auc {longROC}

AUC

Description

Compute area under the ROC curve

Usage

auc(ss) 

Arguments

ss

Matrix with two columns (1-specificities, sensitivities). It can be simply the output of roc function

Details

Area under the ROC curve.

Value

A scalar with the AUC.

Author(s)

Alessio Farcomeni [e-mail]

References

Barbati, G. and Farcomeni, A. (2017) Prognostic assessment of repeatedly measured time-dependent biomarkers, with application to dilated cardiomuopathy, Statistical Methods & Applications, in press

See Also

roc, butstrap, maxauc

Examples

# parameters
n=100
tt=3
Tmax=10
u=1.5
s=2
vtimes=c(0,1,2,5)

# generate data 

ngrid=5000
ts=seq(0,Tmax,length=ngrid)
X2=matrix(rnorm(n*ngrid,0,0.1),n,ngrid)
for(i in 1:n) {
sa=sample(ngrid/6,1)
vals=sample(3,1)-1
X2[i,1:sa[1]]=vals[1]+X2[i,1:sa[1]]
X2[i,(sa[1]+1):ngrid]=vals[1]+sample(c(-2,2),1)+X2[i,(sa[1]+1):ngrid]
}

S1=matrix(sample(4,n,replace=TRUE),n,length(vtimes))
S2=matrix(NA,n,length(vtimes))

S2[,1]=X2[,1]

for(j in 2:length(vtimes)) {
tm=which.min(abs(ts-vtimes[j]))
S2[,j]=X2[,tm]}

cens=runif(n)
ripart=1-exp(-0.01*apply(exp(X2),1,cumsum)*ts/1:ngrid)

Ti=rep(NA,n)
for(i in 1:n) {
Ti[i]=ts[which.min(abs(ripart[,i]-cens[i]))]
}

cens=runif(n,0,Tmax*2)
delta=ifelse(cens>Ti,1,0)
Ti[cens<Ti]=cens[cens<Ti]

## 

## an important marker 

ro=roc(S2,Ti,delta,u,tt,s,vtimes) 
auc(ro)

## an unrelated marker 

ro=roc(S1,Ti,delta,u,tt,s,vtimes) 
auc(ro)