I model survival outcomes using a Cox proportional hazards model and want to evaluate model fit.

Harrel's concordance index C is defined as the proportion of observations that the model can order correctly in terms of survival times. Sometimes C is called the AUC.

The area under the receiver operating characteristic curve AUC is defined as the area under the curve of sensitivity and 1-specificity. At time t the Cox model may be used to obtain a ROC and its AUC. Are C and the ROC-AUC related? How?