drc (version 0.8-2)

braincousens: The Brain-Cousens modification of the logistic function

Description

'braincousens' provides a very general way of specifying Brain-Cousens' modified logistic dose response functions, under various constraints on the parameters.

Usage

braincousens(lowerc = c(-Inf, -Inf, -Inf, -Inf, -Inf), 
  upperc = c(Inf, Inf, Inf, Inf, Inf), fixed = c(NA, NA, NA, NA, NA), 
  names = c("b", "c", "d", "e", "f"), scaleDose = TRUE, useDer = FALSE)

Arguments

lowerc

numeric vector. The lower bound on parameters. Default is minus infinity.

upperc

numeric vector. The upper bound on parameters. Default is plus infinity.

fixed

numeric vector. Specifies which parameters are fixed and at what value they are fixed. NAs for parameter 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'). The order of the parameters is: b, c, d, e, f (see under 'Details').

scaleDose

logical. If TRUE dose values are scaled around 1 during estimation; this is required for datasets where all dose values are small.

useDer

logical. If TRUE derivatives are supplied, otherwise they are not supplied. Not yet implemented!

Value

• The value returned by the 'braincousens' is a list with the following components
• fct
  The dose response function.
• ssfct
  The self starter function.
• deriv1
  The first derivative.
• deriv2
  The second derivative.
• lowerc
  The lower bounds on the parameters.
• upperc
  The upper bounds on the parameters.
• edfct
  The ED function.
• sifct
  The SI function.
• maxfct
  The function for calculating the mean maximum of the dose response curve.

Details

The Brain-Cousens model is given by the expression $$f(x) = c + \frac{d-c+fx}{1+\exp(b(\log(x)-\log(e)))}$$ which is a five-parameter model. It is a modification of the four-parameter logistic curve to take hormesis into account.

References

Brain, P. and Cousens, R. (1989) An equation to describe dose responses where there is stimulation of growth at low doses, Weed Research, 29, 93--96.

See Also

Special cases of the function 'braincousens' are bcl3 and bcl4.

Examples

## Brain-Cousens model with the constraint b>1
model1 <- multdrc(FA, fct=braincousens(fixed=c(NA, NA, NA, NA, NA), 
lowerc=c(1, -Inf, -Inf, -Inf, -Inf)), control=mdControl(constr=TRUE))

summary(model1)

## Brain-Cousens model with the constraint f>0
model2 <- multdrc(FA, fct=braincousens(fixed=c(NA, NA, NA, NA, NA), 
lowerc=c(-Inf, -Inf, -Inf, -Inf, 0)), control=mdControl(constr=TRUE))

summary(model2)
rm(model1, model2)