The area under the receiver operating characteristic 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. These measures are compared using two screening test examples under rare and common disease prevalence rates.
The AP measures the predictive power of a test, which varies when the prevalence rate changes, unlike the AUC, which is prevalence independent. The relationship between the AP and the prevalence rate depends on the underlying screening/diagnostic test. Therefore, the AP provides relevant information to clinical researchers and regulators about how a test is likely to perform in a screening population.
The AP is an attractive alternative to the AUC for the evaluation and comparison of medical screening tests. It could improve the effectiveness of screening programs during the planning stage.