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*) - Preprint: https://biostats.bepress.com/ucbbiostat/paper304

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")`

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 v^{th} 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 v^{th} 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
```

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