var.roc  R Documentation 
These functions compute the variance of the AUC of a ROC curve.
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, ...)
roc, smooth.roc, auc 
a “roc” object from the

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 
boot.n 
for 
boot.stratified 
for 
progress 
the name of progress bar to display. Typically
“none”, “win”, “tk” or “text” (see the

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 
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.
For smoothed ROC curves, smoothing is performed again at each
bootstrap replicate with the parameters originally provided.
If a density smoothing was performed with userprovided
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.
The numeric value of the variance.
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.
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 HajianTilaki (1997) using the algorithm by Sun and Xu (2014).
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
.
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:
norm.x < qnorm(rank(x)/(length(x)+1)) var(roc(response, norm.x, ...), ...)
“delong” and “bootstrap” methods make no such assumption.
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.
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.
Elisabeth R. DeLong, David M. DeLong and Daniel L. ClarkePearson (1988) “Comparing the areas under two or more correlated receiver operating characteristic curves: a nonparametric approach”. Biometrics 44, 837–845.
James A. Hanley and Karim O. HajianTilaki (1997) “Sampling variability of nonparametric estimates of the areas under receiver operating characteristic curves: An update”. Academic Radiology 4, 49–58. DOI: \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/S10766332(97)801614")}.
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: \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1002/(SICI)10970258(19970715)16:13<1529::AIDSIM565>3.0.CO;2H")}.
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: \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1109/LSP.2014.2337313")}.
Hadley Wickham (2011) “The SplitApplyCombine Strategy for Data Analysis”. Journal of Statistical Software, 40, 1–29. URL: \Sexpr[results=rd]{tools:::Rd_expr_doi("10.18637/jss.v040.i01")}.
roc
, cov.roc
CRAN package plyr, employed in this function.
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 redone 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 HajianTilaki, 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)
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