# ci.thresholds

##### Compute the confidence interval of thresholds

This function computes the confidence interval (CI) of the sensitivity and specificity of the thresholds given in argument. By default, the 95% CI are computed with 2000 stratified bootstrap replicates.

- Keywords
- utilities, nonparametric, univar, ROC

##### Usage

```
# ci.thresholds(...)
# S3 method for roc
ci.thresholds(roc, conf.level=0.95, boot.n=2000,
boot.stratified=TRUE, thresholds = "local maximas",
progress=getOption("pROCProgress")$name, parallel=FALSE, ...)
# S3 method for formula
ci.thresholds(formula, data, ...)
# S3 method for smooth.roc
ci.thresholds(smooth.roc, ...)
# S3 method for default
ci.thresholds(response, predictor, ...)
```

##### Arguments

- roc
a “roc” object from the

`roc`

function.- smooth.roc
not available for smoothed ROC curves, available only to catch the error and provide a clear error message.

- response, predictor
arguments for the

`roc`

function.- formula, data
a formula (and possibly a data object) of type response~predictor for the

`roc`

function.- conf.level
the width of the confidence interval as [0,1], never in percent. Default: 0.95, resulting in a 95% CI.

- boot.n
the number of bootstrap replicates. Default: 2000.

- boot.stratified
should the bootstrap be stratified (default, same number of cases/controls in each replicate than in the original sample) or not.

- thresholds
on which thresholds to evaluate the CI. Either the numeric values of the thresholds, a logical vector (as index of

`roc$thresholds`

) or a character “all”, “local maximas” or “best” that will be used to determine the threshold(s) on the supplied curve with`coords`

(not on the resampled curves).- 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

`roc`

and`ci.thresholds.roc`

when calling`ci.thresholds.default`

or`ci.thresholds.formula`

. Arguments for`txtProgressBar`

(only`char`

and`style`

) if applicable. Arguments`best.method`

and`best.weights`

to`coords`

.

##### Details

`ci.thresholds.formula`

and `ci.thresholds.default`

are convenience methods
that build the ROC curve (with the `roc`

function) before
calling `ci.thresholds.roc`

. You can pass them arguments for both
`roc`

and `ci.thresholds.roc`

. Simply use `ci.thresholds`

that will dispatch to the correct method.

This function creates `boot.n`

bootstrap replicate of the ROC
curve, and evaluates the sensitivity and specificity at thresholds
given by the `thresholds`

argument. Then it computes the
confidence interval as the percentiles given by `conf.level`

.

A threshold given as a `logical`

vector or `character`

is converted to the corresponding numeric vector once
*using the supplied ROC curve*, and not at each bootstrap iteration. See `ci.coords`

for the latter behaviour.

For more details about the bootstrap, see the Bootstrap section in this package's documentation.

##### Value

A list of length 2 and class “ci.thresholds”, “ci” and “list” (in this order), with the confidence intervals of the CI and the following items:

a matrix of CI for the specificity. Row (names) are the thresholds, the first column the lower bound, the 2nd column the median and the 3rd column the upper bound.

same than specificity.

the width of the CI, in fraction.

the number of bootstrap replicates.

whether or not the bootstrapping was stratified.

the thresholds, as given in argument.

the object of class “roc” that was used to compute the CI.

##### Warnings

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, 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`

.

##### References

James Carpenter and John Bithell (2000) ``Bootstrap condence intervals:
when, which, what? A practical guide for medical statisticians''.
*Statistics in Medicine* **19**, 1141--1164.
DOI: 10.1002/(SICI)1097-0258(20000515)19:9<1141::AID-SIM479>3.0.CO;2-F.

Tom Fawcett (2006) ``An introduction to ROC analysis''. *Pattern
Recognition Letters* **27**, 861--874. 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: 10.1186/1471-2105-12-77.

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

##### Examples

```
# NOT RUN {
data(aSAH)
# Create a ROC curve:
data(aSAH)
roc1 <- roc(aSAH$outcome, aSAH$s100b)
## Basic example ##
# Compute CI of all local maxima thresholds
# }
# NOT RUN {
ci.thresholds(roc1)
# }
# NOT RUN {
## More options ##
# Customized bootstrap and thresholds:
# }
# NOT RUN {
ci.thresholds(roc1,
thresholds=c(0.5, 1, 2),
boot.n=10000, conf.level=0.9, stratified=FALSE)
# }
# NOT RUN {
## Plotting the CI ##
# }
# NOT RUN {
ci1 <- ci.thresholds(roc1)
# }
# NOT RUN {
plot(roc1)
plot(ci1)
# }
```

*Documentation reproduced from package pROC, version 1.16.2, License: GPL (>= 3)*