A risk-based measure of time-varying prognostic discrimination for survival models

Prognostic survival models are commonly evaluated in terms of both their calibration and their discrimination. Comparing observed and predicted survival curves can assess calibration, while discrimination is typically summarized through comparison of the properties of cases or subjects who experience an event, and the properties of controls represented by event-free individuals. For binary data, discrimination is characterized either by using the relative ranks of cases and controls and a receiver operating characteristic (ROC) curve, or by summarizing the magnitude of risk placed on cases and controls through calculation of the discrimination slope (DS). In this article, we propose a risk-based measure of time-varying discrimination that generalizes the discrimination slope to allow use with incident events and hazard models. We refer to the new measure as the hazard discrimination summary (HDS) since it compares the relative risk among incident cases to their associated dynamic risk set controls. We introduce both a model-based estimation procedure that adopts the Cox model, and an alternative approach that locally relaxes the proportional hazards assumption. We illustrate the proposed methods using both a benchmark survival data set, and an oncology study where primary interest is in the time-varying performance of candidate biomarkers.