IntegrateAUC {risksetROC}

Incident/Dynamic (I/D) ROC curve, AUC and integrated AUC (iAUC) estimation of censored survival data

Description

This function integrates AUC using weights w(t) = 2*f(t)*S(t) as discussed in Heagerty and Zheng, 2005.

Usage

IntegrateAUC(AUC, utimes, St, tmax, weight="rescale")

Arguments

AUC

Area under ROC curve at utimes

utimes

Unique event times for subjects

St

Estimated survival probability at utimes

tmax

Maximum time length to be considered

weight

Either of "rescale" or "conditional"

Details

This function estimates time-dependent concordance measure

P(M_i>M_j|T_i<t, T_i<tmax, T_j>t)

as discussed in the paper from AUC and weights derived from the survival time distribution. The concordance measure is estimated under the assumption that smaller of the two event times happened before time tmax. The resulting measure is an weighted sum of estimated AUC at each unique failure time where weights are proportional to 2*f(t)*S(t), and T is failure time of interest. If weight="rescale", then the weights are rescaled so that the sum of the weights is one. If weight="conditional", it is assumed that both the events happened before tmax.

Value

Returns the following item:

iAUC

Integrated AUC using w(t) as above as weights

Author(s)

Patrick J. Heagerty

References

Heagerty, P.J., Zheng Y. (2005) Survival Model Predictive Accuracy and ROC curves Biometrics, 61, 92 – 105

Examples

library(MASS)
data(VA)
survival.time <- VA$stime
survival.status <- VA$status
score <- VA$Karn
cell.type <- factor(VA$cell )
tx <- as.integer( VA$treat==1 )
age <- VA$age
survival.status[VA$stime > 500 ] <- 0
survival.time[VA$stime > 500 ] <- 500
library(survival)
## first find the estimated survival probabilities at unique failure times
surv.prob <- unique(survfit(Surv(survival.time,survival.status)~1)$surv)
fit0 <- coxph( Surv(survival.time,survival.status)
        ~ score + cell.type + tx + age, na.action=na.omit )
eta <- fit0$linear.predictor
model.score <- eta

utimes <- unique( survival.time[ survival.status == 1 ] )
utimes <- utimes[ order(utimes) ]

## find AUC at unique failure times
AUC <- rep( NA, length(utimes) )
for( j in 1:length(utimes) )
{
out <- CoxWeights( eta, survival.time, survival.status,utimes[j])
AUC[j] <- out$AUC
}
## integrated AUC to get concordance measure
iAUC <- IntegrateAUC( AUC, utimes, surv.prob, tmax=365 )