Comparing median lethal concentration values using confidence interval overlap or ratio tests

Abstract

Experimenters in toxicology often compare the concentration‐response relationship between two distinct populations using the median lethal concentration (LC50). This comparison is sometimes done by calculating the 95% confidence interval for the LC50 for each population, concluding that no significant difference exists if the two confidence intervals overlap. A more appropriate test compares the ratio of the LC50s to 1 or the log(LC50 ratio) to 0. In this ratio test, we conclude that no difference exists in LC50s if the confidence interval for the ratio of the LC50s contains 1 or the confidence interval for the log(LC50 ratio) contains 0. A Monte Carlo simulation study was conducted to compare the confidence interval overlap test to the ratio test. The confidence interval overlap test performs substantially below the nominal α = 0.05 level, closer to p = 0.005; therefore, it has considerably less power for detecting true differences compared to the ratio test. The ratio‐based method exhibited better type I error rates and superior power properties in comparison to the confidence interval overlap test. Thus, a ratio‐based statistical procedure is preferred to using simple overlap of two independently derived confidence intervals.