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Empirical Likelihood Inference for the Area under the ROC Curve
Author(s) -
Qin Gengsheng,
Zhou XiaoHua
Publication year - 2006
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.1541-0420.2005.00453.x
Subject(s) - receiver operating characteristic , confidence interval , statistics , inference , mathematics , empirical likelihood , interval (graph theory) , coverage probability , limiting , chi square test , statistical inference , area under the curve , computer science , artificial intelligence , medicine , mechanical engineering , combinatorics , engineering
Summary For a continuous‐scale diagnostic test, the most commonly used summary index of the receiver operating characteristic curve (ROC) is the area under the curve (AUC) that measures the accuracy of the diagnostic test. In this article, we propose an empirical likelihood (EL) approach for the inference on the AUC. First we define an EL ratio for the AUC and show that its limiting distribution is a scaled chi‐square distribution. We then obtain an EL‐based confidence interval for the AUC using the scaled chi‐square distribution. This EL inference for the AUC can be extended to stratified samples, and the resulting limiting distribution is a weighted sum of independent chi‐square distributions. Additionally we conduct simulation studies to compare the relative performance of the proposed EL‐based interval with the existing normal approximation‐based intervals and bootstrap intervals for the AUC.