Data from toxicology experiments with selenium

Description

Comparison of toxicity of four types of selenium by means of dose-response analysis

Usage

data(selenium)

Format

A data frame with 25 observations on the following 4 variables.

type

a numeric vector indicating the form of selenium applied

conc

a numeric vector of (total) selenium concentrations

total

a numeric vector containing the total number of flies

dead

a numeric vector containing the number of dead flies

Details

The experiment is described in more details by Jeske et al. (2009).

Source

Jeske, D. R., Xu, H. K., Blessinger, T., Jensen, P. and Trumble, J. (2009) Testing for the Equality of EC50 Values in the Presence of Unequal Slopes With Application to Toxicity of Selenium Types, Journal of Agricultural, Biological, and Environmental Statistics, 14, 469–483

Examples

## Analysis similar to what is proposed in Jeske et al (2009)
##  but simply using existing functionality in "drc"

## Fitting the two-parameter log-logistic model with unequal ED50 and slope
sel.m1 <- drm(dead/total~conc, type, weights=total, data=selenium, fct=LL.2(), 
type="binomial")
#sel.m1b <- drm(dead/total~conc, type, weights=total, data=selenium, fct=LN.2(), 
# type="binomial", start=c(1,1,1,1,50,50,50,50))
plot(sel.m1, ylim = c(0, 1.3))
summary(sel.m1)

## Testing for equality of slopes
sel.m2 <- drm(dead/total~conc, type, weights=total, data=selenium, fct=LL.2(), 
type="binomial", pmodels=list(~1, ~factor(type)-1))
sel.m2b <- drm(dead/total~conc, type, weights=total, data=selenium, fct=LN.2(), 
type="binomial", pmodels=list(~1, ~factor(type)-1))
plot(sel.m2, ylim = c(0, 1.3))
summary(sel.m2)
anova(sel.m2, sel.m1)  # 48.654
#anova(sel.m2b, sel.m1b)
# close to the value 48.46 reported in the paper

## Testing for equality of ED50
sel.m3<-drm(dead/total~conc, type, weights=total, data=selenium, fct=LL.2(), 
type="binomial", pmodels=list(~factor(type)-1, ~1))
#sel.m3b<-drm(dead/total~conc, type, weights=total, data=selenium, fct=LN.2(), 
# type="binomial", pmodels=list(~factor(type)-1, ~1), start=c(1,1,1,1,50))
plot(sel.m3, ylim = c(0, 1.3))
summary(sel.m3)

anova(sel.m3, sel.m1)  # 123.56
#anova(sel.m3b, sel.m1b) 
# not too far from the value 138.45 reported in the paper
# (note that the estimation procedure is not exactly the same)
# (and we use the log-logistic model instead of the log-normal model)