Can I calculate or approximate the contribution to AUC on observation level?

Is there a formular to calculate or approximate the observation contribution to AUC? Example based on the interpretation from wikipedia:

When using normalized units, the area under the curve (often referred to as simply the AUC) is equal to the probability that a classifier will rank a randomly chosen positive instance higher than a randomly chosen negative one (assuming 'positive' ranks higher than 'negative')

This is not possible. The $c$-index of concordance, which reduces to AUROC in the binary $Y$ case, is a $U$-statistic whose kernel is a pair of observations. It has no meaning for an individual observation.