  When evaluating medical tests or biomarkers for disease classification, the
area under the receiver-operating characteristic (ROC) curve is a widely used
performance metric that does not require us to commit to a specific decision
threshold. For the same type of evaluations, a different metric known as the
average precision (AP) is used much more widely in the information retrieval
literature. We study both metrics in some depths in order to elucidate their
difference and relationship. More specifically, we explain mathematically why
the AP may be more appropriate if the earlier part of the ROC curve is of
interest. We also address practical matters, deriving an expression for the
asymptotic variance of the AP, as well as providing real-world examples
concerning the evaluation of protein biomarkers for prostate cancer and the
assessment of digital versus film mammography for breast cancer screening.
