ECx {mixtox}

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, rtype = 'quantal', Scaled = TRUE, sav = FALSE)

Arguments

model

a 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

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

effv

a numeric vector with single or multiple effect values

rtype

the response type of endpoint: 'continuous' or 'quantal' data.

Scaled

only for 'continuous' data. To indicate if the effv is scaled by response ranges to 0~1 or not (default is TRUE).

sav

TRUE: save output to a default file; FALSE: output will not be saved; a custom file directory: save output to the custom file directory.

Details

effect concentrations will be calculated with provided equations (model), associated fitting parameters (param), and effect levels (effv). For example, effv should be 0.5 if we want to calculate a concentration causes 50% effect.
The inverse functions of the six quantal 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.

Value

ecx

a numeric vector of effect concentration(s)

effvAbs

absolute effect levels. Only for 'continuous' data with scaled effv. The corresponding absolute effect is calculated.

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), rtype = 'quantal')