butstrap.nri {longROC}

Bootstrapping NRI

Description

Boostrap the AUC for significance testing and confidence interval calculation

Usage

butstrap.nri(risk1,risk2,etime,status,u,tt,nri1,wh,B=1000)

Arguments

risk1

Baseline risk measurements

risk2

Enhanced risk measurements

etime

n vector with follow-up times

status

n vector with event indicators

u

Lower limit for evaluation of sensitivity and specificity

tt

Upper limit (time-horizon) for evaluation of sensitivity and specificity.

nri1

NRI for the original data set

wh

Which NRI to boostrap? wh=1 1/2NRI, wh=2 NRI for events, wh=3 NRI for non-events

B

Number of bootstrap replicates. Defaults to 1000

Details

This function can be used to resample the NRI. The resulting p-value is obtained after assumption that the resampled NRI is Gaussian. Non-parametric confidence interval is obtained as the 2.5 and 97.5 confidence interval is simply given by a Gaussian approximation.

Value

A list with the following elements:

p.value	(Parametric) p-value for H0: NRI=0
se	Standard deviation of the NRI replicates
ci.np	Non-parametric 95% confidence interval for NRI
ci.par	Parametric 95% confidence interval for NRI

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

nri

Examples

# parameters
n=25
tt=3
Tmax=10
u=1.5
s=2
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]

risk1=apply(S1[,1:s],1,sum)
risk1=(risk1-min(risk1))/(max(risk1)-min(risk1))
risk2=apply(S2[,1:s],1,sum)
risk2=(risk2-min(risk2))/(max(risk2)-min(risk2))
butstrap.nri(risk1,risk2,Ti,delta,u,tt,nri(risk1,risk2,Ti,delta,u,tt)$nri,wh=1,B=500)