R: Dose-response model for estimation of no effect concentration...

NEC {drc} | R Documentation

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

### Description

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.

### Usage

      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.

### Author(s)

Christian Ritz

### 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)

    plot(nec.m1)

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

[Package drc version 3.0-1 Index]