Carcinogenic Potency (TD50)

A numerical description of carcinogenic potency, the TD50 is estimated for each set of tumor incidence data reported in the CPDB, thus providing a standardized quantitative measure for comparisons and analyses of many issues in carcinogenesis. In a simplified way, TD50 may be defined as follows: for a given target site(s), if there are no tumors in control animals, then TD50 is that chronic dose-rate in mg/kg body wt/day which would induce tumors in half the test animals at the end of a standard lifespan for the species. Since the tumor(s) of interest often does occur in control animals, TD50 is more precisely defined as: that dose-rate in mg/kg body wt/day which, if administered chronically for the standard lifespan of the species, will halve the probability of remaining tumorless throughout that period. TD50 is analogous to LD50, and a low value of TD50 indicates a potent carcinogen, whereas a high value indicates a weak one. TD50 can be computed for any particular type of neoplasm, for any particular tissue, or for any combination of these.

When an experiment is terminated before the standard lifespan, animals are not at risk of developing tumors later in life. Thus, the number of tumors found will be reduced, and the TD50 will be greater than the true TD50, i.e., the compound will appear to be less potent than it actually is. Because tumor incidence increases markedly with age, our convention for TD50 has been to adopt as a correction factor f2, where f=experiment time/standard lifespan (2 years for rats, mice and hamsters).

Taking an example of male mice fed some test agent for 70 weeks and then continued on test for 30 more weeks, the experiment time would be 100 weeks. The standard lifespan for mice is 104 weeks, so the extrapolation factor for the TD50 value would be (100/104)2, or 0.92. The TD50 would become lower, i.e., more potent. By omitting from the database any experiments lasting less than half the standard lifespan for each species, the necessity for great extrapolation has been reduced.

Note that the correction factor f2 is based on the time the animals are on test, rather than upon age. In an experiment which began when the animals were 6 weeks of age, and which terminated when the animals were 100 weeks of age, the experiment time is 94 weeks. Thus, TD50 is defined in terms of the dose-rate which would be administered throughout life, from birth to death, or the entire standard lifespan.

Statistical Methods for Estimating TD50

For NCI/NTP bioassays and a few experiments from the general literature data were available on the time of death and tumors for each animal, so the TD50 has been estimated using this lifetable data. The symbol “:” appears in the plot for lifetable data. The lifetable methods which we have used to analyze the experimental data have been described in Sawyer et al., 1984. Briefly, a proportional hazards model (Cox, 1972) is assumed for the time-to-tumor data, in which λ(t, d), the tumor-hazard rate at age t for a specific site, is linearly related to d, the administered dose-rate of test chemical in mg/kg body wt/day, as
Equation 1.

λ(t,d) = (1 + β · d)λ0(t).

λ0(t) is the tumor-incidence rate at zero dose. The parameter β and the function λ0 are estimated using maximum likelihood methods. The likelihood ratio statistic tests the hypothesis that the chemical has no carcinogenic effect (i.e., β = 0), and a χ2 goodness-of-fit statistic tests the validity of the linear relationship between dose and tumor incidence expressed by Equation 1. In fitting the model, no attempt is made to distinguish between tumors found in a fatal context and tumors found in an incidental context. Thus the time-to-tumor occurrence is taken to be the time to death of the animal, whether death results from the tumor of interest, or from some other cause, including terminal sacrifice (Peto et al., 1984, Sawyer et al., 1984)

For summary incidence data, we fit by maximum likelihood methods the comparable model
Equation 2.

pd = 1 - exp{-(a + bd)},

where a > 0 and b > 0 and pd is the probability that an animal exposed at dose d for its lifetime develops a tumor. This model is linear at low doses and is often referred to as the “one-hit model.” Here, the number of animals developing tumors at dose d is assumed to follow a binomial distribution with parameters nd and pd, where nd is the number of animals initially exposed at dose d. As with lifetable data, the likelihood ratio statistic is used to test whether the compound is carcinogenic, i.e. whether b = 0, and a χ2 statistic tests the adequacy of the model.

The estimate of TD50 based on summary incidence data is simply log(2)/b, where b is the maximum likelihood estimate (MLE) of b. For lifetable data, the estimate is a more complex function of the MLEs of β and λ0(t) (Sawyer et al., 1984). For either method of estimating TD50, if the χ2 goodness-of-fit test indicated statistically significant departure from linearity, (p<0.05) and this departure was downward, the analysis was repeated eliminating the highest dose group. The purpose of this procedure was to remove the effects of toxicity in summary incidence analyses and to remove the effects of dose saturation in the lifetable analyses. If the goodness-of-fit test indicated an upward departure from linearity, no groups were eliminated when fitting the model.

In our database we have estimated 99 percent confidence intervals for TD50s calculated from lifetable data and for those based on summary incidence data. The method for calculating these intervals from lifetable data is described in Sawyer et al., (1984). For summary incidence data, 99% likelihood-ratio-test-based confidence limits are obtained for b and are then transformed to limits for TD50.


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Last updated: August 6, 2007

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