Harmonic Mean of LTD10 in Excel

Harmonic Mean Of LTD10 in Excel Spreadsheet

An LTD10 value for each species is reported in an Excel spreadsheet for all chemicals in the Carcinogenic Potency Database (CPDB) with a positive evaluation of carcinogenicity by the author of at least one experiment. LTD10 is the lower 95% confidence limit on the dose to induce tumors in 10% of animals in chronic cancer tests. Values in the spreadsheet for each species are averages calculated by taking the harmonic mean of the most potent LTD10 values from among target sites in each positive experiment in the CPDB. If there is only one positive experiment on the chemical in the species, then the most potent LTD10 value from that experiment is reported. When more than one experiment is positive, the reported LTD10 value is a harmonic mean of the most potent LTD10 value 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 in each species, from experiments that may differ, for example, in animal strain, route of compound administration, dose levels tested, duration of experiment, and whether an author published results on survival. In contrast, the most potent site (lowest LTD10 value in any experiment) would use 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 could be estimated because all dosed animals had the tumor of interest, and only summary data (not lifetable) 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. These cases are marked in the spreadsheet with a “P” superscript. For 9 of these chemicals, all animals had tumors at the target site in all positive experiments. The 99% upper confidence limit replaces a harmonic mean in these cases, and the reported value is marked with a “<” symbol to indicate that any LTD10 value would be lower.


  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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