Models used for estimating leukemia risks in the past have expressed the ERR (NRC 1990; NIH 2003) or EAR (ICRP 1991; UNSCEAR 2000b) as a linear-quadratic function of dose and have allowed for dependence on sex, age at exposure, and time since exposure. Both categorical and continuous treatments of age at exposure and time since exposure have been used. The BEIR VII committee models also express the ERR or EAR as a linear-quadratic function of dose with allowance for dependencies on sex, age at exposure, and time since exposure. The committee’s preferred models are of the following form:


where D is dose (Sv), s is sex, and e* is (e − 30) / 10 for e < 30 and 0 for e 30 ( e is age at exposure in years). Table 12-3 shows the parameter estimates, and Figure 12-2 depicts the dependence of the ERR or EAR on age at exposure and time since exposure. The parameter θ indicates the degree of curvature, which does not depend on sex, age at exposure, or time since exposure; βM and βF represent the ERR/Sv or the EAR (expressed as excess deaths per 104 PY-Sv, where PY = person-years), for exposure at age 30 or more at 25 years following exposure. This model was found to fit the data better than analogous models using e instead of e*, or using t instead of log (t), and nearly as well as models with a

TABLE 12-3 Committee’s Preferred ERR and EAR Models for Estimating Leukemia Incidence and Mortalitya,b,c


ERR Model

EAR Model


1.1 per Sv (0.1, 2.6)

1.62 deaths per 104 PY-Sv (0.1, 3.6)


1.2 per Sv (0.1, 2.9)

0.93 deaths per 104 PY-Sv (0.1, 2.0)


−0.40 per decade (−0.78, 0.0)

0.29 per decade (0.0, 0.62)


−0.48 (−1.1, 0.2)


0.42 (0.0, 0.96)

0.56 (0.31, 0.85)


0.87 per Sv (0.16, 15)

0.88 Sv−1 (0.16, 15)

NOTE: Estimated parameters with 95% CIsd based on likelihood ratio profile.

aThe ERR or EAR is of the form βs(D + θ D2) exp [γ e* + δ log (t / 25) + e* log (t / 25)], where D is the dose to the bone marrow (Sv), e is age at exposure (years), e* is (e − 30) / 10 for e < 30 and zero for e 30, and t is time since exposure (years).

bBased on analyses of LSS mortality data (1950–2000), with 296 deaths from leukemia.

cThese models apply only to the period 5 or more years following exposure.

dConfidence intervals based on likelihood ratio profile.

categorical treatment of age at exposure. It was also found to be necessary to allow the dependence on time since exposure to vary by age at exposure by including the term e* log (t / 25). For the EAR model, there was no need to include a term for the main effect of time since exposure; note that with this parameterization, there is no decrease with time since exposure for those exposed at age 30 or more. For application of these models, the reader should consult the section “Use of the Committee’s Preferred Models to Estimate Risks for the U.S. Population.”


To use models developed primarily from Japanese A-bomb survivor data for the estimation of lifetime risks for the U.S. population, several issues must be addressed. These include determining approaches for estimating risks at low doses and low dose rates, projecting risks over time, transporting risks from the Japanese to the U.S. population, and estimating risks from exposure to X-rays. This section describes the approach for addressing each of these issues, as well as the methodology used to estimate lifetime risk. More detailed discussion of some of the issues is given in Chapter 10, and the approach for quantifying the uncertainties associated with some of these issues is discussed later in this chapter.

Estimating Risks from Exposure to Low Doses and Low Dose Rates

The BEIR VII risk models have been developed primarily from analyses of data on the LSS cohort of Japanese A-bomb survivors. Although more than 60% of the exposed members of this cohort were exposed to relatively low doses (0.005–0.1 Sv), survivors who were exposed to doses exceeding 0.5 Gy are still influential in estimating the ERR/Sv. In addition, exposure of A-bomb survivors was at high dose rates, whereas exposure at low dose rates is of primary concern for risk assessment. Based on evidence from experimental data, ICRP (1991), NCRP (1993), EPA (1999), and UNSCEAR (2000b) recommended reducing linear estimates based on A-bomb survivor (or other high-dose-rate) exposure by a dose and dose-rate reduction factor (DDREF) of 2.0.

In Chapter 10, both data on solid cancer risks in the LSS cohort and experimental data pertinent to this issue are evaluated by the committee. Based on this evaluation, the committee found a believable range of DDREF values (for adjusting linear risk estimates based on the LSS cohort) to be 1.1 to 2.3. When a single value is needed, 1.5 (the median of the subjective probability distribution for the LSS DDREF) is used to estimate risk for solid tumors. To estimate the risk of leukemia, the BEIR VII model is linear-quadratic, since this model fitted the data substantially better than the linear model.

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