Study of Rituximab-HCVAD Alternating With Rituximab-Methotrexate-Cytarabine Versus Standard Rituximab-CHOP Every 21 Days for Patients With Newly Diagnosed High Risk Aggressive B-Cell Non-Hodgkin's Lymphomas in Patients 60 Years Old or Younger

Inclusion Criteria:

1. Confirmed diagnosis of previously untreated large B-cell Non Hodgkin's, Large Cell Lymphoma and B-Cell with high grade features. Other aggressive lymphomas such as Primary Mediastinal large B-cell Lymphomas will be also allowed to be included.
2. Patients with performance status of 0-2 (Zubrod Scale).
3. Serum bilirubin \<1.5 mg/dl and serum creatinine \< 2.0 mg/dl unless due to lymphoma; absolute neutrophil count (ANC) \>1000/mm\^3 and platelets \>100,000/mm\^3 unless due to lymphoma.
4. Cardiac ejection fraction 50% or greater.
5. Ages 16 - 60 years (due to the fact that CHOP-R is not studied enough in younger patients and is not considered standard of care).
6. Patients must be willing to receive transfusions of blood products.
7. Age adjusted International Prognostic Index Score of 2 or more
8. Previous steroids are allowed (if used to relieve some symptoms such as SVC, etc).

Exclusion Criteria:

1. Pregnancy (excluded due to the teratogenicity of the involved chemotherapy agents
2. Positive HIV serology because of poor tolerance to this intense chemotherapy regimen
3. Burkitt's lymphomas, and Mantle cell lymphoma, transformed follicular center cell lymphoma, follicular grade III.
4. Any clinical or cytological diagnosis of central nervous system (CNS) involvement
5. Any co-morbid medical, such as Child's Class C liver cirrhosis, end-stage renal disease, and symptomatic congestive heart failure, or psychiatric illnesses that preclude treatment with intense dose chemotherapy as determined by the primary investigator.
6. Concurrent or previous malignancy whose prognosis is poor (\< 90% probability of survival at 5 years)
7. Active Hepatitis B or C. Chronic carriers for Hepatitis B will be excluded.