Investigating the impact of measurement error on AUC estimation using hybrid ROC models: An application to medical and industrial domains

This study addresses the challenge of estimating the Area under the curve (AUC) in the presence of measurement errors (MEs) within two hybrid receiver operating characteristic (ROC) frameworks that incorporate non-normal distributions. Specifically, we examine the combinations of Half-Normal & Exponential, and Half-Normal & Rayleigh distributions. For each hybrid ROC curve, a generalized bias-corrected approximation to the AUC is derived to mitigate the systematic underestimation induced by measurement errors. The performance of the proposed estimators is examined under two classification scenarios: (i) best-case settings characterized by well-separated populations and (ii) worst-case settings involving substantial distributional overlap. The practical applicability and robustness of the proposed methodology are illustrated through real datasets, demonstrating its effectiveness in recovering the true discriminative ability in hybrid and error-contaminated environments.