These functions compute the variance of the AUC of a ROC curve.
Usage
var(...)
## Default S3 method:
var(...)
## S3 method for class 'auc'
var(auc, ...)
## S3 method for class 'roc'
var(roc, method=c("delong", "bootstrap", "obuchowski"),
boot.n = 2000, boot.stratified = TRUE, reuse.auc=TRUE,
progress = getOption("pROCProgress")$name, parallel=FALSE, ...)
## S3 method for class 'smooth.roc'
var(smooth.roc, ...)
Arguments
roc, smooth.roc, auc
a “roc” object from the
roc function, a “smooth.roc” object from the
smooth function or an “auc” object from
the auc function.
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.
reuse.auc
if TRUE (default) and the “roc” objects
contain an “auc” field, re-use these specifications for the
test. See details.
boot.n
for method="bootstrap" only: the number of
bootstrap replicates or permutations. Default: 2000.
boot.stratified
for method="bootstrap" only:
should the bootstrap be stratified (same number
of cases/controls in each replicate than in the original sample) or
not. Default: TRUE.
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 var.roc when calling var,
var.auc and var.smooth.roc. Arguments for
auc (if reuse.auc=FALSE) and
txtProgressBar (only char and style) if
applicable.
Details
The var function computes the variance of the AUC of a ROC
curve. It is typically called with the roc object of
interest. Two methods are available: “delong” and
“bootstrap” (see “Computational
details” section below).
The default is to use “delong” method except for with
partial AUC and smoothed curves where “bootstrap” is employed.
Using “delong” for partial AUC and smoothed ROCs is not
supported (a warning is produced and “bootstrap” is employed
instead).
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.
var.default forces the usage of the
var function in the stats package, so
that other code relying on var should continue to function
normally.
Value
The numeric value of the variance.
AUC specification
var needs a specification of the AUC to compute
the variance of the AUC of the ROC curve.
The specification is defined by:
the “auc” field in the “roc” objects if
reuse.auc is set to TRUE (default)
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” objects do contain an auc field.
As well if the “roc” objects 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 roc.test contains an auc
field and reuse.auc=TRUE, auc is not called and
arguments such as partial.auc are silently ignored.
Computation details
With method="bootstrap", the processing is done as follow:
boot.n bootstrap replicates are drawn from the
data. If boot.stratified is TRUE, each replicate contains
exactly the same number of controls and cases than the original
sample, otherwise if FALSE the numbers can vary.
for each bootstrap replicate, the AUC of the ROC curve
is computed and stored.
the variance of the resampled AUCs are computed and returned.
With method="delong", the processing is done as described in
Hanley and Hajian-Tilaki (1997).
With method="obuchowski", the processing is done as described
in Obuchowski and McClish (1997), Table 1 and Equation 4, p. 1530–1531. The
computation of g for partial area under the ROC curve is
modified as:
expr1 * (2 * pi * expr2) ^ {(-1)} * (-expr4) - A * B * expr1 * (2 * pi * expr2^3) ^ {(-1/2)} * expr3
.
Binormality assumption
The “obuchowski” method makes the assumption that the data is binormal.
If the data shows a deviation from this assumption, it might help to
normalize the data first (that is, before calling roc),
for example with quantile normalization:
“delong” and “bootstrap” methods make no such assumption.
Warnings
If method="delong" and the AUC specification specifies a
partial AUC, the warning “Using DeLong for partial AUC is
not supported. Using bootstrap test instead.” is issued. The
method argument is ignored and “bootstrap” is used instead.
If method="delong" and the ROC
curve is smoothed, the warning “Using DeLong for
smoothed ROCs 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.
When the ROC curve has an auc of 1 (or 100%), the variance will always be null.
This is true for both “delong” and “bootstrap” methods that can
not properly assess the variance in this case. This result is misleading, as the variance is of course not null.
A warning will be displayed to inform of this condition, and of the misleading output.
Errors
If density.cases and density.controls were provided
for smoothing, the error “Cannot compute the covariance on ROC
curves smoothed with density.controls and density.cases.” is
issued.
References
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”. Biometrics44, 837–845.
James A. Hanley and Karim O. Hajian-Tilaki (1997) “Sampling
variability of nonparametric estimates of the areas under receiver
operating characteristic curves: An update”. Academic
Radiology4, 49–58. DOI:
10.1016/S1076-6332(97)80161-4.
Nancy A. Obuchowski, Donna K. McClish (1997). “Sample size
determination for diagnostic accurary studies involving binormal ROC
curve indices”. Statistics in Medicine, 16(13),
1529–1542. DOI: (SICI)1097-0258(19970715)16:13<1529::AID-SIM565>3.0.CO;2-H.
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
roc, cov.roc
CRAN package plyr, employed in this function.
Examples
data(aSAH)
## Basic example
roc1 <- roc(aSAH$outcome, aSAH$s100b)
roc2 <- roc(aSAH$outcome, aSAH$wfns)
var(roc1)
var(roc2)
# We could also write it in one line:
var(roc(aSAH$outcome, aSAH$s100b))
## Not run:
# The latter used Delong. To use bootstrap:
var(roc1, method="bootstrap")
# Decrease boot.n for a faster execution
var(roc1,method="bootstrap", boot.n=1000)
## End(Not run)
# To use obuchowski:
var(roc1, method="obuchowski")
## Not run:
# Variance of smoothed ROCs:
# Smoothing is re-done at each iteration, and execution is slow
var(smooth(roc1))
## End(Not run)
# or from an AUC (no smoothing)
var(auc(roc1))
## Test data from Hanley and Hajian-Tilaki, 1997
disease.present <- c("Yes", "No", "Yes", "No", "No", "Yes", "Yes", "No",
"No", "Yes", "No", "No", "Yes", "No", "No")
field.strength.1 <- c(1, 2, 5, 1, 1, 1, 2, 1, 2, 2, 1, 1, 5, 1, 1)
field.strength.2 <- c(1, 1, 5, 1, 1, 1, 4, 1, 2, 2, 1, 1, 5, 1, 1)
roc3 <- roc(disease.present, field.strength.1)
roc4 <- roc(disease.present, field.strength.2)
# Assess the variance:
var(roc3)
var(roc4)
## Not run:
# With bootstrap:
var(roc3, method="bootstrap")
var(roc4, method="bootstrap")
## End(Not run)