Cumulative Incidence Function in Competing Risks: A Case Study of Primary Biliary Cirrhosis in Liver Disease

Abstract

Competing risks have a potential to cause biased estimates in the context of survival analysis using both traditional tools like the Kaplan-Meier estimator and Cox proportional hazards model. This is especially applicable in Primary Biliary Cirrhosis (PBC) which is a chronic liver disease where the patients can die or undergo liver transplantation as a mutually exclusive outcome. This study used the cumulative incidence function (CIF) and Fine-Gray sub-distribution hazard model to measure competing risks in patients with PBC using data in the Mayo Clinic randomised trial of 312 patients. The likelihoods of death and liver transplantation as time progressed were estimated using CIFs which adequately considered competing events, and Fine-Gray was also used to determine the impact of D-penicillmain therapy versus placebo and the important prognostic factors. The findings revealed that, the cumulative death rates were always higher than the cumulative transplantation rates of the liver during the follow-up time. Even though the patients who were treated with D-penicillmain reported a slightly low mortality and slightly higher rate of transplantation compared to the patients provided with placebo; the difference was considered insignificant. Competing outcomes were found to be significantly predicted by age, ascites, disease stage, and platelet count and not by sex, bilirubin, and albumin. Altogether, the research proves that the competing risks approach is better in terms of its accuracy and clinical significance of assessment outcomes in PBC and the significance of CIF-based methodology in the assessment of treatment effects and prognosis in chronic liver disease.