# Incident/Dynamic (I/D) ROC curve, AUC and integrated AUC (iAUC) estimation of censored survival data This function integrates AUC using weights $w(t) = 2*f(t)*S(t)$ as discussed in Heagerty and Zheng, 2005. ```r 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 $$ P(M_i>M_j|T_it) $$ 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**. ## Returns Returns the following item: - **iAUC**: Integrated AUC using w(t) as above as weights ## References Heagerty, P.J., Zheng Y. (2005) Survival Model Predictive Accuracy and ROC curves **Biometrics**, 61 , 92 -- 105 ## Author(s) Patrick J. Heagerty ## Examples ```r 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 ) ```

IntegrateAUC function