BC: The Brain-Cousens hormesis models

Description Usage Arguments Details Value Note Author(s) References See Also Examples

Description

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

Usage

1
2
3
  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.

...

additional arguments to be passed from the convenience functions.

Details

The model function for the Brain-Cousens model (Brain and Cousens, 1989) is

f(x, b,c,d,e,f) = c + \frac{d-c+fx}{1+\exp(b(\log(x)-\log(e)))}

,

and it is a five-parameter model, obtained by extending the four-parameter log-logistic model (LL.4 to take into account inverse u-shaped hormesis effects.

The parameters have the following interpretations

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)))}

used by van Ewijk and Hoekstra (1993).

Value

See braincousens.

Note

This function is for use with the function drm.

Author(s)

Christian Ritz

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

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
## 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)

drc documentation built on May 1, 2019, 8:43 p.m.

Related to BC in drc...