mixtox (version 1.0)

caPred: Mixture Toxicity Prediction Using CA

Description

Predict the mixture toxicity based on individual concentration-response information. Three optional mixture design methods are provided. One is the arbitrary concentration ratio (acr) for mixture components. Users can arbitrarily deign a random ratio for each component in the mixture. Other two options are equal effect concentration ratio (eecr) and uniform design concentration ratio (udcr).

Usage

caPred(model, param, mixType = c("acr", "eecr", "udcr"), effv)

Arguments

model

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

param

numeric matrix of fitting coefficients with row names (equation selected) and column names (Alpha, Beta, and Gamma). For equations with only two parameters, Gamma can be set as zero or any other numeric value.

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).

Value

• ca
  a series of effect concentrations predicted by CA
• e
  a series of effects associated with the effect concentrations in ca
• 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

Concentration addition (CA) is designed for mixtures of chemicals that have similar mechanisms of action. For a well-defined mixture (e.g., a mixture of n components), CA is expressed mathematically as: $$\sum\limits_{i = 1}^n {\frac{{{c_i}}}{{EC{x_i}}}} = 1$$ where $EC{x_i}$ is the effect concentration of the $i^{th}$ compound that causes x% effect when applied individually at ${c_i}$. The ${c_i}$ can be computed from the following equation: $${c_i} = {p_i} \cdot {c_{mix}} = {p_i} \cdot E{C_{x,mix}}$$ where $p_i$ is the proportion of $i^{th}$ component in the mixture, $c_{mix}$ the mixture concentration and $E{C_{x,mix}}$ the concentration of the mixture at a specific effect x%. The prediction of combined effects of mixture-components based on CA can then be expressed as: $$E{C_{x,mix}} = {\left( {\sum\limits_{i = 1}^n {\frac{{{p_i}}}{{E{C_{x,i}}}}}} \right)^{ - 1}}$$

References

Liang, Yi-zeng, Kai-tai Fang, and Qing-song Xu. 2001. Uniform Design and Its Applications in Chemistry and Chemical Engineering. Chemometrics and Intelligent Laboratory Systems 58(1):43-57. Backhaus, T., Faust, M., 2012. Predictive environmental risk assessment of chemical mixtures: A conceptual framework. Environmental Science and Technology. 46, 2564-2573.

See Also

iaPred

Examples

data(cytotox)
model <- cytotox$sgl$model
param <- cytotox$sgl$param
## example 1
# using CA 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 and four ionic liquids(eight factors).
caPred(model, param, mixType = "eecr", effv = c(0.05, 0.5))

## example 2
# using CA to predict the mixtures designed by uniform design concentration ratio (udcr)
# the udcr mixture design is based on four heavy metals and four ionic liquids (eight factors).
# five levels (EC05, EC10, EC20, EC30, and EC50 ) are allocated in the uniform table using the
# pseudo-level technique (Liang et al., 2001)
model <- cytotox$sgl$model
param <- cytotox$sgl$param
effv <- c(0.05, 0.05, 0.10, 0.10, 0.20, 0.20, 0.30, 0.30, 0.50, 0.50)
caPred(model, param, mixType = "udcr", effv)

## example 3
# using CA to predict the mixtures designed by arbitrary concentration ratio (acr)
# the udcr mixture design is based on four heavy metals and one ionic liquid (five factors).
# the every component in the mixture shares exactly the same ratio (0.20) 
model <- cytotox$sgl$model[1 : 5]
param <- cytotox$sgl$param[1 : 5, ]
effv <- c(0.2, 0.2, 0.2, 0.2, 0.2)
caPred(model, param, mixType = "acr", effv)