approximation (sH in Figure 10-1) at a particular high dose DH is α + βDH, the slope of the low-dose linear approximation (sL in Figure 10-1) is α, and the DDREF corresponding to DH is their ratio, 1 + (β / α)DH (UNSCEAR 1993). A natural numerical quantity for curvature characterization, therefore, is β / α, which is not tied to any particular high dose. This ratio is referred to here as the LQ “curvature” and is represented by the symbol θ (i.e., the reciprocal of the so-called crossover dose).

If the correct curvature, θ, is known, then an LSS DDREF may be defined through the following steps: an LQ model for ERR or EAR is estimated from the LSS data in such a way that the curvature is constrained to be θ, that is, by fitting the relative risk model αLQ(Dose + θDose2) for fixed θ and with unknown linear component αLQ. A separate linear model is estimated from the same data: αLDose, with linear component αL. The LSS DDREF is the estimate of the ratio of the two linear components, αL / αLQ. The resulting DDREF can be used to convert a risk estimate based on the linear model projection to one based on the linear component of an estimated LQ model with curvature determined by a given choice of the value of θ. Figure 10-2 illustrates the definition for two possible choices of this value.

The two definitions of DDREF as a function of LQ curvature must be clearly distinguished: the fixed high-dose DDREF (or UNSCEAR definition), DDREF = 1 + θ × high dose, and the LSS DDREF defined by the estimation process in the preceding paragraph. The first is a function of θ and some particular high dose. The second is a function of θ and the LSS data. Their relationship, as illustrated in Table 10-1, indicates that the LSS DDREF based on A-bomb survivors with doses of 1.5 Sv or less is roughly equivalent to the fixed high-dose DDREF at an effective high dose of about 1 Sv. In other words, in terms of the familiar UNSCEAR single high-dose definition, one can act as if the nonzero LSS doses were concentrated at a dose of 1 Sv.

Table 10-1 may be used as an aid in interpreting radiobiological evidence for curvature. If, for example, radiobiology data indicate that a DDREF of 2 is appropriate for adjusting risks based on a linear model derived at the single high dose of 2 Sv, then the implicit curvature is 0.5 Sv−1 and the corresponding LSS DDREF is 1.5.

The committee estimates LSS DDREF in this report by combining radiobiological and LSS evidence concerning curvature via a Bayesian statistical analysis and applying the definition of LSS DDREF to the result. As detailed in Annex 10B, the

FIGURE 10-2 Illustration of LSS DDREF. Plotted points are the estimated ERRs for solid cancer incidence (averaged over sex, for individuals exposed at age 30 at attained age 60) from LSS subjects in each of 11 dose categories. The vertical lines extend two standard errors above and below the estimates. The solid line is a linear fit to the data for dose range 0–1.5 Sv, with slope αL = 0.56. The other two curves are estimated LQ models for the same dose range, when the curvature, θ, is constrained to be 0.3 Sv−1 (resulting in estimated linear coefficient αLQ = 0.43) and 0.7 Sv−1 (resulting in estimated linear coefficient αLQ = 0.32). The LSS DDREFs that result from these are 0.56 / 0.43 = 1.3 and 0.56 / 0.32 = 1.8, respectively.

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