Calculate confidence regions for the empirical ROC curve

Confidence intervals for TPF and FPF are calculated using the exact method of Clopper and Pearson (1934) each at the level 1 - sqrt(1 - alpha). Based on result 2.4 from Pepe (2003), the cross-product of these intervals yields a 1 - alpha

Usage

StatRocci

stat_rocci(
  mapping = NULL,
  data = NULL,
  geom = "rocci",
  position = "identity",
  show.legend = NA,
  inherit.aes = TRUE,
  ci.at = NULL,
  sig.level = 0.05,
  na.rm = TRUE,
  ...
)

Format

An object of class StatRocci (inherits from Stat, ggproto, gg) of length 6.

Arguments

mapping

Set of aesthetic mappings created by aes(). If specified and inherit.aes = TRUE (the default), it is combined with the default mapping at the top level of the plot. You must supply mapping if there is no plot mapping.

data

The data to be displayed in this layer. There are three options:

If NULL, the default, the data is inherited from the plot data as specified in the call to ggplot().

A data.frame, or other object, will override the plot data. All objects will be fortified to produce a data frame. See fortify() for which variables will be created.

A function will be called with a single argument, the plot data. The return value must be a data.frame, and will be used as the layer data. A function can be created from a formula (e.g. ~ head(.x, 10)).

geom

The geometric object to use to display the data for this layer. When using a stat_*() function to construct a layer, the geom argument can be used to override the default coupling between stats and geoms. The geom argument accepts the following:

A Geom ggproto subclass, for example GeomPoint.
A string naming the geom. To give the geom as a string, strip the function name of the geom_ prefix. For example, to use geom_point(), give the geom as "point".
For more information and other ways to specify the geom, see the layer geom documentation.

position

A position adjustment to use on the data for this layer. This can be used in various ways, including to prevent overplotting and improving the display. The position argument accepts the following:

The result of calling a position function, such as position_jitter(). This method allows for passing extra arguments to the position.
A string naming the position adjustment. To give the position as a string, strip the function name of the position_ prefix. For example, to use position_jitter(), give the position as "jitter".
For more information and other ways to specify the position, see the layer position documentation.

show.legend

logical. Should this layer be included in the legends? NA, the default, includes if any aesthetics are mapped. FALSE never includes, and TRUE always includes. It can also be a named logical vector to finely select the aesthetics to display. To include legend keys for all levels, even when no data exists, use TRUE. If NA, all levels are shown in legend, but unobserved levels are omitted.

inherit.aes

If FALSE, overrides the default aesthetics, rather than combining with them.

ci.at

Vector of cutoffs at which to display confidence regions. If NULL, will automatically choose 3 evenly spaced points to display the regions

sig.level

Significance level for the confidence regions

na.rm

Remove missing observations

...

Other arguments passed on to layer()'s params argument. These arguments broadly fall into one of 4 categories below. Notably, further arguments to the position argument, or aesthetics that are required can not be passed through .... Unknown arguments that are not part of the 4 categories below are ignored.

Static aesthetics that are not mapped to a scale, but are at a fixed value and apply to the layer as a whole. For example, colour = "red" or linewidth = 3. The geom's documentation has an Aesthetics section that lists the available options. The 'required' aesthetics cannot be passed on to the params. Please note that while passing unmapped aesthetics as vectors is technically possible, the order and required length is not guaranteed to be parallel to the input data.
When constructing a layer using a stat_*() function, the ... argument can be used to pass on parameters to the geom part of the layer. An example of this is stat_density(geom = "area", outline.type = "both"). The geom's documentation lists which parameters it can accept.
Inversely, when constructing a layer using a geom_*() function, the ... argument can be used to pass on parameters to the stat part of the layer. An example of this is geom_area(stat = "density", adjust = 0.5). The stat's documentation lists which parameters it can accept.
The key_glyph argument of layer() may also be passed on through .... This can be one of the functions described as key glyphs, to change the display of the layer in the legend.

Aesthetics

stat_rocci understands the following aesthetics (required aesthetics are in bold):

m The continuous biomarker/predictor
d The binary outcome, if not coded as 0/1, the smallest level in sort order is assumed to be 0, with a warning
alpha
color
fill
linetype
size

Computed variables

FPF: estimate of false positive fraction
TPF: estimate of true positive fraction
cutoffs: values of m at which estimates are calculated
FPFL: lower bound of confidence region for FPF
FPFU: upper bound of confidence region for FPF
TPFL: lower bound of confidence region for TPF
TPFU: upper bound of confidence region for TPF

References

Clopper, C. J., and Egon S. Pearson. "The use of confidence or fiducial limits illustrated in the case of the binomial." Biometrika (1934): 404-413.
Pepe, M.S. "The Statistical Evaluation of Medical Tests for Classification and Prediction." Oxford (2003).

Examples

D.ex <- rbinom(50, 1, .5)
rocdata <- data.frame(D = c(D.ex, D.ex), 
                   M = c(rnorm(50, mean = D.ex, sd = .4), rnorm(50, mean = D.ex, sd = 1)), 
                   Z = c(rep("A", 50), rep("B", 50)))

ggplot(rocdata, aes(m = M, d = D)) + geom_roc() + stat_rocci()

ggplot(rocdata, aes(m = M, d = D)) + geom_roc() + 
stat_rocci(ci.at = quantile(rocdata$M, c(.1, .3, .5, .7, .9)))