MLN8237 in Patients With Relapsed or Refractory Aggressive B-Cell Lymphoma Treated With Rituximab +/- Vincristine

Inclusion Criteria: * Histologically confirmed diagnosis of diffuse large B-cell lymphoma (DLBCL)/transformed follicular lymphoma (TFL). Note: Patients with Mantle Cell or Burkitt's lymphoma may be eligible for enrollment to the safety lead-in and dose escalation cohorts, parts 1 \& 2 only * Relapsed or refractory after at least 1 prior systemic treatment for aggressive lymphoma (including anthracycline unless contra-indicated). Relapse following an autologous stem cell transplant is allowed. * Relapsed after autologous stem cell transplantation or not be eligible for autologous stem cell transplantation or refuse autologous stem cell transplantation. Patients enrolled to the phase 2 part must have received prior rituximab. * Measurable disease as specified in study protocol * Eastern Cooperative Oncology Group (ECOG) performance status of 0 to 2 * Female patients who are post menopausal for at least 1 year, surgically sterile, or agree to practice 2 effective methods of contraception through 30 days after the last dose of alisertib (MLN8237) or agree to abstain from heterosexual intercourse. Patients should also use effective contraception for 12 months following the last dose of rituximab and 1 month following the last dose of alisertib (MLN8237. * Male patients who agree to practice effective barrier contraception through 4 months after the last dose of MLN8237 or agree to abstain from heterosexual intercourse * Voluntary written consent Exclusion Criteria * Received more than 4 prior systemic treatment regimens for lymphoma * Known human immunodeficiency virus (HIV) positive or acquired immunodeficiency syndrome (AIDS)-related illness; hepatitis B virus, or hepatitis C virus; known history of Charcot-Marie-Tooth disease or polio * Autologous stem cell transplant less than 3 months prior to enrollment * Patients who have undergone allogeneic stem cell or organ transplantation any time * Systemic antineoplastic therapy, including glucocorticoids or treatment with an investigational agent within 14 days preceding the first dose of study drug treatment. Steroids are permitted for administration with rituximab to prevent or treat infusion reaction * Treatment with nitrosoureas, mitomycin C, rituximab, alemtuzumab, or other unconjugated antibody treatment within 42 days (21 days if clear evidence of progressive disease) prior to the first day of study drug treatment * Treatment with radioimmunoconjugates or toxin immunoconjugates, such as ibritumomab-tiuxetan, or tositumomab, within 12 weeks prior to the first day of study drug treatment * Radiotherapy within 21 days prior to the first dose of study drug treatment * Treatment with enzyme-inducing antiepileptic drugs, such as phenytoin, carbamazepine, or phenobarbital, or with rifampin, rifabutin, rifapentine, or St. John's wort, within 14 days prior to the first dose of alisertib (MLN8237) also not permitted during study * Cardiac status as described in protocol * Major surgery, serious infection, or infection requiring systemic antibiotic therapy within 14 days prior to the first dose of study treatment * History of hemorrhagic or thrombotic cerebrovascular event in the past 12 months * Clinically uncontrolled central nervous system involvement * Inability to receive IV rituximab or vincristine, or to swallow tablets or inability or unwillingness to avoid taking anything by mouth except for water and prescribed medications for 2 hours before and 1 hour after each dose of alisertib (MLN8237) * History of uncontrolled sleep apnea syndrome and other conditions that could result in excessive daytime sleepiness * Female patients who are lactating or pregnant * Serious medical or psychiatric illness or laboratory abnormality that could, in the investigator's opinion, potentially interfere with the completion of treatment according to the protocol * Clinically apparent ≥ Grade 2 neuropathy due to any cause in the 3 months prior to enrollment, or history of ≥ Grade 3 neuropathy related to vincristine at any time * Prior treatment with Aurora A-targeted agents, including alisertib (MLN8237) * Patients who have received myeloid growth factors or platelet transfusion within 14 days prior to the first dose of study treatment * Patients with known hypersensitivity to rituximab, vincristine (or vinca alkaloids), or their diluents