[R] How to compare areas under ROC curves calculated with ROC R package

[Frank E Harrell Jr]

Tuszynski, Jaroslaw W. wrote:
> I might be missing something but I thought that AUC was a measure for
> comparing ROC curves, so there is nothing else needed to "compare" them. The
> larger AUC is the higher correlation of 2 variables compared. No other
> measures or calculations are needed.
> 
> Jarek Tuszynski

A single AUC does not compare two competing predictors; it only measures 
the predictive discrimination of a single predictor (or a single model).

Note that testing for differences in ROC areas results in a test with 
low power.  There are much more powerful approaches such as likelihood 
ratio chi-square tests for embedded models.

The code you included below seems to make some strong assumptions about 
how AUC is estimated.  Nonparametric AUC estimators (related to the 
Wilcoxon test, for example, which is a preferred method) do not have 
simple formulas for standard errors.

Frank Harrell

> 
> -----Original Message-----
> From: r-help-bounces at stat.math.ethz.ch
> [mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Laurent Fanchon
> Sent: Wednesday, March 15, 2006 11:57 AM
> To: r-help at stat.math.ethz.ch
> Subject: [R] How to compare areas under ROC curves calculated with ROCR
> package
> 
> Dear all,
> 
> I try to compare the performances of several parameters to diagnose 
> lameness in dogs.
> I have several ROC curves from the same dataset.
> I plotted the ROC curves and calculated AUC with the ROCR package.
> 
> I would like to compare the AUC.
> I used the following program I found on R-help archives :
>  
> From: Bernardo Rangel Tura
> Date: Thu 16 Dec 2004 - 07:30:37 EST
> 
> seROC<-function(AUC,na,nn){
> a<-AUC
> q1<-a/(2-a)
> q2<-(2*a^2)/(1+a)
> se<-sqrt((a*(1-a)+(na-1)*(q1-a^2)+(nn-1)*(q2-a^2))/(nn*na))
> se
> }
> 
> cROC<-function(AUC1,na1,nn1,AUC2,na2,nn2,r){
> se1<-seROC(AUC1,na1,nn1)
> se2<-seROC(AUC2,na2,nn2)
> 
> sed<-sqrt(se1^2+se2^2-2*r*se1*se2)
> zad<-(AUC1-AUC2)/sed
> p<-dnorm(zad)
> a<-list(zad,p)
> a
> }
> 
> The author of this script says: "The first function (seROC) calculate the
> standard error of ROC curve, the 
> second function (cROC) compare ROC curves."
> 
> What do you think of this script?
> Is there any function to do it better in ROCR?
> 
> Any help would be greatly appreciated. 
> 
> Laurent Fanchon
> DVM, MS
> Ecole Nationale Vétérinaire d'Alfort
> FRANCE
> 
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-- 
Frank E Harrell Jr   Professor and Chair           School of Medicine
                      Department of Biostatistics   Vanderbilt University