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Comparing median lethal concentration values using confidence interval overlap or ratio tests
Author(s) -
Wheeler Matthew W,
Park Robert M.,
Bailer A. John
Publication year - 2006
Publication title -
environmental toxicology and chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.1
H-Index - 171
eISSN - 1552-8618
pISSN - 0730-7268
DOI - 10.1897/05-320r.1
Subject(s) - confidence interval , statistics , mathematics , robust confidence intervals , cdf based nonparametric confidence interval , tolerance interval , population , medicine , environmental health
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.