Comparing predictions among competing risks models with rare events: application to KNOW-CKD study—a multicentre cohort study of chronic kidney disease

A prognostic model to determine an association between survival outcomes and clinical risk factors, such as the Cox model, has been developed over the past decades in the medical field. Although the data size containing subjects’ information gradually increases, the number of events is often relatively low as medical technology develops. Accordingly, poor discrimination and low predicted ability may occur between low- and high-risk groups. The main goal of this study was to evaluate the predicted probabilities with three existing competing risks models in variation with censoring rates. Three methods were illustrated and compared in a longitudinal study of a nationwide prospective cohort of patients with chronic kidney disease in Korea. The prediction accuracy and discrimination ability of the three methods were compared in terms of the Concordance index (C-index), Integrated Brier Score (IBS), and Calibration slope. In addition, we find that these methods have different performances when the effects are linear or nonlinear under various censoring rates.