Compute the confidence interval of the AUC

This function computes the confidence interval (CI) of an area under the curve (AUC).

Usage

# ci.auc(...)
# S3 method for class 'roc'
ci.auc(roc, conf.level=0.95, method=c("delong",
"bootstrap"), boot.n = 2000, boot.stratified = TRUE, reuse.auc=TRUE,
progress = NULL, parallel=FALSE, ...)
# S3 method for class 'smooth.roc'
ci.auc(smooth.roc, conf.level=0.95, boot.n=2000,
boot.stratified=TRUE, reuse.auc=TRUE,
progress = NULL, parallel=FALSE, ...)
# S3 method for class 'auc'
ci.auc(auc, ...)
# S3 method for class 'multiclass.roc'
ci.auc(multiclass.roc, ...)
# S3 method for class 'multiclass.auc'
ci.auc(multiclass.auc, ...)
# S3 method for class 'auc'
ci.auc(auc, ...)
# S3 method for class 'formula'
ci.auc(formula, data, ...)
# Default S3 method
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: DEPRECATED. A value other than NULL will produce a warning. The argument will be removed in a future version.
parallel: DEPRECATED. A value other than FALSE will produce a warning. The argument will be removed in a future version.
...: 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 the “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.

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.

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.

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: 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: 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: 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: doi:10.18637/jss.v040.i01 .