Harmonic Mean of TD50

Harmonic Mean of TD50

In the summary table, a carcinogenic potency value (TD50) is reported for each chemical in each species that has a positive author’s evaluation of carcinogenicity in at least one experiment. TD50 values for each species in the summary table are averages calculated by taking the harmonic mean of the most potent TD50 values from among target sites in each positive experiment from the Carcinogenic Potency Database (CPDB). If there is only one positive experiment on the chemical in the species, then the most potent TD50 value from that experiment is reported. When more than one experiment is positive in the species, the reported TD50 value is a harmonic mean of the most potent TD50 value from each positive experiment, selected from the tissue-tumor combinations (target sites) that were evaluated by he published author of the experiment as evidence of carcinogenicity. The harmonic mean (TH) is defined as:

harmonic mean formula

The harmonic mean TD50 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 administration, dose levels tested, duration of experiment, and whether an author published results on survival. In contrast, use of the most potent site (lowest TD50 value in any experiment) would reflect only results from a single experiment and not take these differences into account.

The harmonic mean TD50 value, as we showed in earlier work, is similar to the most potent site from among all experiments, and more similar than the geometric or arithmetic mean (1). For various purposes one may wish to use different summary measures of TD50. It generally makes little difference in the TD50 value whether one uses the most potent target site in the CPDB or the harmonic mean of the most potent TD50 from all positive experiments (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 TD50 is the same as the most potent site. For 99% of mouse carcinogens and 97% of rat carcinogens, the harmonic mean is within a factor of 3 of the most potent site.

Selection Of TD50 Values Used To Calculate Harmonic Mean

To obtain the harmonic mean, TD50 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) TD50 value from each positive experiment is selected from among values with a statistically significant dose response (p<0.1) for tissue-tumor 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 TD50) 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.

Forty-four chemicals had an experiment for which no TD50 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 of TD50 from that experiment is used in calculating the harmonic mean, as a replacement for the TD50. These cases are marked in the table 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 TD50 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: March 3, 2010

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