# pROC-package

##### pROC

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.

##### 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.

##### Citation

If you use pROC in published research, please cite the following paper:

Xavier Robin, Natacha Turck, Alexandre Hainard, Natalia Tiberti,
Fr<U+00E9>d<U+00E9>rique Lisacek, Jean-Charles Sanchez and Markus M<U+00FC>ller (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 <pROC-cran@xavier.robin.name> 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 |

`ggroc` |
Plot a ROC curve with ggplot2 |

`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 |

`power.roc.test` |
Sample size and power computation |

`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)

##### Experimental: pipelines

Since version 1.15.0, the `roc`

function can be used in pipelines, for instance with dplyr or magrittr. This is still a highly experimental feature and will change significantly in future versions (see issue 54).
The `roc.data.frame`

method supports both standard and non-standard evaluation (NSE), and the `roc_`

function supports standard evaluation only.

library(dplyr) aSAH %>% filter(gender == "Female") %>% roc(outcome, s100b)

By default it returns the `roc`

object, which can then be piped to
the `coords`

function to extract coordinates that can be used
in further pipelines.

aSAH %>% filter(gender == "Female") %>% roc(outcome, s100b) %>% coords(transpose=FALSE) %>% filter(sensitivity > 0.6, specificity > 0.6)

More details and use cases are available in the `roc`

help page.

##### 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`

In Windows, a

`winProgressBar`

bar.In Windows, a

`winProgressBar`

bar.In other systems with or 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

### Algorithms

Over the years, a significant amount of time has been invested in making pROC run faster and faster.
From the naive algorithm iterating over all thresholds implemented in the first version (`algorithm = 1`

), we went to a
C++ implementation (with Rcpp, `algorithm = 3`

), and a different algorithm using cummulative sum of responses sorted
by the predictor, which scales only with the number of data points, independently on the number of thresholds (`algorithm = 2`

).
The curves themselves are identical, but computation time has been decreased massively.

Since version 1.12, pROC was able to automatically select the fastest algorithm for your dataset based on the number of thresholds of the ROC curve.
Initially this number was around 1500 thresholds, above which algorithm 3 was selected. But with pROC 1.15 additional code profiling
enabled us implement additional speedups that brought this number down to less than 100 thresholds.
As the detection of the number of thresholds itself can have a large impact comparatively (up to 10% now), a new `algorithm = 6`

was implemented, which assumes that `ordered`

datasets should have relatively few levels, and hence thresholds. These predictors
are processed with `algorithm = 3`

. Any numeric dataset is now assumed to have a sufficient number of thresholds
to be processed with `algorithm = 2`

efficiently. In the off-chance that you have a very large numeric dataset with very few thresholds,
`algorithm = 3`

can be selected manually (in the call to `roc`

). For instance with 5 thresholds you can
expect a speedup of around to 3 times. This effect disappears altogether as soon as the curve gets to 50-100 thresholds.

This simple selection should work in most cases. However if you are unsure or want to test it for yourself, use `algorithm=0`

to run a quick benchmark 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 (!requireNamespace("microbenchmark")) install.packages("microbenchmark")

# First a ROC curve with many thresholds. Algorithm 2 is much faster. response <- rbinom(5E3, 1, .5) predictor <- rnorm(5E3) rocobj <- roc(response, predictor, algorithm = 0)

# Next a ROC curve with few thresholds but more data points response <- rbinom(1E6, 1, .5) predictor <- rpois(1E6, 1) rocobj <- roc(response, predictor, algorithm = 0)

Other functions have been optimized too, and bottlenecks removed. In particular, the `coords`

function is orders of magnitude faster in pROC 1.15.
The DeLong algorithm has been improved in versions 1.6, 1.7 and 1.9.1, and currently uses a much more efficient algorithm, both
in computation time and memory footprint. We will keep working on improvements to make pROC more suited to large datasets in the future.

### 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)). Since version 1.9, pROC uses the algorithm proposed by Sun and Xu (2014) which has an O(N log N) complexity and is always faster than bootstrapping. By default, pROC will choose the DeLong method whenever possible.

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

##### 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.

Xu Sun and Weichao Xu (2014) ``Fast Implementation of DeLongs Algorithm for Comparing
the Areas Under Correlated Receiver Operating Characteristic Curves''. *IEEE Signal
Processing Letters*, **21**, 1389--1393.
DOI: 10.1109/LSP.2014.2337313.

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

```
# NOT RUN {
data(aSAH)
## Build a ROC object and compute the AUC ##
roc1 <- roc(aSAH$outcome, aSAH$s100b)
print(roc1)
# With a formula
roc(outcome ~ s100b, aSAH)
# With pipes, dplyr-style:
# }
# NOT RUN {
library(dplyr)
aSAH %>% roc(outcome, s100b)
# }
# NOT RUN {
# Create a few more curves for the next examples
roc2 <- roc(aSAH$outcome, aSAH$wfns)
roc3 <- roc(aSAH$outcome, aSAH$ndka)
## AUC ##
auc(roc1, partial.auc = c(1, .9))
## Smooth ROC curve ##
smooth(roc1)
## Summary statistics
var(roc1)
cov(roc1, roc3)
## Plot the curve ##
plot(roc1)
# More plotting options, CI and plotting
# with all-in-one syntax:
roc4 <- 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!
roc5 <- roc(aSAH$outcome, aSAH$wfns,
plot=TRUE, add=TRUE, percent=roc4$percent)
## With ggplot2 ##
library(ggplot2)
# Create multiple curves to plot
rocs <- roc(outcome ~ wfns + s100b + ndka, data = aSAH)
ggroc(rocs)
## 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")
# }
# NOT RUN {
# need to re-add roc2 over the shape
plot(roc2, add=TRUE)
# }
# NOT RUN {
# CI of thresholds
plot(ci.thresholds(roc2))
# }
# NOT RUN {
# In parallel
if (require(doParallel)) {
registerDoParallel(cl <- makeCluster(getOption("mc.cores", 2L)))
# }
# NOT RUN {
ci(roc2, method="bootstrap", parallel=TRUE)
# }
# NOT RUN {
# }
# NOT RUN {
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)
# }
# NOT RUN {
## Power & sample size ##
# Power
# 1 curve
power.roc.test(roc1)
# 2 curves
power.roc.test(roc3, roc2)
# Sample size
# 1 curve
power.roc.test(roc3, power = 0.9)
# 2 curves
power.roc.test(roc1, roc2, power = 0.9)
# Also without ROC objects.
# For instance what AUC would be significantly different from 0.5?
power.roc.test(ncases=41, ncontrols=72, sig.level=0.05, power=0.95)
# }
```

*Documentation reproduced from package pROC, version 1.16.2, License: GPL (>= 3)*