Enrichment Score: a better quantitative metric for evaluating the enrichment capacity of molecular docking models

The standard quantitative metric for evaluating enrichment capacity known as $\textit{LogAUC}$ depends on a cutoff parameter that controls what the minimum value of the log-scaled x-axis is. Unless this parameter is chosen carefully for a given ROC curve, one of the two following problems occurs: either (1) some fraction of the first inter-decoy intervals of the ROC curve are simply thrown away and do not contribute to the metric at all, or (2) the very first inter-decoy interval contributes too much to the metric at the expense of all following inter-decoy intervals. We fix this problem with LogAUC by showing a simple way to choose the cutoff parameter based on the number of decoys which forces the first inter-decoy interval to always have a stable, sensible contribution to the total value. Moreover, we introduce a normalized version of LogAUC known as $\textit{enrichment score}$, which (1) enforces stability by selecting the cutoff parameter in the manner described, (2) yields scores which are more intuitively meaningful, and (3) allows reliably accurate comparison of the enrichment capacities exhibited by different ROC curves, even those produced using different numbers of decoys. Finally, we demonstrate the advantage of enrichment score over unbalanced metrics using data from a real retrospective docking study performed using the program $\textit{DOCK 3.7}$ on the target receptor TRYB1 included in the $\textit{DUDE-Z}$ benchmark.