naac {drda} R Documentation

## Area above the curve

### Description

Evaluate the normalized area above the curve (NAAC).

### Usage

naac(object, xlim, ylim)


### Arguments

 object fit object as returned by drda. xlim numeric vector of length 2 with the lower and upped bound of the integration interval. Default is c(-10, 10) for the logistic function or c(0, 1000) for the log-logistic function. ylim numeric vector of length 2 with the lower and upped bound of the allowed function values. Default is c(0, 1).

### 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.

The normalized area above the curve (NAAC) is simply NAAC = 1 - NAUC.

### Value

Numeric value representing the normalized area above the curve.

nauc for the Normalized Area Under the Curve (NAUC).
drda_fit <- drda(response ~ log_dose, data = voropm2)