title: 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 alpha = 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.
authors.affiliation: National Institute for Occupational Safety and Health, 4676 Columbia Parkway MS-15, Cincinnati, Ohio 45226, USA. mwheeler@cdc.gov
authors.forename: Matthew W
authors.initials: MW
authors.lastname: Wheeler
authors.forename: Robert M
authors.initials: RM
authors.lastname: Park
authors.forename: A John
authors.initials: AJ
authors.lastname: Bailer
mesh_terms: D000818:Animals; D016001:Confidence Intervals; D003530:Cyprinidae; D005449:Fluorenes / Q000633:toxicity; D007814:Larva / Q000187:drug effects; D007928:Lethal Dose 50; D014116:Toxicology
chemical_list: D005449:Fluorenes; C007738:fluoranthene