除了Logistic回归能够计算预测值与真实值的综合一致程度，也即AUC外，生存分析同样能计算AUC。但生存分析假设不同，生存函数的构建也就不尽相同。因而，不同方法计算得到的生存资料的AUC也不尽相同。同时，生存函数ROC曲线的绘制也更加复杂。下面提供几种常用的基于R计算生存资料AUC的方法，并提供两种时间依赖的生存函数的AUC计算示例。

但目前来说，还没有方法可以直接比较两个生存函数的AUC是否存在显著的统计学差异。

install.packages(c("clinfun","CPE","risksetROC", "timeROC",

                   "survivalROC","survC1","survIDINRI"))



library(survival)



set.seed(666)

age <- rnorm(400, 50, 10)

bp  <- rnorm(400,120, 15)

d.time <- rexp(400)

cens   <- runif(400,.5,2)

death  <- d.time <= cens

d.time <- pmin(d.time, cens)



fit <- coxph(Surv(d.time,death) ~ age + bp)

summary(fit) 

# Concordance = 0.502  (se = 0.019 ) 



# Compute the concordance between a right-censored 

# survival time and a single continuous covariate

survConcordance(Surv(d.time,death) ~ predict(fit))

# Concordance = 0.502101  (se = 0.01883032 )

# Concordance = concordant/(concordant+discordant)



library(Hmisc)

# Computes the c index and the corresponding generalization of 

# Somers' Dxy rank correlation for a censored response variable.

rcorrcens(Surv(d.time,death) ~ predict(fit))

# C index: 1 - 0.498 = 0.502 

# C index = (1+aDxy)/2 = (1+0.004)/2 = 0.502



library(risksetROC)

tmax <- max(d.time)

# Create and plot AUC based on incident/dynamic definition of Heagerty

AUC <- risksetAUC(Stime=d.time, status=death,

                  marker=age + bp, method="Cox", tmax=tmax)

AUC$Cindex

# 0.5020833



library(clinfun)

# Calculate Gonen & Heller concordance probability estimate (CPE) for 

# for the Cox proportional hazards model.

coxphCPE(fit)

# CPE= 0.50884256, se.CPE = 0.01678487 



library(CPE)

# Calculate Gonen & Heller concordance probability estimate (CPE) 

# for the Cox proportional hazards model.

phcpe(fit, CPE.SE=TRUE,out.ties=TRUE)

# CPE= 0.5088426, se.CPE = 0.01678487 





library(survivalROC)

# Time-dependent ROC curve estimation from censored survival data

AUC2 <- survivalROC(Stime=d.time, status=death,     

                    marker = eta,     

                    predict.time =  265, method="KM")

AUC2$AUC

# 0.6124465 

plot(AUC2$FP, 

     AUC2$TP, 

     type="l", 

     xlim=c(0,1), ylim=c(0,1),   

     xlab=paste( "FP", "\n", "AUC = ",round(AUC2$AUC,3)), 

     ylab="TP",main="AUC2, Method = KM \n Year = 1")

abline(0,1)



library(timeROC)

# Time-dependent ROC curve estimation

ROC<-timeROC(T=d.time,

             delta=death,

             marker=eta,

             other_markers=as.matrix(bp),

             cause=1,

             weighting="marginal",

             times=quantile(d.time,probs=seq(0.2,0.8,0.1)),

             ROC = TRUE,

             iid = TRUE)

ROC

confint(ROC)