Threshold Free Measures for Assessing the Performance of Medical Screening Tests
The area under the receiver operating curve (AUC) is frequently used as a performance measure for medical tests. It is a threshold-free measure that is independent of the disease prevalence rate. We evaluate the utility of the AUC against an alternate measure called the average positive predictive value (AP), in the setting of many medical screening programs where the disease has a low prevalence rate.
We define the two measures using a common notation system and show that both measures can be expressed as a weighted average of the density function of the diseased subjects. The weights for the AP include prevalence in some form, but those for the AUC do not. An expression for the asymptotic variance of the AP for ordinal data is derived. Lastly, two real-world examples, mammography and prostate cancer biomarkers, are used to compare AUC and AP