`npv`

estimates the npv (a.k.a. positive predictive
value -PPV-) for a nominal/categorical predicted-observed dataset.

`FOR`

estimates the false omission rate, which is the complement
of the negative predictive value for a nominal/categorical predicted-observed dataset.

## Usage

```
npv(
data = NULL,
obs,
pred,
atom = FALSE,
pos_level = 2,
tidy = FALSE,
na.rm = TRUE
)
FOR(
data = NULL,
obs,
pred,
atom = FALSE,
pos_level = 2,
tidy = FALSE,
na.rm = TRUE
)
```

## Arguments

- data
(Optional) argument to call an existing data frame containing the data.

- obs
Vector with observed values (character | factor).

- pred
Vector with predicted values (character | factor).

- atom
Logical operator (TRUE/FALSE) to decide if the estimate is made for each class (atom = TRUE) or at a global level (atom = FALSE); Default : FALSE.

- pos_level
Integer, for binary cases, indicating the order (1|2) of the level corresponding to the positive. Generally, the positive level is the second (2) since following an alpha-numeric order, the most common pairs are

`(Negative | Positive)`

,`(0 | 1)`

,`(FALSE | TRUE)`

. Default : 2.- tidy
Logical operator (TRUE/FALSE) to decide the type of return. TRUE returns a data.frame, FALSE returns a list; Default : FALSE.

- na.rm
Logic argument to remove rows with missing values (NA). Default is na.rm = TRUE.

## Value

an object of class `numeric`

within a `list`

(if tidy = FALSE) or within a
`data frame`

(if tidy = TRUE).

## Details

The npv is a non-normalized coefficient that represents the ratio between the correctly predicted cases (or true positive -TP- for binary cases) to the total predicted observations for a given class (or total predicted positive -PP- for binary cases) or at overall level.

For binomial cases, \(npv = \frac{TP}{PP} = \frac{TP}{TP + FP} \)

The `npv`

metric is bounded between 0 and 1. The closer to 1 the better.
Values towards zero indicate low npv of predictions. It can be estimated
for each particular class or at a global level.

The false omission rate (FOR) represents the proportion of false negatives with respect to the number of negative predictions (PN).

For binomial cases, \(FOR = 1 - npv = \frac{FN}{PN} = \frac{FN}{TN + FN} \)

The `npv`

metric is bounded between 0 and 1. The closer to 1 the better.
Values towards zero indicate low npv of predictions.

For the formula and more details, see online-documentation

## References

Wang H., Zheng H. (2013).
Negative Predictive Value.
*In: Dubitzky W., Wolkenhauer O., Cho KH., Yokota H. (eds) Encyclopedia of Systems Biology.*
_ Springer, New York, NY._ doi:10.1007/978-1-4419-9863-7_234

Trevethan, R. (2017).
*Sensitivity, Specificity, and Predictive Values: Foundations, Pliabilities, and Pitfalls*
_ in Research and Practice. Front. Public Health 5:307_ doi:10.3389/fpubh.2017.00307

## Examples

```
# \donttest{
set.seed(123)
# Two-class
binomial_case <- data.frame(labels = sample(c("True","False"), 100,
replace = TRUE), predictions = sample(c("True","False"), 100, replace = TRUE))
# Multi-class
multinomial_case <- data.frame(labels = sample(c("Red","Blue", "Green"), 100,
replace = TRUE), predictions = sample(c("Red","Blue", "Green"), 100, replace = TRUE))
# Get npv estimate for two-class case
npv(data = binomial_case, obs = labels, pred = predictions, tidy = TRUE)
#> npv
#> 1 0.4259259
# Get fdr estimate for two-class case
FDR(data = binomial_case, obs = labels, pred = predictions, tidy = TRUE)
#> FDR
#> 1 0.4347826
# Get npv estimate for each class for the multi-class case
npv(data = multinomial_case, obs = labels, pred = predictions, tidy = TRUE, atom = TRUE)
#> npv
#> Blue 0.6521739
#> Green 0.7428571
#> Red 0.5245902
# Get npv estimate for the multi-class case at a global level
npv(data = multinomial_case, obs = labels, pred = predictions, tidy = TRUE, atom = TRUE)
#> npv
#> Blue 0.6521739
#> Green 0.7428571
#> Red 0.5245902
# }
```