Bayesian ROC curve estimation under verification bias

• Published in: Statistics in medicine Vol. 33; no. 29; pp. 5081 - 5096
• Main Authors: Gu, Jiezhun, Ghosal, Subhashis, Kleiner, David E.
• Format: Journal Article
• Language: English
• Published: England Blackwell Publishing Ltd 20.12.2014; Wiley Subscription Services, Inc
• Subjects: Accuracy; Bayes Theorem; Bayesian analysis; Bias; binormal model; Computer Simulation; Data Interpretation, Statistical; Diagnostic tests; Estimating techniques; Humans; MAR assumption; Markov Chains; Medical statistics; Models, Biological; Monte Carlo Method; Patient Selection; posterior consistency; Regression Analysis; ROC Curve; Sampling; verification bias-correction; binormal model; verification bias-correction; ROC curve; posterior consistency; MAR assumption
• ISSN: 0277-6715; 1097-0258; 1097-0258
• DOI: 10.1002/sim.6297

Receiver operating characteristic (ROC) curve has been widely used in medical science for its ability to measure the accuracy of diagnostic tests under the gold standard. However, in a complicated medical practice, a gold standard test can be invasive, expensive, and its result may not always be available for all the subjects under study. Thus, a gold standard test is implemented only when it is necessary and possible. This leads to the so‐called ‘verification bias’, meaning that subjects with verified disease status (also called label) are not selected in a completely random fashion. In this paper, we propose a new Bayesian approach for estimating an ROC curve based on continuous data following the popular semiparametric binormal model in the presence of verification bias. By using a rank‐based likelihood, and following Gibbs sampling techniques, we compute the posterior distribution of the binormal parameters intercept and slope, as well as the area under the curve by imputing the missing labels within Markov Chain Monte‐Carlo iterations. Consistency of the resulting posterior under mild conditions is also established. We compare the new method with other comparable methods and conclude that our estimator performs well in terms of accuracy. Copyright © 2014 John Wiley & Sons, Ltd.