drc (version 2.5-12)

CRS.5a: Cedergreen-Ritz-Streibig dose-reponse model for describing hormesis

Description

'CRS.5a', 'CRS.5b' and 'CRS.5c' provide the Cedergreen-Ritz-Streibig modified log-logistic model for describing (inverse u-shaped or j-shaped) hormesis. 'UCRS.5a', 'UCRS.5b' and 'UCRS.5c' provide the Cedergreen-Ritz-Streibig modified log-logistic model for describing u-shaped hormesis.

Usage

CRS.5a(names = c("b", "c", "d", "e", "f"), ...)

  UCRS.5a(names = c("b", "c", "d", "e", "f"), ...)

Arguments

names

a vector of character strings giving the names of the parameters.

...

additional arguments to be passed from the convenience functions.

Value

• See cedergreen.

Details

The model function for inverse u-shaped hormetic patterns is $$f(x) = c + \frac{d-c+f \exp(-1/x^{\alpha})}{1+\exp(b(\log(x)-\log(e)))}$$, which is a five-parameter model. It is a modification of the four-parameter log-logistic curve to take hormesis into account. The parameters have the following interpretations

• $b$: Not direct interpretation
• $c$: Lower horizontal asymptote
• $d$: Upper horizontal asymptote
• $e$: Not direct interpretation
• $f$: Size of the hormesis effect: the larger the value the larger is the hormesis effect.$f=0$corresponds to no hormesis effect and the resulting model is the four-parameter log-logistic model. This parameter should be positive in order for the model to make sense.

The model function for u-shaped hormetic patterns is $$f(x) = c + d - \frac{d-c+f \exp(-1/x^{\alpha})}{1+\exp(b(\log(x)-\log(e)))}$$ This model also simplifies to the four-parameter log-logistic model in case $f=0$ (in a slightly different parameterization as compared to the one used in LL.4). The models denoted a,b,c are obtained by fixing the alpha parameter at 1, 0.5 and 0.25, respectively.

References

See the reference under cedergreen.

See Also

Similar functions are CRS.4a and UCRS.4a, but with the lower limit (the parameter $c$) fixed at 0 (one parameter less to be estimated).

Examples

## Modified logistic model
lettuce.m1 <- drm(lettuce[,c(2,1)], fct=CRS.5a())
summary(lettuce.m1)
ED(lettuce.m1, c(50))

lettuce.m2 <- drm(lettuce[,c(2,1)], fct=CRS.5b())
summary(lettuce.m2)
ED(lettuce.m2, c(50))

lettuce.m3 <- drm(lettuce[,c(2,1)], fct=CRS.5c())
summary(lettuce.m3)
ED(lettuce.m3, c(50))