The four-parameter Weibull functions
'W1.4' and 'W2.4' provide the four-parameter Weibull functions, self starter function and names of the parameters.
W1.4(fixed = c(NA, NA, NA, NA), names = c("b", "c", "d", "e"), ...)
W2.4(fixed = c(NA, NA, NA, NA), names = c("b", "c", "d", "e"), ...)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. The default is reasonable. |
... |
additional arguments to be passed from the convenience functions. |
The equations for the mean functions are given at weibull1.
See weibull1.
This function is for use with the model fitting function drm.
Christian Ritz
Seber, G. A. F. and Wild, C. J (1989) Nonlinear Regression, New York: Wiley \& Sons (pp. 330–331).
Ritz, C (2009) Towards a unified approach to dose-response modeling in ecotoxicology To appear in Environ Toxicol Chem.
## Fitting a four-parameter Weibull (type 1) model
terbuthylazin.m1 <- drm(rgr~dose, data = terbuthylazin, fct = W1.4())
summary(terbuthylazin.m1)
## Fitting a first-order multistage model
## to data from BMDS by EPA
## (Figure 3 in Ritz (2009))
bmds.ex1 <- data.frame(ad.dose=c(0,50,100), dose=c(0, 2.83, 5.67),
num=c(6,10,19), total=c(50,49,50))
bmds.ex1.m1<-drm(num/total~dose, weights=total, data=bmds.ex1,
fct=W2.4(fixed=c(1,NA,1,NA)), type="binomial")
modelFit(bmds.ex1.m1) # same as in BMDS
summary(bmds.ex1.m1) # same background estimate as in BMDS
logLik(bmds.ex1.m1)
## BMD estimate identical to BMDS result
## BMDL estimate differs from BMDS result (different method)
ED(bmds.ex1.m1, 10, ci="delta")
## Better fit
bmds.ex1.m2<-drm(num/total~dose, weights=total, data=bmds.ex1,
fct=W1.4(fixed=c(-1,NA,1,NA)), type="binomial")
modelFit(bmds.ex1.m2)
summary(bmds.ex1.m2)
ED(bmds.ex1.m2, 50, ci = "delta")
## Creating Figure 3 in Ritz (2009)
bmds.ex1.m3 <- drm(num/total~dose, weights=total, data=bmds.ex1,
fct=LL.4(fixed=c(-1,NA,1,NA)), type="binomial")
plot(bmds.ex1.m1, ylim = c(0.05, 0.4), log = "", lty = 3, lwd = 2,
xlab = "Dose (mg/kg/day)", ylab = "",
cex=1.2, cex.axis=1.2, cex.lab=1.2)
mtext("Tumor incidence", 2, line=4, cex=1.2) # tailored y axis label
plot(bmds.ex1.m2, ylim = c(0.05, 0.4), log = "", add = TRUE, lty = 2, lwd = 2)
plot(bmds.ex1.m3, ylim = c(0.05, 0.4), log = "", add = TRUE, lty = 1, lwd = 2)
arrows(2.6 , 0.14, 2, 0.14, 0.15, lwd=2)
text(2.5, 0.14, "Weibull-1", pos=4, cex=1.2)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.