sensitivity
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.
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.
- Keywords
- manip
Usage
sensitivity(data, ...)
## S3 method for class 'default':
sensitivity(data, reference, positive = levels(reference)[1], ...)
## S3 method for class 'table':
sensitivity(data, positive = rownames(data)[1], ...)
## S3 method for class 'matrix':
sensitivity(data, positive = rownames(data)[1], ...)specificity(data, ...)
## S3 method for class 'default':
specificity(data, reference, negative = levels(reference)[-1], ...)
## S3 method for class 'table':
specificity(data, negative = rownames(data)[-1], ...)
## S3 method for class 'matrix':
specificity(data, negative = rownames(data)[-1], ...)
posPredValue(data, ...)
## S3 method for class 'default':
posPredValue(data, reference, positive = levels(reference)[1],
prevalence = NULL, ...)
## S3 method for class 'table':
posPredValue(data, positive = rownames(data)[1], prevalence = NULL, ...)
## S3 method for class 'matrix':
posPredValue(data, positive = rownames(data)[1], prevalence = NULL, ...)
negPredValue(data, ...)
## S3 method for class 'default':
negPredValue(data, reference, negative = levels(reference)[2],
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, ...)
Arguments
- data
- for the default functions, a factor containing the discrete measurements. For the
table
ormatrix
functions, a table or matric object, respectively. - reference
- a factor containing the reference values
- positive
- a character string that defines the factor level corresponding to the "positive" results
- 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
- ...
- not currently used
Details
Suppose a 2x2 table with notation
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 discusions of the statistics.
Value
- A number between 0 and 1 (or NA).
References
Kuhn, M. (2008), ``Building predictive models in R using the caret package, '' Journal of Statistical Software, (
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
Examples
###################
## 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"))