ROC Curves - Different AUC's in SPSS

#1
ROC Curves - Need Help

Independent Samples
I cannot understand why the Area Under the Curve (AUC) is not the same when I calculate the AUC for each of the Groups and when I then compare the two groups.

1) Calculation of AUC, for each of the groups (SPSS: Analyze/Classify/ROC Curve):
Group A ("10"): 3223 observations | AUC=0.752
Group B ("20"): 1834 observations | AUC=0.695

2) Compare two Global Data Groups (SPSS: Analyze/Classify/ROC Analysis)
Global Dada: 5057 observations with Grouping Variable ("10/20")
AUC Group A ("10"): 0.741
AUC Group B ("20"): 0.698

Why do I have different AUC's depending on the statistical test I run in SPSS? I've tried in other software and the difference always occurs. Shouldn't the AUC's be exactly the same, doing the individual calculation or comparing 2 samples?
 

hlsmith

Less is more. Stay pure. Stay poor.
#2
I don't use SPSS and didn't completely follow what you are writing about for "group"? Please add more information.

Are you changing the reference group for a categorical variable?
 
#3
What is at issue is to compare two independent groups of data, that is, the observations of one of the groups do not occur in the other group of data. For example, imagine and first calculate the male group AUC and then calculate the female AUC. The male AUC is 0.752 and the female is 0.695.
But if we run the ROC Curve test on the dataset (male + female) and the grouping variable is the gender, then the male AUC appears as 0.741 and the female as 0.698.
 

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hlsmith

Less is more. Stay pure. Stay poor.
#4
Are you generating these predictions from a logistic regression or other model? If so, each is a different model:

y = male
y = female
y = male + female

So you are going to get different values since the models are conditional on what is in it. You now have more terms in the model.
 
#5
Thank you, you are absolutely right. If I am getting the results of logistic regressions with different covariates, the results will also be different.

In this case, to be able to compare the AUC's, I will have to join the predicted values (probabilities) in a column as if they had been obtained from a single regression. So I will be able to have the same curves graphically represented with the correct AUC's

Once again, thank you very much!