Harmonic Mean of LTD10 for MOE

Use Of Harmonic Mean Of LTD10 In MOE Calculation

The LTD10 value used to calculate MOE is the more potent (lower) value between rats and mice. LTD10 is the lower 95% confidence limit on the dose to induce tumors in 10% of animals in chronic cancer tests. Values in rats and mice used in the MOE are averages calculated by taking the harmonic mean of the most potent LTD10 values from among target sites in each positive experiment in the Carcinogenic Potency Database (CPDB). If there is only one positive experiment on the chemical in the species, then the most potent LTD10 value from that experiment is used for the species. When more than one experiment is positive in the species, the LTD10 value is a harmonic mean of the most potent LTD10 value from each positive experiment, selected from the tissue-tumor combinations (target sites) that were evaluated by the published author of the experiment as evidence of carcinogenicity. The harmonic mean (TH) is defined as:

harmonic mean formula

The harmonic mean LTD10 is a summary measure that takes into account all positive results for a chemical within each species, from experiments that may differ, for example, in animal strain, route of administration, dose levels tested, duration of experiment, and whether an author published results on survival. In contrast, use of the most potent site (lowest LTD10 value in any experiment) would reflect only results from a single experiment and not take these differences into account.

The harmonic mean LTD10, as we showed in earlier work, is similar to the most potent site, and more similar than the geometric or arithmetic mean (1). It generally makes little difference in the LTD10 value whether the most potent target site or the harmonic mean is used (1). In the CPDB overall, for 45% of rat carcinogens and 34% of mouse carcinogens, there is only one positive experiment, and therefore the harmonic mean of LTD10 is the same as the most potent target site. For 99% of mouse carcinogens and 98% of rat carcinogens, the harmonic mean is within a factor of 3 of the most potent site.

Selection Of LTD10 Values Used To Calculate Harmonic Mean

To obtain the harmonic mean, LTD10 values from each experiment are used only from among target sites that the published author evaluated as evidence of carcinogenicity. We use the author’s opinion to determine positivity because it often takes into account more information than statistical significance alone, such as historical control rates for particular sites, survival and latency, and/or dose-response. Generally, this designation by author’s opinion corresponds well with the results of statistical tests for the significance of the dose-response effect (p<0.01).

The most potent (lowest) LTD10 value from each positive experiment is selected from among values with a statistically significant dose response (p<0.1) for target sites that the published author considered to be induced by compound administration. If no target sites have a significant dose response, then the most potent (lowest LTD10) is selected from among positively evaluated target sites with p≥0.1. If some experiments in a species have a positive evaluation and statistically significant results while others have only positive evaluations but statistically non-significant results (p≥0.1), the non-significant experimental results are not used in the calculation of the harmonic mean.

In the CPDB, forty-four chemicals had an experiment for which no LTD10 value could be estimated because all dosed animals had the tumor of interest at all target sites, and only summary (not life table) data on tumor incidence were available. The 99% upper confidence limit on TD10 is used for these experiments as a replacement for the LTD10 in calculating the harmonic mean.


  1. Gold, L.S., Slone, T.H., and Bernstein, L. Summary of carcinogenic potency (TD50) and positivity for 492 rodent carcinogens in the Carcinogenic Potency Database. Environ. Health Perspect. 79: 259-272 (1989). abstractAbstract PDF
  2. Gold, L. S., Slone, T. H., and Ames, B. N. What do animal cancer tests tell us about human cancer risk? Overview of analyses of the Carcinogenic Potency Database. Drug Metabolism Reviews 30: 359-404 (1998). abstractAbstract PDF
  3. Gold, L.S., Slone, T.H., and Ames, B.N. Overview of analyses of the Carcinogenic Potency Database. In: Gold, L.S., and Zeiger, E., Eds. Handbook of Carcinogenic Potency and Genotoxicity Databases. Boca Raton, FL: CRC Press, 1997, pp. 661-685.
  4. Gold, L.S., Gaylor, D.W., and Slone, T.H. Comparison of Cancer Risk Estimates Based on a Variety of Risk Assessment Methodologies. Regul. Toxicol. Pharmacol. 37: 45-53 (2003). PDF
  5. Gold, L.S., Wright, C., Bernstein, L., and de Veciana, M. Reproducibility of results in “near-replicate” carcinogenesis bioassays. Journal of the National Cance r Institute 78: 1149-1158 (1987). abstractAbstract PDF

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Last updated: February 26, 2009

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