drc (version 1.6-0)

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(fixed = c(NA, NA, NA, NA, NA), names = c("b", "c", "d", "e", "f"))

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

Arguments

fixed

numeric vector specifying which parameters are fixed and at which values they are fixed. NAs designate parameters that are not fixed.

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.

See Also

More details are found for the general model function braincousens.

Examples

## Fitting the data in van Ewijk and Hoekstra (1993)
lettuce.bcm1 <- drm(weight ~ conc, data = lettuce, fct=BC.5())
modelFit(lettuce.bcm1)
plot(lettuce.bcm1)

lettuce.bcm2 <- drm(weight ~conc, data = lettuce, fct=BC.4())
summary(lettuce.bcm2)
ED(lettuce.bcm2, c(50))  
# compare the parameter estimate and 
# its estimated standard error 
# to the values in the paper by 
# van Ewijk and Hoekstra (1993)


## Brain-Cousens model with the constraint b>3
ryegrass.bcm1 <- drm(rootl ~conc, data = ryegrass, fct = BC.5(), 
lower = c(3, -Inf, -Inf, -Inf, -Inf), control = drmc(constr=TRUE))

summary(ryegrass.bcm1)

## Brain-Cousens model with the constraint f>0 
## (no effect as the estimate of f is positive anyway)
ryegrass.bcm2 <- drm(rootl ~conc, data = ryegrass, fct = BC.5(), 
lower = c(-Inf, -Inf, -Inf, -Inf, 0), control = drmc(constr=TRUE))

summary(ryegrass.bcm2)