Inverse function of Hill equation

For the dose-response Hill equation of a drug defined by \(E(x) = E_{inf}+\frac{1-E_{inf}}{1+(\frac{x}{EC50})^(\frac{1}{HS})}\), that computes the response in viability from a dose in micromole for a drug, this function is the inverse function of the Hill curve that computes the dose required to produce a given response: \( f^{-1}(E) = EC50 ( \frac{1-E}{E-E_{inf}} )^{\frac{1}{HS}} ) \)

Usage

effectToDose(viability, EC50, HS, E_inf, is_pct = FALSE)

Arguments

viability

numeric is a vector whose entries are the viability values in the range [0, 1] if is_pct is FALSE or [0, 100] if it is TRUE.

EC50

numeric is a vector of relative EC50 for drug-response equation.

HS

numeric Hill coefficient of the drug-response equation that represents the sigmoidity of the curve.

E_inf

numeric the maximum attanable effect of a drug when it is administered with a infinitely high concentration.

is_pct

logical whether both the input viabiliy and E_inf are given in percentage ([0, 100]) rather than decimal ([0, 1]). Default FALSE.

Value

numeric concentrations in micromoles required to produce viability in the corresponding entries.

Examples

dose <- effectToDose(viability = 80,
                     EC50 = 42,
                     HS = 1,
                     E_inf = 10,
                     is_pct = TRUE)