Interval estimation for the Youden index of a continuous diagnostic test with verification biased data

In medical diagnostic studies, the Youden index plays a crucial role as a comprehensive measurement of the diagnostic test effectiveness, aiding in determining the optimal threshold values by maximizing the sum of sensitivity and specificity. However, in clinical practice, verification of true disease status might be partially missing and estimators based on partially validated subjects are usually biased. While verification bias-corrected estimation methods for the receiver operating characteristic curve have been widely studied, no such results have been specifically developed for the Youden index. In this paper, we propose bias-corrected interval estimation methods for the Youden index of a continuous test under the missing-at-random assumption. Based on four estimators (full imputation (FI), mean score imputation, inverse probability weighting, and the semiparametric efficient (SPE)) introduced by Alonzo and Pepe for handling verification bias, we develop multiple confidence intervals for the Youden index by applying bootstrap resampling and the method of variance estimates recovery (MOVER). Extensive simulation and real data studies show that when the disease model is correctly specified, MOVER-FI intervals yield better coverage probability. We also observe a tradeoff between methods when the verification proportion is low: Bootstrap approaches achieve higher accuracy, while MOVER approaches deliver greater precision. Remarkably, bootstrap-SPE interval exhibit appealing doubly robustness to model misspecification and perform adequately across almost all scenarios considered. Based on our findings, we recommend using the bootstrap-SPE intervals when the true disease model is unknown, and the MOVERws-FI interval if the true disease model can be well approximated.