Bias-corrected methods for estimating the receiver operating characteristic surface of continuous diagnostic tests

TL;DR

This paper addresses verification bias in evaluating continuous diagnostic tests for three-class diseases, proposing bias-corrected estimators for ROC surface and volume under the curve, with theoretical validation and simulation studies.

Contribution

It introduces new verification bias-corrected estimators for ROC surface and volume under the curve for three-class diagnostic tests, with proven consistency and asymptotic normality.

Findings

Estimators are consistent and asymptotically normal.

Simulation studies demonstrate good finite sample performance.

Applications illustrate practical utility.

Abstract

Verification bias is a well-known problem that may occur in the evaluation of predictive ability of diagnostic tests. When a binary disease status is considered, various solutions can be found in the literature to correct inference based on usual measures of test accuracy, such as the receiver operating characteristic (ROC) curve or the area underneath. Evaluation of the predictive ability of continuous diagnostic tests in the presence of verification bias for a three-class disease status is here discussed. In particular, several verification bias-corrected estimators of the ROC surface and of the volume underneath are proposed. Consistency and asymptotic normality of the proposed estimators are established and their finite sample behavior is investigated by means of Monte Carlo simulation studies. Two illustrations are also given.