Combination Chemotherapy With or Without Autologous Stem Cell Transplant in Treating Patients With Central Nervous System B-Cell Lymphoma

Primary Objective: To compare the two-year progression-free survival (PFS) of patients treated with the myeloablative consolidation treatment strategy of HDT/ASCT versus those treated with non-myeloablative consolidation chemotherapy with cytarabine and etoposide Secondary Objectives: 1. To compare the two-year event-free survival (EFS) of patients treated with consolidation HDT/ASCT versus those treated with consolidation chemotherapy consisting of etoposide and cytarabine 2. To compare the overall survival (OS) of patients treated with the consolidation HDT/ASCT versus those treated with consolidation chemotherapy consisting of etoposide and cytarabine 3. To assess the toxicities associated with consolidation HDT/ASCT versus consolidation consisting of etoposide and cytarabine 4. To determine diffusion MRI metrics (ADCmini, ADC25%, and ADCmean) prior to induction chemotherapy, after one full induction chemotherapy cycle, and at the end of induction chemotherapy as a predictor of response and outcome (CALGB 581101) 5. To determine brain FDG-PET metrics (tumor SUV and tumor versus background SUV) prior to induction chemotherapy, after one full induction chemotherapy cycle, and at the end of induction chemotherapy as a predictor of response and outcome (CALGB 581101) 6. To determine whether low baseline ADC measurements are associated with shorter PFS and OS (CALGB 581101) 7. To determine whether reduction in tumor SUV by \> 25% on brain FDG-PET/CT after one cycle of induction therapy is associated with improved PFS and OS (CALGB 581101) 8. To determine which IHC-based biomarkers are predictive of an adverse prognosis (CALGB 151113) 9. To determine which IHC-based biomarkers are predictive of a favorable prognosis (CALGB 151113) for BCL6 (B-cell CLL/lymphoma 6), and STAT 6 (signal transducer and activator of transcription 6, interleukin-4 induced) 10. To analyze tumor tissue for gene expression profiles, and to correlate these profiles with treatment outcomes (CALGB 151113) 11. To determine whether CSF proteome is a predictor of outcomes (prognostic marker) irrespective of treatment arm (CALGB 151113) for (IL-10 (interleukin 10) and C3 (complement component 3) 12. To assess the neurocognitive function of patients treated with consolidation HDT/ASCT versus those treated with consolidation chemotherapy (etoposide and cytarabine) as measured by serial administration of the International PCNSL Collaborative Group (IPCG) neurocognitive battery and evaluate the long-term survivorship differences between the two arms (CALGB 71105)