Key result
New hazard discrimination summary metric generalizes the discrimination slope for incident events and hazard models.
Introduces the hazard discrimination summary (HDS) as a new statistical measure for evaluating time-varying prognostic discrimination in survival models.
Both calibration and discrimination require joint evaluation in prognostic survival models; leaves open optimal metrics for clinical application.
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.
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Liang et al. (2016) studied this question. A new risk-based measure of time-varying discrimination, the hazard discrimination summary (HDS), was proposed to generalize the discrimination slope for incident events and hazard models.