mixtox (version 1.0)

CEx: Effect Calculation

Description

Effects can be calculated at particular concentrations based on the inverse function of Hill, Weibull, Logit, BCW, BCL, GL.

Usage

CEx(model, param, conc)

Arguments

model

character vector of equation names: Hill, Weibull, Logit, BCW, BCL, GL

param

numeric matrix of fitting coefficients with rownames (equation selected) and colnames (ALpha, Beta, and Gamma). For equations with two parameters, Gamma can be set as zero or any other numeric value.

conc

numeric vector with single or multiple concentrations.

Value

• a numeric vector of effect(s)

Details

effects will be calculated with provided equations (model), associated fitting parameters (param), and concentrations(conc). The inverse function of those six sigmoidal equations are as follows: inverse Hill: $${c = \beta E/\left( {\alpha - E} \right)}$$ 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) Scholze, M. et al. 2001. A General Best-Fit Method for Concentration-Response Curves and the Estimation of Low-Effect Concentrations. Environmental Toxicology and Chemistry 20(2):448-457.

See Also

ECx

Examples

data(cytotox)

## example 1
# calculate the effect of heavy metal Ni(2+) at the concentration of 0.00005 mol/L on the MCF-7
model.ni <- cytotox$sgl$model
param.ni <- cytotox$sgl$param
CEx(model.ni, param.ni, conc = 0.00005)

## example 2
# calculate the effect caused by four heavy metals and four ionic liquids at the concentration of
# 0.00001 and 0.00002 mol/L on the MCF-7 cells
model <- cytotox$sgl$model
param <- cytotox$sgl$param
CEx(model, param, conc = c(0.00001, 0.00002))