pROC (version 1.3.1)

ci.se: Compute the confidence interval of sensitivities at given specificities

Description

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

Usage

ci.se(...)
## S3 method for class 'roc':
ci.se(roc, specificities = seq(0, 1, .1) * ifelse(roc$percent,
100, 1), conf.level=0.95, boot.n=2000, boot.stratified=TRUE,
progress=getOption("pROCProgress")$name, ...) 
## S3 method for class 'smooth.roc':
ci.se(smooth.roc, specificities = seq(0, 1, .1) *
ifelse(smooth.roc$percent, 100, 1), conf.level=0.95, boot.n=2000,
boot.stratified=TRUE, progress=getOption("pROCProgress")$name, ...)
## S3 method for class 'formula':
ci.se(formula, data, ...)
## S3 method for class 'default':
ci.se(response, predictor, ...)

Arguments

roc, smooth.roc

a roc object from the roc function, or a smooth.roc object from the smooth.roc function.

response, predictor

arguments for the roc function.

formula, data

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

specificities

on which specificities to evaluate the CI.

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.

progress

the name of progress bar to display. Typically none, win, tk or text (see the name argument to create_progress_b

...

further arguments passed to or from other methods, especially arguments for roc and ci.se.roc when calling ci.se.default or ci.se.formula. Arguments for

Value

• A matrix of CI for the given sensitivities. Row (names) are the specificities, the first column the lower bound, the 2nd column the median and the 3rd column the upper bound.

  Additionally, the list has the following attributes:

• conf.level
  the width of the CI, in fraction.
• boot.n
  the number of bootstrap replicates.
• boot.stratified
  whether or not the bootstrapping was stratified.
• specificities
  the specificities as given in argument.
• roc
  the object of class roc that was used to compute the CI.

encoding

UTF-8

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, 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.

Errors

If density.cases and density.controls were provided for smoothing, the error Cannot compute the statistic on ROC curves smoothed with density.controls and density.cases. is issued.

Details

ci.se.formula and ci.se.default are convenience methods that build the ROC curve (with the roc function) before calling ci.se.roc. You can pass them arguments for both roc and ci.se.roc. Simply use ci.se that will dispatch to the correct method. The ci.se.roc function creates boot.n bootstrap replicate of the ROC curve, and evaluates the sensitivity at specificities given by the specificities argument. Then it computes the confidence interval as the percentiles given by conf.level.

Stratification of bootstrap can be controlled with boot.stratified. In stratified bootstrap, each replicate contains the same number of cases and controls than the original sample. Stratification is especially useful if one group has only little observations, or if groups are not balanced. Higher numbers of boot.n will give a more precise estimate of the CI, but take more time to compute. 2000 is recommanded by Carpenter and Bithell.

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.

References

Tom Fawcett (2006) ``An introduction to ROC analysis''. Pattern Recognition Letters 27, 861--874. DOI: 10.1016/j.patrec.2005.10.010.

James Carpenter and John Bithell (2000) ``Bootstrap condence intervals: when, which, what? A practical guide for medical statisticians''. Statistics in Medicine 19, 1141--1164.

See Also

roc, ci, ci.sp, plot.ci

Examples

data(aSAH)

# Syntax (response, predictor):
ci.se(aSAH$outcome, aSAH$s100b)

# With a roc object and less bootstrap:
rocobj <- roc(aSAH$outcome, aSAH$s100b)
ci.se(rocobj, boot.n=100)

# Customized bootstrap and specific specificities:
ci.se(rocobj, c(.95, .9, .85), boot.n=500, conf.level=0.9, stratified=FALSE)

# Alternatively, you can get the CI directly from roc():
rocobj <- roc(aSAH$outcome,
              aSAH$s100b, ci=TRUE, of="se", boot.n=100)
rocobj$ci

# Plotting the CI
plot(rocobj)
plot(rocobj$ci)

# On a smoothed ROC, the CI is re-computed automatically
smooth(rocobj)
# Or you can compute a new one:
ci.se(smooth(rocobj, method="density", reuse.ci=FALSE), boot.n=100)