negPredValue

0th

Percentile

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.

Keywords
manip
Usage
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

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).

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

Aliases
  • negPredValue
  • negPredValue.default
  • negPredValue.table
  • negPredValue.matrix
  • posPredValue
  • posPredValue.default
  • posPredValue.table
  • posPredValue.matrix
  • sensitivity
  • sensitivity.default
  • sensitivity.table
  • sensitivity.matrix
  • specificity
  • specificity.default
  • specificity.table
  • specificity.matrix
  • posPredValue
  • posPredValue.default
  • posPredValue.table
  • posPredValue.matrix
  • negPredValue
  • negPredValue.default
  • negPredValue.table
  • negPredValue.matrix
  • sensitivity.default
  • sensitivity.table
  • sensitivity.matrix
Examples
# 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 {
# }
Documentation reproduced from package caret, version 6.0-80, License: GPL (>= 2)

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