TABLE 10-2 Maximum Likelihood Estimates of Curvature and Corresponding Estimates of LSS DDREFa and the Posterior Median from the Bayesian Analysis that Combines the Two

Estimate of θ

(95 % interval)


(95% interval)

Radiobiology animal experiments

0.5 Sv

(0.1, 3.2)

1.5 (1.0, 4.4)

LSS data (0–1.5 Sv dose range)

0.3 Sv

(−0.1, 1.5)

1.3 (0.8, 2.6)

Combined (posterior)

0.5 Sv

( 0.1, 1.2)

1.5 (1.1, 2.3)

NOTE: The 95% intervals are confidence intervals (likelihood ratio) in the first two rows and Bayesian posterior probability intervals in the last row.

aFrom radiobiological animal experiment results and LSS data.

logical data and from LSS data are sensitive to the range of doses used for estimation.

As shown in Annex 10B and evident in Figure 10B-1, there is a statistically significant difference in curvatures for the different mouse strains, sex, and cancer outcome combinations investigated (p-value < .001). Some results indicate large curvature, some no curvature, and some curvature in the opposite direction. The combined effect is weak evidence for small curvature. Because of the wide variability, the analysis is sensitive to the particular studies chosen and the approach for estimating a curvature that is presumed to be constant across studies.

The numerical results also are not robust because of the somewhat arbitrary choice in dose range subset for estimating linear-quadratic models, both from animal experiments and from LSS data. If the LQ model is fitted to a dose range that includes doses at which leveling off of the dose-response curve has occurred (as illustrated in Figure 10-1), the result will be biased for the intended purpose. If the dose range is too low, meaning it excludes doses for which the LQ approximation is still good, the estimates will be less precise than what is possible but will not lead to any bias. Given these consequences, it is judged preferable to choose a cutoff dose that is too low rather than one that is too high. The cutoffs of 1.5–2 Gy for animal experiments and 1.5 Sv for LSS data were chosen subjectively, based on the belief that these were sufficiently low that leveling off is not of great concern. Nevertheless, the fact remains that the relationships shown in Figure 10-3 would be quite different if different dose ranges were used.

The cutoff of 1.5 Sv for the LSS data is important for assessing curvature. The resulting LSS DDREF is appropriate for adjusting risks from linear models based on the same dose range. Since the LSS estimated linear model is insensitive to the choice of subset however, the particular choice of dose range upon which to estimate the linear model is not critical.

More generally, since a linear model fits the LSS data over the entire range (for cancers other than leukemia), it is important to question why the expected curvature fails to materialize and whether the absence of curvature necessarily implies that the LSS low-dose slope is too large. It could be that a linear relationship is the result of some cancelation of inward curvature and high-dose leveling-off. It is not obvious that the linear relationship resulting from such cancelation overestimates low-dose risk.

Given these unresolved issues, it is comforting that the estimate of LSS DDREF is consistent with the best-fitting LQ model based on LSS data alone; that is, low-dose risk estimates based on LSS linear models with DDREF adjustment will be essentially the same as risk estimates based on the best-fitting LQ model from LSS data over the range 0 to 1.5 Sv. In Figure 10-2, for example, it is clear that the linear component of an LQ curve with curvature 0.5 Sv−1 over the low-dose range is consistent with the data. The difference between that estimate and one based on the unadjusted linear model will be small relative to the size of the associated confidence interval.

The DDREF analysis has used LSS data on solid cancer incidence. A recent similar analysis on cancer mortality (Preston and others 2004) has provided the somewhat larger estimated curvature 0.94 Sv−1 (90% CI 0.16, 8.4) for the best-fitting LQ model over the range 0 to 2 Sv. Since there is considerable imprecision in the calculations, this result is not inconsistent with the committee’s conclusions.

In summary, the approach used by the committee to make an analytical judgment about the value of DDREF has employed a combined Bayesian analysis of dose-response curvature for cancer risk using animal radiobiological data and human evidence from the LSS. The committee found a believable range of DDREF values for adjusting linear risk estimates from the LSS cohort to be 1.1–2.3. Based on this analysis, the committee elected to use the value of 1.5 for solid tumors; also, a linear-quadratic model was used for leukemia. The committee recognizes the limitations of the data and the uncertainties in estimating the DDREF.


This report has given much attention to biological responses to radiation that, although not well understood, may influence the development of views on tumorigenic mechanisms and the modeling of epidemiologic data.

Adaptive Responses

Adaptive responses to radiation are represented in a range of studies that purport to demonstrate that a low priming dose of radiation can influence the subsequent response of cells or experimental animals to subsequent challenge by a second higher dose. It is claimed by some that these adaptive

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