mixtox (version 1.0)

iaPred: Mixture Toxicity Prediction Using IA

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 random ratios for components in the mixture. Other two options are equal effect concentration ratio(eecr) and uniform design concentration ratio (udcr).

Usage

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

Arguments

model

character vector of equations: Hill, Weibull, Logit, BCW, BCL, GL

param

numeric matrix of fitting coefficients with row names (selected equations) and column names (Alpha, Beta, and Gamma). For equations with 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

• ia
  a series of effect concentrations predicted by IA
• e
  a series of effects associated with the effect concentrations in ia
• 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

Independent action (IA) is designed for mixtures of chemicals that have distinct mechanisms of action. The IA model is commonly defined as: $${\rm{E}}({c_{mix}}) = 1 - (1 - {\rm{E}}({c_1}))(1 - {\rm{E}}({c_2})) \cdot \cdot \cdot (1 - {\rm{E}}({c_n})) = 1 - \prod\limits_{i = 1}^n {\left( {1 - {\rm{E}}({c_i})} \right)}$$ where $E\left( {{c_{mix}}} \right)$ is the overall effect caused by $c_{mix}$, and $E({c_i})$ is the effect elicited by $c_i$ when applied individually. For a fitted function $f_i$ based on the concentration-response data of the $i^{th}$ component, $E({c_i})$ is equal to ${f_i}({c_i})$. When $E({c_{mix}}) = x$, the equation can be expressed as: $$x% = 1 - \prod\limits_{i = 1}^n {\left( {1 - {f_i}\left( {{p_i}\left( {E{C_{x,mix}}} \right)} \right)} \right)}$$ This equation can be used to predict the combined effects of mixture-components based on IA. The dichotomy technique can be used to solve the constructed equation.

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

caPred

Examples

data(cytotox)
model <- cytotox$sgl$model
param <- cytotox$sgl$param
## example 1
# using IA 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 ion liquids(eight factors).
iaPred(model, param, mixType = "eecr", effv = c(0.05, 0.5))

## example 2
# using IA to predict the mixtures designed by uniform design concentration ratio (udcr)
# the udcr mixture design is based on four heavy metals and four ion 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)
iaPred(model, param, mixType = "udcr", effv)

## example 3
# using IA 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) 
model <- cytotox$sgl$model[1 : 4]
param <- cytotox$sgl$param[1 : 4, ]
effv <- c(0.25, 0.25, 0.25, 0.25)
iaPred(model, param, mixType = "acr", effv)