Evaluating the Performances of Biomarkers over a Restricted Domain of High Sensitivity

The burgeoning advances in high-throughput technologies have posed a great challenge to the identification of novel biomarkers for diagnosing, by contemporary models and methods, through bioinformatics-driven analysis. Diagnostic performance metrics such as the partial area under the $ROC$ ($pAUC$) indexes exhibit limitations to analysing genomic data. Among other issues, the inability to differentiate between biomarkers whose $ROC$ curves cross each other with the same $pAUC$ value, the inappropriate expression of non-concave $ROC$ curves, and the lack of a convenient interpretation, restrict their use in practice. Here, we have proposed the fitted partial area index ($FpAUC$), which is computable through an algorithm valid for any $ROC$ curve shape, as an alternative performance summary for the evaluation of highly sensitive biomarkers. The proposed approach is based on fitter upper and lower bounds of the $pAUC$ in a high-sensitivity region. Through variance estimates, simulations, and case studies for diagnosing leukaemia, and ovarian and colon cancers, we have proven the usefulness of the proposed metric in terms of restoring the interpretation and improving diagnostic accuracy. It is robust and feasible even when the $ROC$ curve shows hooks, and solves performance ties between competitive biomarkers.