plotAUC.s {longROC}

AUC as a function of time

Description

Compute area under the ROC curve for several values of the time horizon

Usage

plotAUC.s(X,etime,status,u=NULL,tt,s,vtimes,fc=NULL,plot=TRUE)

Arguments

X

n by S matrix of longitudinal score/biomarker for i-th subject at j-th occasion (NA if unmeasured)

etime

n vector with follow-up times

status

n vector with event indicators

u

Lower limit for evaluation of sensitivity and specificity. Defaults to vtimes[s] (see below)

tt

A vector of upper limits (time-horizons) for evaluation of sensitivity and specificity.

s

n vector of measurements/visits to use for each subject. all(s<=S)

vtimes

S vector with visit times

fc

Events are defined as fc = 1. Defaults to $I(cup X(t_j)>cutoff)$

plot

Do we plot the AUCs? Defaults to TRUE

Details

Area under the ROC curve is computed for each value of the vector tt. The resulting vector is returned. If plot=TRUE (which is the default) also a plot of tt vs AUC is displayed.

Value

A vector with AUCs

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.s, butstrap.s, auc

Examples

# parameters
n=25
tt=3
Tmax=10
u=1.5
s=sample(3,n,replace=TRUE)
vtimes=c(0,1,2,5)

# generate data 

ngrid=1000
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 

aucs=plotAUC.s(S2,Ti,delta,u,seq(2,5,length=5),s,vtimes)