Dose-response model for estimation of no effect concentration (NEC).

The no effect concentration has been proposed as an alternative to both the classical no observed effect concentration (NOEC) and the regression-based EC/ED approach. The NEC model is a dose-response model with a threshold below which the response is assumed constant and equal to the control response.

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

  NEC.2(upper = 1, fixed = c(NA, NA), names = c("b", "e"), ...)

  NEC.3(fixed = c(NA, NA, NA), names = c("b", "d", "e"), ...)

  NEC.4(fixed = c(NA, NA, NA, NA), names = c("b", "c", "d", "e"), ...)

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.
upper	numeric value. The fixed, upper limit in the model. Default is 1.
...	additional arguments in NEC

Details

The NEC model function proposed by Pires et al (2002) is defined as follows

$$ f(x) = c + (d-c)\exp(-b(x-e)I(x-e)) + \frac{d2}{1+\exp(b2(\log(x)-\log(e2)))}$$

where \(I(x-e)\) is the indicator function. It is equal to 0 for \(x<=e\) and equal 1 for \(x>e\).

In other words: The parameter e in NEC in "drc" corresponds to the parameter c' in Pires et al (2002), the parameter b in NEC in "drc" corresponds to the parameter m' in Pires et al (2002), the parameter d in NEC in "drc" corresponds to the parameter l' in Pires et al (2002), and finally the parameter c in NEC in "drc" (the lower horizontal limit) is (implictly) fixed at 0 in Pires et al (2002)

Value

The value returned is a list containing the nonlinear function, the self starter function and the parameter names.

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.

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  393.27256  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)

abline(v=coef(nec.m1)[4], lty=2)  # showing the estimated threshold