I'm actually not sure, so you may be able to help me answer that question!
I am using the ROC curve to assess the sensitivity and specificity of three measures, and using a the presence/absence of a diagnosis as the dichotomous variable (i.e., yes/no the participant has a diagnosis).
I hadn't thought of using that method as I have been advised by my supervisors to conduct a ROC analysis first and see what that comes up with. It seems that the ROC curve is used widely in my area of research and so I think that is why they would like to continue to use it.
It is strange that I cannot seem to find any information on whether there are any assumptions to conduct this test though!
I think it is just an optimization algorithm, so you can feed any data into it. I will try to look up if there are any assumptions in the morning.
I recommended the decision tree based on thinking you are trying to create a decision rule based on 3 variable at the same time, correct or not? Look up what it takes to do a power calculation related to ROC curve, that may help with possible assumption or components to keep in mind.
Well, I got busy - so my response will be terse. I was thinking about the ROC curve, and to take a step back, it is just a graph - that is it. So you plot all of the observed operating points (possible SEN vs SPEC) in the sample then connect them creating the empiral ROC curve.
So do scatterplots or bar graphs have assumptions? Probably just the intuitive basics related to what type of data it can handle. I think when it comes to assumptions, they may come into play related to using the Whitney-Mann test or comparing models. But the ROC Curve itself is just a graph.
I would highly recommend the book "Analyzing Receiver Operating Characteristic Curves with SAS: by Gonen. It provides a gentle introduction to many ROC Curve concepts including bias, and applying curves to ordinal and survival data. Plus, I think the book is fairly cheap and Gonen seems to be a person who regularly publishes technical papers in this area.
Take home thoughts, its just a graph and theory and assumptions may come into play downstream when finding a cut-point or making hypotheses related to AUC.