The ideal mathematical model for predicting survival for individual patients with primary biliary cirrhosis should be based on a small number of inexpensive, noninvasive measurements that are universally available. Such a model would be useful in medical management by aiding in the selection of patients for and timing of orthotopic liver transplantation. This paper describes the development, testing and use of a mathematical model for predicting survival. The Cox regression method and comprehensive data from 312 Mayo Clinic patients with primary biliary cirrhosis were used to derive a model based on patient's age, total serum bilirubin and serum albumin concentrations, prothrombin time and severity of edema. When cross-validated on an independent set of 106 Mayo Clinic primary biliary cirrhosis patients, the model predicted survival accurately. Our model was found to be comparable in quality to two other primary biliary cirrhosis survival models reported in the literature and to have the advantage of not requiring liver biopsy.
Orthotopic liver transplantation is considered to be potentially life-saving for selected patients with advanced or end-stage primary biliary cirrhosis. The availability of a model to predict survival probability for an individual patient would improve selection of patients for transplantation and the timing of that transplantation. Also, such a model could be used to help to decide which patients are appropriate, medically and ethically, for clinical trials of other treatment modalities. In addition, the model could be used for education and counseling of the patient and the family.
Using the Cox proportional hazards regression procedure (l), Roll et al. at Yale (2) and Christensen et al. in Europe (3) independently developed multivariate survival models. The Yale model used patient's age, serum bilirubin concentration, hepatomegaly and presence of portal fibrosis or cirrhosis to predict survival. The European model used age, bilirubin and albumin concentra-