roc: Build a ROC curve
In pROC: Display and Analyze ROC Curves
roc R Documentation
Build a ROC curve
Description
This is the main function of the pROC package. It builds a ROC
curve and returns a “roc” object, a list of class
“roc”. This object can be printed, plotted, or
passed to the functions auc, ci,
smooth.roc and coords. Additionally, two
roc objects can be compared with roc.test.
Usage
roc(...)
## S3 method for class 'formula'
roc(formula, data, ...)
## S3 method for class 'data.frame'
roc(data, response, predictor,
ret = c("roc", "coords", "all_coords"), ...)
## Default S3 method:
roc(response, predictor, controls, cases,
density.controls, density.cases,
levels=base::levels(as.factor(response)), percent=FALSE, na.rm=TRUE,
direction=c("auto", "<", ">"), algorithm = 6, quiet = FALSE,
smooth=FALSE, auc=TRUE, ci=FALSE, plot=FALSE, smooth.method="binormal",
smooth.n=512, ci.method=NULL, density=NULL, ...)
roc_(data, response, predictor, ret = c("roc", "coords", "all_coords"), ...)
Arguments
response
a factor, numeric or character vector of
responses (true class), typically encoded with 0 (controls) and 1 (cases).
Only two classes can be used in a ROC curve. If the vector
contains more than two unique values, or if their order could be
ambiguous, use levels to specify which values must be used as
control and case value.
If the first argument was a data.frame, response
should be the name of the column in data containing the
response, quoted for roc_, and optionally quoted for
roc.data.frame (non-standard evaluation or NSE).
predictor
a numeric or ordered vector
of the same length than response, containing the predicted
value of each observation.
If the first argument was a data.frame, predictor
should be the name of the column in data containing the
predictor, quoted for roc_, and optionally quoted for
roc.data.frame (non-standard evaluation or NSE).
controls, cases
instead of response, predictor,
the data can be supplied as two numeric or
ordered vectors containing the predictor
values for control and case observations.
density.controls, density.cases
a smoothed ROC curve can be
built directly from two densities on identical x points, as in
smooth.
formula, data
a formula of the type response~predictor. If mulitple predictors
are passed, a named list of roc objects will be returned. Additional arguments
data and subset, but not na.action are supported, see
model.frame for more details.
levels
the value of the response for controls and cases
respectively. By default, the first two values of
levels(as.factor(response)) are taken, and the remaining levels are ignored.
It usually captures two-class factor data correctly, but will
frequently fail for other data types (response factor with more than 2 levels,
or for example if your response is coded “controls” and “cases”,
the levels will be inverted) and must then be specified here.
If your data is coded as 0 and 1 with 0
being the controls, you can safely omit this argument.
percent
if the sensitivities, specificities and AUC must be
given in percent (TRUE) or in fraction (FALSE, default).
na.rm
if TRUE, the NA values will be removed
(ignored by roc.formula).
direction
in which direction to make the comparison?
“auto” (default): automatically define in which group the
median is higher and take the direction accordingly.
“>”: if the predictor values for the control group are
higher than the values of the case group (controls > t >= cases).
“<”: if the predictor values for the control group are lower
or equal than the values of the case group (controls < t <= cases).
You should set this explicity to “>” or “<” whenever
you are resampling or randomizing the data, otherwise the
curves will be biased towards higher AUC values.
algorithm
the method used to compute sensitivity and specificity,
an integer of length 1 between 0 and 6.
1: a safe, well-tested, pure-R code that is efficient when the
number of thresholds is low. It goes with O(T*N).
2: an alternative pure-R algorithm that goes in
O(N). Typically faster than 1 when the number of thresholds of
the ROC curve is above 1000. Less tested than 1.
3: a C++
implementation of 1, about 3-5x faster. Typically the fastest with
ROC curves with less than 50-100 thresholds, but has a very bad worst-case
when that number increases.
4 (debug only, slow):
runs algorithms 1 to 3 and makes sure they return the same values.
5: select 2 or 3 based on the number of thresholds.
6 (default): quickly select the algorithm on the class of the data: 2
for numeric and 3 for ordered.
0: use microbenchmark to choose between 2 and 3.
ret
for roc.data.frame only, whether to return the
threshold sensitivity and specificity at all thresholds (“coords”),
all the coordinates at all thresholds (“all_coords”) or the
roc object (“roc”).
quiet
set to TRUE to turn off messages
when direction and levels are auto-detected.
smooth
if TRUE, the ROC curve is passed to smooth
to be smoothed.
auc
compute the area under the curve (AUC)? If TRUE
(default), additional arguments can be passed to auc.
ci
compute the confidence interval (CI)? If set to TRUE,
additional arguments can be passed to ci.
plot
plot the ROC curve? If TRUE, additional
arguments can be passed to plot.roc.
smooth.method, smooth.n, ci.method
in roc.formula and
roc.default, the method and n arguments to
smooth (if smooth=TRUE) and
of="auc") must be passed as
smooth.method, smooth.n and ci.method to avoid confusions.
density
density argument passed to smooth.
...
further arguments passed to or from other methods, and
especially:
-
auc: partial.auc, partial.auc.focus, partial.auc.correct.
-
ci: of, conf.level, boot.n, boot.stratified, progress
-
ci.auc:, reuse.auc, method
-
ci.thresholds: thresholds
-
ci.se: sensitivities
-
ci.sp: specificities
-
plot.roc: add, col and most
other arguments to the plot.roc function. See
plot.roc directly for more details.
-
smooth: method, n, and all other
arguments. See smooth for more details.
Details
This function's main job is to build a ROC object. See the
“Value” section to this page for more details. Before
returning, it will call (in this order) the smooth,
auc, ci and plot.roc
functions if smooth auc, ci and plot.roc
(respectively) arguments are set to TRUE. By default, only auc
is called.
Data can be provided as response, predictor, where the
predictor is the numeric (or ordered) level of the evaluated signal, and
the response encodes the observation class (control or case). The
level argument specifies which response level must be taken as
controls (first value of level) or cases (second). It can
safely be ignored when the response is encoded as 0 and
1, but it will frequently fail otherwise. By default, the first
two values of levels(as.factor(response)) are taken, and the
remaining levels are ignored. This means that if your response is
coded “control” and “case”, the levels will be
inverted.
In some cases, it is more convenient to pass the data as
controls, cases, but both arguments are ignored if
response, predictor was specified to non-NULL values.
It is also possible to pass density data with density.controls,
density.cases, which will result in a smoothed ROC curve even if
smooth=FALSE, but are ignored if response, predictor or
controls, cases are provided.
Specifications for auc, ci and
plot.roc are not kept if auc, ci or plot are set to
FALSE. Especially, in the following case:
myRoc <- roc(..., auc.polygon=TRUE, grid=TRUE, plot=FALSE)
plot(myRoc)
the plot will not have the AUC polygon nor the grid. Similarly, when
comparing “roc” objects, the following is not possible:
roc1 <- roc(..., partial.auc=c(1, 0.8), auc=FALSE)
roc2 <- roc(..., partial.auc=c(1, 0.8), auc=FALSE)
roc.test(roc1, roc2)
This will produce a test on the full AUC, not the partial AUC. To make
a comparison on the partial AUC, you must repeat the specifications
when calling roc.test:
roc.test(roc1, roc2, partial.auc=c(1, 0.8))
Note that if roc was called with auc=TRUE, the latter syntax will not
allow redefining the AUC specifications. You must use reuse.auc=FALSE for that.
Value
If the data contained any NA value and na.rm=FALSE, NA is
returned. Otherwise, if smooth=FALSE, a list of class
“roc” with the following fields:
auc
if called with auc=TRUE, a numeric of class “auc” as
defined in auc.
ci
if called with ci=TRUE, a numeric of class “ci” as
defined in ci.
response
the response vector. Patients whose response is not
%in% levels are discarded. If NA values
were removed, a na.action attribute similar
to na.omit stores the row numbers.
predictor
the predictor vector converted to numeric as used to build the ROC
curve. Patients whose response is not %in% levels are discarded. If
NA values were removed, a na.action attribute similar
to na.omit stores the row numbers.
original.predictor, original.response
the response and predictor vectors as passed in argument.
levels
the levels of the response as defined in argument.
controls
the predictor values for the control observations.
cases
the predictor values for the cases.
percent
if the sensitivities, specificities and AUC are
reported in percent, as defined in argument.
direction
the direction of the comparison, as defined in argument.
fun.sesp
the function used to compute sensitivities and specificities.
Will be re-used in bootstrap operations.
sensitivities
the sensitivities defining the ROC curve.
specificities
the specificities defining the ROC curve.
thresholds
the thresholds at which the sensitivities and
specificities were computed. See below for details.
call
how the function was called. See match.call for
more details.
If smooth=TRUE a list of class “smooth.roc” as returned
by smooth, with or without additional elements
auc and ci (according to the call).
Thresholds
Thresholds are selected as the means between any two consecutive values
observed in the data. This choice is aimed to facilitate their interpretation,
as any data point will be unambiguously positive or negative
regardless of whether the comparison operator includes equality
or not.
In rare cases it might not be possible to represent the
mean between two consecutive values, or one might want to use a custom
threshold. In those cases, the semantic of the comparison
is as follows: with direction = '>',
observations are positive when they are smaller than or equal
(<=) to the threshold.
With direction = '<', observations are positive when they
are greater than or equal (>=) to the threshold.
As a corollary, thresholds do not correspond to actual values
in the data.
Experimental: pipelines
Since version 1.15.0, the roc function can be used in pipelines, for instance with dplyr or magrittr. This is still a highly experimental feature and will change significantly in future versions (see issue 54).
The roc.data.frame method supports both standard and non-standard evaluation (NSE):
library(dplyr)
# Standard evaluation:
aSAH %>%
filter(gender == "Female") %>%
roc("outcome", "s100b")
# Non-Standard Evaluation:
aSAH %>%
filter(gender == "Female") %>%
roc(outcome, s100b)
For tasks involving programming and variable column names, the roc_ function provides
standard evaluation:
# Standard evaluation:
aSAH %>%
filter(gender == "Female") %>%
roc_("outcome", "s100b")
By default it returns the roc object, which can then be piped to
the coords function to extract coordinates that can be used
in further pipelines.
# Returns thresholds, sensitivities and specificities:
aSAH %>%
roc(outcome, s100b) %>%
coords(transpose = FALSE) %>%
filter(sensitivity > 0.6,
specificity > 0.6)
# Returns all existing coordinates, then select precision and recall:
aSAH %>%
roc(outcome, s100b) %>%
coords(ret = "all", transpose = FALSE) %>%
select(precision, recall)
Errors
If no control or case observation exist for the given levels of
response, no ROC curve can be built and an error is triggered with
message “No control observation” or “No case
observation”.
If the predictor is not a numeric or ordered, as defined by
as.numeric or as.ordered, the message
“Predictor must be numeric or ordered” is returned.
The message “No valid data provided” is issued when the data
wasn't properly passed. Remember you need both response and
predictor of the same (not null) length, or both controls
and cases. Combinations such as predictor and
cases are not valid and will trigger this error.
Infinite values of the predictor cannot always be thresholded by
infinity and can cause ROC curves to not reach 0 or 100%
specificity or sensitivity. Since version 1.13.0, pROC returns NaN
with a warning message “Infinite value(s) in predictor” if
predictor contains any infinite values.
References
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")}.
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: \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1186/1471-2105-12-77")}.
See Also
auc, ci, plot.roc, print.roc, roc.test
Examples
data(aSAH)
# Basic example
roc(aSAH$outcome, aSAH$s100b,
levels=c("Good", "Poor"))
# As levels aSAH$outcome == c("Good", "Poor"),
# this is equivalent to:
roc(aSAH$outcome, aSAH$s100b)
# In some cases, ignoring levels could lead to unexpected results
# Equivalent syntaxes:
roc(outcome ~ s100b, aSAH)
roc(aSAH$outcome ~ aSAH$s100b)
with(aSAH, roc(outcome, s100b))
with(aSAH, roc(outcome ~ s100b))
# With a formula:
roc(outcome ~ s100b, data=aSAH)
## Not run:
library(dplyr)
aSAH %>%
filter(gender == "Female") %>%
roc(outcome, s100b)
## End(Not run)
# Using subset (only with formula)
roc(outcome ~ s100b, data=aSAH, subset=(gender == "Male"))
roc(outcome ~ s100b, data=aSAH, subset=(gender == "Female"))
# With numeric controls/cases
roc(controls=aSAH$s100b[aSAH$outcome=="Good"], cases=aSAH$s100b[aSAH$outcome=="Poor"])
# With ordered controls/cases
roc(controls=aSAH$wfns[aSAH$outcome=="Good"], cases=aSAH$wfns[aSAH$outcome=="Poor"])
# Inverted the levels: "Poor" are now controls and "Good" cases:
roc(aSAH$outcome, aSAH$s100b,
levels=c("Poor", "Good"))
# The result was exactly the same because of direction="auto".
# The following will give an AUC < 0.5:
roc(aSAH$outcome, aSAH$s100b,
levels=c("Poor", "Good"), direction="<")
# If we are sure about levels and direction auto-detection,
# we can turn off the messages:
roc(aSAH$outcome, aSAH$s100b, quiet = TRUE)
# If we prefer counting in percent:
roc(aSAH$outcome, aSAH$s100b, percent=TRUE)
# Plot and CI (see plot.roc and ci for more options):
roc(aSAH$outcome, aSAH$s100b,
percent=TRUE, plot=TRUE, ci=TRUE)
# Smoothed ROC curve
roc(aSAH$outcome, aSAH$s100b, smooth=TRUE)
# this is not identical to
smooth(roc(aSAH$outcome, aSAH$s100b))
# because in the latter case, the returned object contains no AUC
pROC documentation built on Nov. 2, 2023, 6:05 p.m.
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| roc | R Documentation |
Build a ROC curve
Description
This is the main function of the pROC package. It builds a ROC
curve and returns a “roc” object, a list of class
“roc”. This object can be printed, plotted, or
passed to the functions auc, ci,
smooth.roc and coords. Additionally, two
roc objects can be compared with roc.test.
Usage
roc(...)
## S3 method for class 'formula'
roc(formula, data, ...)
## S3 method for class 'data.frame'
roc(data, response, predictor,
ret = c("roc", "coords", "all_coords"), ...)
## Default S3 method:
roc(response, predictor, controls, cases,
density.controls, density.cases,
levels=base::levels(as.factor(response)), percent=FALSE, na.rm=TRUE,
direction=c("auto", "<", ">"), algorithm = 6, quiet = FALSE,
smooth=FALSE, auc=TRUE, ci=FALSE, plot=FALSE, smooth.method="binormal",
smooth.n=512, ci.method=NULL, density=NULL, ...)
roc_(data, response, predictor, ret = c("roc", "coords", "all_coords"), ...)
Arguments
response |
a factor, numeric or character vector of
responses (true class), typically encoded with 0 (controls) and 1 (cases).
Only two classes can be used in a ROC curve. If the vector
contains more than two unique values, or if their order could be
ambiguous, use |
predictor |
a |
controls, cases |
instead of |
density.controls, density.cases |
a smoothed ROC curve can be
built directly from two densities on identical |
formula, data |
a formula of the type |
levels |
the value of the response for controls and cases
respectively. By default, the first two values of
|
percent |
if the sensitivities, specificities and AUC must be
given in percent ( |
na.rm |
if |
direction |
in which direction to make the comparison? “auto” (default): automatically define in which group the median is higher and take the direction accordingly. “>”: if the predictor values for the control group are higher than the values of the case group (controls > t >= cases). “<”: if the predictor values for the control group are lower or equal than the values of the case group (controls < t <= cases). You should set this explicity to “>” or “<” whenever you are resampling or randomizing the data, otherwise the curves will be biased towards higher AUC values. |
algorithm |
the method used to compute sensitivity and specificity,
an integer of length 1 between |
ret |
for |
quiet |
set to |
smooth |
if TRUE, the ROC curve is passed to |
auc |
compute the area under the curve (AUC)? If |
ci |
compute the confidence interval (CI)? If set to |
plot |
plot the ROC curve? If |
smooth.method, smooth.n, ci.method |
in |
density |
|
... |
further arguments passed to or from other methods, and especially:
|
Details
This function's main job is to build a ROC object. See the
“Value” section to this page for more details. Before
returning, it will call (in this order) the smooth,
auc, ci and plot.roc
functions if smooth auc, ci and plot.roc
(respectively) arguments are set to TRUE. By default, only auc
is called.
Data can be provided as response, predictor, where the
predictor is the numeric (or ordered) level of the evaluated signal, and
the response encodes the observation class (control or case). The
level argument specifies which response level must be taken as
controls (first value of level) or cases (second). It can
safely be ignored when the response is encoded as 0 and
1, but it will frequently fail otherwise. By default, the first
two values of levels(as.factor(response)) are taken, and the
remaining levels are ignored. This means that if your response is
coded “control” and “case”, the levels will be
inverted.
In some cases, it is more convenient to pass the data as
controls, cases, but both arguments are ignored if
response, predictor was specified to non-NULL values.
It is also possible to pass density data with density.controls,
density.cases, which will result in a smoothed ROC curve even if
smooth=FALSE, but are ignored if response, predictor or
controls, cases are provided.
Specifications for auc, ci and
plot.roc are not kept if auc, ci or plot are set to
FALSE. Especially, in the following case:
myRoc <- roc(..., auc.polygon=TRUE, grid=TRUE, plot=FALSE)
plot(myRoc)
the plot will not have the AUC polygon nor the grid. Similarly, when comparing “roc” objects, the following is not possible:
roc1 <- roc(..., partial.auc=c(1, 0.8), auc=FALSE)
roc2 <- roc(..., partial.auc=c(1, 0.8), auc=FALSE)
roc.test(roc1, roc2)
This will produce a test on the full AUC, not the partial AUC. To make
a comparison on the partial AUC, you must repeat the specifications
when calling roc.test:
roc.test(roc1, roc2, partial.auc=c(1, 0.8))
Note that if roc was called with auc=TRUE, the latter syntax will not
allow redefining the AUC specifications. You must use reuse.auc=FALSE for that.
Value
If the data contained any NA value and na.rm=FALSE, NA is
returned. Otherwise, if smooth=FALSE, a list of class
“roc” with the following fields:
auc |
if called with |
ci |
if called with |
response |
the response vector. Patients whose response is not
|
predictor |
the predictor vector converted to numeric as used to build the ROC
curve. Patients whose response is not |
original.predictor, original.response |
the response and predictor vectors as passed in argument. |
levels |
the levels of the response as defined in argument. |
controls |
the predictor values for the control observations. |
cases |
the predictor values for the cases. |
percent |
if the sensitivities, specificities and AUC are reported in percent, as defined in argument. |
direction |
the direction of the comparison, as defined in argument. |
fun.sesp |
the function used to compute sensitivities and specificities. Will be re-used in bootstrap operations. |
sensitivities |
the sensitivities defining the ROC curve. |
specificities |
the specificities defining the ROC curve. |
thresholds |
the thresholds at which the sensitivities and specificities were computed. See below for details. |
call |
how the function was called. See |
If smooth=TRUE a list of class “smooth.roc” as returned
by smooth, with or without additional elements
auc and ci (according to the call).
Thresholds
Thresholds are selected as the means between any two consecutive values observed in the data. This choice is aimed to facilitate their interpretation, as any data point will be unambiguously positive or negative regardless of whether the comparison operator includes equality or not.
In rare cases it might not be possible to represent the
mean between two consecutive values, or one might want to use a custom
threshold. In those cases, the semantic of the comparison
is as follows: with direction = '>',
observations are positive when they are smaller than or equal
(<=) to the threshold.
With direction = '<', observations are positive when they
are greater than or equal (>=) to the threshold.
As a corollary, thresholds do not correspond to actual values in the data.
Experimental: pipelines
Since version 1.15.0, the roc function can be used in pipelines, for instance with dplyr or magrittr. This is still a highly experimental feature and will change significantly in future versions (see issue 54).
The roc.data.frame method supports both standard and non-standard evaluation (NSE):
library(dplyr)
# Standard evaluation:
aSAH %>%
filter(gender == "Female") %>%
roc("outcome", "s100b")
# Non-Standard Evaluation:
aSAH %>%
filter(gender == "Female") %>%
roc(outcome, s100b)
For tasks involving programming and variable column names, the roc_ function provides
standard evaluation:
# Standard evaluation:
aSAH %>%
filter(gender == "Female") %>%
roc_("outcome", "s100b")
By default it returns the roc object, which can then be piped to
the coords function to extract coordinates that can be used
in further pipelines.
# Returns thresholds, sensitivities and specificities:
aSAH %>%
roc(outcome, s100b) %>%
coords(transpose = FALSE) %>%
filter(sensitivity > 0.6,
specificity > 0.6)
# Returns all existing coordinates, then select precision and recall:
aSAH %>%
roc(outcome, s100b) %>%
coords(ret = "all", transpose = FALSE) %>%
select(precision, recall)
Errors
If no control or case observation exist for the given levels of response, no ROC curve can be built and an error is triggered with message “No control observation” or “No case observation”.
If the predictor is not a numeric or ordered, as defined by
as.numeric or as.ordered, the message
“Predictor must be numeric or ordered” is returned.
The message “No valid data provided” is issued when the data
wasn't properly passed. Remember you need both response and
predictor of the same (not null) length, or both controls
and cases. Combinations such as predictor and
cases are not valid and will trigger this error.
Infinite values of the predictor cannot always be thresholded by
infinity and can cause ROC curves to not reach 0 or 100%
specificity or sensitivity. Since version 1.13.0, pROC returns NaN
with a warning message “Infinite value(s) in predictor” if
predictor contains any infinite values.
References
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")}.
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: \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1186/1471-2105-12-77")}.
See Also
auc, ci, plot.roc, print.roc, roc.test
Examples
data(aSAH)
# Basic example
roc(aSAH$outcome, aSAH$s100b,
levels=c("Good", "Poor"))
# As levels aSAH$outcome == c("Good", "Poor"),
# this is equivalent to:
roc(aSAH$outcome, aSAH$s100b)
# In some cases, ignoring levels could lead to unexpected results
# Equivalent syntaxes:
roc(outcome ~ s100b, aSAH)
roc(aSAH$outcome ~ aSAH$s100b)
with(aSAH, roc(outcome, s100b))
with(aSAH, roc(outcome ~ s100b))
# With a formula:
roc(outcome ~ s100b, data=aSAH)
## Not run:
library(dplyr)
aSAH %>%
filter(gender == "Female") %>%
roc(outcome, s100b)
## End(Not run)
# Using subset (only with formula)
roc(outcome ~ s100b, data=aSAH, subset=(gender == "Male"))
roc(outcome ~ s100b, data=aSAH, subset=(gender == "Female"))
# With numeric controls/cases
roc(controls=aSAH$s100b[aSAH$outcome=="Good"], cases=aSAH$s100b[aSAH$outcome=="Poor"])
# With ordered controls/cases
roc(controls=aSAH$wfns[aSAH$outcome=="Good"], cases=aSAH$wfns[aSAH$outcome=="Poor"])
# Inverted the levels: "Poor" are now controls and "Good" cases:
roc(aSAH$outcome, aSAH$s100b,
levels=c("Poor", "Good"))
# The result was exactly the same because of direction="auto".
# The following will give an AUC < 0.5:
roc(aSAH$outcome, aSAH$s100b,
levels=c("Poor", "Good"), direction="<")
# If we are sure about levels and direction auto-detection,
# we can turn off the messages:
roc(aSAH$outcome, aSAH$s100b, quiet = TRUE)
# If we prefer counting in percent:
roc(aSAH$outcome, aSAH$s100b, percent=TRUE)
# Plot and CI (see plot.roc and ci for more options):
roc(aSAH$outcome, aSAH$s100b,
percent=TRUE, plot=TRUE, ci=TRUE)
# Smoothed ROC curve
roc(aSAH$outcome, aSAH$s100b, smooth=TRUE)
# this is not identical to
smooth(roc(aSAH$outcome, aSAH$s100b))
# because in the latter case, the returned object contains no AUC
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