How to interpret the overlap of AUC-CI(95%) of two logistic regression models Here is my question. I am comparing two logistic regression models which use the same data and endpoint but different variables. My goal is to see if the model improves based on the performance using AUC. In the first model, my reference model's AUC is 0.754(95% CI: 0.634-0.873). After including the new variable in the model's AUC increased to 0.792(95% CI: 0.686-0.903). This would indicate that the model performance is improved from reference. However, even though the new variable is a statistically significant addition to the model(p-value: 0.016) there is considerable overlap in the AUC-CI of both models.
When comparing the means of two groups, it is understood that if the confidence intervals for those groups overlap, the difference between groups is not statistically significant. However, I see that in publications similar to mine, the overlap in AUC-CI is regularly observed. Furthermore, the findings of these publications report the overlap but don't justify or discuss the overlap and still declare that the addition of the new variable improves the model's performance.
Am I missing something about how to interpret the AUC-CI in logistic regression models? Can someone explain this to me and provide textual justification? I have a reviewer complaining about the overlap but I don't know how to respond.
I also provided some publication examples that have overlap in AUC-CI but still declare the model is significantly improved:
https://www.sciencedirect.com/science/article/pii/S0167814016311999
https://www.sciencedirect.com/science/article/pii/S0167814017325471
https://www.sciencedirect.com/science/article/pii/S0167814018333097

It is not true that overlapping confidence intervals precludes a significant difference, even in simple situations like testing for mean differences (and a reviewer brought in to evaluate the statistics should know this). Consequently, if some reasonable test shows that the difference between AUCs is significant, feel free to go with that, despite the overlapping confidence intervals.
There are multiple issues with AUC (discussed elsewhere on this Stack, particularly by Frank Harrell), and you might be more interested in evaluating based on log-loss or Brier score, but overlapping confidence intervals is not among the strikes against AUC.
That same Frank Harrell has a blog post about how to evaluate the value of a new variable that you might find helpful, too.
