Is multidimensional ROC Curve Analysis a thing?

#1
Hi, I'm a student of statistics and right now, in my course, we're studying validation of diagnostic tests. While learning about ROC Curves and AUC, I was wondering if does considering ROC Curves in the multivariate context make sense, and if so, how's the analysis performed and which are the application of such a tool. Thank you for any info you will be able to provide me.
 

hlsmith

Less is more. Stay pure. Stay poor.
#2
Can you provide more information or an example to what you are referencing? Thanks.

ROC curves plot SEN vs 1-SPEC, so 2-D. You can compare multiple models by plotting more than one curve in that 2-D space. If you had multiple outcomes (multivariate) what would you be looking for via the ROC beyond plotting more than one curve.

You could have more than 2-D if you incorporated another variable associated with both SEN and SPEC, but I am not sure what that would be. There is a trade off in false positives and false negative between these metrics.
 

fed2

Active Member
#3
for many predictors most logit regression packages compute the ROC curve based on the propensity scores, ie the predicted probablity of event. There are certain theories which say this is the best way as i recall.

For multiple outcomes, this would lead to more than 2 states, ie a tri-state model, if it can be placed into an ordinal classification. https://pubmed.ncbi.nlm.nih.gov/23794784/

There's an r package for that, but i have not thought about that in so long id have to go look in the stats crypt...