ROCc {glmtoolbox}

The Receiver Operating Characteristic (ROC) Curve

Description

Computes the exact area under the ROC curve (AUROC), the Gini coefficient, and the Kolmogorov-Smirnov (KS) statistic for a binary classifier. Optionally, this function can plot the ROC curve, that is, the plot of the estimates of Sensitivity versus the estimates of 1-Specificity. This function also computes confidence intervals for AUROC and Gini coefficient using the method proposed by DeLong et al. (1988).

Usage

ROCc(
  object,
  plot.it = TRUE,
  verbose = TRUE,
  level = 0.95,
  digits = max(3, getOption("digits") - 2),
  ...
)

Arguments

object

a matrix with two columns: the first one is a numeric vector of 1's and 0's indicating whether each row is a "success" or a "failure"; the second one is a numeric vector of values indicating the probability (or propensity score) of each row to be a "success". Optionally, object can be an object of the class glm which is obtained from the fit of a generalized linear model where the distribution of the response variable is assumed to be binomial.

plot.it

an (optional) logical switch indicating if the plot of the ROC curve is required or just the data matrix in which it is based. As default, plot.it is set to TRUE.

verbose

an (optional) logical switch indicating if should the report of results be printed. As default, verbose is set to TRUE.

level

an (optional) value indicating the required confidence level. As default, level is set to 0.95.

digits

an (optional) integer value indicating the number of decimal places to be used. As default, digits is set to max(3, getOption("digits") - 2).

...

further arguments passed to or from other methods. For example, if plot.it=TRUE then ... may to include graphical parameters as col, pch, cex, main, sub, xlab, ylab.

Value

A list which contains the following objects:

roc

A matrix with the Cutoffs and the associated estimates of Sensitivity and Specificity.

auroc

The exact area under the ROC curve.

ci.auroc

Confidence interval for the area under the ROC curve.

gini

The value of the Gini coefficient computed as 2(auroc-0.5).

ci.gini

Confidence interval for the Gini coefficient.

ks

The value of the Kolmogorov-Smirnov statistic computed as the maximum value of |1-Sensitivity-Specificity|.

References

Cho H., Matthews G.J., Harel O. (2019) Confidence Intervals for the Area Under the Receiver Operating Characteristic Curve in the Presence of Ignorable Missing Data. International statistical review 87, 152–177.

DeLong E.R., DeLong D.M., Clarke-Pearson D.L. (1988). Comparing the areas under two or more correlated receiver operating characteristic curves: a nonparametric approach. Biometrics 44, 837–845.

Nahm F.S. (2022). Receiver operating characteristic curve: overview and practical use for clinicians. Korean journal of anesthesiology 75, 25–36.

Hanley J.A., McNeil B.J. (1982) The Meaning and Use of the Area under a Receiver Operating Characteristic (ROC) Curve. Radiology 143, 29–36.

Examples

###### Example: Patients with burn injuries
burn1000 <- aplore3::burn1000
burn1000 <- within(burn1000, death2 <- ifelse(death=="Dead",1,0))

### splitting the sample: 70% for the training sample and 30% for the validation sample
train <- sample(1:nrow(burn1000),size=nrow(burn1000)*0.7)
traindata <- burn1000[train,]
testdata <- burn1000[-train,]

fit <- glm(death ~ age*inh_inj + tbsa*inh_inj, family=binomial("logit"), data=traindata)
probs <- predict(fit, newdata=testdata, type="response")

### ROC curve for the validation sample
ROCc(cbind(testdata[,"death2"],probs), col="red", col.lab="blue", col.axis="black",
     col.main="black", family="mono")