curvature of interest can be ascertained by fitting an LQ model to the reciprocal of the mean survival.
Figure 10B-3 shows the reciprocal mean survival times plotted versus dose, with different plotting characters for means based on acutely and chronically exposed mice. Also shown on the plot are the fits to the model that has the age-specific death rate equal to a constant plus αDose for chronically exposed mice and the same constant plus α(Dose + θDose2) for acutely exposed mice, following the reasoning in the first section of this Annex. (The estimates are maximum likelihood estimates based on normality of the reciprocal means, which are estimates from a large number of mice.) The estimates depend highly on the dose range considered. This presents a difficulty since leveling off of the dose-response is expected (as shown in Figure 10-1), but the dose at which leveling off occurs is difficult to determine, both theoretically and empirically. The decision was made by the committee to use the 0–1.5 Gy dose range, but this is subjective and open to debate.
The (profile) likelihood function for θ is shown in Figure 10B-4. It is evident that the life-shortening data indicate slightly more curvature than the direct cancer risk results. While it is appropriate to multiply two likelihoods from independent data sets, these data sets are not independent. Instead, an average of the two is obtained, shown as the solid curve in Figure 10B-4, to represent an average effect based on the two ways of dealing with the data. The maximum likelihood estimate of θ from the average likelihood is 0.5, corresponding to an LSS DDREF of 1.5.
Evidence of curvature at the cellular level comes primarily from studies of chromosomal aberrations in human cells. Table 10B-1 shows estimated LQ models for the regression of chromosome aberration induction on dose. These results may be included weakly, by specifying a probability distribution with mean and variance equal to the sample mean and sample variance of the three curvatures in the table. The result of including such a distribution in the averaging of Figure 10B-4 is to increase the width of the resulting average likelihood, with little effect on the center of the distribution. Since they do not alter the results and because of the extra theoretical demand in incorporating cellular data into models for human cancer rates, chromosome aberration data were not included in the analysis.
The final step in the LSS DDREF estimation involves combining animal radiobiological information with LSS information about curvature. The average likelihood in Figure 10B-4