Code to reproduce https://mbq.me/blog/augh-roc

auroc.R

#AUROC calculation code
auroc<-function(score,cls){
 n1<-sum(!cls); sum(cls)->n2;
 U<-sum(rank(score)[!cls])-n1*(n1+1)/2;
 return(1-U/n1/n2);
}

#... as a cryptic one-liner
auroc1l<-function(score,cls)
 mean(rank(score)[cls]-1:sum(cls))/sum(!cls)

#... caTools-like version
colAuroc<-function(score,cls)
 colMeans(apply(score,2,rank)[cls,]-1:sum(cls))/sum(!cls)

#AUROC significance
pAuroc<-function(auroc,nx,ny){
 W<-round((1-auroc)*nx*ny);
 pwilcox(W,nx,ny)
}

#Minimal significant AUROC (p=p), for a given nx, ny
qAuroc<-function(nx,ny,p=.05){
 ca<-1-(qwilcox(p,nx,ny)-1)/nx/ny
 #Even AUROC=1 won't be significant
 ca[!is.finite(ca)]<-NaN;
 ca[ca>1]<-NaN;
 ca
}

plot-sig-auroc-space.R

source('auroc.R')
library(gpclib)

mergeSeries<-function(s){
 if(length(s)<2) return(s);
 ans<-as(s[[1]],"gpc.poly");s[-1]->s;
 for(ss in s) ans<-union(ans,as(ss,"gpc.poly"))
 return(ans@pts)
}

optimiseRects<-function(xmin,ymin,xmax,ymax,cls){
 lapply(1:length(xmin),function(i)
  cbind(
   c(xmin[i],xmax[i],xmax[i],xmin[i]),
   c(ymin[i],ymin[i],ymax[i],ymax[i])
  ))->polys;
 lapply(split(polys,cls),mergeSeries)
}

makePlot<-function(maxN=110,maxNt=21){
 do.call(rbind,lapply(c(7:maxN),function(N){
  M<-1:floor(N/2);
  qAuroc(N-M,M)->ca;
  data.frame(
   N=N,
   fra=M/N,
   fram=(M-1/2)/N,
   frap=(M+1/2)/N,
   ca=ca)[is.finite(ca),];
 }))->QQ;

 QQ$aurocClass<-cut(QQ$ca,c(.5,.55,.6,.65,.7,.75,.8,.85,.9,.95,1,Inf),right=FALSE)
 QQ$aurocClass<-factor(QQ$aurocClass);
 acl<-levels(QQ$aurocClass);
 cc<-rev(
  c("#000000","#00ccff","#00d4aa","#80ff80","#ffcc00","#ff7f2a","#ff2a2a",
    "#d40000","#5500d4","#b380ff","#ff00cc"));

 plot(.2,1,type='n',
  xlim=c(0,.55),ylim=c(7,maxN),
  log="y",
  xlab="Fraction of the smaller class",
  ylab="Number of objects",
  main="Minimal AUROC significant at p=.05");
 abline(v=(1:10)/20);
 abline(h=7:maxNt)
 optimiseRects(QQ$fram,QQ$N-.5,QQ$frap,QQ$N+.5,QQ$aurocClass)->polys;
 lapply(names(polys),function(pn)
  lapply(polys[[pn]],polygon,col=cc[which(acl==pn)]));
 QQ[QQ$N<=maxNt,]->QQ;
 legend("bottomleft",fill=cc,acl,bg="white")
}