ROC Analyses Based on Measuring Evidence

TL;DR

This paper explores ROC analysis under various distributional assumptions, proposing a Bayesian framework with prior elicitation to evaluate AUC, cutoff points, and classification errors.

Contribution

It introduces a Bayesian methodology for ROC analysis that incorporates prior distributions and provides algorithms for prior elicitation.

Findings

Bayesian approach effectively estimates AUC and cutoff points.

Method accommodates both parametric and nonparametric models.

Provides practical algorithms for prior selection.

Abstract

ROC analyses are considered under a variety of assumptions concerning the distributions of a measurement $X$ in two populations. These include the binormal model as well as nonparametric models where little is assumed about the form of distributions. The methodology is based on a characterization of statistical evidence which is dependent on the specification of prior distributions for the unknown population distributions as well as for the relevant prevalence $w$ of the disease in a given population. In all cases, elicitation algorithms are provided to guide the selection of the priors. Inferences are derived for the AUC as well as the cutoff $c$ used for classification and the associated error characteristics.