# ci.auc

##### Compute the confidence interval of the AUC

This function computes the confidence interval (CI) of an area under the curve (AUC). By default, the 95% CI is computed with 2000 stratified bootstrap replicates.

- Keywords
- utilities, nonparametric, univar, ROC

##### Usage

```
# ci.auc(...)
# S3 method for roc
ci.auc(roc, conf.level=0.95, method=c("delong",
"bootstrap"), boot.n = 2000, boot.stratified = TRUE, reuse.auc=TRUE,
progress = getOption("pROCProgress")$name, parallel=FALSE, ...)
# S3 method for smooth.roc
ci.auc(smooth.roc, conf.level=0.95, boot.n=2000,
boot.stratified=TRUE, reuse.auc=TRUE,
progress=getOption("pROCProgress")$name, parallel=FALSE, ...)
# S3 method for auc
ci.auc(auc, ...)
# S3 method for multiclass.roc
ci.auc(multiclass.roc, ...)
# S3 method for multiclass.auc
ci.auc(multiclass.auc, ...)
# S3 method for auc
ci.auc(auc, ...)
# S3 method for formula
ci.auc(formula, data, ...)
# S3 method for default
ci.auc(response, predictor, ...)
```

##### Arguments

- roc, smooth.roc
a “roc” object from the

`roc`

function, or a “smooth.roc” object from the`smooth`

function.- auc
an “auc” object from the

`auc`

function.- multiclass.roc, multiclass.auc
not implemented.

- response, predictor
arguments for the

`roc`

function.- formula, data
a formula (and possibly a data object) of type response~predictor for the

`roc`

function.- conf.level
the width of the confidence interval as [0,1], never in percent. Default: 0.95, resulting in a 95% CI.

- method
the method to use, either “delong” or “bootstrap”. The first letter is sufficient. If omitted, the appropriate method is selected as explained in details.

- boot.n
the number of bootstrap replicates. Default: 2000.

- boot.stratified
should the bootstrap be stratified (default, same number of cases/controls in each replicate than in the original sample) or not.

- reuse.auc
if

`TRUE`

(default) and the “roc” object contains an “auc” field, re-use these specifications for the test. If false, use optional`…`

arguments to`auc`

. See details.- progress
the name of progress bar to display. Typically “none”, “win”, “tk” or “text” (see the

`name`

argument to`create_progress_bar`

for more information), but a list as returned by`create_progress_bar`

is also accepted. See also the “Progress bars” section of this package's documentation.- parallel
if TRUE, the bootstrap is processed in parallel, using parallel backend provided by plyr (foreach).

- …
further arguments passed to or from other methods, especially arguments for

`roc`

and`roc.test.roc`

when calling`roc.test.default`

or`roc.test.formula`

. Arguments for`auc`

and`txtProgressBar`

(only`char`

and`style`

) if applicable.

##### Details

This function computes the CI of an AUC. Two methods are available:
“delong” and “bootstrap” with the parameters defined in “roc$auc” to
compute a CI. When it is called with two vectors (response, predictor)
or a formula (response~predictor) arguments, the `roc`

function is called to build the ROC curve first.

The default is to use
“delong” method except for comparison of partial AUC and smoothed
curves, where `bootstrap`

is used. Using “delong” for
partial AUC and smoothed ROCs is not supported.

With `method="bootstrap"`

, the function calls `auc`

`boot.n`

times. For more details about the bootstrap, see the Bootstrap section in
this package's documentation.

For smoothed ROC curves, smoothing is performed again at each
bootstrap replicate with the parameters originally provided.
If a density smoothing was performed with user-provided
`density.cases`

or `density.controls`

the bootstrap cannot
be performed and an error is issued.

With `method="delong"`

, the variance of the AUC is computed as
defined by DeLong *et al.* (1988) using the algorithm by Sun and Xu (2014)
and the CI is deduced with `qnorm`

.

CI of multiclass ROC curves and AUC is not implemented yet. Attempting to call these methods returns an error.

##### Value

A numeric vector of length 3 and class “ci.auc”, “ci” and “numeric” (in this order), with the lower bound, the median and the upper bound of the CI, and the following attributes:

the width of the CI, in fraction.

the method employed.

the number of bootstrap replicates.

whether or not the bootstrapping was stratified.

an object of class “auc” stored for reference about the compued AUC details (partial, percent, ...)

The aucs item is not included in this list since version 1.2 for consistency reasons.

##### AUC specification

The comparison of the CI needs a specification of the AUC. This allows to compute the CI for full or partial AUCs. The specification is defined by:

the “auc” field in the “roc” object if

`reuse.auc`

is set to`TRUE`

(default). It is naturally inherited from any call to`roc`

and fits most cases.passing the specification to

`auc`

with … (arguments`partial.auc`

,`partial.auc.correct`

and`partial.auc.focus`

). In this case, you must ensure either that the`roc`

object do not contain an`auc`

field (if you called`roc`

with`auc=FALSE`

), or set`reuse.auc=FALSE`

.

If `reuse.auc=FALSE`

the `auc`

function will always
be called with `…`

to determine the specification, even if
the “roc” object do contain an `auc`

field.

As well if the “roc” object do not contain an `auc`

field, the `auc`

function will always be called with
`…`

to determine the specification.

Warning: if the roc object passed to ci contains an `auc`

field and `reuse.auc=TRUE`

, auc is not called and
arguments such as `partial.auc`

are silently ignored.

##### Warnings

If `method="delong"`

and the AUC specification specifies a
partial AUC, the warning “Using DeLong's test for partial AUC is
not supported. Using bootstrap test instead.” is issued. The
`method`

argument is ignored and “bootstrap” is used
instead.

If `boot.stratified=FALSE`

and the sample has a large imbalance between
cases and controls, it could happen that one or more of the replicates
contains no case or control observation, or that there are not enough
points for smoothing, producing a `NA`

area.
The warning “NA value(s) produced during bootstrap were ignored.”
will be issued and the observation will be ignored. If you have a large
imbalance in your sample, it could be safer to keep
`boot.stratified=TRUE`

.

##### Errors

If `density.cases`

and `density.controls`

were provided
for smoothing, the error “Cannot compute the statistic on ROC
curves smoothed with density.controls and density.cases.” is issued.

##### 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.

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.

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

##### Examples

```
# NOT RUN {
# Create a ROC curve:
data(aSAH)
roc1 <- roc(aSAH$outcome, aSAH$s100b)
## Basic example ##
ci.auc(roc1)
# You can also write:
ci(roc1)
ci(auc(roc1))
## More options ##
# Partial AUC and customized bootstrap:
# }
# NOT RUN {
ci.auc(roc1,
conf.level=0.9,
partial.auc=c(1, .8), partial.auc.focus="se", partial.auc.correct=TRUE,
boot.n=10000, stratified=FALSE)
# }
# NOT RUN {
# Note that the following will NOT give a CI of the partial AUC:
# }
# NOT RUN {
ci.auc(roc1,
partial.auc=c(1, .8), partial.auc.focus="se", partial.auc.correct=FALSE)
# }
# NOT RUN {
# This is because rocobj$auc is not a partial AUC and reuse.auc = TRUE by default.
# You can overcome this problem by passing an AUC instead:
auc1 <- auc(roc1, partial.auc=c(1, .8), partial.auc.focus="se",
partial.auc.correct=FALSE)
# }
# NOT RUN {
ci.auc(auc1)
# }
# NOT RUN {
## On smoothed ROC curves with bootstrap ##
# }
# NOT RUN {
ci.auc(smooth(roc1, method="density"))
# }
```

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