cedergreen {drc} | R Documentation |
'cedergreen' provides a very general way of specifying then Cedergreen-Ritz-Streibig modified log-logistic model for describing hormesis, under various constraints on the parameters.
CRS.6
is the extension of link{cedergreen}
with freely varying alpha parameter.
For u-shaped hormesis data 'ucedergreen' provides a very general way of specifying the Cedergreen-Ritz-Streibig modified log-logistic model, under various constraints on the parameters.
cedergreen(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"), alpha, scaleDose = TRUE) CRS.6(lowerc=c(-Inf, -Inf, -Inf, -Inf, -Inf, -Inf), upperc=c(Inf, Inf, Inf, Inf, Inf, Inf), fixed=c(NA, NA, NA, NA, NA, NA), names=c("b","c","d","e","f","g")) ucedergreen(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"), alpha, scaleDose = TRUE)
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'). |
alpha |
numeric. The degree of hormesis. Needs to be specified! |
scaleDose |
logical. If TRUE dose values are scaled around 1 during estimation; this is required for datasets where all dose values are small. |
The model is given by the expression
f(x) = c + frac{d-c+f exp(-1/(x^{α}))}{1+exp(b(log(x)-log(e)))}
which is a five-parameter model (alpha is fixed or freely varying). Not all features (eg EC/ED calculation) are available for the model with freely varying alpha.
It is a modification of the four-parameter logistic curve to take hormesis into account.
The u-shaped model is given by the expression
f(x) = cd - frac{d-c+f exp(-1/x^{α})}{1+exp(b(log(x)-log(e)))}
The value returned is a list containing the non-linear function, the self starter function and the parameter names.
The functions are for use with the functions drm
or multdrc
.
Christian Ritz
Cedergreen, N. and Ritz, C. and Streibig, J. C. (2005) Improved empirical models describing hormesis, Environmental Toxicology and Chemistry 24, 3166–3172.
Special cases are CRS.4a
, CRS.4a
,
UCRS.5a
and UCRS.5a
where a,b and c coresspond to
the pre-specified alpha values 1, 0.5 and 0.25, respectively.
## Modified logistic model with the constraint f>0 lettuce.m1 <- multdrc(weight~conc,data=lettuce, fct=cedergreen(fixed=c(NA, NA, NA, NA, NA), lowerc=c(-Inf, -Inf, -Inf, -Inf, 0), alpha=1), control=mdControl(constr=TRUE)) summary(lettuce.m1) ED(lettuce.m1, c(10, 50, 90)) ## Estimating alpha lettuce.m2<-drm(weight~conc,data=lettuce,fct=CRS.6()) summary(lettuce.m2) plot(lettuce.m2) # oops: not increasing until hormesis peak