with the exception of leukemia, there has been little statistical evidence of a need for curvature in the LSS dose-response models and substantial reliance on models in which risk is simply a linear function of radiation dose (Pierce and Preston 2000; Preston and others 2003). There is stronger evidence of curvature from radiobiological considerations and experimental results. The DDREF has been used in the past as a device for allowing risk estimates to conform to this expected curvature but without abandoning the LSS linear models (ICRP 1991; NCRP 1993; EPA 1999; UNSCEAR 2000b; NIH 2003).

A rationale for DDREF is illustrated in Figure 10-1 for a setting that mimics a simple animal experiment on cancer induction by acute-dose low-LET radiation in which risks are observed only at two doses: zero and some particular “high dose.” If the true dose-response relationship is concave up to that dose, as the radiobiological data tend to suggest, then a line connecting the excess risk at high dose to the origin would tend to have a larger slope than a line that approximates the dose-response curve at doses near zero. The DDREF in this case is the ratio of these two slopes (i.e., the risk per unit of dose at high dose divided by the risk per unit of dose at low dose). If this ratio is known then it can be used to convert a risk estimate from the high-dose linear approximation to the more appropriate low-dose linear approximation, as shown in the figure. The association between the form of the dose-response at acute doses and the effects of dose-rate is discussed in Chapter 2 and in Annex 10B.

This DDREF clearly must depend on what is meant by high dose and should not be mistakenly thought of as a universal low-dose correction factor. Furthermore, of particular interest here is what might more appropriately be called an LSS DDREF, where a curvature adjustment to risk estimates from LSS-estimated linear models is based on a wide range of doses. The line analogous to the “high-dose linear approximation” of Figure 10-1 is the one that results from linear model estimation with the LSS data. If a certain degree of curvature is presumed, then it is possible to define an LSS DDREF that correctly adjusts LSS linear risk in order to estimate cancer risk at low doses. Such a definition is provided after the discussion of a numerical characterization of dose-response curvature upon which it is based.

If, over some dose range of interest, the dose-response curve can be approximated by a linear-quadratic (LQ) function, αDose + βDose2, then the slope of the high-dose linear

FIGURE 10-1 A hypothetical dose-response curve with a linear approximation for low doses (i.e., the tangent of the curve at dose zero) and a linear approximation based on risk at one particular high dose (i.e., the line that passes through the origin and the true dose-response curve at the high dose), when the high dose is taken to be 2 Gy. The DDREF at this high dose is the larger slope divided by the smaller slope. An explanation of why this low-dose effect also applies to low-dose-rate effects is provided in Chapter 3.

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