naac: Area above the curve

In drda: Dose-Response Data Analysis

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.

See Also

nauc for the Normalized Area Under the Curve (NAUC).

Examples

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

drda documentation built on April 3, 2025, 6 p.m.