aFor incidence of solid cancers and based on doses between 0 and 1.5 Sv, as in Figure 10-2.
bDDREF = 1 + θ × high dose.
cFrom estimating LQ models forced to have curvature θ.
10B, the radiobiological information comes from mouse experiments, via models estimated from direct cancer risk data and models estimated from cancer-associated life-shortening data. The resulting posterior distribution for possible values of LSS DDREF is displayed in Figure 10-3.
Table 10-2 summarizes the graphical results of Figure 10-3. A single estimate of curvature is the median of the posterior distribution: 0.5 Sv−1, corresponding to an LSS DDREF of 1.5. On the basis of these analyses, there is little disagreement between the radiobiological and LSS estimates of LSS DDREF. While a quadratic term in an LSS LQ model is not significantly different from zero (twosided p-value = .2, for the 0–1.5 Sv dose range), the single best estimate of LSS DDREF from the LSS subset is 1.3. If the radiobiological estimate of 1.5 seems low, the committee believes that it is due not to a new interpretation of radiobiological curvature but rather to the use of an LSS DDREF that is specific to the needs of LSS linear model adjustment to account for the curvature. As evident in Table 10-1, a DDREF suitable for LSS adjustment is less than that expected for low-dose extrapolation of estimates based on high doses of 2 to 3 Sv.
The Bayesian approach formalizes the connection among the DDREF, the LQ curvature in radiobiology, and the LSS data. However, there are two reasons for the continuing uncertainty in the estimation of DDREF: (1) there is substantial inconsistency and imprecision in the data from animal experiments; and (2) the curvature estimates from radiobio-
FIGURE 10-3 Results of a Bayesian statistical analysis of dose-response curvature and associated LSS DDREF values. The probability density labeled “radiobiological prior” expresses the belief about curvature deduced from animal data, as detailed in Annex 11B. Regions of high density correspond to more believable values of curvature. The LSS likelihood is the likelihood function of curvature θ from the data displayed in Figure 10-2. The “combined” density is the Bayesian posterior obtained by updating the radiobiological density to account for information from the LSS data. The scale below the plot shows the implied values of LSS DDREFs corresponding to the θ scale. NOTE: The committee judges it preferable to choose a cutoff dose that lies within the lower rather the higher portion of the possible range.