nauc {drda} | R Documentation |

## Area under the curve

### Description

Evaluate the normalized area under the curve (NAUC).

### Usage

```
nauc(object, xlim, ylim)
```

### Arguments

`object` |
fit object as returned by |

`xlim` |
numeric vector of length 2 with the lower and upped bound of the
integration interval. Default is |

`ylim` |
numeric vector of length 2 with the lower and upped bound of the
allowed function values. Default is |

### Details

The area under the curve (AUC) is the integral of the chosen model
`y(x; theta)`

with respect to `x`

.

In real applications the response variable is usually contained within a
known interval. For example, if our response represents relative viability
against a control compound, the curve is expected to be between 0 and 1.
Let `ylim = c(yl, yu)`

represent the admissible range of our function
`y(x; theta)`

, that is `yl`

is its lower bound and `yu`

its upper bound.
Let `xlim = c(xl, xu)`

represent the admissible range of the predictor
variable `x`

. For example, when `x`

represent the dose, the boundaries
are the minimum and maximum doses we can administer.

To make the AUC value comparable between different compounds and/or studies,
this function sets a hard constraint on both the `x`

variable and the
function `y`

. The intervals can always be changed if needed.

The integral calculated by this function is of the piece-wise function
`f(x; theta)`

defined as

`f(x; theta) = yl`

, if `y(x; theta) < yl`

`f(x; theta) = y(x; theta)`

, if `yl <= y(x; theta) <= yu`

`f(x; theta) = yu`

, if `y(x; theta) > yu`

The AUC is finally normalized by its maximum possible value, that is the
area of the rectangle with width `xu - xl`

and height `yu - yl`

.

### Value

Numeric value representing the normalized area under the curve.

### See Also

`naac`

for the Normalized Area Above the Curve
(NAAC).

### Examples

```
drda_fit <- drda(response ~ log_dose, data = voropm2)
nauc(drda_fit)
nauc(drda_fit, xlim = c(6, 8), ylim = c(0.2, 0.5))
```

*drda*version 2.0.3 Index]