# Statistical Methods for Estimating LTD_{10} from
TD_{50} and Its Lower Confidence Limit

LTD_{10} is the lower 95% confidence
limit on the dose to induce tumors in 10% of animals.
LTD_{10} values are estimated from the CPDB using the
TD_{50} and 99% lower confidence limit as follows:

Both the TD_{50} and the
two-sided 99% confidence limits (LoConf, UpConf) are reported in
the CPDB from fitting the one-hit
model to experimental dose-response data using maximum likelihood
methods. The one-hit model was selected because it is the most
conservative of the multistage models. When both the
TD_{50} and the two-sided 99% confidence limits are
available, it is shown in Gold *et al.* (2003) for the one-hit
model that the lower 95% confidence limit for the TD_{10},
i.e., LTD_{10} is:

**LTD**_{10} = [(TD_{50})^{0.36}
× (LoConf)^{0.64}] / 6.6

Since the one-hit model is the most conservative form of the family
of multistage models of carcinogenesis, the above estimate of the
LTD_{10} provides at least 95% confidence that the true
value of the TD_{10} is above this lower confidence limit
for this family of models.
This method gave similar estimates to the LTD_{10}
obtained by fitting the multistage model to the tumor incidence
data for both linear and curved dose responses with high or low
tumor rates in the controls and tight or wide confidence limits for
the TD_{50} (Gold *et al.*, 2003). Thus, relatively
precise estimates of the LTD_{10} can be readily calculated
from the TD_{50} and LoConf from the CPDB.

LTD_{10} values are reported in
an Excel spreadsheet in each species
for all chemicals in the CPDB with a positive evaluation of
carcinogenicity by the author of at least one experiment.

See also Statistical Methods for
Estimating TD_{50}.

## References

- 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
- U.S. Environmental Protection Agency (2005).
*Guidelines for
Carcinogen Risk Assessment*. PDF

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Last updated: August 6, 2007

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