# cvAUC v1.1.0

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## Cross-Validated Area Under the ROC Curve Confidence Intervals

This package contains various tools for working with and evaluating cross-validated area under the ROC curve (AUC) estimators. The primary functions of the package are ci.cvAUC and ci.pooled.cvAUC, which report cross-validated AUC and compute confidence intervals for cross-validated AUC estimates based on influence curves for i.i.d. and pooled repeated measures data, respectively. One benefit to using influence curve based confidence intervals is that they require much less computation time than bootstrapping methods. The utility functions, AUC and cvAUC, are simple wrappers for functions from the ROCR package.

# cvAUC

The cvAUC R package provides a computationally efficient means of estimating confidence intervals (or variance) of cross-validated Area Under the ROC Curve (AUC) estimates.

In binary classification problems, the AUC is commonly used to evaluate the performance of a prediction model. Often, it is combined with cross-validation in order to assess how the results will generalize to an independent data set. In order to evaluate the quality of an estimate for cross-validated AUC, we obtain an estimate of its variance.

For massive data sets, the process of generating a single performance estimate can be computationally expensive. Additionally, when using a complex prediction method, the process of cross-validating a predictive model on even a relatively small data set can still require a large amount of computation time. Thus, in many practical settings, the bootstrap is a computationally intractable approach to variance estimation. As an alternative to the bootstrap, a computationally efficient influence curve based approach to obtaining a variance estimate for cross-validated AUC can be used.

The primary functions of the package are ci.cvAUC and ci.pooled.cvAUC, which report cross-validated AUC and compute confidence intervals for cross-validated AUC estimates based on influence curves for i.i.d. and pooled repeated measures data, respectively. One benefit to using influence curve based confidence intervals is that they require much less computation time than bootstrapping methods. The utility functions, AUC and cvAUC, are simple wrappers for functions from the ROCR package.

Erin LeDell, Maya L. Petersen & Mark J. van der Laan, "Computationally Efficient Confidence Intervals for Cross-validated Area Under the ROC Curve Estimates." (In Review)

## Install cvAUC

You can install:

• the latest released version from CRAN with

install.packages("cvAUC")

• the latest development version from GitHub with

if (packageVersion("devtools") < 1.6) {
install.packages("devtools")
}
devtools::install_github("ledell/cvAUC")


## Using cvAUC

Here is a quick demo of how you can use the package. In this example we do the following:

• Load an i.i.d. data set with a binary outcome.
• We will use 10-fold cross-validation, so we need to divide the indices randomly into 10 folds. In this step, we stratify the folds by the outcome variable. Stratification is not necessary, but is commonly performed in order to create validation folds with similar distributions. This information is stored in a 10-element list called folds. Below, the function that creates the folds is called .cvFolds.
• For the vth iteration of the cross-validation (CV) process, fit a model on the training data (i.e. observations in folds {1,...,10}\v) and then using this saved fit, generate predicted values for the observations in the vth validation fold. The .doFit function below does this procedure. In this example, we the Random Forest algorithm.
• Next, this function is applied across all folds to generate predicted values for each validation fold.
• These predicted values is stored in vector called predictions.
• Lastly, we use the ci.cvAUC function to calculate CV AUC and to generate a 95% confidence interval for this CV AUC estimate.

First, we define a few utility functions:

.cvFolds <- function(Y, V){
# Create CV folds (stratify by outcome)
Y0 <- split(sample(which(Y==0)), rep(1:V, length=length(which(Y==0))))
Y1 <- split(sample(which(Y==1)), rep(1:V, length=length(which(Y==1))))
folds <- vector("list", length=V)
for (v in seq(V)) {folds[[v]] <- c(Y0[[v]], Y1[[v]])}
return(folds)
}

.doFit <- function(v, folds, train){
# Train & test a model; return predicted values on test samples
set.seed(v)
ycol <- which(names(train)==y)
params <- list(x = train[-folds[[v]],-ycol],
y = as.factor(train[-folds[[v]],ycol]),
xtest = train[folds[[v]],-ycol])
fit <- do.call(randomForest, params)
pred <- fit$test$votes[,2]
return(pred)
}


This function will execute the example:

iid_example <- function(train, y = "V1", V = 10, seed = 1) {

# Create folds
set.seed(seed)
folds <- .cvFolds(Y = train[,c(y)], V = V)

# Generate CV predicted values
cl <- makeCluster(detectCores())
registerDoParallel(cl)
predictions <- foreach(v = 1:V, .combine="c",
.packages=c("randomForest")) %dopar% .doFit(v, folds, train)
stopCluster(cl)
predictions[unlist(folds)] <- predictions

# Get CV AUC and 95% confidence interval
runtime <- system.time(res <- ci.cvAUC(predictions = predictions,
labels = train[,c(y)],
folds = folds,
confidence = 0.95))
print(runtime)
return(res)
}


Load a sample binary outcome training set into R:

train_csv <- "http://www.stat.berkeley.edu/~ledell/data/higgs_10k.csv"
train <- read.table(train_csv, sep=",")


Run the example:

library(randomForest)
library(doParallel)
library(cvAUC)

res <- iid_example(train = train, y = "V1", V = 10, seed = 1)
print(res)

# $cvAUC # [1] 0.7813759 # #$se
# [1] 0.004534395
#
# $ci # [1] 0.7724886 0.7902631 # #$confidence
# [1] 0.95


## cvAUC Performance

For the example above (10,000 observations), it took ~0.2 seconds to calculate the cross-validated AUC and the influence curve based confidence intervals. This was benchmarked on a 2.3 GHz Intel Core i7 processor using cvAUC package version 1.1.0.

For bigger (i.i.d.) training sets, here are a few rough benchmarks:

• 100,000 observations: ~0.5 seconds
• 1 million observations: ~13.0 seconds

## Functions in cvAUC

 Name Description AUC Area Under the ROC Curve ci.cvAUC Confidence Intervals for Cross-validated Area Under the ROC Curve (AUC) Estimates cvAUC Cross-validated Area Under the ROC Curve (AUC) cvAUC-package Cross-Validated Area Under the ROC Curve Confidence Intervals ci.pooled.cvAUC Confidence Intervals for Cross-validated Area Under the ROC Curve (AUC) Estimates for Pooled Repeated Measures Data admissions Data set: Simulated Admissions Data with Binary Outcome adherence Data set: Simulated Pooled Repeated Measures Data No Results!