Concordance vs. Sensitivity I am confused between these two terms: sensitivity and concordance. What I understand about these two terms:
Concordance: the number of pairs where actual 1s have higher predicted probability of becoming 1s than 0s divided by total number of pairs.
Sensitivity: percentage of 1s correctly predicted as 1.
By their definitions, both seems to be the same.
I have read somewhere that concordance = (true positive  + true negative) / sample size.
I have tried to calculate concordance using this formula. But it seems to be incorrect.
First, I have run logistic regression in SAS using PROC LOGISTIC with the CTABLE PPROB=0.5 options. Then I have calculated true positive pairs from (sensitivity percentage $\times$ number of 1s) and true negative pairs from (specificity percentage $\times$ number of 0s). I added them up and divided by total responses. This is not matching up with concordance score.
 A: I have always found the Wikipedia article on sensitivity and specificity to quite well summarize the various measures. The formula for concordance you mention above is the same that the Wikipedia article calls accuracy. This is not the same as concordance, which also goes with names c-statistic or area under the receiver operating characteristic curve (AUC). Concordance is also different from specificity. Your formula for the specificity seems to be correct, but the formula for concordance is not.
The difference between accuracy and AUC is that accuracy is measured at a certain cut-off point that was used for dicotomizing the probability distribution given by logistic model whereas AUC measures overall accuracy over a range of cutoff points, so to say. 
There's a well written article on concordance in Austin, P. C. and Steyerberg, E. W. (2012). Interpreting the concordance statistic of a logistic regression model: relation to the variance and odds ratio of a continuous explanatory variable. BMC Medical Research Methodology, 12(82):1–8.. The second paragraph of the Background gives several definitions for concordance. There's also some information specifically on the SAS implementation and how to invoke the ROC curve and to produce an AUC value in SAS.
