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Background  Incremental value (IncV) evaluates the performance change between an existing risk model and a new model. Different IncV metrics do not always agree with each other. For example, compared with a prescribed-dose model, an ovarian-dose model for predicting acute ovarian failure has a slightly lower area under the receiver operating characteristic curve (AUC) but increases the area under the precision-recall curve (AP) by 48%. This phenomenon of disagreement is not uncommon, and can create confusion when assessing whether the added information improves the model prediction accuracy.    Methods  In this article, we examine the analytical connections and differences between the AUC IncV ( Δ AUC) and AP IncV ( Δ AP). We also compare the true values of these two IncV metrics in a numerical study. Additionally, as both are semi-proper scoring rules, we compare them with a strictly proper scoring rule: the IncV of the scaled Brier score ( Δ sBrS) in the numerical study.    Results  We demonstrate that  Δ AUC and  Δ AP are both weighted averages of the changes (from the existing model to the new one) in separating the risk score distributions between events and non-events. However,  Δ AP assigns heavier weights to the changes in higher-risk regions, whereas  Δ AUC weights the changes equally. Due to this difference, the two IncV metrics can disagree, and the numerical study shows that their disagreement becomes more pronounced as the event rate decreases. In the numerical study, we also find that  Δ AP has a wide range, from negative to positive, but the range of  Δ AUC is much smaller. In addition,  Δ AP and  Δ sBrS are highly consistent, but  Δ AUC is negatively correlated with  Δ sBrS and  Δ AP when the event rate is low.    Conclusions   Δ AUC treats the wins and losses of a new risk model equally across different risk regions. When neither the existing or new model is the true model, this equality could attenuate a superior performance of the new model for a sub-region. In contrast,  Δ AP accentuates the change in the prediction accuracy for higher-risk regions.    Supplementary Information  The online version contains supplementary material available at (10.1186/s41512-021-00102-w).

A relationship between the incremental values of area under the ROC curve and of area under the precision-recall curve