Confidence intervals for the length of the receiver-operating characteristic curve based on a smooth estimator

A good diagnostic test should show different behavior on both the positive and the negative populations. However, this is not enough for having a good classification system. The binary classification problem is a complex task, which implies to define decision criteria. The knowledge of the level of...

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Bibliographic Details
Published in:Statistical methods in medical research Vol. 32; no. 5; p. 978
Main Author: Martínez-Camblor, Pablo
Format: Journal Article
Language:English
Published: England 01.05.2023
Subjects:
Algorithms
Area Under Curve
Biomarkers
Confidence Intervals
Monte Carlo Method
ROC Curve
binary classification problem
Asymptotic distribution
kernel density estimator
length of the curve
receiver-operating characteristic curve
ISSN:1477-0334, 1477-0334
Online Access:Get more information
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Summary:A good diagnostic test should show different behavior on both the positive and the negative populations. However, this is not enough for having a good classification system. The binary classification problem is a complex task, which implies to define decision criteria. The knowledge of the level of dissimilarity between the two involved distributions is not enough. We also have to know how to define those decision criteria. The length of the receiver-operating characteristic curve has been proposed as an index of the optimal discriminatory capacity of a biomarker. It is related not with the actual but with the optimal classification capacity of the considered diagnostic test. One particularity of this index is that its estimation should be based on parametric or smoothed models. We explore here the behavior of a kernel density estimator-based approximation for estimating the length of the receiver-operating characteristic curve. We prove the asymptotic distribution of the resulting statistic, propose a parametric bootstrap algorithm for confidence intervals construction, discuss the role that the bandwidth parameter plays in the quality of the provided estimations and, via Monte Carlo simulations, study its finite-sample behavior considering four different criteria for the bandwidth selection. The practical use of the length of the receiver-operating characteristic curve is illustrated through two real-world examples.
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ISSN:1477-0334
1477-0334
DOI:10.1177/09622802231160053