Evaluation of Diagnostic Accuracy under Measurement Error using a new Hybrid ROC Model

Hybrid ROC Modeling under Measurement Error

Resumen

In recent years, Receiver Operating Characteristic (ROC) analysis has gained wide importance in medical research for evaluating the performance of diagnostic tests. It helps in classifying subjects into healthy and diseased populations based on biomarker values. While hybrid ROC models based on mixed distributional assumptions have been explored in the literature, limited attention has been given to modelling scenarios where healthy population exhibit right-skewed baseline characteristics while diseased populations show variability consistent with magnitude-type biological measurements. In this study, we propose a hybrid ROC model in which the test scores of the healthy population follow an Exponential distribution and those of the diseased population follow a Rayleigh distribution. This pairing provides a flexible yet analytically tractable framework for modelling asymmetric biomarker behaviour frequently observed in medical data. Closed-form expressions for the ROC curve and the corresponding Area under the Curve (AUC) are derived to study the discriminative ability of the model. A key contribution of this work is the explicit incorporation of measurement error into the hybrid ROC setting and the development of a bias-corrected estimator to improve diagnostic accuracy in the presence of measurement error. The performance of the proposed method is evaluated through extensive simulation studies across varying sample sizes and contamination levels. The methodology is further illustrated using a real dataset, demonstrating that the bias-corrected estimator substantially improves accuracy and provides reliable classification in the presence of measurement error.