Hematology, serum chemistry, and iron status will be assessed at intervals throughout the study. The number of units of blood transfused, pre-transfusion Hb level, and the reasons for transfusion will be collected. Clinical laboratory results, vital signs, and the incidence and severity of adverse events will be assessed and monitored during the study. Patients will receive epoetin alfa under the skin (SC) at a dose of 10,000 units (U) every week, 20,000 U every 2 weeks, 20,000 U every 4 weeks or 40,000 U every 4 weeks for 16 weeks. Protocol Addendum: Patients will receive epoetin alfa 40,000 U every 6 weeks over 12 weeks.