**Suggested Citation:**"ANNEX C: ADJUSTMENT OF POTENCY VALUES FOR LESS THAN LIFETIME EXPOSURE." National Research Council. 1993.

*Issues in Risk Assessment*. Washington, DC: The National Academies Press. doi: 10.17226/2078.

"shrinking" the Y_{i} toward the mean . The estimators of *µ*_{i} have the correct dispersion in that

In fitting the Weibull model in (A.1), we found that the estimate of the variance of the log_{10}TD*_{50} based on (A.9) appeared to be excessively large in a small number of cases. In order not to underestimate the between-study variability based on (B.2), we used a trimmed mean S*s_{i}^{2}/n*, in which the largest and smallest 10% of the observed values of s_{i}^{2} were omitted (Hampel et al., 1986, p. 79). Specifically, the summation S* covers only those n* = 153 observations falling in the central 80% of the distribution of the s_{i}^{2}.

**Annex C:** **Adjustment of Potency Values for Less than Lifetime Exposure**

In order to ensure that TD_{50} values for different chemicals are comparable, some adjustment for differences in the duration of the experimental period is desirable. Gold et al. (1984) adjusted TD_{50} values by a multiplicative factor of f^{2}, where f represents the fraction of a two year period encompassed by the study period. This effectively scales the TD_{50} values to a standard two year rodent lifetime. Specifically, we have

where the TD_{50} denotes the estimate of carcinogenic potency based on the observed data for the actual experimental period, and denotes the standardized value.

To motivate the use of the adjustment factor f^{2}, consider the extended Weibull model

**Suggested Citation:**"ANNEX C: ADJUSTMENT OF POTENCY VALUES FOR LESS THAN LIFETIME EXPOSURE." National Research Council. 1993.

*Issues in Risk Assessment*. Washington, DC: The National Academies Press. doi: 10.17226/2078.

depending on both dose d and time t. Under this model, the TD_{50}(t) evaluated at time t is given by

Thus, the ratio of TD_{50}'s at two distinct times t_{1} and t_{2} is

where f = t_{1}/t_{2}. In the CPDB, Gold et al. (1984) use a one-stage model with k = 1 and set p = 2 based on empirical observations reported by Peto et al. (1984), leading to their adjustment factor f^{2}. In our applications of the Weibull model in (A.1), we will use a similar adjustment factor of f^{2/k} to standardize TD_{50} values to a two year rodent lifetime.

For a multi-stage model of the form

allowing for the effects of both dose d and time t, the TD_{50} at time t is obtained as the solution of the equation

It follows that the standardized value of the TD_{50} is obtained as the solution of the equation

As with the Weibull model, we set p = 2 in the applications considered in this paper.