Doubly robust estimation of the area under the receiver-operating characteristic curve in the presence of verification bias

The area under the receiver operating characteristic curve (AUC) is a popular summary measure of the efficacy of a medical diagnostic test to discriminate between healthy and diseased subjects. A frequently encountered problem in studies that evaluate a new diagnostic test is that not all patients undergo disease verification because the verification test is expensive, invasive, or both. Furthermore, the decision to send patients to verification often depends on the new test and on other predictors of true disease status. In such cases, usual estimators of the AUC based on verified patients only are biased. In this article we develop estimators of the AUC of markers measured on any scale that adjust for selection to verification. These estimators adjust for measured patient covariates and diagnostic test results and also for an assumed degree of residual selection bias. They can then be used in a sensitivity analysis to examine how the AUC estimates change when different plausible degrees of residual association are assumed. As with other missing-data problems, due to the curse of dimensionality, a model for disease or a model for selection is needed to obtain well-behaved estimators of the AUC when the marker and/or the measured covariates are continuous. We describe a doubly robust estimator that has the attractive feature of being consistent and asymptotically normal if either the disease or the selection model (but not necessarily both) is correct.