pROC (version 1.8)

pROC-package: pROC

Description

Tools for visualizing, smoothing and comparing receiver operating characteristic (ROC curves). (Partial) area under the curve (AUC) can be compared with statistical tests based on U-statistics or bootstrap. Confidence intervals can be computed for (p)AUC or ROC curves. Sample size / power computation for one or two ROC curves are available.

Citation

If you use pROC in published research, please cite the following paper: Xavier Robin, Natacha Turck, Alexandre Hainard, Natalia Tiberti, Frédérique Lisacek, Jean-Charles Sanchez and Markus Müller (2011). ``pROC: an open-source package for R and S+ to analyze and compare ROC curves''. BMC Bioinformatics, 12, p. 77. DOI: 10.1186/1471-2105-12-77 Type citation("pROC") for a BibTeX entry. The authors would be glad to hear how pROC is employed. You are kindly encouraged to notify Xavier Robin about any work you publish.

Abbreviations

The following abbreviations are employed extensively in this package:

• ROC: receiver operating characteristic
• AUC: area under the ROC curve
• pAUC: partial area under the ROC curve
• CI: confidence interval
• SP: specificity
• SE: sensitivity

Functions

roc

Build a ROC curve

are.paired

Dertermine if two ROC curves are paired

auc

Compute the area under the ROC curve

ci

Compute confidence intervals of a ROC curve

ci.auc

Compute the CI of the AUC

ci.coords

Compute the CI of arbitrary coordinates

ci.se

Compute the CI of sensitivities at given specificities

ci.sp

Compute the CI of specificities at given sensitivities

ci.thresholds

Compute the CI of specificity and sensitivity of thresholds

ci.coords

Compute the CI of arbitrary coordinates

coords

Coordinates of the ROC curve

cov

Covariance between two AUCs

has.partial.auc

Determine if the ROC curve have a partial AUC

lines.roc

Add a ROC line to a ROC plot

plot.ci

Plot CIs

plot

Plot a ROC curve

print

Print a ROC curve object

roc.test

Compare the AUC of two ROC curves

smooth

Smooth a ROC curve

Dataset

This package comes with a dataset of 141 patients with aneurysmal subarachnoid hemorrhage: aSAH.

Installing and using

To install this package, make sure you are connected to the internet and issue the following command in the R prompt:

    install.packages("pROC")
  

To load the package in R:

    library(pROC)
  

Bootstrap

All the bootstrap operations for significance testing, confidence interval, variance and covariance computation are performed with non-parametric stratified or non-stratified resampling (according to the stratified argument) and with the percentile method, as described in Carpenter and Bithell (2000) sections 2.1 and 3.3. Stratification of bootstrap can be controlled with boot.stratified. In stratified bootstrap (the default), each replicate contains the same number of cases and controls than the original sample. Stratification is especially useful if one group has only little observations, or if groups are not balanced. The number of bootstrap replicates is controlled by boot.n. Higher numbers will give a more precise estimate of the significance tests and confidence intervals but take more time to compute. 2000 is recommanded by Carpenter and Bithell (2000) for confidence intervals. In our experience this is sufficient for a good estimation of the first significant digit only, so we recommend the use of 10000 bootstrap replicates to obtain a good estimate of the second significant digit whenever possible. Progress bars A progressbar shows the progress of bootstrap operations. It is handled by the plyr package (Wickham, 2011), and is created by the progress_* family of functions. Sensible defaults are guessed during the package loading:

• In non-interactive mode, no progressbar is displayed.
• In embedded GNU Emacs “ESS”, a txtProgressBar windows In Windows, a winProgressBar bar. unix In Windows, a winProgressBar bar.
• In other systems with a graphical display, a tkProgressBar.
• In systems without a graphical display, a txtProgressBar.

The default can be changed with the option “pROCProgress”. The option must be a list with a name item setting the type of progress bar (“none”, “win”, “tk” or “text”). Optional items of the list are “width”, “char” and “style”, corresponding to the arguments to the underlying progressbar functions. For example, to force a text progress bar:

options(pROCProgress = list(name = "text", width = NA, char = "=", style = 3)

To inhibit the progress bars completely:

options(pROCProgress = list(name = "none"))

Handling large datasets

Versions 1.6 and 1.7 of pROC focused on execution speed to handle large datasets. Let's say we have the following dataset with 100 thousands observations:

response <- round(runif(1E5))
predictor <- rnorm(1E5)
system.time(rocobj <- roc(response, predictor)) # Very slow!
  

Choosing an algorithm for roc By default, pROC uses an algorithm that linearly depends on the number of thresholds. An naive optimization is to reduce the precision of the predictor by generating ties in the data

system.time(rocobj <- roc(response, round(predictor))) # Faster - but losing precision
    

Since version 1.6, pROC contains an alternative algorithm with an overhead growing linearly as a function of the number of observations. Use the algorithm=2 arguments when calling roc.

system.time(rocobj <- roc(response, predictor, algorithm = 2)) # Better
    

When unsure about the fastest algorithm, use algorithm=0 to choose between 2 and 3. Make sure microbenchmark is installed. Beware, this is very slow as it will repeat the computation 10 times to obtain a decent estimate of each algorithm speed.

if (!require(microbenchmark))
  install.packages("microbenchmark")
rocobj <- roc(response, round(predictor), algorithm = 0)
rocobj <- roc(response, predictor, algorithm = 0) # Very slow!
    

Boostrap Bootstrap is typically slow because it involves repeatedly computing the ROC curve (or a part of it). Some bootstrap functions are faster than others. Typically, ci.thresholds is the fastest, and ci.coords the slowest. Use ci.coords only if the CI you need cannot be computed by the specialized CI functions ci.thresholds, ci.se and ci.sp. Note that ci.auc cannot be replaced anyway. A naive way to speed-up the boostrap is by removing the progress bar:

rocobj <- roc(response, round(predictor))
system.time(ci(rocobj))
system.time(ci(rocobj, progress = "none"))
    

It is of course possible to reduce the number of boostrap iterations. See the boot.n argument to ci. This will reduce the precision of the bootstrap estimate. Parallel processing Bootstrap operations can be performed in parallel. The backend provided by the plyr package is used, which in turn relies on the foreach package. To enable parallell processing, you first need to load an adaptor for the foreach package (doMC, doMPI, doParallel, doRedis, doRNG or doSNOW)), register the backend, and set parallel=TRUE.

library(doParallel)
registerDoParallel(cl <- makeCluster(getOption("mc.cores", 2)))
ci(rocobj, method="bootstrap", parallel=TRUE)
stopCluster(cl)
  		

Progress bars are not available when parallel processing is enabled. Using DeLong instead of boostrap DeLong is an asymptotically exact method to evaluate the uncertainty of an AUC (DeLong et al. (1988)) which is typically faster than boostrapping. By default, pROC will choose the DeLong method whenever possible. Since version 1.7, pROC does not allocate an m * n matrix (with m = number of controls and n = number of case observations) in all DeLong computations, so it is in practice nearly always faster than bootstrapping. However it still goes with O(m*n) so it might be slower than bootstrap in some very edge cases (i.e. when generating a roc curve with algorithm=3 that has a small number of thresholds but a large number of observations).

rocobj <- roc(response, round(predictor), algorithm=3)
system.time(ci(rocobj, method="delong"))
system.time(ci(rocobj, method="bootstrap", parallel = TRUE))
    

Details

The basic unit of the pROC package is the roc function. It will build a ROC curve, smooth it if requested (if smooth=TRUE), compute the AUC (if auc=TRUE), the confidence interval (CI) if requested (if ci=TRUE) and plot the curve if requested (if plot=TRUE).

The roc function will call smooth, auc, ci and plot as necessary. See these individual functions for the arguments that can be passed to them through roc. These function can be called separately.

Two paired (that is roc objects with the same response) or unpaired (with different response) ROC curves can be compared with the roc.test function.

References

James Carpenter and John Bithell (2000) ``Bootstrap condence intervals: when, which, what? A practical guide for medical statisticians''. Statistics in Medicine 19, 1141--1164. DOI: 10.1002/(SICI)1097-0258(20000515)19:9<1141::aid-sim479>3.0.CO;2-F.

Elisabeth R. DeLong, David M. DeLong and Daniel L. Clarke-Pearson (1988) ``Comparing the areas under two or more correlated receiver operating characteristic curves: a nonparametric approach''. Biometrics 44, 837--845.

Tom Fawcett (2006) ``An introduction to ROC analysis''. Pattern Recognition Letters 27, 861--874. DOI: 10.1016/j.patrec.2005.10.010. Xavier Robin, Natacha Turck, Alexandre Hainard, et al. (2011) ``pROC: an open-source package for R and S+ to analyze and compare ROC curves''. BMC Bioinformatics, 7, 77. DOI: 10.1186/1471-2105-12-77. Hadley Wickham (2011) ``The Split-Apply-Combine Strategy for Data Analysis''. Journal of Statistical Software, 40, 1--29. URL: www.jstatsoft.org/v40/i01.

See Also

CRAN packages ROCR, verification or Bioconductor's roc for ROC curves.

CRAN packages plyr, MASS and logcondens employed in this package.

Examples

data(aSAH)

# Build a ROC object and compute the AUC
roc(aSAH$outcome, aSAH$s100b)
roc(outcome ~ s100b, aSAH)

# Smooth ROC curve
roc(outcome ~ s100b, aSAH, smooth=TRUE)

# more options, CI and plotting
roc1 <- roc(aSAH$outcome,
            aSAH$s100b, percent=TRUE,
            # arguments for auc
            partial.auc=c(100, 90), partial.auc.correct=TRUE,
            partial.auc.focus="sens",
            # arguments for ci
            ci=TRUE, boot.n=100, ci.alpha=0.9, stratified=FALSE,
            # arguments for plot
            plot=TRUE, auc.polygon=TRUE, max.auc.polygon=TRUE, grid=TRUE,
            print.auc=TRUE, show.thres=TRUE)

# Add to an existing plot. Beware of 'percent' specification!
roc2 <- roc(aSAH$outcome, aSAH$wfns,
            plot=TRUE, add=TRUE, percent=roc1$percent)

## Coordinates of the curve ##
coords(roc1, "best", ret=c("threshold", "specificity", "1-npv"))
coords(roc2, "local maximas", ret=c("threshold", "sens", "spec", "ppv", "npv"))

## Confidence intervals ##

# CI of the AUC
ci(roc2)

## Not run: 
# # CI of the curve
# sens.ci <- ci.se(roc1, specificities=seq(0, 100, 5))
# plot(sens.ci, type="shape", col="lightblue")
# plot(sens.ci, type="bars")
# ## End(Not run)

# need to re-add roc2 over the shape
plot(roc2, add=TRUE)

## Not run: 
# # CI of thresholds
# plot(ci.thresholds(roc2))
# ## End(Not run)

# In parallel
if (require(doParallel)) {
    registerDoParallel(cl <- makeCluster(getOption("mc.cores", 2L)))
    ## Not run: ci(roc2, method="bootstrap", parallel=TRUE)
    
    stopCluster(cl)
}

## Comparisons ##

# Test on the whole AUC
roc.test(roc1, roc2, reuse.auc=FALSE)

## Not run: 
# # Test on a portion of the whole AUC
# roc.test(roc1, roc2, reuse.auc=FALSE, partial.auc=c(100, 90),
#          partial.auc.focus="se", partial.auc.correct=TRUE)
# 
# # With modified bootstrap parameters
# roc.test(roc1, roc2, reuse.auc=FALSE, partial.auc=c(100, 90),
#          partial.auc.correct=TRUE, boot.n=1000, boot.stratified=FALSE)
# ## End(Not run)