A placement-value based approach to concave ROC analysis

TL;DR

This paper introduces a novel placement value-based method to ensure concave ROC curves, improving decision-theoretic optimality, using Bayesian estimation in both parametric and semiparametric frameworks, validated through simulations and real data.

Contribution

It proposes a new placement value-based approach to enforce ROC curve concavity and employs Bayesian methods for estimation, advancing ROC analysis.

Findings

The method produces more optimal ROC curves in simulations.

Bayesian estimation improves robustness across scenarios.

Application to pancreatic cancer data demonstrates practical utility.

Abstract

The receiver operating characteristic (ROC) curve is an important graphic tool for evaluating a test in a wide range of disciplines. While useful, an ROC curve can cross the chance line, either by having an S-shape or a hook at the extreme specificity. These non-concave ROC curves are sub-optimal according to decision theory, as there are points that are superior than those corresponding to the portions below the chance line with either the same sensitivity or specificity. We extend the literature by proposing a novel placement value-based approach to ensure concave curvature of the ROC curve, and utilize Bayesian paradigm to make estimations under both a parametric and a semiparametric framework. We conduct extensive simulation studies to assess the performance of the proposed methodology under various scenarios, and apply it to a pancreatic cancer dataset.