Comparison of Lethal Doses Calculated Using Logit/Probit–Log(Dose) Regressions With Arbitrary Slopes Using R

Abstract

The median lethal dose (LD50) is commonly used to indicate acute toxicity of an insecticide to an insect species. Approximate confidence intervals for LD50s are often calculated using the Fieller and delta methods. It is often necessary to compare the relative potencies of several insecticides with a population or of one insecticide with different populations. Comparing the LD50s using probit/logit-log(dose) regressions with parallel slopes can be implemented in many software packages, but for the cases with arbitrary slopes are not generally available. We used the glm function in R to calculate and compare lethal doses without assuming equal slopes. Bioassay datasets from the literature fitted using the logit model gave the 95% confidence limits (95% CLs) for the lethal doses using Fieller's theorem and incorporating a heterogeneity factor identical to the 95% CLs determined using the PoloPlus software. The delta method gave 95% CLs identical to the 95% CLs determined using the R drc package. The same datasets fitted using the probit model gave 95% CLs similar to the 95% CLs determined using PoloPlus and the drc package. The natural response rates for the control group were included using Abbott's equation. When the potency ratio method and the z-test were used to identify differences between two lethal doses, and when the χ2 and log likelihood ratio tests were used to determine whether the regression lines were parallel, the conclusions were the same as those gave by PoloPlus and the drc package.