Cedergreen-Ritz-Streibig Model

Provides the Cedergreen-Ritz-Streibig function, a five-parameter model for describing dose-response curves that exhibit hormesis (a stimulatory or beneficial effect at low doses). This function generates a model object suitable for use with non-linear regression functions like drm.

Usage

cedergreen(
  fixed = c(NA, NA, NA, NA, NA),
  names = c("b", "c", "d", "e", "f"),
  method = c("loglinear", "anke", "method3", "normolle"),
  ssfct = NULL,
  alpha,
  fctName,
  fctText
)

Arguments

fixed: A numeric vector of length 5 specifying any parameters to be held fixed during the estimation. The order is c(b, c, d, e, f). Use NA for parameters that should be estimated. The default is to estimate all parameters.
names: A character vector of length 5 providing names for the parameters. The default is c("b", "c", "d", "e", "f").
method: A character string specifying the method for the self-starter function to use for finding initial parameter values. Options are "loglinear", "anke", "method3", and "normolle". This is only used if ssfct is NULL.
ssfct: A custom self-starter function. If NULL (the default), a self-starter is automatically generated by calling cedergreen.ssf with the specified method, fixed, and alpha arguments.
alpha: A mandatory numeric value specifying the fixed shape parameter $\alpha$. The function will stop if this is not provided.
fctName: An optional character string to name the function object.
fctText: An optional character string providing a descriptive text for the model.

Value

A list of class mllogistic, containing the model function (fct), the self-starter function (ssfct), parameter names (names), and other components required for use with modeling functions like drm.

Details

The Cedergreen-Ritz-Streibig model is defined by the following equation: $$f(x) = c + \frac{d - c + f \exp(-1/x^{\alpha})}{1 + \exp(b(\log(x) - \log(e)))}$$ The parameter $f$ determines the size of the hormetic effect (stimulation). If $f=0$, the model simplifies to the standard four-parameter log-logistic model. The parameter $\alpha$ is a shape parameter that must be specified by the user.

Author

Christian Ritz, Hannes Reinwald

Examples

dose <- c(0, 0.1, 0.5, 1, 5, 10, 20)
response <- c(100, 102, 95, 80, 40, 25, 20)
my_data <- data.frame(dose = dose, response = response)
model_fit <- drm(response ~ dose, data = my_data,
                 fct = cedergreen(alpha = 0.5))
summary(model_fit)
#> 
#> Model fitted: Cedergreen-Ritz-Streibig (5 parms)
#> 
#> Parameter estimates:
#> 
#>               Estimate Std. Error t-value   p-value    
#> b:(Intercept)   1.1619     0.2153  5.3965 0.0326651 *  
#> c:(Intercept)  13.5774     4.5892  2.9585 0.0977776 .  
#> d:(Intercept) 101.4210     2.0399 49.7190 0.0004043 ***
#> e:(Intercept)   1.3820     1.1363  1.2162 0.3479717    
#> f:(Intercept)  72.5388   126.6937  0.5726 0.6247324    
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> Residual standard error:
#> 
#>  2.513311 (2 degrees of freedom)