drc (version 1.5-5)

BC.5: The Brain-Cousens hormesis models

Description

'BC.4' and 'BC.5' provide the Brain-Cousens modified log-logistic models for describing u-shaped hormesis.

Usage

BC.5(names = c("b", "c", "d", "e", "f"))

  BC.4(names = c("b", "d", "e", "f"))

Arguments

names

a vector of character strings giving the names of the parameters. The default is reasonable.

Value

• See braincousens.

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 log-logistic curve to take u-shaped hormesis into account. Fixing the lower limit at 0 yields the four-parameter model $$f(x) = 0 + \frac{d-0+fx}{1+\exp(b(\log(x)-\log(e)))}$$

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. van Ewijk, P. H. and Hoekstra, J. A. (1993) Calculation of the EC50 and its Confidence Interval When Subtoxic Stimulus Is Present, ECOTOXICOLOGY AND ENVIRONMENTAL SAFETY, 25, 25--32.

Examples

lettuce.m1 <- drm(lettuce[,c(2,1)], fct=BC.5())
anova(lettuce.m1)
plot(lettuce.m1)

lettuce.m2 <- drm(lettuce[,c(2,1)], fct=BC.4())
summary(lettuce.m2)
ED(lettuce.m2, c(50))  # compare the parameter estimate and 
                   # its estimated standard error 
                   # to the values in the paper by 
                   # van Ewijk and Hoekstra