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Concordance Statistic (C-Statistic / AUC)

Source: R/cStat.R
cStat.Rd

Computes the concordance statistic (C-statistic), equivalent to the area under the ROC curve (AUC), for predicted values and a binary outcome.

Usage

cStat(x, ...)

# S3 method for class 'glm'
cStat(x, ...)

# Default S3 method
cStat(x, resp, conf.level = NA, ...)

Arguments

x

an object for which the C-statistic should be computed; for the default method, a numeric vector of predicted values

...

additional arguments passed to methods

resp

a binary response vector (numeric, logical, or factor)

conf.level

confidence level for the interval; NA (default) suppresses interval calculation

Value

if conf.level = NA, an unnamed numeric scalar between 0 and 1; otherwise a named numeric vector with elements:

est

point estimate of the C-statistic.

lci

lower confidence interval bound.

uci

upper confidence interval bound.

Details

The C-statistic is defined as the probability that, for a randomly chosen pair of observations with different outcomes, the observation with the higher predicted value has the higher observed outcome.

Ties in predicted values are handled by assigning a weight of 0.5.

resp is converted with as.numeric(factor(resp)) - 1, so the second level in sort order counts as the event - 1 for a 0/1 coding, TRUE for a logical, and the second factor level otherwise. Getting this backwards returns \(1 - C\) rather than an error, so check the level order when the response is a factor with unusual labels.

This implementation uses:

  • O(n log n) concordance computation

  • Parallel bootstrap confidence intervals via RcppParallel

  • Efficient memory handling

The number of bootstrap samples can be supplied through ... as R; the default is 1000.

Random number generation

A confidence level triggers a bootstrap, which draws a seed from R's global random number generator and therefore advances it. Call base::set.seed() beforehand for reproducible intervals.

See also

Other assoc.ordinal: conDisPairs(), kendallW(), ordAssocs()

Examples

# Default method
set.seed(1)
x <- runif(100)
y <- rbinom(100, 1, 0.5)
cStat(x, resp = y)
#> [1] 0.4569243

# GLM method
r.mod <- glm(complaint ~ temperature + wrongpizza + wine_ordered,
             data = bedrock::Pizza, family = binomial)
cStat(r.mod, conf.level = 0.95)
#>       est       lci       uci 
#> 0.6251552 0.5786945 0.6705040