| 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))