Patients receive doxorubicin hydrochloride liposome IV over 90 minutes, rituximab IV over 5-7 hours, cyclophosphamide IV over 1 hour, and vincristine IV over 1-2 minutes on day 1 and oral prednisone on days 1-5. Patients also receive filgrastim (G-CSF), sargramostim (GM-CSF), or pegfilgrastim beginning on day 3 and continuing until blood counts recover. Treatment repeats every 21-28 days for up to 8 courses in the absence of disease progression or unacceptable toxicity.