Can concordance statistic be performed and subsequently presented without at he same time calculating AIC?
In technical sense, it is not necessary to compute the AIC to be able to compute the c-statistic. To compute the c-statistic you do need to approximate the AUC. Here's a thorough example:
https://stats.stackexchange.com/questions/145566/how-to-calculate-area-under-the-curve-auc-or-the-c-statistic-by-hand
The AIC and c-statistic address different aspects of model fit. Whether either needs to be reported depends on you modelling setting. For example, if you have a host of candidate models that you compare, AIC may be a useful statistic to use (although there may be better information criteria for that purpose - depends again on the specifics of your analysis situation). With this in mind, you may find this discussion relevant:
https://stats.stackexchange.com/questions/51275/what-is-the-difference-in-what-aic-and-c-statistic-auc-actually-measure-for-mo
Regards,
Timo
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