Receiver operating characteristic (ROC) movies, universal ROC (UROC) curves, and coefficient of predictive ability (CPA)

TL;DR

This paper introduces ROC movies, universal ROC (UROC) curves, and a new coefficient of predictive ability (CPA) that extend ROC analysis to any linearly ordered outcome, providing more versatile tools for predictive performance assessment.

Contribution

The paper presents novel ROC-based tools that generalize classical ROC analysis to ordered outcomes and introduces CPA as a new measure of predictive ability.

Findings

CPA equals AUC for binary outcomes

CPA relates linearly to Spearman's coefficient

Applications demonstrate new insights in biomedicine and meteorology

Abstract

Throughout science and technology, receiver operating characteristic (ROC) curves and associated area under the curve (AUC) measures constitute powerful tools for assessing the predictive abilities of features, markers and tests in binary classification problems. Despite its immense popularity, ROC analysis has been subject to a fundamental restriction, in that it applies to dichotomous (yes or no) outcomes only. Here we introduce ROC movies and universal ROC (UROC) curves that apply to just any linearly ordered outcome, along with an associated coefficient of predictive ability (CPA) measure. CPA equals the area under the UROC curve, and admits appealing interpretations in terms of probabilities and rank based covariances. For binary outcomes CPA equals AUC, and for pairwise distinct outcomes CPA relates linearly to Spearman's coefficient, in the same way that the C index relates linearly to Kendall's coefficient. ROC movies, UROC curves, and CPA nest and generalize the tools of classical ROC analysis, and are bound to supersede them in a wealth of applications. Their usage is illustrated in data examples from biomedicine and meteorology, where rank based measures yield new insights in the WeatherBench comparison of the predictive performance of convolutional neural networks and physical-numerical models for weather prediction.