Patients undergoing major orthopedic surgery frequently require blood transfusions both during and after the operation. These transfusions can result in adverse reactions, such as a blood clot in a deep vein. Agents that can reduce the need for transfusions would improve the overall safety of the surgery. In previous studies with epoetin alfa, patients have generally experienced an increase in the percentage of red blood cells in whole blood, a decrease in blood transfusions, and a decrease in the number of surgery-related adverse reactions, with good tolerance of the drug. This is a randomized, double-blind, placebo-controlled, parallel group, multicenter study. The study will evaluate the safety of epoetin alfa and to determine whether epoetin alfa will reduce the need for blood transfusions in patients who are expected to require at least 2 units of blood during the period of time around major orthopedic hip or knee surgery. Before the start of the study, patients are screened for eligibility and a test is performed to determine the amount of hemoglobin present in each patient's blood. Based on these results, patients are then divided into 3 groups: patients with hemoglobin <=10 grams/deciliter (g/dL), patients with hemoglobin >10 and <=13 g/dL, and patients with hemoglobin >10 g/dL. Within each of these groups, patients will be randomly assigned to receive 1 of 3 treatments: epoetin alfa 300 units/kilogram (U/kg), epoetin alfa 100 U/kg, or placebo, by injection beneath the skin, beginning 10 days before scheduled surgery and ending 4 days after surgery. Additionally, from 10 days before surgery until 4 days after surgery all patients will receive a 150 milligram iron supplement daily by mouth, and from the day of surgery (following surgery) until 6 days after surgery, all patients will be given Coumadin 5 milligrams daily (a drug to prevent a blood clot in a deep vein). Safety evaluations include laboratory tests, physical examination, vital signs, and the recording of adverse events performed throughout the study until the patient is discharged from the hospital. In addition, six weeks after surgery, laboratory tests are performed, vital signs are measured, and any adverse events are recorded. Ultrasound is performed before the start of the study and on Day 5 after surgery to determine if there is a blood clot in a deep vein. Effectiveness will be determined by reduction in the need for transfusions during the period of time around the surgery. The study hypothesis is that patients treated with epoetin alfa will require fewer transfusions during the period of time around surgery than patients treated with placebo. Epoetin alfa 300 units/kilogram (U/kg), epoetin alfa 100 U/kg, or placebo, by injection beneath the skin beginning 10 days before scheduled surgery and ending 4 days after surgery.