Calculate sensitivity, specificity and predictive values

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.

negPredValue(data, ...)

# S3 method for default
negPredValue(data, reference,
  negative = levels(reference)[2], prevalence = NULL, ...)

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

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

posPredValue(data, ...)

# S3 method for default
posPredValue(data, reference,
  positive = levels(reference)[1], prevalence = NULL, ...)

# S3 method for table
posPredValue(data, positive = rownames(data)[1],
  prevalence = NULL, ...)

# S3 method for matrix
posPredValue(data, positive = rownames(data)[1],
  prevalence = NULL, ...)

sensitivity(data, ...)

# S3 method for default
sensitivity(data, reference,
  positive = levels(reference)[1], na.rm = TRUE, ...)

# S3 method for table
sensitivity(data, positive = rownames(data)[1], ...)

# S3 method for matrix
sensitivity(data, positive = 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

Value

A number between 0 and 1 (or NA).

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.

References

Kuhn, M. (2008), ``Building predictive models in R using the caret package, '' Journal of Statistical Software, (http://www.jstatsoft.org/article/view/v028i05/v28i05.pdf).

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.

See also

confusionMatrix

Examples

if (FALSE) {
###################
## 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"))
}