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

Area of Science:

• Toxicology
• Insecticide Resistance
• Statistical Modeling

Background:

• Median lethal dose (LD50) is a standard metric for insecticide acute toxicity.
• Comparing insecticide potencies across populations or species often requires LD50 analysis.
• Existing methods for LD50 comparison often assume parallel regression slopes, limiting their applicability.

Purpose of the Study:

• To develop and validate a statistical method using R for calculating and comparing LD50 values.
• To assess the accuracy of this new method against established software (PoloPlus, R drc package).
• To enable LD50 comparisons without the restrictive assumption of parallel slopes.

Main Methods:

• Utilized the generalized linear model (glm) function in R for logit and probit regression analyses.
• Applied Fieller's theorem and the delta method for calculating 95% confidence limits (CLs) of LD50.
• Incorporated Abbott's equation for natural response rates and compared results with PoloPlus and the R drc package.

Main Results:

• The R function, using the logit model, produced 95% CLs identical to PoloPlus when Fieller's theorem and a heterogeneity factor were used.
• The delta method in R yielded 95% CLs consistent with the R drc package.
• Probit model analysis in R also generated comparable 95% CLs to established software.
• Statistical tests for potency and slope parallelism in R aligned with conclusions from PoloPlus and the drc package.

Conclusions:

• The R-based glm function offers a flexible and accurate alternative for calculating and comparing LD50 values, particularly when slopes are not parallel.
• This method enhances the ability to conduct robust insecticide toxicity and potency assessments in entomological research.
• The findings support the use of R for advanced statistical analysis in toxicology and pest management.