I conduted ROC curve, the area under the curve is .911
I want to know how to identify cases that make area under th curve is less than 1
You can see, the x-axis of ROC is 1-specificity and the y-axis of ROC is sensitivity. That means the ROC is drawn with lots of sensitivity and specificity values under different cutoffs. Each cutoff will divide all subjects into different groups. So, back to your question. ROC and AUC are like a summary of a Diagnostic test, all subject s are involved in the curve. Therefore you cannot and you don't need to identify any cases. I hope that will help you.
Arwa, take a look at this blog post: https://towardsdatascience.com/understanding-auc-roc-curve-68b2303cc9c5. Notice especially images 6 & 7. In order to have AUC=1, you need complete separation of the test score distributions for those with and without the condition you are trying to detect. For every cut-point, sensitivity must equal 1. HTH.
PS- Here's another webpage with an interactive demo that might help.
- http://arogozhnikov.github.io/2015/10/05/roc-curve.html
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