Liver Transplant Eligibility: Referral Criteria and Requirements. When you have end stage liver disease, and no longer see results with medical therapy, you may be eligible for a liver transplant at UPMC.. At the UPMC Liver Transplant Program, we consider each person referred to our program - even if other centers have said that you are not a candidate.Transplant Process‧Living-Donor Liver Transplant‧Patient Stories.