auc  R Documentation 
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
.
auc(...)
## S3 method for class 'roc'
auc(roc, partial.auc=FALSE, partial.auc.focus=c("specificity",
"sensitivity"), partial.auc.correct=FALSE,
allow.invalid.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, ...)
## Default S3 method:
auc(response, predictor, ...)
roc, smooth.roc, multiclass.roc 
a “roc” object from the

response, predictor 
arguments for the 
formula, data 
a formula (and possibly a data object) of type response~predictor for the 
partial.auc 
either 
partial.auc.focus 
if 
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
nondiscriminant AUC of 0.5 whatever the 
allow.invalid.partial.auc.correct 
logical indicating if
the correction must return 
... 
further arguments passed to or from other methods,
especially arguments for 
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 a partial AUC (pAUC)
can be
specified 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 in relation 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. It is recommended to
plot
the ROC curve with auc.polygon=TRUE
in order to
make sure the specification is correct.
If a pAUC is defined, it can be standardized (corrected). This correction is
controled by the partial.auc.correct
argument. If partial.auc.correct=TRUE
,
the correction by McClish will be applied:
\frac{1+\frac{aucmin}{maxmin}}{2}
where auc is the uncorrected pAUC computed in the region defined by partial.auc
,
min is the value of the nondiscriminant AUC (with an AUC of 0.5 or 50
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. This correction is fully compatible with percent
.
Note that this correction is undefined for curves below the diagonal (auc < min). Attempting
to correct such an AUC will return NA
with a warning.
The numeric AUC value, of class c("auc", "numeric")
(or
c("multiclass.auc", "numeric")
or c("mv.multiclass.auc", "numeric")
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. 
There is no difference in the computation of the area under a smoothed
ROC curve, except for curves smoothed with method="binomial"
. In this case
and only if a full AUC is requested, the classical binormal AUC formula is applied:
auc=\phi\frac{a}{\sqrt{1 + b^2}}.
If the ROC curve is smoothed with any other method
or if a partial AUC
is requested, the empirical AUC described in the previous section is applied.
With an object of class “multiclass.roc”, a multiclass AUC is computed as an average AUC as defined by Hand and Till (equation 7).
auc=\frac{2}{c(c1)}\sum{aucs}
with aucs all the pairwise roc curves.
Tom Fawcett (2006) “An introduction to ROC analysis”. Pattern Recognition Letters 27, 861–874. DOI: \Sexpr[results=rd]{tools:::Rd_expr_doi("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: \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1023/A:1010920819831")}.
Donna Katzman McClish (1989) “Analyzing a Portion of the ROC Curve”. Medical Decision Making 9(3), 190–195. DOI: \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1177/0272989X8900900307")}.
Xavier Robin, Natacha Turck, Alexandre Hainard, et al. (2011) “pROC: an opensource package for R and S+ to analyze and compare ROC curves”. BMC Bioinformatics, 7, 77. DOI: \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1186/147121051277")}.
roc
, ci.auc
# Create a ROC curve:
data(aSAH)
roc.s100b < roc(aSAH$outcome, aSAH$s100b)
# Get the full AUC
auc(roc.s100b)
# Get the partial AUC:
auc(roc.s100b, partial.auc=c(1, .8), partial.auc.focus="se", partial.auc.correct=TRUE)
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.