Net reclassification index at event rate: properties and relationships.

The net reclassification improvement (NRI) is an attractively simple summary measure quantifying improvement in performance because of addition of new risk marker(s) to a prediction model. Originally proposed for settings with well-established classification thresholds, it quickly extended into applications with no thresholds in common use. Here we aim to explore properties of the NRI at event rate. We express this NRI as a difference in performance measures for the new versus old model and show that the quantity underlying this difference is related to several global as well as decision analytic measures of model performance. It maximizes the relative utility (standardized net benefit) across all classification thresholds and can be viewed as the Kolmogorov-Smirnov distance between the distributions of risk among events and non-events. It can be expressed as a special case of the continuous NRI, measuring reclassification from the 'null' model with no predictors. It is also a criterion based on the value of information and quantifies the reduction in expected regret for a given regret function, casting the NRI at event rate as a measure of incremental reduction in expected regret. More generally, we find it informative to present plots of standardized net benefit/relative utility for the new versus old model across the domain of classification thresholds. Then, these plots can be summarized with their maximum values, and the increment in model performance can be described by the NRI at event rate. We provide theoretical examples and a clinical application on the evaluation of prognostic biomarkers for atrial fibrillation.