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

TLDR

In toxicology, researchers compare LC50 values between populations, sometimes using 95 % confidence interval overlap to infer no difference. This study evaluates whether a ratio‑based test of LC50s is preferable to the conventional confidence interval overlap method. A Monte Carlo simulation compared the two approaches, defining the ratio test as significant when the confidence interval for the LC50 ratio excludes 1 (or its log excludes 0). Results show the CI overlap test has inflated type I error (~0.005) and lower power, whereas the ratio test maintains nominal error and higher power, making it the preferred method.

Abstract

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.