mixtox (version 1.3)

iaPred: Mixture Toxicity Prediction Based on Independent Action

Description

Predict the mixture toxicity based on individual concentration-response information fitted only based on the following six models: Hill, Weibull, Logit, BCW, BCL, and GL. Three optional mixture design methods are provided:(1)arbitrary concentration ratio (acr), users can set an arbitary proportion for each component in a mixture; (2)equal effect concentration ratio (eecr); (3) uniform design concentration ratio (udcr).

Usage

iaPred(model, param, mixType = c("acr", "eecr", "udcr"), effv, effPoints, 
		lb = 1e-9, ub = 6)

Arguments

model

character vector of models: 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 to 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

effPoints

numeric vector [0 ~ 1] to predict effect concentrations.

lb

lower bound for solving constructed IA using diochotomy method.

ub

upper bound bound for solving constructed IA using diochotomy method.

Value

• ia
  a series of effect concentrations predicted by IA
• e
  a series of effects (effPoints) associated with the effect concentrations in ia
• pct
  the proportion of every component in a mixture
• uniTab
  the uniform design table to construct the mixture when mixType is 'udcr'

Details

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 is 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)

## 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).
model <- cytotox$sgl$model
param <- cytotox$sgl$param
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 seven antibiotics (seven 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 <- antibiotox$sgl$model
param <- antibiotox$sgl$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 antibiotics (four factors).
# the every component in the mixture shares exactly the same ratio (0.25) 
model <- antibiotox$sgl$model[1 : 4]
param <- antibiotox$sgl$param[1 : 4, ]
effv <- c(0.25, 0.25, 0.25, 0.25)
iaPred(model, param, mixType = "acr", effv)