discSurv (version 1.1.2)

aucUno: Area under the Curve Estimation

Description

Estimates the time dependent area under the curve given calculated true positive rate and false positive rate. Both objects ("tprObj", "fprObj") and must have identical input arguments, e. g. same relationship of discrete response and covariates and supplied data sources. The values should be above 0.5 for a well predicting model, because random guessing would get this score.

Usage

aucUno(tprObj, fprObj)

Arguments

tprObj

Object of class "discSurvTprUno". See function tprUno

fprObj

Object of class "discSurvFprUno". See function fprUno

Value

• • Output:
  {A list with objects:}
  • Output:
  {Named numeric vector with auc value}
• Input:
• {A list of given argument input values (saved for reference)}

Details

The auc is estimated by numerical integration of the ROC curve.

References

Hajime Uno and Tianxi Cai and Lu Tian and L. J. Wei, (2007), Evaluating Prediction Rules for t-Year Survivors With Censored Regression Models, Journal of the American Statistical Association Patrick J. Heagerty and Yingye Zheng, (2005), Survival Model Predictive Accuracy and ROC Curves, Biometrics 61, 92-105

See Also

tprUno, fprUno

Examples

#####################################################
# Example with cross validation and unemployment data 

library(Ecdat)
library(caret)
data(UnempDur)
summary(UnempDur$spell)

# Extract subset of data
set.seed(635)
IDsample <- sample(1:dim(UnempDur)[1], 100)
UnempDurSubset <- UnempDur [IDsample, ]
head(UnempDurSubset)
range(UnempDurSubset$spell)
set.seed(7550)
CVfolds <- createFolds (y=UnempDurSubset$spell, returnTrain=TRUE, k=2)

# Estimate true positive rate of time interval 7: 
# Correspondes to three and a half month duration (each interval is of length two weeks)
tryTPR <- tprUno (timepoint=7, dataSet=UnempDurSubset, trainIndices=CVfolds, 
survModelFormula=spell ~ age + logwage, censModelFormula=censor1 ~ 1, 
linkFunc="logit", idColumn=NULL)
tryTPR
plot(tryTPR)

# Estimate false positive rate of time interval 7:
tryFPR <- fprUno (timepoint=7, dataSet=UnempDurSubset, trainIndices=CVfolds,  
survModelFormula=spell ~ age + logwage, censModelFormula=censor1 ~ 1, 
linkFunc="logit", idColumn=NULL)
tryFPR
plot(tryFPR)

# Estimate auc
tryAUC <- aucUno (tprObj=tryTPR, fprObj=tryFPR)
tryAUC
plot(tryAUC)

#####################################
# Example National Wilm's Tumor Study

library(survival)
head(nwtco)
summary(nwtco$rel)

# Select subset
set.seed(-375)
Indices <- sample(1:dim(nwtco)[1], 500)
nwtcoSub <- nwtco [Indices, ]

# Convert time range to 30 intervals
intLim <- quantile(nwtcoSub$edrel, prob=seq(0, 1, length.out=30))
intLim [length(intLim)] <- intLim [length(intLim)] + 1
nwtcoSubTemp <- contToDisc(dataSet=nwtcoSub, timeColumn="edrel", intervalLimits=intLim)
nwtcoSubTemp$instit <- factor(nwtcoSubTemp$instit)
nwtcoSubTemp$histol <- factor(nwtcoSubTemp$histol)
nwtcoSubTemp$stage <- factor(nwtcoSubTemp$stage)

# Split in training and test sample
set.seed(-570)
TrainingSample <- sample(1:dim(nwtcoSubTemp)[1], round(dim(nwtcoSubTemp)[1]*0.75))
nwtcoSubTempTrain <- nwtcoSubTemp [TrainingSample, ]
nwtcoSubTempTest <- nwtcoSubTemp [-TrainingSample, ]

# Convert to long format
nwtcoSubTempTrainLong <- dataLong(dataSet=nwtcoSubTempTrain, timeColumn="timeDisc", 
censColumn="rel")

# Estimate glm
inputFormula <- y ~ timeInt + histol + instit + stage
glmFit <- glm(formula=inputFormula, data=nwtcoSubTempTrainLong, family=binomial())
linPreds <- predict(glmFit, newdata=cbind(nwtcoSubTempTest, 
timeInt=nwtcoSubTempTest$timeDisc))

# Estimate tpr given one training and one test sample at time interval 5
tprFit <- tprUnoShort (timepoint=5, marker=linPreds, 
newTime=nwtcoSubTempTest$timeDisc, newEvent=nwtcoSubTempTest$rel, 
trainTime=nwtcoSubTempTrain$timeDisc, trainEvent=nwtcoSubTempTrain$rel)

# Estimate fpr given one training and one test sample at time interval 5
fprFit <- fprUnoShort (timepoint=5, marker=linPreds, 
newTime=nwtcoSubTempTest$timeDisc)

# Estimate auc
tryAUC <- aucUno (tprObj=tprFit, fprObj=fprFit)
tryAUC
plot(tryAUC)