pROC (version 1.4.3)

auc: Compute the area under the ROC curve

Description

This function computes the numeric value of area under the ROC curve (AUC) with the trapezoidal rule. Two syntaxes are possible: one object of class roc, or either two vectors (response, predictor) or a formula (response~predictor) as in the roc function. By default, the total AUC is computed, but a portion of the ROC curve can be specified with partial.auc.

Usage

auc(...)
## S3 method for class 'roc':
auc(roc, partial.auc=FALSE, partial.auc.focus=c("specificity",
"sensitivity"), partial.auc.correct=FALSE, ...)
## S3 method for class 'smooth.roc':
auc(smooth.roc, ...)
## S3 method for class 'multiclass.roc':
auc(multiclass.roc, ...)
## S3 method for class 'formula':
auc(formula, data, ...)
## S3 method for class 'default':
auc(response, predictor, ...)

Arguments

roc, smooth.roc, multiclass.roc

a roc object from the roc function, a smooth.roc object from the smooth.roc function, or a multiclass.roc

response, predictor

arguments for the roc function.

formula, data

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

partial.auc

either FALSE (default: consider total area) or a numeric vector of length 2: boundaries of the AUC to consider in [0,1] (or [0,100] if percent is TRUE).

partial.auc.focus

if partial.auc is not FALSE and a partial AUC is computed, specifies if partial.auc specifies the bounds in terms of specificity (default) or sensitivity. Can be shortened to spec/sens or even sp/se. Igno

partial.auc.correct

logical indicating if the correction of AUC must be applied in order to have a maximal AUC of 1.0 and a non-discriminant AUC of 0.5 whatever the partial.auc defined. Ignored if partial.auc=FALSE. Default: FALSE<

...

further arguments passed to or from other methods, especially arguments for roc when calling auc.default, auc.formula, auc.smooth.roc. Note that the auc

Value

• The numeric AUC value, of class auc (or multiclass.auc if a multiclass.roc was supplied), in fraction of the area or in percent if percent=TRUE, with the following attributes:
• partial.auc
  if the AUC is full (FALSE) or partial (and in this case the bounds), as defined in argument.
• partial.auc.focus
  only for a partial AUC, if the bound specifies the sensitivity or specificity, as defined in argument.
• partial.auc.correct
  only for a partial AUC, was it corrected? As defined in argument.
• percent
  whether the AUC is given in percent or fraction.
• roc
  the original ROC curve, as a roc, smooth.roc or multiclass.roc object.

encoding

UTF-8

Multi-class AUCs

With an object of class multiclass.roc, a multi-class AUC is computed as an average AUC as defined by Hand and Till (equation 7).

$$auc=\frac{2}{c(c-1)}\sum{aucs}$$

with aucs all the pairwise roc curves.

Details

This function is typically called from roc when auc=TRUE (default). It is also used by ci. When it is called with two vectors (response, predictor) or a formula (response~predictor) arguments, the roc function is called and only the AUC is returned.

By default, the total area under the curve is computed, but you can specify a partial AUC with the partial.auc argument. It specifies the bounds of specificity or sensitivity (depending on partial.auc.focus) between which the AUC will be computed. As it specifies specificities or sensitivities, you must adapt it accordingly to the 'percent' specification (see details in roc). partial.auc.focus is ignored if partial.auc=FALSE (default). If a partial AUC is computed, partial.auc.focus specifies if the bounds specified in partial.auc must be interpreted as sensitivity or specificity. Any other value will produce an error. partial.auc.correct is ignored if partial.auc=FALSE (default). If TRUE, the correction by McClish will be applied: $$\frac{1+\frac{auc-min}{max-min}}{2}$$ where min is the value of the non-discriminant AUC in the region and max is the maximum possible AUC in the region. With this correction, the AUC will be 0.5 if non discriminant and 1.0 if maximal, whatever the region defined. Fully compatible with percent.

There is no difference in the computation of the area under a smoothed ROC curve.

References

Tom Fawcett (2006) ``An introduction to ROC analysis''. Pattern Recognition Letters 27, 861--874. DOI: http://dx.doi.org/10.1016/j.patrec.2005.10.010{10.1016/j.patrec.2005.10.010}.

David J. Hand and Robert J. Till (2001). A Simple Generalisation of the Area Under the ROC Curve for Multiple Class Classification Problems. Machine Learning 45(2), p. 171--186. DOI: http://dx.doi.org/10.1023/A:1010920819831{10.1023/A:1010920819831}.

Donna Katzman McClish (1989) ``Analyzing a Portion of the ROC Curve''. Medical Decision Making 9(3), 190--195. DOI: http://dx.doi.org/10.1177/0272989X8900900307{10.1177/0272989X8900900307}. 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: http://dx.doi.org/10.1186/1471-2105-12-77{10.1186/1471-2105-12-77}.

See Also

roc, ci.auc

Examples

data(aSAH)

# Syntax (response, predictor):
auc(aSAH$outcome, aSAH$s100b)

# With a roc object:
rocobj <- roc(aSAH$outcome, aSAH$s100b)
# Full AUC:
auc(rocobj)
# Partial AUC:
auc(rocobj, partial.auc=c(1, .8), partial.auc.focus="se", partial.auc.correct=TRUE)

# Alternatively, you can get the AUC directly from roc():
roc(aSAH$outcome, aSAH$s100b)$auc
roc(aSAH$outcome, aSAH$s100b,
    partial.auc=c(1, .8), partial.auc.focus="se",
    partial.auc.correct=TRUE)$auc