more than 4 weeks earlier * Patients who are receiving any other investigational agents * Known CNS involvement by lymphoma. Patients at high risk for secondary CNS involvement but without neurologic symptoms suspected to be due to lymphoma are allowed to be enrolled and receive intrathecal chemotherapy including but not limited to methotrexate, cytarabine and glucocorticoids. Patients who are enrolled and subsequently identified to have pathologic confirmation of CNS involvement by lymphoma may be continued on study at the discretion of the principal investigator. * History of allergic reactions attributed to compounds of similar chemical or biologic composition to carfilzomib or other agents (R-CHOP) used in this study * Active congestive heart failure (New York heart Association Class III or IV), symptomatic ischemia, or conduction abnormalities uncontrolled by conventional intervention or myocardial infarction within four months prior to enrollment * Patients with uncontrolled intercurrent illness including, but not limited to ongoing or active infection, or psychiatric illness/social situations that would limit compliance with study requirements * Pregnant or breastfeeding women are excluded from this study because Carfilzomib is a proteasome inhibitor with the potential for teratogenic or abortifacient effects. Because there is an unknown, but potential risk for adverse events in nursing infants secondary to treatment of the mother with Carfilzomib, breastfeeding should be discontinued if the mother is treated with Carfilzomib. These potential risks may also apply to other agents used in this study. * HIV-positive patients on combination antiretroviral therapy are ineligible because of the potential for pharmacokinetic interactions with Carfilzomib. In addition, these patients are at increased risk of lethal infections when treated with marrow suppressive therapy. Appropriate studies will be undertaken in patients receiving combination antiretroviral therapy when indicated. * Other malignancies within the past 3 years except for adequately treated carcinoma of the cervix or basal or squamous cell carcinomas of the skin, or low-risk prostate cancer after curative therapy, or low risk melanoma if treated with definitive therapy (such as excision) and expected to have a low likelihood of recurrence. * Patients who have had major surgical procedures or significant traumatic injury within 28 days prior to study treatment * Patients who are reported to be of direct Asian-Pacific (China, Japan, Taiwan, Singapore, Republic of Korea, and Thailand) ancestry.