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

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.

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.

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.

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.