Optimizing classification accuracy under non-normal measurement errors: a unified approach using Half-Normal and Exponential ROC curves

The area under the Receiver Operating Characteristic (ROC) curve is a widely used metric to evaluate how well diagnostic markers can differentiate between individuals with a disease and those who do not have a disease. In the medical field, these markers are generally subject to measurement errors, which can significantly impact the accuracy of the ROC analysis. The existing literature has predominantly focused on estimating the accuracy of an ROC curve in the presence of measurement errors under the assumption that the population comes from a normal distribution. However, in real-life scenarios, we mostly encounternon-normal data characteristics, and existing procedures do not adequately address the problem of non-normal measurement errors. To address this, we considered two non-normal (Half-Normal & Exponential) ROC curves and proposed a unified approach of bias-corrected approximation to correctly estimate their accuracies in the presence of measurement errors. The performance of the proposed estimators is evaluated through extensive simulation studies under both well-separated and overlapping scenarios, demonstrating minimal bias and mean squared error. The methodology is further assessed using real clinical datasets under Half-Normal and Exponential assumptions, confirming improved AUC estimation in the presence of measurement errors.