# How to interpret the output for calculating concordance index (c-index)?

I have posted a "similar" question in another thread. But I think that question is not specific/concrete enough to get the answer I expected.

I know that, in survival analysis, the concordance index (c-index) can be used to measure how well a ranking list is w.r.t survival times of subjects (F. E. Harrell, 1996, section 5.5). That is, if subjects with higher survival times get higher scores from the model, the c-index of the model will be large.

My question is: can the score be interpreted as the risk of the subject? In other words, do subjects with smaller scores (which indicates shorter survival times) correspond to larger failure risk?

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It is certainly not the same as the risk you would you to calculate relative risk between two survival curves. But it does seem apparent that the concordance measures how one ranking is correlated with ranking based on survival. So if the concordance index is high for a particular ranking then the ranking is good at separating the high risk subjects from low risk based on rank. –  Michael Chernick Jun 5 '12 at 11:33
@MichaelChernick thank you again. In your last sentence, what do you mean exactly by "high risk" subjects? The risk of failure eventually? or the risk of failure at any time? For example, suppose subject A is ranked higher than subject B, we then know that the estimated survival time of A is shorter than B, does it also means that the failure risk of A is larger than B at any particular time T? –  Yoanh27 Jun 6 '12 at 1:41

The index of concordance is a "global" index for validating the predictive ability of a survival model. It is the fraction of pairs in your data, where the observation with the higher survival time has the higher probability of survival predicted by your model. As far as I remember it it equivalent to a rank correlation.

The index is not calculated for every observation/subject. So the c-index can not be interpreted as the risk of a subject. High values mean that your model predicts higher probabilities of survival for higher observed survival times.

If you are interested in the risk of a subject in a timeperiod t, I think you have to estimate the survival and hazard function for a given set of regressors. My main reference on this subject is Harrell (2001): Rgression Modeling Strategies, Springer

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High risk by your definition means likely to have short survival times.

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OK, finally we get here! But do you think it is reasonable to think that subjects with shorter survival times are more likely to failure at any particular time T? –  Yoanh27 Jun 6 '12 at 2:17
You could write it as a calculation using Bayes' rule. –  Glen_b Dec 3 '12 at 4:21