Correcting diagnostic information loss in hybrid ROC analysis under measurement errors

Accurate evaluation of diagnostic performance is fundamental to medical decision-making, however this evaluation becomes particularly challenging when biomarker measurements exhibit non-normal and heterogeneous distributional characteristics. In practical diagnostic studies, healthy and diseased populations often differ substantially in skewness and tail behavior, a pattern that limits the adequacy of conventional single-distribution ROC models. To address this limitation, this paper introduces a hybrid Receiver Operating Characteristic (ROC) framework in which biomarker values from the healthy population follow an Exponential distribution, while those from the diseased population are modeled using a Lindley distribution. Closed-form expressions for the corresponding ROC curve and Area under the Curve (AUC) are derived to quantify the discriminative ability of the proposed model. Theoretical properties of the proposed ROC model are established to ensure its validity. Since diagnostic measurements are frequently contaminated by laboratory and instrumental errors, a bias-corrected AUC estimator is also developed to account for measurement errors. The performance of the proposed estimator is evaluated through extensive simulation studies under varying contamination levels and sample sizes. A real-data application further demonstrates that the bias-corrected estimator substantially improves the accuracy and reliability of diagnostic assessment in the presence of measurement error.