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

Arm A: Rituximab 375 mg/m² by vein on day 1, Cycle 1 and alternating cycles. Arm B: Rituximab 375 mg/m² on day 1, Cycle 2 and alternating cycles.

"Arm A: Cyclophosphamide 300 mg/m\^2 by vein (IVPB) over 3 hours every 12 hours x 6 doses on Days 2-4, Cycle 1 and alternating cycles.~Arm B: Cyclophosphamide 750 mg/m² by vein day 1"

Arm A: Doxorubicin 50 mg/m\^2/day by vein over 15 minutes (12 hours after last dose of cyclophosphamide) on Day 5, Cycle 1 and alternating cycles.

"Arm A: Vincristine 1.4 mg/m\^2 (maximum 2 mg) by vein (IVPB) on Days 5 (1-24 hours after last cyclophosphamide) and on day 12, Cycle 1 and alternating cycles.~Arm B: Vincristine 1.4 mg/m\^2 (maximum 2 mg) by vein (IVPB) on Days 5 (1-24 hours after last cyclophosphamide) and on day 12 of each cycle."

Arm A: Dexamethasone 40 mg by vein or by mouth daily x 4 on Days 2-5 and on days 12-15 of cycle 1 and alternating cycles.

Arm A: Methotrexate after finishing Rituximab, 200 mg/m2 by vein over 2 hours, then 800 mg/m2 by vein over 22 hours day 1 cycle 2.

Arm B: Cytarabine 3 g/m\^2 by vein over 2 hours every 12 hours X 4 doses on days 3 \& 4, cycle 2 and alternating cycles.

Arm B: Prednisone 100 mg by mouth (as a pill, capsule, or tablet) once a day on Days 1-5, each cycle.