No Effect Concentration (NEC) dose-response model

The NEC model is a dose-response model with a threshold below which the response is assumed constant and equal to the control response. It has been proposed as an alternative to both the classical NOEC and the regression-based EC/ED approach.

Usage

NEC(fixed = c(NA, NA, NA, NA), names = c("b", "c", "d", "e"), fctName, fctText)

Arguments

fixed: numeric vector specifying which parameters are fixed and at what value they are fixed. NAs are used for parameters that are not fixed.
names: a vector of character strings giving the names of the parameters (should not contain ":"). The default is reasonable (see under 'Usage').
fctName: optional character string used internally by convenience functions.
fctText: optional character string used internally by convenience functions.

Value

A list containing the nonlinear function, the self starter function and the parameter names.

Details

The NEC model function proposed by Pires et al (2002) is: $$f(x) = c + (d-c)\exp(-b(x-e)I(x-e))$$ where $I(x-e)$ is the indicator function equal to 0 for $x<=e$ and 1 for $x>e$.

References

Pires, A. M., Branco, J. A., Picado, A., Mendonca, E. (2002) Models for the estimation of a 'no effect concentration', Environmetrics, 13, 15–27.

Author

Christian Ritz

Examples

nec.m1 <- drm(rootl ~ conc, data = ryegrass, fct = NEC.4())
summary(nec.m1)
#> 
#> Model fitted: NEC (4 parms)
#> 
#> Parameter estimates:
#> 
#>                Estimate Std. Error t-value   p-value    
#> b:(Intercept)   3.16938  393.27265  0.0081  0.993650    
#> c:(Intercept)   0.67201    0.23463  2.8641  0.009592 ** 
#> d:(Intercept)   7.39666    0.20260 36.5091 < 2.2e-16 ***
#> e:(Intercept)   3.41729   41.27705  0.0828  0.934842    
#> ---
#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#> 
#> Residual standard error:
#> 
#>  0.7017905 (20 degrees of freedom)
plot(nec.m1)