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I am analysing diagnostic accuracy. I have a dataset with a ground truth and 3 predictors.

  • Ground truth = binary (0/1)
  • Predictor 1-2 = binary (0/1)
  • Predictor 3 = continuous (0-100)

I have 50,000 observations, and each observation can maximum have ground truth = 1 once.

I have made ROC-curves with corresponding AUC-values for ground truth and predictor 1-3.

I have also made some subanalyses, where the definition of ground truth has changed a bit, and thus, it is here possible for the observations to have ground truth = 1 multiple times (yet, this is still rare).

My professor (who is not an statistics expert) has asked me to do the ROC-AUC curves for the main data (as I have done) and to perhaps include the c-statistics for the subanalyses.

My question is: What is the difference between the c-statistic and the AUC? As far as I can read, it is basically the same?

  • Perhaps the c-statistic take in mind that the outcome (ground truth) can happen multiple times?

I hope one of you are able to help me :)

user12541161
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  • Does this answer your question? AUC in ordinal logistic regression The first sentence of Harrell’s answer seems to confirm your suspicion that the concordance index for a binary outcome equals the area under the ROC curve. – Dave Aug 14 '23 at 15:11
  • The AUC and c-statistic are the same thing, unless perhaps you're doing something unusual and the setting in which they are the same thing does not apply. It's hard to understand the question Perhaps the c-statistic take in mind that the outcome (ground truth) can happen multiple times? because you haven't explained what it means for an outcome to happen multiple times -- AUC is most often used for binary outcomes, so the outcome is at most 1. Can you [edit] to explain what you're analyzing and how AUC and c-statistic fit into the analysis? What makes you doubt that they are the same? – Sycorax Aug 14 '23 at 15:15

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