Why do smooth ROC Curves?

[oli.m]

In a nutshell:
What is the reason why people smooth ROC Curves?

When I plot a ROC Curve, the emperical data gives me always a parametric function which looks like stairs going up.

This is due to the fact that you either have:

• a non-continuous tests (e.g.: a medical test which can have 0 -10 full points) . So I could only calculate 10 differnt thresholds, because there are no values like "1.45" .

or:

• even if the data is continuous, there is never a measurement for every value.

-> actually all ROC functions are parametric

During my research I found out that there are many different methods to smoothen the graphs (see Figure below). Apparently this is relevant in some cases, but unfortunately I could not find out why exactly?

Does anyone know why?

I want to do a ROCAUC analysis about a medical test with 0-7 full points.

Soure

Thank you!
Oli

[nirgrahamuk]

I suppose its that you are stepping away from the precise model and data for which you have the empirical result and slightly generalising to what might be considered 'similar models with similar data'.
There is of course an empirical approach to this which would be to bootstrap model builds and average out the ROC curves, the more you do the smoother the result would be. obviously the number of evaluation points for which any single ROC curve is calculated will influence the degree of 'smoothness' also.