AUC below 0.5


I am calculating area under the curve (AUC) values for the individual independent variables of a conditional logistic regression model. I am using Stata's rocreg command.

Half of the ten variables show AUC values below 0.5, specifically values as 0.32, 0.38 and 0.45.

Do AUC values below 0.5 indicate data error? If not, can the values simply ble inverted (so that I present AUC of 0.32 rather as 0.68), or must they be reported as they are?

The study is a matched case control study with 12 cases and two matched controls for each case.

Thank you in advance.


Omega Contributor
have not used that package. does it control for the paired data?

ideally you want confidence intervals on your auc estimates. if the upper bound is below 0.5 it just means the variable significantly predicts the outcomes reference group. if the independent variable is binary you could also switch its reference level.
Thank you for the reply.

I don't know how the rocreg command handles matched data and more than control for each case, good question. And after your reply, I will also present confidence intervals for the AUC values. Note that I do present p-values, means and standard deviations for each variable, but from the conditional logistic regression (which takes into account the matching). Of note, I see that it is only insignificant variables that show AUC values below 0.05.
Having calculated 95% CI for all variables, I run into another issue: Even if the p-value from the conditional logistic regression is statistically significant (<.05), the 95 % CI is not (involves 0.5). I guess the AUC does not take into account the matching. Does anybody have experience on this matter?