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Direct estimation of the area under the receiver operating characteristic curve in the presence of verification bias
Author(s) -
He Hua,
Lyness Jeffrey M.,
McDermott Michael P.
Publication year - 2009
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.3388
Subject(s) - receiver operating characteristic , estimator , statistics , mathematics , resampling , statistic , variance (accounting) , wilcoxon signed rank test , weighting , area under the curve , econometrics , mann–whitney u test , medicine , accounting , business , radiology
The area under a receiver operating characteristic (ROC) curve (AUC) is a commonly used index for summarizing the ability of a continuous diagnostic test to discriminate between healthy and diseased subjects. If all subjects have their true disease status verified, one can directly estimate the AUC nonparametrically using the Wilcoxon statistic. In some studies, verification of the true disease status is performed only for a subset of subjects, possibly depending on the result of the diagnostic test and other characteristics of the subjects. Because estimators of the AUC based only on verified subjects are typically biased, it is common to estimate the AUC from a bias‐corrected ROC curve. The variance of the estimator, however, does not have a closed‐form expression and thus resampling techniques are used to obtain an estimate. In this paper, we develop a new method for directly estimating the AUC in the setting of verification bias based on U ‐statistics and inverse probability weighting (IPW). Closed‐form expressions for the estimator and its variance are derived. We also show that the new estimator is equivalent to the empirical AUC derived from the bias‐corrected ROC curve arising from the IPW approach. Copyright © 2008 John Wiley & Sons, Ltd.