Kidney Graft Failure and Patient Survival Modelling Based on Competing Risks Under Nonproportional Hazards

Abstract

We analyze data on Silesian patients after kidney transplantation under competing events scenarios where time to death and time to graft failure are considered as absorbing competing events. Our objectives are to use model diagnostics in identifying violations of proportionality assumption under the framework of subdistribution and cause-specific hazards. We use the Fine-Gray proportional hazards model for the subdistribution. Under the cause-specific hazards (CSH) scenario we use the Cox proportional hazards model and Gray's time-varying coefficients model and available model diagnostics. We show that violation of proportional subdistribution hazards assumption may be conveniently identified using residual diagnostics and properly accounted for by involving time interactions with appropriate model predictors. We also show that although the nonproportional effects on cumulative incidence do not necessarily translate in those on cause-specific hazards, they often take place simultaneously, and a violation of the proportionality assumption needs to be checked rigorously. Time-varying effects have a profound impact on clinical inference under competing risks. They do not translate directly between the frameworks of subdistribution and cause-specific hazards because the cumulative incidence is obtained via integrating the cause-specific hazard weighted by the overall survival function. Also, a different definition of the risk set is in place under the cumulative incidence and CSH framework, respectively. However, a simultaneous violation of the proportionality assumption under both frameworks is still possible. Clinical inference may change considerably when such a violation occurs. Nonproportional effects may be properly identified under each framework using available model diagnostics.