| evalHillEqn {braidrm} | R Documentation |
Calculate and Invert Hill Equation
Description
Calculates the response of a four-parameter Hill (or log-logistic) dose-response model, or determines the concentrations which yield the given response.
Usage
evalHillEqn(conc, parv)
invertHillEqn(val, parv)
Arguments
conc |
a vector of concentrations to be passed as input into the model |
parv |
a four-element vector specifying the full parameter set of a particular Hill model |
val |
a vector of responses to be inverted in a particular Hill model |
Details
There is some ambiguity in how the parameters of a Hill or log-logistic model are specified. We have chosen to use the following equation:
E(D) = E_0 + \frac{E_f-E_0}{1+\left(\frac{D}{{ID}_M}\right)^{-n}}
where the Hill slope n is always positive. Using this equation, the parameter vector for a Hill model is
(n,E_0,E_f,ln{{ID}_M}) (note that the fourth parameter value is log-transformed in the
parameter vector).
Value
For evalHillEqn a vector of responses resulting from the given concentrations. For invertHillEqn, a vector
of concentrations that produce the given responses; responses beyond the model's maximal effect will produce a value of Inf,
while responses that do not reach the model's baseline effect produce a value of 0.
Author(s)
Nathaniel R. Twarog
See Also
Examples
act <- evalHillEqn(exp(seq(log(10^-8),log(10^-5),length=100)),parv=c(2,0,100,log(10^-6)))
ec90 <- invertHillEqn(90,parv=c(2,0,100,log(10^-6)))