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. If only one experiment is positive for the chemical in the species, then the most potent TD₅₀ value from that test is reported in the table. When more than one experiment is positive, the reported potency value is a harmonic mean of the most potent TD₅₀ values from each positive experiment. The harmonic mean is used because it encompasses more of the biological data than the most potent site from among all experiments, thereby providing an improved estimate. We have shown that the harmonic mean is similar to the most potent TD₅₀ value for chemicals with more than one positive test (1). The harmonic mean (T_H) is defined as:

To obtain the harmonic mean, the lowest TD₅₀ value from each positive experiment is selected from among positively evaluated target sites with a statistically significant dose response (two-tailed p<0.1). If no positive sites have a significant dose response, then the most potent (lowest TD₅₀) is selected from among positively evaluated 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 on tumor incidence were available. For these cases the 99% upper confidence limit of TD₅₀ is used in 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.

References

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). Abstract Text
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). Abstract PDF
3. Gold, L.S., Slone, T.H., Manley, N.M., and Ames, B.N. Misconceptions About the Causes of Cancer. Vancouver, Canada: Frase r Institute (2002). PDF

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Last updated: August 6, 2007