pROC (version 1.18.0)

# ci.auc: Compute the confidence interval of the AUC

## Description

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.

## 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.

## 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:

conf.level

the width of the CI, in fraction.

method

the method employed.

boot.n

the number of bootstrap replicates.

boot.stratified

whether or not the bootstrapping was stratified.

auc

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:

1. 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.

2. 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.

## 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.

## 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.

`roc`, `auc`, `ci`

## Examples

Run this code
```# 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"))
# }
```

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