maxauc.s {longROC}

Optimal Score

Description

Compute optimal score for AUC

Usage

maxauc.s(X,etime,status,u=NULL,tt,s,vtimes,fc=NULL)

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 max(vtimes[s]) (see below)

tt

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

s

n vector of number 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 $I(cup X(t_j)>cutoff)$

Details

This function can be used to find an optimal linear combination of p scores/biomarkers repeatedly measured over time. The resulting score is optimal as it maximizes the AUC among all possible linear combinations. The first biomarker in array X plays a special role, as by default its coefficient is unitary.

Value

A list with the following elements:

beta	Beta coefficients for the optimal score
score	Optimal score

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

auc, butstrap, maxauc

Examples

# parameters
n=20
tt=3
Tmax=10
u=1.5
s=sample(3,n,replace=TRUE)
vtimes=c(0,1,2,5)

# generate data 

ngrid=500
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]

## 

X=array(NA,c(2,nrow(S1),ncol(S1)))
X[1,,]=round(S2) #fewer different values, quicker computation 
X[2,,]=S1

sc=maxauc.s(X,Ti,delta,u,tt,s,vtimes)

# beta coefficients

sc$beta

# final score (X[1,,]+X[2,,]*sc$beta[1]+...+X[p,,]*sc$beta[p-1])

sc$score