evaluation of GLM by ROC analysis

Hi,
I was wondering if someone could give me hints/references as to how to
proceed with the following.
Take logistic regression with input variables a,b,c and a dicotomous
outcome variable d.
The model can then evaluated by ROC analysis of the distribution d^
(the model estimate) using d as clasifier.
I hope I have manaed to make myself clear so far.

If one was to hypothesize that a parameter c' made a better model than
c above one could of course fit the new model, determine the parameters
and re-evalute the new model using ROC analysis.
Here is the question: In stead of going through this potentially large
hazzle could one in stead compare the ROC curves generated on c and c'?
Ie. if c' has a higher area under the ROC curve than c - then will a
model tranied with c' have higher overall area under the AUC?

It is assumed that the model is additive only with no interaction term.

What way would I need to take to prove this or is it simply wrong?


Thanks,
Soren

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