Application of the skew exponential power distribution to ROC curves

Abstract

The bi-Normal ROC model and corresponding metrics are commonly used in medical studies to evaluate the discriminatory ability of a biomarker. However, in practice, many clinical biomarkers tend to have skewed or other non-Normal distributions. And while the bi-Normal ROC model’s AUC tends to be unbiased in this setting, providing a reasonable measure of global performance, the corresponding decision thresholds tend to be biased. To correct this bias, we propose using an ROC model based on the skew exponential power (SEP) distribution, whose additional parameters can accommodate skewed, heavy tailed, or other non-Normal distributions. Additionally, the SEP distribution can be used to evaluate whether the bi-Normal model would be appropriate. The performance of these ROC models and the non-parametric approach are evaluated via a simulation study and applied to a real data set involving infections from Klebsiella pneumoniae. The SEP based ROC-model provides some efficiency gains with respect to estimation of the AUC and provides cut-points with improved classification rates. As such, in the presence non-Normal data, we suggest using the proposed SEP ROC model.