Inference about time-dependent prognostic accuracy measures in the presence of competing risks

BACKGROUND: Evaluating a candidate marker or developing a model for predicting risk of future conditions is one of the major goals in medicine. However, model development and assessment for a time-to-event outcome may be complicated in the presence of competing risks. In this manuscript, we propose a local and a global estimators of cause-specific AUC for right-censored survival times in the presence of competing risks. METHODS: The local estimator - cause-specific weighted mean rank (cWMR) - is a local average of time-specific observed cause-specific AUCs within a neighborhood of given time t. The global estimator - cause-specific fractional polynomials (cFPL) - is based on modelling the cause-specific AUC as a function of t through fractional polynomials. RESULTS: We investigated the performance of the proposed cWMR and cFPL estimators through simulation studies and real-life data analysis. The estimators perform well in small samples, have minimal bias and appropriate coverage. CONCLUSIONS: The local estimator cWMR and the global estimator cFPL will provide computationally efficient options for assessing the prognostic accuracy of markers for time-to-event outcome in the presence of competing risks in many practical settings.