# sensitivity: Calculate sensitivity, specificity and predictive values In caret: Classification and Regression Training

 negPredValue R Documentation

## Calculate sensitivity, specificity and predictive values

### Description

These functions calculate the sensitivity, specificity or predictive values of a measurement system compared to a reference results (the truth or a gold standard). The measurement and "truth" data must have the same two possible outcomes and one of the outcomes must be thought of as a "positive" results.

### Usage

```negPredValue(data, ...)

## Default S3 method:
negPredValue(
data,
reference,
negative = levels(reference),
prevalence = NULL,
...
)

## S3 method for class 'table'
negPredValue(data, negative = rownames(data)[-1], prevalence = NULL, ...)

## S3 method for class 'matrix'
negPredValue(data, negative = rownames(data)[-1], prevalence = NULL, ...)

posPredValue(data, ...)

## Default S3 method:
posPredValue(
data,
reference,
positive = levels(reference),
prevalence = NULL,
...
)

## S3 method for class 'table'
posPredValue(data, positive = rownames(data), prevalence = NULL, ...)

## S3 method for class 'matrix'
posPredValue(data, positive = rownames(data), prevalence = NULL, ...)

sensitivity(data, ...)

## Default S3 method:
sensitivity(
data,
reference,
positive = levels(reference),
na.rm = TRUE,
...
)

## S3 method for class 'table'
sensitivity(data, positive = rownames(data), ...)

## S3 method for class 'matrix'
sensitivity(data, positive = rownames(data), ...)

specificity(data, ...)

## Default S3 method:
specificity(
data,
reference,
negative = levels(reference)[-1],
na.rm = TRUE,
...
)

## S3 method for class 'table'
specificity(data, negative = rownames(data)[-1], ...)
```

### Arguments

 `data` for the default functions, a factor containing the discrete measurements. For the `table` or `matrix` functions, a table or matric object, respectively. `...` not currently used `reference` a factor containing the reference values `negative` a character string that defines the factor level corresponding to the "negative" results `prevalence` a numeric value for the rate of the "positive" class of the data `positive` a character string that defines the factor level corresponding to the "positive" results `na.rm` a logical value indicating whether `NA` values should be stripped before the computation proceeds

### Details

The sensitivity is defined as the proportion of positive results out of the number of samples which were actually positive. When there are no positive results, sensitivity is not defined and a value of `NA` is returned. Similarly, when there are no negative results, specificity is not defined and a value of `NA` is returned. Similar statements are true for predictive values.

The positive predictive value is defined as the percent of predicted positives that are actually positive while the negative predictive value is defined as the percent of negative positives that are actually negative.

Suppose a 2x2 table with notation

 Reference Predicted Event No Event Event A B No Event C D

The formulas used here are:

Sensitivity = A/(A+C)

Specificity = D/(B+D)

Prevalence = (A+C)/(A+B+C+D)

PPV = (sensitivity * Prevalence)/((sensitivity*Prevalence) + ((1-specificity)*(1-Prevalence)))

NPV = (specificity * (1-Prevalence))/(((1-sensitivity)*Prevalence) + ((specificity)*(1-Prevalence)))

See the references for discussions of the statistics.

### Value

A number between 0 and 1 (or NA).

Max Kuhn

### References

Kuhn, M. (2008), “Building predictive models in R using the caret package, ” Journal of Statistical Software, (doi: 10.18637/jss.v028.i05).

Altman, D.G., Bland, J.M. (1994) “Diagnostic tests 1: sensitivity and specificity,” British Medical Journal, vol 308, 1552.

Altman, D.G., Bland, J.M. (1994) “Diagnostic tests 2: predictive values,” British Medical Journal, vol 309, 102.

`confusionMatrix`

### Examples

```
## Not run:
###################
## 2 class example

lvs <- c("normal", "abnormal")
truth <- factor(rep(lvs, times = c(86, 258)),
levels = rev(lvs))
pred <- factor(
c(
rep(lvs, times = c(54, 32)),
rep(lvs, times = c(27, 231))),
levels = rev(lvs))

xtab <- table(pred, truth)

sensitivity(pred, truth)
sensitivity(xtab)
posPredValue(pred, truth)
posPredValue(pred, truth, prevalence = 0.25)

specificity(pred, truth)
negPredValue(pred, truth)
negPredValue(xtab)
negPredValue(pred, truth, prevalence = 0.25)

prev <- seq(0.001, .99, length = 20)
npvVals <- ppvVals <- prev  * NA
for(i in seq(along = prev))
{
ppvVals[i] <- posPredValue(pred, truth, prevalence = prev[i])
npvVals[i] <- negPredValue(pred, truth, prevalence = prev[i])
}

plot(prev, ppvVals,
ylim = c(0, 1),
type = "l",
ylab = "",
xlab = "Prevalence (i.e. prior)")
points(prev, npvVals, type = "l", col = "red")
abline(h=sensitivity(pred, truth), lty = 2)
abline(h=specificity(pred, truth), lty = 2, col = "red")
legend(.5, .5,
c("ppv", "npv", "sens", "spec"),
col = c("black", "red", "black", "red"),
lty = c(1, 1, 2, 2))

###################
## 3 class example

library(MASS)

fit <- lda(Species ~ ., data = iris)
model <- predict(fit)\$class

irisTabs <- table(model, iris\$Species)

## When passing factors, an error occurs with more
## than two levels
sensitivity(model, iris\$Species)

## When passing a table, more than two levels can
## be used
sensitivity(irisTabs, "versicolor")
specificity(irisTabs, c("setosa", "virginica"))

## End(Not run)

```

caret documentation built on Aug. 9, 2022, 5:11 p.m.