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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')

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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.

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