mixtox (version 1.3)

gcaHill: Mixture Toxicity Prediction Using GCA (Hill_two)

Description

Predict the mixture toxicity based on individual concentration-response information fitted by Hill_two equation. An explicit formula for gca prediction were used instead of the dichotomy algorithm in gcaPred. Three optional mixture design methods are provided. One is the arbitrary concentration ratio (acr) for mixture components. Users can deign random ratios for components in the mixture. Other two options are equal effect concentration ratio (eecr) and uniform design concentration ratio (udcr).

Usage

gcaHill(model, param, mixType = c("acr", "eecr", "udcr"), effv, refEffv = c(0.10, 0.50))

Arguments

model

character vector of equation names, just Hill_two

param

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

mixType

experimental design of the mixture. acr: arbitrary concentration ratio; eecr: equal effect concentration ratio; udcr: uniform design concentration ratio.

effv

numeric vector with single or multiple effect values (0 ~ 1).

refEffv

to determine the concentration ranges for predicting effect.

Value

• x
  a series of concentrations
• e
  a series of effects caused by the concentrations (x) as predicted by gca
• pct
  the concentration ratio (percent) of every component in the mixture
• uniTab
  the uniform design table used to construct the mixture when mixType is udcr

Details

The generalized concentration addition (GCA) model was proposed by Howard and Webster to predict mixtures containing partial agonists (Howard and Webster, 2009). Empirical data are used to fit concentration-response function, and then predict the mixture response using the inverse function. $$E_{mix}^{GCA} = \frac{{\sum\limits_{i = 1}^n {\frac{{{\alpha _i}{c_i}}}{{{K_i}}}}}} {{1 + \sum\limits_{i = 1}^n {\frac{{{c_i}}}{{{K_i}}}} }}$$ where $c_i$ is the concentration of component $i$ in the mixture. Parameter $\alpha _i$ and $K_i$ are fitted coefficient of $i^{th}$ component, which are the same as $\beta$ and $\alpha$ in Hill_two equation. Right, the $\alpha _i$ and $K_i$ are corresponding to $\beta$ and $\alpha$ in Hill_two equation.

References

Howard, G.J., Schlezinger, J.J., Hahn, M.E., Webster, T.F., 2010. Generalized Concentration Addition Predicts Joint Effects of Aryl Hydrocarbon Receptor Agonists with Partial Agonists and Competitive Antagonists. Environ. Health Perspect. 118, 666-672. Howard, G.J., Webster, T.F., 2009. Generalized concentration addition: A method for examining mixtures containing partial agonists. J. Theor. Biol. 259, 469-477. Hadrup, N., Taxvig, C., Pedersen, M., Nellemann, C., Hass, U., Vinggaard, A.M., 2013. Concentration addition, independent action and generalized concentration addition models for mixture effect prediction of sex hormone synthesis in vitro. PLoS One 8, e70490.

See Also

gcaPred

Examples

model <- c("Hill_two", "Hill_two", "Hill_two", "Hill_two")
param <- matrix(c(3.94e-5, 0.97, 0, 5.16e-4, 1.50, 0, 3.43e-6, 1.04, 0, 9.18e-6, 0.77, 0), 
				nrow = 4, ncol = 3, byrow = TRUE)
rownames(param) <- c('Ni', 'Zn', 'Cu', 'Mn')
colnames(param) <- c('Alpha', 'Beta', 'Gamma')
## example 1
# using GCA to predict the mixtures designed by equal effect concentration ratio (eecr) at
# the effect concentration of EC05 and EC50
# the eecr mixture design is based on four heavy metals (four factors).
gcaHill(model, param, mixType = "eecr", effv = c(0.05, 0.5))

## example 2
# using GCA to predict the mixtures designed by uniform design concentration ratio (udcr)
# the udcr mixture design is based on four heavy metals (four factors).
# Seven levels (EC05, EC10, EC15, EC20, EC25, EC30, and EC50 ) are allocated in 
# the uniform table
effv <- c(0.05, 0.10, 0.15, 0.20, 0.25, 0.30, 0.50)
gcaHill(model, param, mixType = "udcr", effv)

## example 3
# using GCA to predict the mixtures designed by arbitrary concentration ratio (acr)
# the udcr mixture design is based on four heavy metals (four factors).
# the every component in the mixture shares exactly the same ratio (0.25) 
effv <- c(0.25, 0.25, 0.25, 0.25)
gcaHill(model, param, mixType = "acr", effv)