True verification probabilities should not be used in estimating the area under receiver operating characteristic curve

• Published in: Statistics in medicine Vol. 39; no. 27; pp. 3937 - 3946
• Main Author: Wu, Yougui
• Format: Journal Article
• Language: English
• Published: England Wiley Subscription Services, Inc 30.11.2020
• Subjects: area under a ROC curve; Diagnostic tests; Estimation bias; inverse probability weighting; Medical research; Probability; Statistical analysis; two‐phase design; verification bias; verification probability; two-phase design; inverse probability weighting; area under a ROC curve; verification bias; verification probability
• ISSN: 0277-6715; 1097-0258; 1097-0258
• DOI: 10.1002/sim.8700

In medical research, a two‐phase study is often used for the estimation of the area under the receiver operating characteristic curve (AUC) of a diagnostic test. However, such a design introduces verification bias. One of the methods to correct verification bias is inverse probability weighting (IPW). Since the probability a subject is selected into phase 2 of the study for disease verification is known, both true and estimated verification probabilities can be used to form an IPW estimator for AUC. In this article, we derive explicit variance formula for both IPW AUC estimators and show that the IPW AUC estimator using the true values of verification probabilities even when they are known are less efficient than its counterpart using the estimated values. Our simulation results show that the efficiency loss can be substantial especially when the variance of test result in disease population is small relative to its counterpart in nondiseased population.