smooth: Smooth a ROC curve
In pROC: Display and Analyze ROC Curves
smooth R Documentation
Smooth a ROC curve
Description
This function smoothes a ROC curve of numeric predictor. By default, a
binormal smoothing is performed, but density or custom smoothings are
supported.
Usage
smooth(...)
## Default S3 method:
smooth(...)
## S3 method for class 'roc'
smooth(roc,
method=c("binormal", "density", "fitdistr", "logcondens",
"logcondens.smooth"), n=512, bw = "nrd0", density=NULL,
density.controls=density, density.cases=density,
start=NULL, start.controls=start, start.cases=start,
reuse.auc=TRUE, reuse.ci=FALSE, ...)
## S3 method for class 'smooth.roc'
smooth(smooth.roc, ...)
Arguments
roc, smooth.roc
a “roc” object from the
roc function, or a “smooth.roc” object from the
smooth function.
method
“binormal”, “density”, “fitdistr”,
“logcondens”, “"logcondens.smooth"”.
n
the number of equally spaced points where the smoothed curve will be
calculated.
bw
if method="density" and density.controls and
density.cases are not provided, bw is passed to
density to determine the bandwidth of the
density Can be a character string (“nrd0”, “nrd”,
“ucv”, “bcv” or “SJ”, but any name
matching a function prefixed with “bw.” is
supported) or a numeric value, as described in density.
Defaults to “nrd0”.
density, density.controls, density.cases
if
method="density", a numeric value of density (over the y
axis) or a function returning a density (such as
density. If method="fitdistr", a densfun
argument for fitdistr.
If the value is different for control and case observations,
density.controls and density.cases can be employed
instead, otherwise density will be propagated to both
density.controls and density.cases.
start, start.controls, start.cases
if
method="fitdistr", optionnal start
arguments for . start.controls
and start.cases allows to specify different distributions for
controls and cases.
reuse.auc, reuse.ci
if TRUE (default for reuse.auc) and the “roc” objects
contain “auc” or “ci” fields, re-use these
specifications to regenerate auc or ci
on the smoothed ROC curve with the original parameters. If
FALSE, the object returned will not contain
“auc” or “ci” fields. It is currently not possible to
redefine auc and ci options directly: you need to call auc or
ci later for that.
...
further arguments passed to or from other methods, and
especially to density (only cut, adjust,
and kernel, plus window for compatibility with S+) and
fitdistr.
Details
If method="binormal", a linear model is fitted to the quantiles of
the sensitivities and specificities. Smoothed sensitivities and
specificities are then generated from this model on n points.
This simple approach was found to work well for most ROC curves, but
it may produce hooked smooths in some situations (see in Hanley (1988)).
With method="density", the density
function is employed to generate a smooth kernel
density of the control and case observations as described by Zhou
et al. (1997), unless
density.controls or density.cases are provided
directly. bw can be given to
specify a bandwidth to use with density. It can be a
numeric value or a character string (“nrd0”, “nrd”,
“ucv”, “bcv” or “SJ”, but any name
matching a function prefixed with “bw.” is
supported). In the case of a character
string, the whole predictor data is employed to determine the numeric
value to use on both controls and cases.
Depending on your data, it might be a good idea to specify the
kernel argument for density. By default,
“gaussian” is used, but “epanechnikov”,
“rectangular”, “triangular”, “biweight”,
“cosine” and “optcosine” are supported. As all the
kernels are symetrical, 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))
smooth(roc(response, norm.x, ...), ...)
Additionally, density can be a function which must return
either a numeric vector of densities over the y axis or a list
with a “y” item like the density function. It
must accept the following input:
density.fun(x, n, from, to, bw, kernel, ...)
It is important to honour n, from and to in order
to have the densities evaluated on the same points for controls and
cases. Failing to do so and returning densities of different length
will produce an error. It is also a good idea to use a constant
smoothing parameter (such as bw) especially when controls and
cases have a different number of observations, to avoid producing
smoother or rougher densities.
If method="fitdistr", the fitdistr
function from the MASS package is employed to fit parameters for
the density function density with optionnal start parameters
start. The density function are fitted
separately in control (density.controls, start.controls)
and case observations (density.cases,
start.cases). density can be one of the character values
allowed by fitdistr or a density function (such
as dnorm, dweibull, ...).
The method="logcondens" and method="logcondens.smooth" use the
logcondens package to generate a non smoothed or smoothed
(respectively) log-concave density estimate of of the control and case
observation with the logConROC function.
smooth.default forces the usage of the
smooth function in the stats package, so
that other code relying on smooth should continue to function
normally.
Smoothed ROC curves can be passed to smooth again. In this case, the
smoothing is not re-applied on the smoothed ROC curve but the
original “roc” object will be re-used.
Note that a smooth.roc curve has no threshold.
Value
A list of class “smooth.roc” with the following fields:
sensitivities
the smoothed sensitivities defining the ROC curve.
specificities
the smoothed specificities defining the ROC curve.
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.
call
how the function was called. See match.call for
more details.
smoothing.args
a list of the arguments used for the
smoothing. Will serve to apply the smoothing again in further
bootstrap operations.
auc
if the original ROC curve contained an AUC, it is computed
again on the smoothed ROC.
ci
if the original ROC curve contained a CI, it is computed
again on the smoothed ROC.
fit.controls, fit.cases
with method="fitdistr" only:
the result of MASS's
fitdistr function for controls and cases, with an
additional “densfun” item indicating the density function, if
possible as character.
logcondens
with method="logcondens" and method="logcondens.smooth" only:
the result of logcondens's logConROC function.
model
with method="binormal" only:
the linear model from lm used to smooth the ROC curve.
Attributes
Additionally, the original roc object is stored as a
“roc” attribute.
Errors
The message “The 'density' function must return a numeric
vector or a list with a 'y' item.” will be displayed if the
density function did not return a valid output. The message
“Length of 'density.controls' and 'density.cases' differ.”
will be displayed if the returned value differ in length.
Binormal smoothing cannot smooth ROC curve defined by only one
point. Any such attempt will fail with the error “ROC curve not
smoothable (not enough points).”.
If the smooth ROC curve was generated by roc with
density.controls and density.cases numeric arguments, it
cannot be smoothed and the error “Cannot smooth a ROC curve
generated directly with numeric 'density.controls' and
'density.cases'.” is produced.
fitdistr and density smoothing methods require a
numeric predictor. If the ROC curve to smooth was
generated with an ordered factor only binormal smoothing can be
applied and the message “ROC curves of ordered predictors can
be smoothed only with binormal smoothing.” is displayed otherwise.
fitdistr, logcondens and logcondens.smooth methods
require additional packages. If not available, the following message
will be displayed with the required command to install the package:
“Package ? not available, required with method='?'.
Please install it with 'install.packages("?")'.
”
References
James E. Hanley (1988) “The robustness of the “binormal” assumptions
used in fitting ROC curves”. Medical Decision Making 8, 197–203.
Lutz Duembgen, Kaspar Rufibach (2011) “logcondens: Computations Related
to Univariate Log-Concave Density Estimation”. Journal of Statistical
Software, 39, 1–28. URL: \Sexpr[results=rd]{tools:::Rd_expr_doi("10.18637/jss.v039.i06")}.
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")}.
Kaspar Rufibach (2011) “A Smooth ROC Curve Estimator Based on Log-Concave Density Estimates”.
The International Journal of Biostatistics, 8, accepted. DOI:
\Sexpr[results=rd]{tools:::Rd_expr_doi("10.1515/1557-4679.1378")}. arXiv:
arXiv:1103.1787.
William N. Venables, Brian D. Ripley (2002). “Modern Applied Statistics with S”. New York, Springer.
Google books.
Kelly H. Zou, W. J. Hall and David E. Shapiro (1997) “Smooth
non-parametric receiver operating characteristic (ROC) curves for
continuous diagnostic tests”. Statistics in Medicine
18, 2143–2156. DOI:
\Sexpr[results=rd]{tools:::Rd_expr_doi("10.1002/(SICI)1097-0258(19971015)16:19<2143::AID-SIM655>3.0.CO;2-3")}.
See Also
roc
CRAN packages MASS and logcondens employed in this function.
Examples
data(aSAH)
## Basic example
rocobj <- roc(aSAH$outcome, aSAH$s100b)
smooth(rocobj)
# or directly with roc()
roc(aSAH$outcome, aSAH$s100b, smooth=TRUE)
# plotting
plot(rocobj)
rs <- smooth(rocobj, method="binormal")
plot(rs, add=TRUE, col="green")
rs2 <- smooth(rocobj, method="density")
plot(rs2, add=TRUE, col="blue")
rs3 <- smooth(rocobj, method="fitdistr", density="lognormal")
plot(rs3, add=TRUE, col="magenta")
if (requireNamespace("logcondens")) {
rs4 <- smooth(rocobj, method="logcondens")
plot(rs4, add=TRUE, col="brown")
rs5 <- smooth(rocobj, method="logcondens.smooth")
plot(rs5, add=TRUE, col="orange")
}
legend("bottomright", legend=c("Empirical", "Binormal", "Density", "Log-normal",
"Log-concave density", "Smoothed log-concave density"),
col=c("black", "green", "blue", "magenta", "brown", "orange"), lwd=2)
## Advanced smoothing
# if we know the distributions are normal with sd=0.1 and an unknown mean:
smooth(rocobj, method="fitdistr", density=dnorm, start=list(mean=1), sd=.1)
# different distibutions for controls and cases:
smooth(rocobj, method="fitdistr", density.controls="normal", density.cases="lognormal")
# with densities
bw <- bw.nrd0(rocobj$predictor)
density.controls <- density(rocobj$controls, from=min(rocobj$predictor) - 3 * bw,
to=max(rocobj$predictor) + 3*bw, bw=bw, kernel="gaussian")
density.cases <- density(rocobj$cases, from=min(rocobj$predictor) - 3 * bw,
to=max(rocobj$predictor) + 3*bw, bw=bw, kernel="gaussian")
smooth(rocobj, method="density", density.controls=density.controls$y,
density.cases=density.cases$y)
# which is roughly what is done by a simple:
smooth(rocobj, method="density")
## Not run:
## Smoothing artificial ROC curves
rand.unif <- runif(1000, -1, 1)
rand.exp <- rexp(1000)
rand.norm <-
rnorm(1000)
# two normals
roc.norm <- roc(controls=rnorm(1000), cases=rnorm(1000)+1, plot=TRUE)
plot(smooth(roc.norm), col="green", lwd=1, add=TRUE)
plot(smooth(roc.norm, method="density"), col="red", lwd=1, add=TRUE)
plot(smooth(roc.norm, method="fitdistr"), col="blue", lwd=1, add=TRUE)
if (requireNamespace("logcondens")) {
plot(smooth(roc.norm, method="logcondens"), col="brown", lwd=1, add=TRUE)
plot(smooth(roc.norm, method="logcondens.smooth"), col="orange", lwd=1, add=TRUE)
}
legend("bottomright", legend=c("empirical", "binormal", "density", "fitdistr",
"logcondens", "logcondens.smooth"),
col=c(par("fg"), "green", "red", "blue", "brown", "orange"), lwd=c(2, 1, 1, 1))
# deviation from the normality
roc.norm.exp <- roc(controls=rnorm(1000), cases=rexp(1000), plot=TRUE)
plot(smooth(roc.norm.exp), col="green", lwd=1, add=TRUE)
plot(smooth(roc.norm.exp, method="density"), col="red", lwd=1, add=TRUE)
# Wrong fitdistr: normality assumed by default
plot(smooth(roc.norm.exp, method="fitdistr"), col="blue", lwd=1, add=TRUE)
# Correct fitdistr
plot(smooth(roc.norm.exp, method="fitdistr", density.controls="normal",
density.cases="exponential"), col="purple", lwd=1, add=TRUE)
if (requireNamespace("logcondens")) {
plot(smooth(roc.norm.exp, method="logcondens"), col="brown", lwd=1, add=TRUE)
plot(smooth(roc.norm.exp, method="logcondens.smooth"), col="orange", lwd=1, add=TRUE)
}
legend("bottomright", legend=c("empirical", "binormal", "density",
"wrong fitdistr", "correct fitdistr",
"logcondens", "logcondens.smooth"),
col=c(par("fg"), "green", "red", "blue", "purple", "brown", "orange"), lwd=c(2, 1, 1, 1, 1))
# large deviation from the normality
roc.unif.exp <- roc(controls=runif(1000, 2, 3), cases=rexp(1000)+2, plot=TRUE)
plot(smooth(roc.unif.exp), col="green", lwd=1, add=TRUE)
plot(smooth(roc.unif.exp, method="density"), col="red", lwd=1, add=TRUE)
plot(smooth(roc.unif.exp, method="density", bw="ucv"), col="magenta", lwd=1, add=TRUE)
# Wrong fitdistr: normality assumed by default (uniform distributions not handled)
plot(smooth(roc.unif.exp, method="fitdistr"), col="blue", lwd=1, add=TRUE)
if (requireNamespace("logcondens")) {
plot(smooth(roc.unif.exp, method="logcondens"), col="brown", lwd=1, add=TRUE)
plot(smooth(roc.unif.exp, method="logcondens.smooth"), col="orange", lwd=1, add=TRUE)
}
legend("bottomright", legend=c("empirical", "binormal", "density",
"density ucv", "wrong fitdistr",
"logcondens", "logcondens.smooth"),
col=c(par("fg"), "green", "red", "magenta", "blue", "brown", "orange"), lwd=c(2, 1, 1, 1, 1))
## End(Not run)
# 2 uniform distributions with a custom density function
unif.density <- function(x, n, from, to, bw, kernel, ...) {
smooth.x <- seq(from=from, to=to, length.out=n)
smooth.y <- dunif(smooth.x, min=min(x), max=max(x))
return(smooth.y)
}
roc.unif <- roc(controls=runif(1000, -1, 1), cases=runif(1000, 0, 2), plot=TRUE)
s <- smooth(roc.unif, method="density", density=unif.density)
plot(roc.unif)
plot(s, add=TRUE, col="grey")
## Not run:
# you can bootstrap a ROC curve smoothed with a density function:
ci(s, boot.n=100)
## End(Not run)
pROC documentation built on Nov. 2, 2023, 6:05 p.m.
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| smooth | R Documentation |
Smooth a ROC curve
Description
This function smoothes a ROC curve of numeric predictor. By default, a binormal smoothing is performed, but density or custom smoothings are supported.
Usage
smooth(...)
## Default S3 method:
smooth(...)
## S3 method for class 'roc'
smooth(roc,
method=c("binormal", "density", "fitdistr", "logcondens",
"logcondens.smooth"), n=512, bw = "nrd0", density=NULL,
density.controls=density, density.cases=density,
start=NULL, start.controls=start, start.cases=start,
reuse.auc=TRUE, reuse.ci=FALSE, ...)
## S3 method for class 'smooth.roc'
smooth(smooth.roc, ...)
Arguments
roc, smooth.roc |
a “roc” object from the
|
method |
“binormal”, “density”, “fitdistr”, “logcondens”, “"logcondens.smooth"”. |
n |
the number of equally spaced points where the smoothed curve will be calculated. |
bw |
if |
density, density.controls, density.cases |
if
|
start, start.controls, start.cases |
if
|
reuse.auc, reuse.ci |
if |
... |
further arguments passed to or from other methods, and
especially to |
Details
If method="binormal", a linear model is fitted to the quantiles of
the sensitivities and specificities. Smoothed sensitivities and
specificities are then generated from this model on n points.
This simple approach was found to work well for most ROC curves, but
it may produce hooked smooths in some situations (see in Hanley (1988)).
With method="density", the density
function is employed to generate a smooth kernel
density of the control and case observations as described by Zhou
et al. (1997), unless
density.controls or density.cases are provided
directly. bw can be given to
specify a bandwidth to use with density. It can be a
numeric value or a character string (“nrd0”, “nrd”,
“ucv”, “bcv” or “SJ”, but any name
matching a function prefixed with “bw.” is
supported). In the case of a character
string, the whole predictor data is employed to determine the numeric
value to use on both controls and cases.
Depending on your data, it might be a good idea to specify the
kernel argument for density. By default,
“gaussian” is used, but “epanechnikov”,
“rectangular”, “triangular”, “biweight”,
“cosine” and “optcosine” are supported. As all the
kernels are symetrical, 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))
smooth(roc(response, norm.x, ...), ...)
Additionally, density can be a function which must return
either a numeric vector of densities over the y axis or a list
with a “y” item like the density function. It
must accept the following input:
density.fun(x, n, from, to, bw, kernel, ...)
It is important to honour n, from and to in order
to have the densities evaluated on the same points for controls and
cases. Failing to do so and returning densities of different length
will produce an error. It is also a good idea to use a constant
smoothing parameter (such as bw) especially when controls and
cases have a different number of observations, to avoid producing
smoother or rougher densities.
If method="fitdistr", the fitdistr
function from the MASS package is employed to fit parameters for
the density function density with optionnal start parameters
start. The density function are fitted
separately in control (density.controls, start.controls)
and case observations (density.cases,
start.cases). density can be one of the character values
allowed by fitdistr or a density function (such
as dnorm, dweibull, ...).
The method="logcondens" and method="logcondens.smooth" use the
logcondens package to generate a non smoothed or smoothed
(respectively) log-concave density estimate of of the control and case
observation with the logConROC function.
smooth.default forces the usage of the
smooth function in the stats package, so
that other code relying on smooth should continue to function
normally.
Smoothed ROC curves can be passed to smooth again. In this case, the smoothing is not re-applied on the smoothed ROC curve but the original “roc” object will be re-used.
Note that a smooth.roc curve has no threshold.
Value
A list of class “smooth.roc” with the following fields:
sensitivities |
the smoothed sensitivities defining the ROC curve. |
specificities |
the smoothed specificities defining the ROC curve. |
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. |
call |
how the function was called. See |
smoothing.args |
a list of the arguments used for the smoothing. Will serve to apply the smoothing again in further bootstrap operations. |
auc |
if the original ROC curve contained an AUC, it is computed again on the smoothed ROC. |
ci |
if the original ROC curve contained a CI, it is computed again on the smoothed ROC. |
fit.controls, fit.cases |
with |
logcondens |
with |
model |
with |
Attributes
Additionally, the original roc object is stored as a
“roc” attribute.
Errors
The message “The 'density' function must return a numeric
vector or a list with a 'y' item.” will be displayed if the
density function did not return a valid output. The message
“Length of 'density.controls' and 'density.cases' differ.”
will be displayed if the returned value differ in length.
Binormal smoothing cannot smooth ROC curve defined by only one point. Any such attempt will fail with the error “ROC curve not smoothable (not enough points).”.
If the smooth ROC curve was generated by roc with
density.controls and density.cases numeric arguments, it
cannot be smoothed and the error “Cannot smooth a ROC curve
generated directly with numeric 'density.controls' and
'density.cases'.” is produced.
fitdistr and density smoothing methods require a
numeric predictor. If the ROC curve to smooth was
generated with an ordered factor only binormal smoothing can be
applied and the message “ROC curves of ordered predictors can
be smoothed only with binormal smoothing.” is displayed otherwise.
fitdistr, logcondens and logcondens.smooth methods
require additional packages. If not available, the following message
will be displayed with the required command to install the package:
“Package ? not available, required with method='?'.
Please install it with 'install.packages("?")'.
”
References
James E. Hanley (1988) “The robustness of the “binormal” assumptions used in fitting ROC curves”. Medical Decision Making 8, 197–203.
Lutz Duembgen, Kaspar Rufibach (2011) “logcondens: Computations Related to Univariate Log-Concave Density Estimation”. Journal of Statistical Software, 39, 1–28. URL: \Sexpr[results=rd]{tools:::Rd_expr_doi("10.18637/jss.v039.i06")}.
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")}.
Kaspar Rufibach (2011) “A Smooth ROC Curve Estimator Based on Log-Concave Density Estimates”. The International Journal of Biostatistics, 8, accepted. DOI: \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1515/1557-4679.1378")}. arXiv: arXiv:1103.1787.
William N. Venables, Brian D. Ripley (2002). “Modern Applied Statistics with S”. New York, Springer. Google books.
Kelly H. Zou, W. J. Hall and David E. Shapiro (1997) “Smooth non-parametric receiver operating characteristic (ROC) curves for continuous diagnostic tests”. Statistics in Medicine 18, 2143–2156. DOI: \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1002/(SICI)1097-0258(19971015)16:19<2143::AID-SIM655>3.0.CO;2-3")}.
See Also
roc
CRAN packages MASS and logcondens employed in this function.
Examples
data(aSAH)
## Basic example
rocobj <- roc(aSAH$outcome, aSAH$s100b)
smooth(rocobj)
# or directly with roc()
roc(aSAH$outcome, aSAH$s100b, smooth=TRUE)
# plotting
plot(rocobj)
rs <- smooth(rocobj, method="binormal")
plot(rs, add=TRUE, col="green")
rs2 <- smooth(rocobj, method="density")
plot(rs2, add=TRUE, col="blue")
rs3 <- smooth(rocobj, method="fitdistr", density="lognormal")
plot(rs3, add=TRUE, col="magenta")
if (requireNamespace("logcondens")) {
rs4 <- smooth(rocobj, method="logcondens")
plot(rs4, add=TRUE, col="brown")
rs5 <- smooth(rocobj, method="logcondens.smooth")
plot(rs5, add=TRUE, col="orange")
}
legend("bottomright", legend=c("Empirical", "Binormal", "Density", "Log-normal",
"Log-concave density", "Smoothed log-concave density"),
col=c("black", "green", "blue", "magenta", "brown", "orange"), lwd=2)
## Advanced smoothing
# if we know the distributions are normal with sd=0.1 and an unknown mean:
smooth(rocobj, method="fitdistr", density=dnorm, start=list(mean=1), sd=.1)
# different distibutions for controls and cases:
smooth(rocobj, method="fitdistr", density.controls="normal", density.cases="lognormal")
# with densities
bw <- bw.nrd0(rocobj$predictor)
density.controls <- density(rocobj$controls, from=min(rocobj$predictor) - 3 * bw,
to=max(rocobj$predictor) + 3*bw, bw=bw, kernel="gaussian")
density.cases <- density(rocobj$cases, from=min(rocobj$predictor) - 3 * bw,
to=max(rocobj$predictor) + 3*bw, bw=bw, kernel="gaussian")
smooth(rocobj, method="density", density.controls=density.controls$y,
density.cases=density.cases$y)
# which is roughly what is done by a simple:
smooth(rocobj, method="density")
## Not run:
## Smoothing artificial ROC curves
rand.unif <- runif(1000, -1, 1)
rand.exp <- rexp(1000)
rand.norm <-
rnorm(1000)
# two normals
roc.norm <- roc(controls=rnorm(1000), cases=rnorm(1000)+1, plot=TRUE)
plot(smooth(roc.norm), col="green", lwd=1, add=TRUE)
plot(smooth(roc.norm, method="density"), col="red", lwd=1, add=TRUE)
plot(smooth(roc.norm, method="fitdistr"), col="blue", lwd=1, add=TRUE)
if (requireNamespace("logcondens")) {
plot(smooth(roc.norm, method="logcondens"), col="brown", lwd=1, add=TRUE)
plot(smooth(roc.norm, method="logcondens.smooth"), col="orange", lwd=1, add=TRUE)
}
legend("bottomright", legend=c("empirical", "binormal", "density", "fitdistr",
"logcondens", "logcondens.smooth"),
col=c(par("fg"), "green", "red", "blue", "brown", "orange"), lwd=c(2, 1, 1, 1))
# deviation from the normality
roc.norm.exp <- roc(controls=rnorm(1000), cases=rexp(1000), plot=TRUE)
plot(smooth(roc.norm.exp), col="green", lwd=1, add=TRUE)
plot(smooth(roc.norm.exp, method="density"), col="red", lwd=1, add=TRUE)
# Wrong fitdistr: normality assumed by default
plot(smooth(roc.norm.exp, method="fitdistr"), col="blue", lwd=1, add=TRUE)
# Correct fitdistr
plot(smooth(roc.norm.exp, method="fitdistr", density.controls="normal",
density.cases="exponential"), col="purple", lwd=1, add=TRUE)
if (requireNamespace("logcondens")) {
plot(smooth(roc.norm.exp, method="logcondens"), col="brown", lwd=1, add=TRUE)
plot(smooth(roc.norm.exp, method="logcondens.smooth"), col="orange", lwd=1, add=TRUE)
}
legend("bottomright", legend=c("empirical", "binormal", "density",
"wrong fitdistr", "correct fitdistr",
"logcondens", "logcondens.smooth"),
col=c(par("fg"), "green", "red", "blue", "purple", "brown", "orange"), lwd=c(2, 1, 1, 1, 1))
# large deviation from the normality
roc.unif.exp <- roc(controls=runif(1000, 2, 3), cases=rexp(1000)+2, plot=TRUE)
plot(smooth(roc.unif.exp), col="green", lwd=1, add=TRUE)
plot(smooth(roc.unif.exp, method="density"), col="red", lwd=1, add=TRUE)
plot(smooth(roc.unif.exp, method="density", bw="ucv"), col="magenta", lwd=1, add=TRUE)
# Wrong fitdistr: normality assumed by default (uniform distributions not handled)
plot(smooth(roc.unif.exp, method="fitdistr"), col="blue", lwd=1, add=TRUE)
if (requireNamespace("logcondens")) {
plot(smooth(roc.unif.exp, method="logcondens"), col="brown", lwd=1, add=TRUE)
plot(smooth(roc.unif.exp, method="logcondens.smooth"), col="orange", lwd=1, add=TRUE)
}
legend("bottomright", legend=c("empirical", "binormal", "density",
"density ucv", "wrong fitdistr",
"logcondens", "logcondens.smooth"),
col=c(par("fg"), "green", "red", "magenta", "blue", "brown", "orange"), lwd=c(2, 1, 1, 1, 1))
## End(Not run)
# 2 uniform distributions with a custom density function
unif.density <- function(x, n, from, to, bw, kernel, ...) {
smooth.x <- seq(from=from, to=to, length.out=n)
smooth.y <- dunif(smooth.x, min=min(x), max=max(x))
return(smooth.y)
}
roc.unif <- roc(controls=runif(1000, -1, 1), cases=runif(1000, 0, 2), plot=TRUE)
s <- smooth(roc.unif, method="density", density=unif.density)
plot(roc.unif)
plot(s, add=TRUE, col="grey")
## Not run:
# you can bootstrap a ROC curve smoothed with a density function:
ci(s, boot.n=100)
## End(Not run)
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