With the development of personalized medicine, the study of individual prognosis appears to be a major contemporary scientific issue. Dynamic models are particularly well adapted to such studies by allowing some potential changes in the follow-up to be taken into account. In particular, this leads to more accurate predictions by updating the available information throughout the patient monitoring. Some mathematical tools have been developed to quantify and compare the effectiveness of dynamic predictions using dynamic versions of the area under the receiver operating characteristic curve and the Brier score in the competing risks setting. Nevertheless, only two predictive abilities can be compared. This may be too restrictive in a clinical context where more and more information can be collected during patient follow-up thanks to recent technological advances. Here we propose a new procedure that allows multiple comparisons of the predictive abilities of different biomarkers, based on the dynamic area under the receiver operating characteristic curve or Brier score. Performances of our testing procedure were assessed by simulations. Moreover, a motivating application in hepatology will be presented. Finally, this work compares more than two dynamic predictive abilities of biomarkers and is available via R functions on GitHub.
Keywords: Competing risks; dynamic Brier score; dynamic area under the receiver operating characteristic curve; dynamic prediction; multiple tests; prediction accuracy.