drc (version 4.0-0)

W1.4: The four-parameter Weibull functions

Description

'W1.4' and 'W2.4' provide the four-parameter Weibull functions, self starter function and names of the parameters.

Usage

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"), ...)

Value

See weibull1.

Arguments

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.

...

additional arguments to be passed from the convenience functions.

Author

Christian Ritz

Details

The equations for the mean functions are given at weibull1.

References

Seber, G. A. F. and Wild, C. J (1989) Nonlinear Regression, New York: Wiley and Sons (pp. 330--331).

Ritz, C (2010) Towards a unified approach to dose-response modeling in ecotoxicology, Environ Toxicol Chem 29, 220--229, https://doi.org/10.1002/etc.7

See Also

Setting \(c=0\) yields W1.3. A more flexible function, allowing fixing or constraining parameters, is available through weibull1.

Examples

## 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)