This study will have a Screening Phase of up to one week when patients will be evaluated for study eligibility followed by an open-label Treatment Phase of 16 weeks when patients will be randomly assigned to receive epoetin alfa administered under the skin at one of four dosing regimens. Patients will then complete a Post-Treatment Follow-Up Phase of 1 week (Week 17). Hemoglobin will be measured weekly. There will be no dose adjustments during the initial 4 weeks of the study, however, the dose may be withheld during this time if necessary. Further dose increases may occur at 4-week intervals and dose reductions may occur as frequently as the dosing interval assigned at randomization.