mixtox (version 1.3)

ECx: Effect Concentration Calculation for Sigmoidal Models

Description

Effect concentrations are calculated at particular effects based on the fitting coefficients of 13 Sigmoidal models.

Usage

ECx(model, param, effv)

Arguments

model

character vector of equations:("Hill", "Hill_two", "Hill_three", "Hill_four", "Weibull", "Weibull_three", "Weibull_four", "Logit", "Logit_three", "Logit_four", "BCW(Box-Cox-Weibull)", "BCL(Box-Cox-Logit)", "GL(Generalized Logit)")

param

numeric matrix of fitting coefficients with rownames (equations) and colnames (Alpha, Beta, Gamma, Delta, and Epsilon).

effv

numeric vector with single or multiple effect values

Value

• ecx
  a numeric vector of effect concentration(s)

Details

effect concentrations will be calculated with provided equations (model), associated fitting parameters (param), and effects (effv). $effv$ should be 0.5 if we want to calculate a concentration causes 50% effect. As an example, the inverse function of the six sigmoidal equations are listed as follows: inverse Hill_two: $${c = \beta E/\left( {\alpha - E} \right)}$$ inverse Weibull: $$c = {10^{\left( {\ln ( - \ln (1 - E)) - \alpha } \right)/\beta }}$$ inverse Logit: $$c = {10^{\left( {\ln (E/(1 - E)) - \alpha } \right)/\beta }}$$ inverse BCW: $$c = {\left( {(\gamma /\beta )(\ln ( - \ln (1 - E)) - \alpha ) + 1} \right)^{1/\gamma }}$$ inverse BCL: $$c = {((\gamma /\beta )( - \ln ((1 - E)/E) - \alpha ) + 1)^{1/\gamma }}$$ inverse GL: $$c = {10^{(( - \ln ({{(1/E)}^{1/\gamma }} - 1) - \alpha )/\beta )}}$$ where $E$ is effect and $c$ is the concentration.

References

Hill equation (biochemistry) http://en.wikipedia.org/wiki/Hill_equation_(biochemistry) Reference to {curveFit}

Examples

## example 1
# calculate EC5 and EC50 of seven antibiotics on the photobacteria
model <- antibiotox$sgl$model
param <- antibiotox$sgl$param
effv <- c(0.05, 0.5)
ECx(model, param, effv = c(0.05, 0.50))

## example 2
# calculate EC5 and EC50 of four heavy metals and four ionic liquids on the MCF-7 cells
model <- cytotox$sgl$model
param <- cytotox$sgl$param
ECx(model, param, effv = c(0.05, 0.50))