Data from toxicology experiments with selenium
Comparison of toxicity of four types of selenium by means of dose-response analysis
data(selenium)
A data frame with 25 observations on the following 4 variables.
typea numeric vector indicating the form of selenium applied
conca numeric vector of (total) selenium concentrations
totala numeric vector containing the total number of flies
deada numeric vector containing the number of dead flies
The experiment is described in more details by Jeske et al. (2009).
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
## 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)
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