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

• 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.
• Patients with performance status of 0-2 (Zubrod Scale).
• Serum bilirubin 1000/mm^3 and platelets >100, 000/mm^3 unless due to lymphoma.
• Cardiac ejection fraction 50% or greater.
• 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).
• Patients must be willing to receive transfusions of blood products.
• Age adjusted International Prognostic Index Score of 2 or more
• Previous steroids are allowed (if used to relieve some symptoms such as SVC, etc).

Exclusion Criteria

• Pregnancy (excluded due to the teratogenicity of the involved chemotherapy agents
• Positive HIV serology because of poor tolerance to this intense chemotherapy regimen
• Burkitt's lymphomas, and Mantle cell lymphoma, transformed follicular center cell lymphoma, follicular grade III.
• Any clinical or cytological diagnosis of central nervous system (CNS) involvement
• 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.
• Concurrent or previous malignancy whose prognosis is poor (< 90% probability of survival at 5 years)
• Active Hepatitis B or C. Chronic carriers for Hepatitis B will be excluded.