R: Cedergreen-Ritz-Streibig dose-reponse model for describing...

CRS.5a {drc} | R Documentation

## 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.

### Details

The model function for inverse u-shaped hormetic patterns is

f(x) = c + \frac{d-c+f \exp(-1/x^{α})}{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^{α})}{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.

### Value

See `cedergreen`.

### Note

This function is for use with the function `drm`.

### Author(s)

Christian Ritz

### 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))

[Package drc version 3.0-1 Index]