A numerical description of carcinogenic potency,
the TD_{50} 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, TD_{50} may be defined
as follows: for a given target site(s), if there are no tumors in
control animals, then TD_{50} 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,
TD_{50} 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. TD_{50} is
analogous to LD_{50}, and a low value of TD_{50}
indicates a potent carcinogen, whereas a high value indicates a
weak one. TD_{50} 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 TD_{50} will be greater than the true
TD_{50}, i.e., the compound will appear to be less potent
than it actually is. Because tumor incidence increases markedly
with age, our convention for TD_{50} has been to adopt as a
correction factor f^{2}, 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 TD_{50}
value would be (100/104)^{2}, or 0.92. The TD_{50}
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 f^{2} 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, TD_{50} is defined in
terms of the dose-rate which would be administered throughout life,
from birth to death, or the entire standard lifespan.

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 TD_{50} 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 _{0}(t)* is the
tumor-incidence rate at zero dose. The parameter

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

Equation 2.

where *a > 0* and
*b > 0* and *p _{d}* is the
probability that an animal exposed at dose

The estimate of TD_{50} 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 *λ _{0}(t)* (Sawyer

In our database we have estimated 99 percent
confidence intervals for TD_{50}s 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 TD_{50}.

- Cox, D.R. Regression models and life
tables (with discussion)
*J. R. Stat. Soc. Brit. Series B*34: 187-220 (1972). - Peto, R., Pike, M.C., Bernstein, L.,
Gold, L.S., and Ames, B.N. The TD
_{50}: A proposed general convention for the numerical description of the carcinogenic potency of chemicals in chronic-exposure animal experiments.*Environmental Health Perspectives*58: 1-8 (1984). Abstract PDF - Sawyer, C., Peto, R., Bernstein,
L., and Pike, M.C. Calculation of carcinogenic potency from
long-term animal carcinogenesis experiments.
*Biometrics*40: 27-40 (1984). Abstract PDF

Return to the Carcinogenic Potency Project (CPDB) Home Page:

Last updated: August 6, 2007

PDF documents are best viewed with the free Adobe® Reader http://get.adobe.com/reader

Excel documents are best viewed with the free Excel® Viewer http://www.microsoft.com/en-us/download/details.aspx?id=10