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], ...)

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

A number between 0 and 1 (or NA).

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.

Kuhn, M. (2008), ``Building predictive models in R using the
caret package, '' *Journal of Statistical Software*,
(https://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.

# NOT RUN { # } # 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")) # } # NOT RUN { # }