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Health Risks from Exposure to Low Levels of Ionizing Radiation: Beir VII Phase 2
12
Estimating Cancer Risk
INTRODUCTION
This chapter presents models that allow one to estimate the lifetime risk of cancer resulting from any specified dose of ionizing radiation and applies these models to example exposure scenarios for the U.S. population. Models are developed for estimating lifetime risks of cancer incidence and mortality and take account of sex, age at exposure, dose rate, and other factors. Estimates are given for all solid cancers, leukemia, and cancers of several specific sites. Like previous BEIR reports addressing low-LET (linear energy transfer) radiation, risk models are based primarily from data on Japanese atomic bomb survivors. However, the vast literature on both medically exposed persons and nuclear workers exposed at relatively low doses has been reviewed to evaluate whether findings from these studies are compatible with A-bomb survivor-based models. In many cases, results of fitting models similar to those in this chapter have been published.
Risk estimates are subject to several sources of uncertainty due to inherent limitations in epidemiologic data and in our understanding of exactly how radiation exposure increases the risk of cancer. In addition to statistical uncertainty, the populations and exposures for which risk estimates are needed nearly always differ from those for whom epidemiologic data are available. This means that assumptions are required, many of which involve considerable uncertainty. Risk may depend on the type of cancer, the magnitude of the dose, the quality of the radiation, the dose-rate, the age and sex of the person exposed, exposure to other carcinogens such as tobacco, and other characteristics of the exposed individual. Despite the abundance of epidemiologic and experimental data on the health effects of exposure to radiation, data are not adequate to quantify these dependencies precisely. Uncertainties in the BEIR VII risk models are discussed, and a quantitative assessment of selected sources of uncertainty is made.
In recent years, several national and international organizations have developed models for estimating cancer risk from exposure to low levels of low-LET ionizing radiation. These include the work of the BEIR V committee (NRC 1990), the International Commission on Radiological Protection (ICRP 1991), the National Council on Radiation Protection and Measurements (NCRP 1993), the Environmental Protection Agency (EPA 1994, 1999), the United Nations Scientific Committee on the Effects of Atomic Radiation (UNSCEAR 2000b), and the National Institutes of Health (NIH 2003). The approaches used in these past assessments are described in Annex 12A.
DATA EVALUATED FOR BEIR VII MODELS
As in earlier BEIR reports addressing health effects from exposure to low-LET radiation, the committee’s models for risk estimation are based primarily on the Life Span Study (LSS) cohort of survivors of the atomic bombings in Hiroshima and Nagasaki. As discussed in Chapter 6, the LSS cohort offers several advantages for developing quantitative estimates of risk from exposure to ionizing radiation. These include its large size, the inclusion of both sexes and all ages, a wide range of doses that have been estimated for individual subjects, and high-quality mortality and cancer incidence data. In addition, because the exposure was to the whole body, the LSS cohort offers the opportunity to assess risks for cancers of a large number of specific sites and to evaluate the comparability of site-specific risks.
Another consideration in the choice of data was that it was considered essential that the data used by the committee eventually be available to other investigators. The Radiation Effects Research Foundation (RERF) has developed a policy of making summarized data available to those who request it, thus enabling other investigators to analyze data used by the BEIR VII committee. This is not the case for data sets on most other radiation-exposed cohorts.
Although the committee’s models have been developed from A-bomb survivor data, attention has been given to their compatibility with data from other cohorts. Fortunately, for
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most cohorts with suitable data for developing quantitative risk models, analyses based on models similar to those used by the committee have been conducted and published. This facilitated the committee’s evaluation of data from other studies. Pooled analyses of thyroid cancer risks (Ron and others 1995a) and of breast cancer risks (Preston and others 2002a) were especially helpful in this regard, as were several meta-analyses by Little and colleagues. In addition, the many published analyses based on A-bomb survivor data have guided and facilitated the committee’s efforts in its choice of models. The committee notes particularly the main publications on mortality (Preston and others 2003) and incidence data (Thompson and others 1994) and the models developed by UNSCEAR (2000b) and NIH (2003).
The use of data on persons exposed at low doses and low dose rates merits special mention. Of these studies, the most promising for quantitative risk assessment are the studies of nuclear workers who have been monitored for radiation exposure through the use of personal dosimeters. These studies, which are reviewed in Chapter 8, were not used as the primary source of data for risk modeling principally because of the imprecision of the risk estimates obtained. For example, in a large combined study of nuclear workers in three countries, the estimated relative risk per gray (ERR/Gy) for all cancers other than leukemia was negative, and the confidence interval included negative values and values larger than estimates based on A-bomb survivors (Cardis and others 1995).
Since the publication of BEIR V, data on cancer incidence in the LSS cohort from the Hiroshima Tumor Registry have become available, whereas previously only data from the Nagasaki Tumor Registry were available. Thus, the committee could use both incidence and mortality data to develop its models. The incidence data offer the advantages of including nonfatal cancers and of better diagnostic accuracy. However, the mortality data offer the advantages of covering a longer period (1950–2000) than the incidence data (1958–1998) and of including deaths of LSS members who migrated from Hiroshima and Nagasaki to other parts of Japan.
MEASURES OF RISK AND CHOICE OF CANCER END POINTS
To express the health impact of whole-body exposures to radiation, the lifetime risk of total cancer, without distinction as to site, is usually of primary concern. Estimates of risk for both mortality and incidence are of interest, the former because it is the most serious consequence of exposure to radiation and the latter because it reflects public health impact more fully. The time or age of cancer occurrence is also of interest, and for this reason, estimates of cancer mortality risks are sometimes accompanied by estimates of the years of life lost or years of life lost per death. Because leukemia exhibits markedly different patterns of risk with time since exposure and other variables, and also because the excess relative risk for leukemia is clearly greater than that for solid cancers, all recent risk assessments have provided separate models and estimates for leukemia.
For exposure scenarios in which various tissues of the body receive substantially different doses, estimates of risks for cancers of specific sites are needed. Adjudication of compensation claims for possible radiation-related cancer, which is usually specific to organ site, also requires site-specific estimates. Furthermore, site-specific cancers vary in their causes and baseline risks, and it might thus be expected that models for estimating excess risks from radiation exposure could also vary by site. For this reason, even for estimating total cancer risk, it is desirable to estimate risks for each of several specific cancer sites and then sum the results.
The development of site-specific models is limited by data characteristics. For A-bomb survivor data on solid cancers, parameter estimates based on site-specific data are less precise than those based on all solid cancers analyzed as a group, particularly for less common cancers. It is especially difficult to detect and quantify the modifying effects of variables such as sex, age at exposure, and attained age for site-specific cancers. It was for these reasons that the BEIR V committee provided estimates for only five broad cancer categories.
In addition to statistical uncertainties, it has recently been recognized that estimates of the modifying effects of age at exposure based on A-bomb survivor data can be influenced strongly by secular trends in Japanese baseline rates (Pierce 2002; Preston and others 2003). This occurs because age at exposure in the LSS cohort is confounded with birth cohort, making it impossible to estimate their separate effects without additional information on the relation of baseline and radiation-related risks. (See Annex 12B for further discussion of this issue.) Japanese rates for several cancer sites changed over the period 1950–1998 as Japan became more Westernized, including rates for cancers of the stomach, colon, lung, and female breast. A related problem is that baseline risks for the United States and Japan differ substantially for many cancer sites, and it is unclear how to account for these differences in applying models developed from A-bomb survivor data to estimate risks for the U.S. population.
Pierce and colleagues (1996) and, more recently, Preston and colleagues (2003) found little evidence of heterogeneity among excess relative risk (ERR)1 models developed for several specific cancer sites. Although these authors caution that this finding should be taken mainly as a warning against overinterpreting apparent differences in sites, some grouping of cancers seems justified. In developing its models, the committee has tried to strike a balance between allowing for differences among cancer sites and statistical precision. As discussed later in this chapter, most of the committee’s mod-
1
ERR is the rate of disease in an exposed population divided by the rate of disease in an unexposed population minus 1.0.
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els for site-specific cancers make use of data on all solid cancers to estimate the modifying effects of age at exposure and attained age, but make use only of data for the site of interest to estimate the overall level of risk.
Considerations in deciding on the sites for which individual estimates should be provided are whether or not the cancer has been linked clearly with radiation exposure and the adequacy of the data for developing reliable risk estimates. On the first point, it can be argued that the range of uncertainty for risk of a particular cancer is of interest regardless of whether or not a statistically significant dose-response had been observed, a position taken by NIH (2003). Cancers of the salivary glands, stomach, colon, liver, lung, breast, bladder, ovary, and thyroid and nonmelanoma skin cancer have all been linked clearly with radiation exposure in A-bomb survivor data, with evidence somewhat more equivocal for a few additional sites such as esophagus, gall bladder, and kidney. Other studies support many of these associations, and bone cancer has been linked with exposure to α-irradiation from 224Ra. Leukemia has been strongly linked with radiation exposure in several studies including those of atomic bomb survivors.
Another consideration in selecting sites for evaluation is the likelihood of exposure scenarios that will irradiate the site selectively. Here it is noted that inhalation exposures will selectively irradiate the lung, exposures from ingestion will selectively irradiate the digestive organs, exposure to strontium selectively irradiates the bone marrow, and exposure to uranium selectively irradiates the kidney.
Based on these considerations, the committee has provided models and mortality and incidence estimates for cancers of the stomach, colon, liver, lung, female breast, prostate, uterus, ovary, bladder, and all other solid cancers. Incidence estimates are also provided for thyroid cancer.
The inclusion of cancers of the prostate and uterus merits comment because these cancers are not usually thought to be radiation-induced and have not been evaluated separately in previous risk assessments. However, the committee did not want to include these cancers in the residual category of “all other solid cancers,” particularly since prostate cancer is much more common in the United States than in Japan.
THE BEIR VII COMMITTEE’S PREFERRED MODELS
Approach to Analyses
This section describes the results of analyses of data on cancer incidence and mortality in the LSS cohort that were conducted by the committee with the help of RERF personnel acting as agents of the National Academies. Analyses of cancer incidence were based on cases diagnosed in the period 1958–1998. Analyses of cancer mortality from all solid cancers and from leukemia were based on deaths occurring in the period 1950–2000 (Preston and others 2004), whereas analyses of mortality from cancer of specific sites were based on deaths occurring in the period 1950–1997 (Preston and others 2003). Both excess relative risk models and excess absolute risk (EAR)2 models were evaluated. Methods were generally similar to those that have been used in recent reports by RERF investigators (Pierce and others 1996; Preston and others 2003) and were based on Poisson regression using the AMFIT module of the software package EPICURE (Preston and others 1991). Additional detail is given in Annex 12B.
All analyses were based on the newly implemented DS02 dose estimates. Doses were expressed in sieverts, with a constant weighting factor of 10 for the neutron dose; that is, the doses were calculated as γ-ray absorbed dose (Gy) + 10 × neutron absorbed dose (Gy). The DS02 system provides estimates of doses to several organs of the body. For site-specific estimates, the committee used dose to the organ being evaluated, with colon dose used for the residual category of “other” cancers. The weighted dose, d, to the colon was used for the combined category of all solid cancer or all solid cancers excluding thyroid and nonmelanoma skin cancer. Additional discussion of the doses used in the analyses is given in Annex 12B.
Models for All Solid Cancers
Risk estimates for all solid cancers were obtained by summing the estimates for cancers of specific sites. However, the general form of the model and the estimates of the parameters that quantify the modifying effects of age at exposure and attained age were (with some exceptions) based on analyses of data on all solid cancers. Such analyses offer the advantage of larger numbers of cancer cases and deaths, which increases statistical precision.
As discussed in Chapter 6, most recent analyses of data on the LSS cohort have been based on either ERR models, in which the excess risk is expressed relative to the background risk, or EAR models, in which the excess risk is expressed as the difference in the total risk and the background risk. With linear dose-response functions, the general models for the ERR and EAR are given below:
or
where λ(c, s, a, b) denotes the background rate at zero dose, and depends on city (c), sex (s), attained age (a), and birth cohort (b). The terms βs ERR(e, a) and βs EAR(e, a) are, respectively, the ERR and the EAR per unit of dose expressed in sieverts, which may depend on sex (s), age at exposure (e), and attained age (a).
2
EAR is the rate of disease in an exposed population minus the rate of disease in an unexposed population.
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FIGURE 12-1A Age-time patterns in radiation-associated risks for solid cancer incidence excluding thyroid and nonmelanoma skin cancer. Curves are sex-averaged estimates of the risk at 1 Sv for people exposed at age 10 (solid lines), age 20 (dashed lines), and age 30 or more (dotted lines). Estimates were computed using the parameter estimates shown in Table 12-1.
FIGURE 12-1B Age-time patterns in the radiation-associated risks for all solid cancer mortality. Curves are sex-averaged estimates of the risk at 1 Sv for people exposed at age 10 (solid lines), age 20 (dashed lines), and age 30 or more (dotted lines). Estimates were computed using the parameter estimates shown in Table 12-1.
The most recent analyses of A-bomb survivor cancer incidence and mortality data (e.g., Preston and others 2003, 2004) are based on models in which ERR (e, a) and EAR (e, a) are of the form below:
(12-1)
The parameters γ and η quantify the dependence of the ERR or EAR on e and a. These models, with dependence on both age at exposure and attained age, were chosen because of difficulties in distinguishing the fits of models with only one of those variables and because, with the incidence data, analyses of all solid cancers indicated dependence on both variables.
The committee’s models were developed from analyses of both LSS incidence and LSS mortality data. Analyses of incidence data were based on the category consisting of all solid cancers excluding thyroid and nonmelanoma skin cancers. These exclusions were made because both thyroid cancer and nonmelanoma skin cancer exhibit exceptionally strong age-at-exposure dependencies that do not seem typi-
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cal of cancer of other sites (Thompson and others 1994). Because the most recent mortality data (1950–2000) available to the committee did not include site-specific solid cancers and because thyroid cancer and nonmelanoma skin cancer are rarely fatal, analyses of mortality data were based on the category of all solid cancers. The committee’s preferred models for estimating solid cancer risks are similar to the RERF model, except that the ERR and EAR depend on age at exposure only for exposure ages under 30 years and are constant for exposure ages over 30. That is,
(12-2)
where e is age at exposure in years, e* is equal to e − 30 when e < 30, and equal to zero when e 30, and a is attained age in years.
Figure 12-1A shows plots of the ERR and EAR for incidence of all solid cancers excluding thyroid cancer and nonmelanoma skin cancer as a function of exposure age and attained age using the BEIR VII model. Figure 12-1B shows similar plots for mortality from all solid cancers. Although the ERR and EAR models have the same form, the values and interpretation of the parameters are different. In particular, the ERR shows a decrease with attained age, whereas the EAR shows a strong increase with attained age. Both the ERR and the EAR decrease with increasing age at exposure for those exposed under age 30.
The committee chose the model shown in Equation (122) because it fitted both incidence and mortality data on all solid cancers excluding thyroid cancer and nonmelanoma skin cancer slightly better than the RERF model shown in Equation (12-1). There was no indication of a continued decrease with exposure age in the ERR or EAR after exposure age 30, and there was even a suggestion of an increase at older ages. Further discussion of the rationale for choosing the Equation (12-2) model, including a detailed description of analyses that were conducted by the committee, can be found in Annex 12B. In that annex, the committee evaluates several alternative model choices, including models that allow for dependence on age at exposure alone, on attained age alone, and on time since exposure instead of attained age. Also evaluated are models that use different functional forms to express the dependence on exposure age, attained age, or time since exposure. Although several alternative models provided reasonable descriptions of the data, the BEIR VII preferred model shown in Equation (12-2) provided the best fit.
Table 12-1 shows estimates of the parameters of the ERR and EAR models obtained from analyses of LSS incidence data (1958–1998) for all solid cancers excluding thyroid and nonmelanoma skin cancers and of LSS mortality data (1950–2000) for all solid cancers. Further description of these results and how they were obtained can be found in Annex 12B.
TABLE 12-1 ERR and EAR Models for Estimating Incidence of All Solid Cancers Excluding Thyroid and Nonmelanoma Skin Cancers and Mortality from All Solid Cancersa,b
ERR Models
No. of Cases or Deaths
ERR/Sv (95% CI) at Age 30 and Attained Age 60
Per-Decade Increase in Age at Exposure Over the Range 0–30 Yearsc (95% CI), γ
Exponent of Attained Age (95% CI), η
Males (βM)
Females (βF)
Incidenced
12,778
0.33 (0.24, 0.47)
0.57 (0.44, 0.74)
−0.30 (−0.51, −0.10)
−1.4 (−2.2, −0.7)
Mortalitye
10,127
0.23 (0.15, 0.36)
0.47 (0.34, 0.65)
−0.56 (−0.80, −0.32)
−0.67 (−1.6, 0.26)
EAR Models
EAR per 104 PY-Sv (95% CI)
Males (βM)
Females (βF)
Incidenced
12,778
22 (15, 30)
28 (22, 36)
−0.41 (−0.59, −0.22)
2.8 (2.15, 3.41)
Mortalitye
10,127
11 (7.5, 17)
13 (9.8, 18)
−0.37 (−0.59, −0.15)
3.5 (2.71, 4.28)
NOTE: Estimated parameters with 95% CIs. PY = person-years.
aThe ERR or EAR is of the form βs D exp (γe*) (a / 60)η, where D is the dose (Sv), e is age at exposure (years), e* is (e − 30) / 10 for e < 30 and zero for e 30, and a is attained age (years).
bThe committee’s preferred estimates of risks from all solid cancers are obtained as sums of estimates based on models for site-specific cancers (see Table 12-2 and text).
cChange in ERR/Sv or EAR per 104 PY-Sv (per-decade increase in age at exposure) is obtained as 1 − exp (γ ).
dBased on analyses of LSS incidence data 1958–1998 for all solid cancers excluding thyroid and nonmelanoma skin cancer.
eBased on analyses of LSS mortality data 1950–2000 for all solid cancers.
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Models for Site-Specific Solid Cancers Other Than Breast and Thyroid
Although the committee provides risk estimates for both cancer incidence and mortality, models for site-specific cancers were based on cancer incidence data. This was done primarily because site-specific cancer incidence data are based on diagnostic information that is more detailed and accurate than death certificate data and because, for several sites, the number of incident cases is considerably larger than the number of deaths (see annex Table 12B-2). However, models developed from incidence data were checked for consistency with mortality data. Since there is little evidence that radiation-induced cancers are more rapidly fatal than cancer that occurs for other reasons, ERR models based on incidence data can be used directly to estimate risks of cancer mortality, whereas EAR models require adjustment. (See “Method of Calculating Lifetime Risks” for a description of how the models are used to estimate risks of cancer incidence and mortality.)
Models for estimating risks of solid cancers of specific sites other than breast and thyroid were also of the form shown in Equation (12-2). The committee’s approach to quantifying the parameters γ and η was to use the estimates obtained from analyzing incidence data on all solid cancers excluding thyroid and nonmelanoma skin cancers (shown in Table 12-1) unless site-specific analyses indicated significant departure from these estimates. This approach is similar to that used by UNSCEAR (2000b) except that the committee estimated the parameters βM and βF separately for each site of interest.
The committee’s preferred ERR and EAR models for site-specific cancer incidence and mortality are shown in Table 12-2. The estimates of βM and βF are for a person exposed at age 30 or older at an attained age of 60. Models for breast and thyroid cancer were based on published analyses that included data on medically exposed persons as discussed in the next two sections. For other sites, common values of the parameter γ indicating dependence on age at exposure could be used in all cases. With the ERR models, common values of the parameter indicating the dependence of risks on attained age (η) could be used in all cases except the category “all other solid cancers.” With the EAR models, it was necessary to estimate the attained-age parameter, η, separately for cancers of the liver, lung, and bladder, which may reflect variation in the pattern of increase with age for site-specific baseline rates.
The committee emphasizes that there is considerable uncertainty in models for site-specific cancers. Statistical uncertainty in the estimates of the main effect parameter βs is
TABLE 12-2 Committee’s Preferred ERR and EAR Models for Estimating Site-Specific Solid Cancer Incidence and Mortalitya
Cancer Site
No. of Cases
ERR Models
EAR Models
βMb (95% CI)
βFb (95% CI)
γc
ηd
βMe (95% CI)
βFe (95% CI)
γc
ηd
Stomach
3602
0.21 (0.11, 0.40)
0.48 (0.31, 0.73)
−0.30
−1.4
4.9 (2.7, 8.9)
4.9 (3.2, 7.3)
−0.41
2.8
Colon
1165
0.63 (0.37, 1.1)
0.43 (0.19, 0.96)
−0.30
−1.4
3.2 (1.8, 5.6)
1.6 (0.8, 3.2)
−0.41
2.8
Liver
1146
0.32 (0.16, 0.64)
0.32 (0.10, 1.0)
−0.30
−1.4
2.2 (1.9, 5.3)
1.0 (0.4, 2.5)
−0.41
4.1 (1.9, 6.4)
Lung
1344
0.32 (0.15, 0.70)
1.40 (0.94, 2.1)
−0.30
−1.4
2.3 (1.1, 5.0)
3.4 (2.3, 4.9)
−0.41
5.2 (3.8, 6.6)
Breastf
952
—
0.51 (0.28, 0.83)
0
−2.0
—
9.4 (6.7, 13.3)
−0.51
3.5, 1.1g
Prostate
281
0.12 (<0, 0.69)
—
−0.30
−1.4
0.11 (<0, 1.0)
—
−0.41
2.8
Uterus
875
—
0.055 (<0, 0.22)
−0.30
−1.4
—
1.2 (< 0, 2.6)
−0.41
2.8
Ovary
190
—
0.38 (0.10, 1.4)
−0.30
−1.4
—
0.70 (0.2, 2.1)
−0.41
2.8
Bladder
352
0.50 (0.18, 1.4)
1.65 (0.69, 4.0)
−0.30
−1.4
1.2 (0.4, 3.7)
0.75 (0.3, 1.7)
−0.41
6.0 (3.1, 9.0)
Other solid cancers
2969
0.27 (0.15, 0.50)
0.45 (0.27, 0.75)
−0.30
−2.8 (−4.1, −1.5)
6.2 (3.8, 10.0)
4.8 (3.2, 7.3)
−0.41
2.8
Thyroidh
0.53 (0.14, 2.0)
1.05 (0.28, 3.9)
−0.83
0
NOTE: Estimated parameters with 95% CIs. PY = person-years.
aThe ERR or EAR is of the form βs D exp (γ e*) (a / 60)η, where D is the dose (Sv), e is age at exposure (years), e* is (e − 30) / 10 for e < 30 and zero for e 30, and a is attained age (years). Models for breast and thyroid cancer are based on e instead of e*, although γ is still expressed per decade.
bERR/Sv for exposure at age 30+ at attained age 60.
cPer-decade increase in age at exposure over the range 0–30 years (γ).
dExponent of attained age (η).
eEAR per 104 PY-Sv for exposure at age 30+ and attained age 60; these values are for cancer incidence and must be adjusted as described in the text to estimate cancer mortality risks.
fBased on a pooled analysis by Preston and others (2002a). See text for details. Parameter estimates presented by Preston and colleagues were for exposure at age 25 at attained age 50, while estimates in this table are for exposure at age 30 at attained age 60.
gThe first number is for attained ages less than 50; the second number is for attained ages 50 or greater.
hBased on a pooled analyses by Ron and others (1995a) and NIH (2003). Confidence intervals are based on standard errors of non-sex-specific estimates with allowance for heterogeneity among studies.
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often large. Although the common values of the parameters γ and η that have been used to quantify the modifying effects of age at exposure and attained age are compatible with site-specific data, estimates of these parameters based on site-specific data are often quite different from the common values. Annex 12B shows the site-specific estimates of γ and η.
Models for Female Breast Cancer
The committee’s preferred models for estimating breast cancer incidence and mortality are those developed by Preston and colleagues (2002a) from analyses of combined data on breast cancer incidence in several cohorts including the LSS. The LSS data used in these analyses were for the period 1958–1993, whereas the committee’s analyses included data through 1998. Although these models were developed for estimating breast cancer incidence, they may also be used to estimate breast cancer mortality using the same approach as that for other site-specific solid cancers.
Preston and colleagues (2002a) found that common models could be used to describe data from the LSS cohort, the original Massachusetts tuberculosis fluoroscopy cohort and an extension of this cohort (Boice and others 1991b), and the Rochester infant thymus irradiation cohort (Hildreth and others 1989). Models for both the ERR and the EAR were developed for these cohorts. The ERR model was as follows:
where a is attained age. With this model, it was necessary to estimate β separately for the LSS and the remaining U.S. women. Parameter estimates were β = 1.46 for the LSS and 0.51 for the remaining U.S. cohorts. The committee’s preferred ERR model for estimating risks for U.S. women uses β = 0.51. In the formulation above, the committee has parameterized the model so that β indicates the ERR at an attained age of 60 instead of 50 as given in Preston and colleagues. The pooled EAR model from Preston and colleagues (2002b) was as follows:
where e is exposure age and a is attained age (years); η = 3.5 for a < 50 and η = 1 for a 50. For the EAR, a common value of the overall level of risk (9.4) could be used for all four cohorts. Again, the model has been parameterized so that the value of 9.4 is for a woman exposed at age 30 at attained age 60 (instead of a woman exposed at age 25 at attained age 50 as in Preston and others).
Although the committee calculates lifetime risk estimates based on both the ERR and the EAR models described above, its preferred estimates are based on the EAR model. With this model the estimated main effect is more stable because it is based on both LSS and U.S. women. In addition, this model includes both age at exposure and attained age as modifying factors and is thus more comparable to models used for other sites.
Model for Thyroid Cancer
The committee’s preferred model for estimating thyroid cancer incidence is based on a pooled analysis of data from seven thyroid cancer incidence studies conducted by Ron and colleagues (1995a). The NIH (2003) adapted the results of data from five cohorts of persons exposed under age 15 to develop a thyroid cancer incidence model. The five studies were the A-bomb survivors (including only those exposed under age 15; Thompson and others 1994), the Rochester thymus study (Shore and others 1993b), the Israel tinea capitis study (Ron and others 1989), children treated for enlarged tonsils and other conditions (Pottern and others 1990; Schneider and others 1993), and an international childhood cancer study (Tucker and others 1991). Ron and colleagues found that the ERR/Gy for females was about twice that for males although the difference was not statistically significant. Although the NIH (2003) used a non-sex-specific model, for consistency with the treatment of cancers of other sites, the committee has used a sex-specific model. From data presented in NIH (2003, Table IV.D.8), it can be determined that the model takes the form ERR/Gy = 0.79 exp [−0.083 (e − 30)], where e is exposure age in years. The BEIR VII model is as follows:
and
The estimate of the ERR per Gy given by Ron and colleagues was 7.7 (95% CI 2.1, 29) in a model without modification by age at exposure. With the committee’s model, this would be the ERR/Gy, averaged over the two sexes, for exposure at about 2.5 years of age, which was about the average exposure age in the data analyzed by Ron and colleagues.
Ron and colleagues (1995a) did not present results for ERR or EAR models that allowed for modification by both age at exposure and attained age.
Model for Leukemia
The committee’s models for estimating leukemia risks were based on analyses of LSS leukemia mortality data for the period 1950–2000 (Preston and others 2004). The quality of diagnostic information for the non-type-specific leukemia mortality used in these analyses is thought to be high. Data on medically exposed cohorts have indicated that chronic lymphocytic leukemia (CLL) is not likely to be induced by radiation exposure (Boice and others 1987; Curtis and others 1994; Weiss and others 1995), but CLL is extremely rare in Japan. Details of the committee’s leukemia analyses are given in Annex 12B.
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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:
(12-3)
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
Parameter
ERR Model
EAR Model
βM
1.1 per Sv (0.1, 2.6)
1.62 deaths per 104 PY-Sv (0.1, 3.6)
βF
1.2 per Sv (0.1, 2.9)
0.93 deaths per 104 PY-Sv (0.1, 2.0)
γ
−0.40 per decade (−0.78, 0.0)
0.29 per decade (0.0, 0.62)
δ
−0.48 (−1.1, 0.2)
0.0
0.42 (0.0, 0.96)
0.56 (0.31, 0.85)
θ
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.”
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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FIGURE 12-2 Age-time patterns in radiation-associated risks for leukemia mortality. Curves are sex-averaged estimates of the risk at 1 Sv for people exposed at age 10 (solid lines), age 20 (dashed lines), and age 30 or more (dotted lines). Estimates were computed using the parameter estimates shown in Table 12-3.
Projection of Risks over Time
The LSS cohort has now been followed for more than 50 years, so that lifetime follow-up is nearly complete for all but the youngest survivors (under age 20 at exposure). Although the extrapolation involved in estimating lifetime risks based on limited follow-up has been a major source of uncertainty in past risk assessments, it is now much less so. The BEIR VII models allow for dependencies of both the ERR and the EAR on attained age, and it is assumed that the identified patterns persist until the end of life for the youngest survivors. Additional discussion of this issue is found in Chapter 10.
For leukemia, the early years of follow-up also must be addressed. Ascertainment of leukemia cases for the LSS cohort did not begin until 1950, while data on medically exposed cohorts have demonstrated that excess leukemia cases can occur as early as a year or two after exposure (Boice and others 1987; Curtis and others 1992, 1994; Inskip and others 1993; Weiss and others 1994, 1995). In several of these studies, relative risks were highest in the period 1–5 years after exposure. In addition, a recent analysis of data on Mayak workers found that leukemia risks 3–5 years following external radiation exposure were more than an order of magnitude higher than risks for later periods (Shilnikova and others 2003). The UNSCEAR (2000b) committee addressed this problem by assuming that excess risks for the first 5 years after exposure were half those observed 5 years after exposure. The BEIR VII committee has instead assumed that excess absolute risk in the period 2–5 years following exposure is equal to that observed 5 years after exposure. Clearly there is uncertainty in the magnitude of the risk during the initial years following exposure.
Transport of Risks from a Japanese to a U.S. Population
Baseline risks for many site-specific cancers are different for the United States and Japan. For example, baseline risks for cancers of the colon, lung, and female breast are higher in the United States, whereas baseline risks for cancers of the stomach and liver are much higher in Japan. The BEIR V committee based its estimates on relative risk transport, where it is assumed that the excess risk due to radiation is proportional to baseline risks; that is, the ERR is the same for the United States and Japan. However, the BEIR III committee based its estimates on absolute risk transport, where it is assumed that the excess risk does not depend on baseline risks; that is, the EAR is the same for the United States and Japan. The EPA (1994) used the geometric mean of the two estimates, whereas UNSCEAR (2000b) presented estimates based on both approaches without indicating a preference. Estimates based on relative and absolute risk can differ substantially. For example, the UNSCEAR stomach cancer estimates for the U.S. population based on absolute risk transport are nearly an order of magnitude larger than those based on relative risk transport.
For breast and thyroid cancer, the committee’s models are based on combined analyses that include Caucasian subjects. For other solid cancer sites including leukemia, the committee has calculated risks using both relative and absolute risk transport, which provides an indication of the uncertainty from this source. The recommended point estimates are weighted means of estimates obtained under the two models (adjusted by a DDREF of 1.5 as discussed above). For sites other than breast, thyroid, and lung, a weight of 0.7 is used for the estimate obtained using relative risk transport and a weight of 0.3 for the estimate obtained using absolute
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risk transport, with the weighting done on a logarithmic scale. This choice was made because, as discussed in Chapter 10, there is somewhat greater support for relative risk than for absolute risk transport. In addition, the ERR models used to obtain relative risk transport estimates may be less vulnerable to possible bias from underascertainment of cases. For lung cancer, the weighting scheme is reversed, and a weight of 0.7 is used for the absolute risk transport estimate and a weight of 0.3 for the relative risk transport estimate. This departure was made because of evidence that the interaction of radiation and smoking in A-bomb survivors is additive (Pierce and others 2003). Although it is likely that the correct transport model varies by cancer site, for sites other than breast, thyroid, and lung the committee judged that current knowledge was insufficient to allow the approach to vary by cancer site.
Transport has not generally been considered an important source of uncertainty for estimating leukemia risks. The committee has nevertheless developed both ERR and EAR models for leukemia and obtained estimates based on both relative and absolute risk transport. As shown later, the EAR model leads to substantially lower lifetime risks than the ERR model (Table 12-7). Since there is no reason to suspect underascertainment of leukemia deaths, apparently this comes about because baseline risks in the LSS cohort are different than those for a modern U.S. population. Because of the small number of deaths in the early period among those who were unexposed, it might be thought that the uncertainty in the estimated ERR/Sv would be large; however in fact, it is only slightly larger than that for the EAR model (Table 12-3).
Relative Effectiveness of X-Rays and γ-Rays
Risk estimates in this report have been developed primarily from data on A-bomb survivors and are thus directly relevant to exposure from high-energy photons. However, the report is concerned with low-LET radiation generally, which includes γ-rays, X-rays, and fast electrons. There is no principal difference between the action of these different types of radiation, because they all work through fast electrons that either are incident on the body or are released within the body by electrons or photons. The various types of low-LET radiation vary in their ability to penetrate to greater depths in the body. The more penetrating, high-energy radiation tends to produce electrons with linear energy transfer less than 1 keV / μm, while the softer X-rays release slower electrons with linear energy transfer up to several kiloelectronvolts per micrometer.
With regard to setting dose limits in radiation protection, γ-rays, fast electrons, and X-rays are all given the radiation weighting factor 1; that is, an absorbed dose of 1 Gy of these radiations is taken to be equal to the effective dose 1 Sv (ICRP 1991), which expresses the fact that the differences of effectiveness between different photon radiations are not considered of sufficient consequence to require explicit accounting in radiation protection regulations. However, the significant difference between the (dose average) unrestricted LET of 60Co (about 0.4keV / μm) or 137Cs γ-rays (about 0.8keV / μm) and that of 200 kVp X-rays (about 3.5keV / μm) makes it clear that the relative biological effectiveness (RBE) at low doses can differ appreciably for γ-rays and X-rays. For actual risk estimates it is, therefore, necessary to consider these differences in terms of the radiobiological findings, the dosimetric and microdosimetric parameters of radiation quality, and the radioepidemiologic evidence.
As discussed in ICRP (2004) and in Chapters 1 and 3 of this report, there is evidence based on chromosomal aberration data and on biophysical considerations that, at low doses, the effectiveness per unit absorbed dose of standard X-rays may be about twice that of high-energy photons. The effectiveness of lower-energy X-rays may be even higher. How this translates into risks of late effects in man is an open question. Estimates based on studies of persons exposed to X-rays for medical reasons tend to be lower than those based on A-bomb survivors (Little 2001; ICRP 2004), but a number of other differences may confound these comparisons. In addition, doses in many medically exposed populations are higher than those at which the energy of the radiation (based on biophysical considerations) would be expected to be important.
Because of the lack of adequate epidemiologic data on this issue, the committee makes no specific recommendation for applying risk estimates in this report to estimate risk from exposure to X-rays. However, it may be desirable to increase risk estimates in this report by a factor of 2 or 3 for the purpose of estimating risks from low-dose X-ray exposure.
Relative Effectiveness of Internal Exposure
Internal exposure through inhalation or ingestion is also of interest. For example, internal exposure to 131I, strontium, and cesium may occur from atmospheric fallout from nuclear weapons testing. Epidemiologic studies involving these exposures are reviewed in Chapter 9. Studies of thyroid cancer in relation to 131I include those of persons exposed to atmospheric fallout in Utah, to releases from the Hanford plant, and as a result of the Chernobyl accident. There are also studies of persons exposed to cesium and strontium from releases from the Mayak nuclear facility in Russia into the Techa River. To date, these studies are not adequate to quantify carcinogenic risk reliably as a function of dose. Although there are no strong reasons to think that the dose-response from internal low-LET exposure would differ from that for external exposure, there is additional uncertainty in applying the BEIR VII risk models to estimate risks from internal exposure.
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Method of Calculating Lifetime Risks
Several measures of lifetime risk have been used to express radiation risks and are discussed by Vaeth and Pierce (1990), Thomas and colleagues (1992), UNSCEAR (2000b), and Kellerer and colleagues (2001). The BEIR VII committee has chosen to use what Kellerer and coworkers refer to as the lifetime attributable risk (LAR), which was earlier called the risk of untimely death by Vaeth and Pierce (1990). The LAR is an approximation of the risk of exposure-induced death (REID), the measure used by UNSCEAR (2000b), which estimates the probability that an individual will die from (or develop) cancer associated with the exposure. Although the nomenclature is recent, the LAR was used by the BEIR III committee (1980b) and by the EPA (1994).
The LAR and the REID both differ from the excess lifetime risk (ELR) used by the BEIR V committee in that the former include deaths or incident cases of cancer that would have occurred without exposure but occurred at a younger age because of the exposure. As noted by Thomas and colleagues (1992) and earlier by Pierce and Vaeth (1989), the ratio of ELR to REID is approximately 1 − Qc where Qc is the lifetime risk of dying from the cause of interest. For example, the ELR for all cancer mortality would be about 20% lower than the REID. The LAR differs from the REID in that the survival function used in calculating the LAR does not take account of persons dying of radiation-induced disease, thus simplifying the computations. This difference may be important for estimating risks at higher doses (1+ Sv), but not at the low doses of interest for this report. Kellerer and colleagues show that the REID and the LAR are nearly identical at low doses and discuss other aspects of the LAR compared to the REID.
The LAR for a person exposed to dose D at age e is calculated as follows:
(12-4)
where the summation is from a = e + L to l00, where a denotes attained age (years) and L is a risk-free latent period (L = 5 for solid cancers; L = 2 for leukemia). The M(D, e, a) is the EAR, S(a) is the probability of surviving until age a, and S(a)/S(e) is the probability of surviving to age a conditional on survival to age e. All calculations are sex-specific; thus, the dependence of all quantities on sex is suppressed.
The quantities S(a) were obtained from a 1999 unabridged life table for the U.S. population (Anderson and DeTurk 2002). Lifetime risk estimates using relative risk transport were based on ERR models. For these calculations,
for cancer incidence, and
for cancer mortality. The ERR(D, e, a) was obtained from models shown in Tables 12-1, 12-2, and 12-3. The λIc(a) represents sex- and age-specific 1995–1999 U.S. cancer incidence rates from Surveillance Epidemiology, and End Results (SEER) registries, whereas the λMc (a) are sex- and age-specific 1995–1999 U.S. cancer mortality rates (http://seer.cancer.gov/csr/1975_2000), where c designates the cancer site or category. These rates were available for each 5-year age group with linear interpolation used to develop estimates for single years of age. With the exception of the category “all solid cancers,” the same ERR models were used to estimate both cancer incidence and mortality.
Lifetime risk estimates using absolute risk transport were based on EAR models (see “Transport of Risks from a Japanese to a U.S. Population”). For estimating cancer incidence, M(D, e, a) is taken to be the EAR(D, e, a) based on the models shown in Tables 12-1, 12-2, and 12-3. For estimating mortality from all solid cancers, the EAR mortality model shown in Table 12-1 was used directly. For estimating site-specific cancer mortality, it was necessary to adjust the EAR(D, e, a) from Tables 12-2 and 12-3 by multiplying by λMc (a)/λIc (a), the ratio of the sex- and age-specific mortality and incidence rates for the U.S. population. That is, for site-specific mortality,
Leukemia merits special comment. The approach for deriving incidence and mortality estimates based on relative and absolute risk transport is the same for leukemia as for other site-specific cancers, despite the fact that leukemia models were developed from LSS mortality data rather than incidence data as for other sites. This is because LSS leukemia data were obtained at a time when this disease was nearly always rapidly fatal, so that estimates of leukemia mortality should closely approximate those for leukemia incidence. In the last few decades, however, marked progress has been made in treating leukemia, and the disease is not always fatal. Thus, the committee has used the EAR model shown in Table 12-3 to estimate leukemia incidence, but has adjusted the EAR(D, s, e, a) from Table 12-3 in the manner described above to obtain estimates of leukemia mortality. In all cases, the U.S. leukemia baseline rates were for all leukemias excluding CLL.
Models for leukemia differ from those for solid cancers in that risk is expressed as a function of age at exposure (e) and time since exposure (t) instead of age at exposure and attained age (a). Since t = a − e, ERR(D, e, a) or EAR(D, e, a) is obtained by substituting a − e for t in the models presented in Table 12-3. Note further that for the period 2–5 years after exposure, the EAR is assumed to be the same as that at 5 years after exposure. That is, for a = e + 2 to e + 5, M(D, e, a) = M(D, e, e + 5).
The approach described above for obtaining estimates based on absolute transport differs from that used by UNSCEAR (2000b) and NIH (2003), where M(D, e, a) for
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were more than eight times those for the 45–60 exposure age group (p = .02), while for the remaining solid cancers this ratio was less than 2 and did not differ significantly from unity (p > .5).
The increased ERR/Sv and EAR per 104 PY-Sv for the oldest age-at-exposure group was one of the reasons the committee selected the BEIR VII model with no decline with exposure age after age 30 in preference to the RERF model with a decline throughout the entire range of exposure age. The committee notes particularly that stomach and liver cancers, for which this effect was strongest, are far more prevalent in Japan than in the United States. With the incidence data, about 37% of the cancers in the solid cancer category that the committee analyzed were cancers of the stomach and liver; by contrast, SEER data for the United States (see Table 12-3) indicate that only about 3% of incident cancers are of these types. Furthermore, risks for stomach and liver cancers may be affected by infectious agents such as Helicobacter pylori for stomach cancer and the hepatitis virus for liver cancer (Parsonnet and others 1994; Aromaa and others 1996; Goldstone and others 1996). Infection rates might differ by birth cohort (and thus exposure age), which could affect risks due to radiation in ways that are not currently understood. Although the reason for the relatively high ERR/Sv among those exposed at older ages is not fully understood the committee does not think that this effect is likely to generalize to a modern U.S. population.
Based on the analyses of A-bomb survivor data described above, the committee has selected the model shown in Equation (12B-6) as its preferred model for estimating solid cancer risks. However, several alternative choices, including the RERF model shown in Equation (12B-3), fitted the data nearly as well and would also have been reasonable choices. Both ERR and EAR models are evaluated. Table 12B-4 shows the estimated parameters (with 95% confidence intervals) for ERR and EAR models obtained from both incidence and mortality data. With the ERR models, the effect of exposure age is stronger for mortality than for incidence data, while the effect of attained age is weaker. The two EAR models show similar exposure age effects, but the rate of increase with attained age is greater for the mortality data than for the incidence data.
The committee also evaluated mortality data on all solid cancers to compare the use of 5- and 10-year minimal latent periods. This was done by fitting the BEIR VII ERR model, and estimating the ERR/Sv separately for the period 5–9 years following exposure and for the period 10 or more years following exposure. Although the estimate for the 5–9-year period was not quite statistically significant with a two-sided test (p = .10), there was no evidence that it differed from the estimate for the later follow-up period (p = .44). The committee accordingly has used a minimal latent period of 5 years in its calculations of lifetime risks.
TABLE 12B-4 ERR and EAR Models for Estimating Incidence of All Solid Cancers Excluding Thyroid and Nonmelanoma Skin Cancers and Mortality from All Solid Cancersa,b
ERR Models
No. of Cases or Deaths
ERR/Sv (95% CI) at Age 30 and Attained Age 60
Per-Decade Increase in Age at Exposure Over the Range 0–30 Yearsc (95% CI), γ
Exponent of Attained Age (95% CI), η
Males (βM)
Females (βF)
Incidenced
12,778
0.33 (0.24, 0.47)
0.57 (0.44, 0.74)
−0.30 (−0.51, −0.10)
−1.4 (−2.2, −0.7)
Mortalitye
10,127
0.23 (0.15, 0.36)
0.47 (0.34, 0.65)
−0.56 (−0.80, −0.32)
−0.67 (−1.6, 0.26)
EAR models
EAR per 104 PY-Sv (95% CI)
Males (βM)
Females (βF)
Incidenced
12,778
22 (15, 30)
28 (22, 36)
−0.41 (−0.59, −0.22)
2.8 (2.15, 3.41)
Mortalitye
10,127
11 (7.5, 17)
13 (9.8, 18)
−0.37 (−0.59, −0.15)
3.5 (2.71, 4.28)
NOTE: Estimated parameters with 95% CIs. PY = person-years.
aThe ERR or EAR is of the form βs D exp (γe*) (a / 60)η, where D is the dose (Sv), e is age at exposure (years), e* is (e − 30) / 10 for e < 30 and zero for e 30, and a is attained age (years).
bThe committee’s preferred estimates of risks from all solid cancers are obtained as sums of estimates based on models for site-specific cancers (see Table 12-2 and text).
cChange in ERR/Sv or EAR per 104 PY-Sv (per-decade increase in age at exposure) is obtained as 1 − exp (γ).
dBased on analyses of LSS incidence data 1958–1998 for all solid cancers excluding thyroid and nonmelanoma skin cancer.
eBased on analyses of LSS mortality data 1950–2000 for all solid cancers.
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Analyses of Incidence and Mortality Data on Site-Specific Solid Cancers
Although the committee provides risk estimates for both cancer incidence and mortality, models for site-specific cancers were based mainly on cancer incidence data. This was done primarily because site-specific cancer incidence data are based on diagnostic information that is more detailed and accurate than death certificate data and because, for several sites, the number of incident cases is considerably larger than the number of deaths. For cancers of the colon, breast, prostate, and bladder, the number of cases in the LSS cohort is more than double the number of deaths (Table 12B-1B). In addition, mortality data may be more subject than incidence data to changes over time brought about because of improved survival. Models developed from incidence data were however evaluated for consistency with mortality data. Since there is little evidence that radiation-induced cancers are more rapidly fatal than cancer that occurs for other reasons, ERR models based on incidence data can be used directly to estimate risks of cancer mortality. EAR models require adjustment as discussed in the chapter.
Models for site-specific cancers were based on the BEIR VII model indicated by Equation (12B-6). The committee’s approach to quantifying the parameters γ and η was to use the estimates obtained from analyzing incidence data on all solid cancers excluding thyroid and nonmelanoma skin cancers unless site-specific analyses indicated significant departure from these estimates. Table 12B-5A shows the results of fitting ERR site-specific models to the incidence data. Results are shown for a model in which all four of the parameters βM, βF, γ, and η were estimated and are also shown for a model in which the parameters quantifying the modifying effects of age of exposure and attained age γ and η were set equal to the values obtained from analysis of the category all solid cancers excluding thyroid and nonmelanoma skin cancers; these values are referred to subsequently as the “common values.” The final column gives the deviance difference between the two models and the resulting p-value based on a two-degree-of-freedom test comparing the fits of the two models. This test does not take account of uncertainty in the estimates of the common values of γ and η. In addition, the committee fitted models in which just one of the parameters γ and η was fixed, with the other estimated allowing a one-degree-of-freedom test for each of the parameters.
The only sites with even modest evidence (p < .10) of departure from the fixed values of γ and η were cancer of the uterus and the category “all other solid cancers.” For cancer of the uterus, the estimated ERR/Sv was very small and nonsignificant so that it was not possible to obtain stable estimates of the modifying parameters; thus the common values were used. For other solid cancers, a test for the parameter η alone resulted in a p-value of .025; thus, results are also
TABLE 12B-5A Results of Fitting Stratified ERR Models to Site-Specific Cancer Incidence Data Using the Model ERR(D, s, e, a) = βs D exp [γ e* + η log (a / 60)]a
Cancer Site
No. of Cases
All Parameters Estimated
Fixed Parameters: γ = −0.30; η = −1.4
Deviance Differenceb (p-value)
βM
βF
γ
η
βM
βF
Solid cancerc
12,778
0.33
0.57
−0.30
−1.4
0.33
0.57
Stomach
3602
0.25
0.54
−0.13
−1.9
0.21
0.48
0.5 (> 0.5)
Colon
1165
0.72
0.54
−0.16
−3.1
0.63
0.43
1.0 (> 0.5)
Liver
1146
0.40
0.36
−0.15
−1.5
0.32
0.32
0.2 (> 0.5)
Lung
1344
0.39
1.68
0.05
−1.1
0.32
1.40
2.9 (0.23)
Breast
847
—
1.19
−0.04
−2.0
—
0.91
2.4 (0.34)
Prostated
281
—
—
—
—
0.12
—
—
Uterus
875
—
0.027
−2
5.6
—
0.055
5.8 (0.055)
Ovary
190
—
0.47
−0.13
−1.6
—
0.38
0.05 (> 0.5)
Bladder
352
0.51
1.62
−0.04
0.28
0.50
1.65
2.7 (0.26)
Other solid cancers
2969
0.27
0.45
−0.29
−2.8
0.33
0.51
5.0 (0.081)
Other solid cancers (alternative)
2969
0.27
0.45
Fixed at −0.30
−2.8
0.003e (>0.5)
aD is dose (Sv); e* = (e − 30) / 10 for e < 30, where e is age at exposure (years); e* = 0 for e 30; and a is attained age (years). βM and βF are the ERR/Sv for males and females exposed at age 30 at attained age 60, γ is expressed per decade increase in age at exposure over the range 0–30 years, and a is the exponent of attained age.
bDifference in deviance for model shown in columns 7 and 8 and model shown in columns 3–6.
cSolid cancer excluding thyroid and nonmelanoma skin cancers.
dModel with all parameters estimated would not converge.
eDifference in deviance for this model and that shown in columns 3–6 in the row immediately above.
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shown for an alternative model with η estimated separately for this category.
Table 12B-5B shows results based on mortality data on site-specific cancers. As in Table 12B-5A, columns 3–6 show results with all four of the parameters βM, βF, γ, and η estimated using data on that site alone. Columns 7 and 8 show the results of testing the compatibility of these models with models developed from the incidence data with γ and η fixed as indicated in columns 7 and 8 of Table 12B-5A. Column 7 is based on analyses in which γ was set equal to −0.30 per decade and η was set equal to −1.4, and the parameters βM and βF were estimated, and thus tests whether the fixed values of data γ and η are compatible with the mortality data. Column 8 is based on analyses in which all four of the parameters βM, βF, γ and η were set equal to the values estimated from the incidence data (Table 12B-5A). The alternative model for “all other solid cancers,” based on the incidence data, was also evaluated. Because of difficulties in fitting four-parameter models for cancers of the prostate and uterus, these sites are not shown in Table 12B-4B. Only for colon cancer and for all other solid cancers was there a suggestion (p < .10) that the models based on incidence data did not fit the mortality data. Because there was no evidence against using the common values of η and γ for colon cancer based on the incidence data, the committee chose to use the common values for this site. For all other solid cancers, the alternative model developed from the incidence data was also more compatible with the mortality data, and this was chosen as the preferred model.
Table 12B-5C shows results of fitting EAR models to the cancer incidence data and is analogous to Table 12B-5A for the ERR models. There is clear evidence that common values of the parameters γ and η are not appropriate for cancers of lung, breast, and bladder. For all three of these sites, and also for liver cancer (see below), alternative models in which η was estimated and γ was set at the common value (−0.41) provided acceptable fits.
For breast cancer, the committee fitted additional EAR models with separate parameters for attained ages under 50 and over 50, similar to the model used by Preston and colleagues (2002a) in a pooled analysis of breast cancer incidence data from several cohorts including the LSS data. This model (labeled alternative 2) provided a significantly better fit (p < .001) than did the model with a single parameter for attained age. As discussed in this chapter, the committee’s preferred models for breast cancer were based on pooled analyses by Preston and colleagues (2002a). However, it was of interest to compare these results with those obtained from models based on the same approach as most other cancer sites.
Table 12B-5D shows results of fitting EAR models to the mortality data. All but the last column are analogous to those in Table 12B-4C for the ERR models. The last column of Table 12B-5D shows the deviance differences for models based on the mortality data and the alternative models shown in Table 12B-5C. Only for cancers of the liver, lung, breast, and bladder was there evidence (p < .10) of departure from the main incidence models. However, for these sites, there
TABLE 12B-5B Results of Fitting Stratified ERR Models to Site-Specific Cancer Mortality Data Using the Model ERR(D, s, e, a) = βs D exp [γ e* + η log (a / 60)]a
Cancer Site
No. of Deaths
All Parameters Estimated
Fixed Parameters γ = −0.30; η = −1.4
βM
βF
γ
η
βM
βF
Deviance Difference for Testing γ and ηb (p-value)
Deviance Difference for Testing βM, βF, γ, and η (p-value)c
Stomach
2,867
0.11
0.41
−0.65
0.29
0.14
0.46
2.6 (0.28)
3.3 (>0.5)
Colon
478
0.65
0.79
−0.19
−5.3
0.68
0.68
4.8 (0.09)
5.8 (0.22)
Liver
1,236
0.23
0.25
−0.51
0.82
0.28
0.29
1.8 (0.40)
2.0 (>0.50)
Lung
1,264
0.36
0.80
−0.36
0.34
0.45
0.93
3.0 (0.23)
6.6 (0.16)
Breast
272
—
0.56
−0.72
−1.5
—
0.94
1.9 (0.38)
2.0 (>0.5)
Ovary
136
—
0.34
−0.10
−5.1
—
0.65
1.3 (> 0.5)
2.1 (>0.5)
Bladder
150
1.27
1.65
0.10
−0.65
0.90
1.18
3.3 (0.20)
3.8 (0.44)
All other solid cancers
2,211
0.24
0.30
−0.68
−1.7
0.35
0.53
5.1 (0.079)
5.1 (0.28)
All other solid cancer (alternative)
Fixed at −0.30
Fixed at −2.8
0.32
0.44
3.3 (0.20)
3.5 (0.48)
aD is dose (Sv); e* = (e − 30) / 10 for e < 30, where e is age at exposure (years); e* = 0 for e 30; and a is attained age (years). βM and βF are the ERR/Sv for males and females exposed at age 30 at attained age 60, γ is expressed per decade increase in age at exposure over the range 0–30 years, and η is the exponent of attained age.
bDifference in deviance for model shown in columns 7 and 8 (with γ = −0.30 and η = −1.4) and model shown in columns 3–6 (2 degrees of freedom).
cDifference in deviance for model shown in columns 7 and 8 of Table 12B-5A and model shown in columns 3–6 of this table (4 degrees of freedom for cancers occurring in both sexes; 3 degrees of freedom for cancers of the breast, prostate, uterus, and ovary).
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TABLE 12B-5C Results of Fitting Parametric EAR Models to Site-Specific Cancer Incidence Data Using the Model EAR(D, s, e, a) = βs D exp [γ e* + η log (a / 60)]a
Cancer Site
No. of Cases
All Parameters Estimated
Fixed Parameters: γ = −4.1; η = 2.8
Deviance Differenceb (p-value)
βM
βF
γ
η
βM
βF
Solid cancerc
12,778
22
28
−0.41
2.8
22
28
Stomach
3,602
7.0
7.1
0.002
1.8
4.9
4.9
3.4 (0.18)
Colon
1,165
2.2
0.84
−1.0
5.7
3.2
1.6
4.0 (0.14)
Liver
1,146
1.8
0.81
−0.64
4.8
1.9
0.83
1.9 (0.39)
Liverd (alternative)
1,146
2.2
1.0
Fixed at −0.41
4.1
0.3e (> 0.5)
Lung
1,344
3.1
4.6
−0.3
4.4
1.5
3.3
15.4 (<0.001)
Lung (alternative)
1,344
2.3
3.4
Fixed at −0.41
5.2
2.0e (0.16)
Breast
847
—
5.6
−0.51
1.5
—
6.3
16.5 (<0.001)
Breast (alternative 1)
847
—
6.1
Fixed at −0.41
1.3
0.42e (> 0.5)
Breast (alternative 2)
847
—
5.9
Fixed at −0.41
3.4, −2.4f
−13.9g (<0.001)
Prostateh
281
—
—
—
—
0.11
—
—
Uterus
875
—
0.28
−1.6
6.3
—
1.2
2.7 (0.27)
Ovary
190
—
0.50
−0.66
2.7
—
0.7
1.2 (> 0.5)
Bladder
352
1.3
0.88
−0.23
5.6
1.1
0.62
6.4 (0.04)
Bladder (alternative)
352
1.2
0.75
Fixed at −0.41
6.0
0.1e (>0.5)
Other solid cancers
2,969
5.1
4.2
−0.39
1.9
6.2
4.8
3.1 (0.22)
aD is dose (Sv); e* = (e − 30) / 10 for e < 30, where e is age at exposure in years; e* = 0 for e 30; and a is attained age in years. βM and βF are the number of excess cases per 104 PY-Sv for males and females exposed at age 30 at attained age 60, γ is expressed per decade increase in age at exposure over the range 0–30 years, and a is the exponent of attained age.
bDifference in deviance for model shown in columns 7 and 8 and model shown in columns 3–6.
cSolid cancer excluding thyroid and nonmelanoma skin cancers.
dThis alternative was developed to obtain a model that was consistent with mortality data.
eDifference in deviance for this model and that shown in columns 3–6 in the row immediately above.
fThe first coefficient is for attained age under 50; the second coefficient is for attained age over 50.
gDifference in deviance for alternative 1 breast model and this model.
hModel with all parameters estimated would not converge.
was no evidence of departure from the alternate incidence models. In fact, the alternative liver cancer model was developed because of the large attained age effect identified in the mortality data. In general, the numbers of excess deaths per 104 PY-Sv would be expected to be less than the numbers of excess cases; thus, it was not sensible to evaluate the compatibility of the estimated βM and βF as was done for the ERR models. However, for sites common to both sexes, the committee tested whether or not the ratio βF / βM estimated from the mortality data was compatible with that estimated from the incidence data (with the latter treated as a fixed value). The p-values for the sites tested, based on a single-degree-of-freedom test, were as follows: stomach (p = .19), colon (p = .35), liver (p > .5), lung (p = .28), and all other solid cancers (p > .5).
The analyses of site-specific cancer presented in the last few paragraphs address the use of common parameters to quantify the modifying effects of age at exposure and attained age, but do not address the possibility of common parameters for the overall level of the ERR or EAR (βM and βF). Because at least some of the variation among cancer sites in these estimated parameters is due to sampling variation, one might consider using common parameters for sites where there is no evidence of statistical differences. The committee chose not to use such an approach because it seems likely that there are true differences among the sites and because it was considered desirable to use site-specific data to reflect the uncertainty in site-specific estimates. A promising approach for the future is to use methods that draw both on data for individual sites and on data for the combined category of all solid cancers. With this approach, the variance of the site-specific estimate and the degree of deviation from the all-solid-cancer estimate are considered in developing site-specific estimates that draw both on data for the specific individual site and on data for all solid cancers. The National Research Council (2000) gives a simple il-
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TABLE 12B-5D Results of Fitting Parametric EAR Models to Site-Specific Cancer Mortality Data Using the Model EAR(D, s, e, a) = βs D exp [γ e* + η log (a / 60)]a
Cancer Site
No. of Deaths
All Parameters Estimated
Fixed Parameters: γ = −4.1; η = 2.8
βM
βF
γ
η
βM
βF
Deviance Differenceb (p-value)
Stomach
2867
2.6
4.3
0.008
2.7
1.4
2.8
2.8 (0.25)
Colon
478
0.82
0.66
−0.66
3.6
0.96
0.83
0.6 (> 0.5)
Liver
1236
0.61
0.30
−1.2
7.9
1.1
0.56
6.9 (0.033)
Liver (alternative)
Fixed at −0.41
4.1
1.7
0.72
3.0 (0.23)
Lung
1264
2.1
1.8
−0.36
6.1
1.2
1.4
19.3 (<0.001)
Lung (alternative)
Fixed at −0.41
Fixed at 5.2
2.1
1.9
1.8 (0.41)
Breast
272
—
0.90
−0.90
2.8
—
1.5
5.1 (0.077)
Breast (alternative 2)
—
2.0
−0.60
6.5, −2.9c
—
2.0
3.2d (0.36)
Ovary
136
—
0.78
−0.19
2.0
0.66
0.2 (> 0.5)
Bladder
150
0.76
0.21
0.76
6.7
0.20
< 0
6.6 (0.037)
Bladder (alternative)
0.53
0.13
Fixed at −0.41
Fixed at 6.0
2.7 (0.26)
All other solid cancers
2211
2.2
2.0
−0.61
2.9
2.9
2.6
0.8 (>0.5)
aD is dose (Sv); e* = (e − 30) / 10 for e < 30, where e is age at exposure (years); e* = 0 for e 30; and a is attained (years). βM and βF are the number of excess cases per 104 PY-Sv for males and females exposed at age 30 at attained age 60, γ is expressed per decade increase in age at exposure over the range 0–30 years, and η is the exponent of attained age.
bDifference in deviance for models shown in columns 7 and 8 (with γ = −0.41 and η = 2.8) and model shown in columns 3–6 (2 degrees of freedom).
cThe first parameter is for attained age under 50; the second coefficient is for attained age over 50.
dDifference in deviance for alternative 2 breast model with γ = −0.41 and the two attained age parameters set at the values shown in Table 12B-5C and the model shown in columns 3–6 of this table (3 degrees of freedom).
lustration of this approach, using methods described in DerSimonian and Laird (1986) for estimating site-specific excess relative risks for the purpose of developing radioepidemiologic tables.
The committee’s preferred models for estimating site-specific cancer incidence and mortality are summarized in Table 12-2. With the exception of the category of all other solid cancers, the ERR models are based on common values of the parameters γ and η that quantify the modifying effects of age at exposure and attained age. For the EAR models, the preferred models are based on site-specific estimates of η for cancers of the liver, lung, and bladder; for the remaining sites (other than breast), common values of γ and η were used. For breast and thyroid cancers, models developed by Preston and colleagues (2002a) and by Ron and coworkers (1995a) are used as discussed in this chapter. The EAR coefficients βM and βF shown in Table 12-2 can be used directly only for cancer incidence and must be adjusted as described in this chapter for cancer mortality.
As stated earlier, the committee’s models for mortality from all solid cancers were based on mortality data. An alternative might have been to use incidence data for this purpose as was done for site-specific cancers. However, the two main reasons for using incidence data for estimating mortality from site-specific data were the better diagnostic quality and the larger number of cases for several cancer sites. These considerations do not apply when evaluating risks for the broad category of all solid cancers. In addition, the mix of cancers is different for incidence and mortality data so that one might expect greater differences than for site-specific data as evidenced from the parameter estimates shown in Table 12B-4. Nevertheless, the committee conducted analyses of the solid cancer mortality data with parameters set equal to the estimates obtained from the incidence data (as in columns 7 and 8 of Tables 12B-5B and 12B-5D). With the solid cancer ERR model, a joint test of γ = −0.30 per decade and η = −1.4 (the values from the incidence data) resulted in a p-value of .06. However, there was no evidence of further differences when main effects parameters βM and βF were set equal to those for the incidence data (βM = 0.33; βF = 0.57).
With EAR models, the estimated main effects (βM and βF) based on the incidence data were about twice those based on mortality data, reflecting the fact that not all cancers are fatal. The estimates of γ, the parameter quantifying the effects of age at exposure, were similar, whereas the increase with attained age (quantified by η) was stronger for the mortality data than for the incidence data. When mortality data
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were analyzed with the parameters γ and η set equal to the values estimated from incidence data, the joint test resulted in a p-value of .041; the evidence for differences came about mainly from differences in the attained age parameter η (p = .047) with little evidence of differences in the exposure age parameter γ (p > .5).
Analyses of Data on Leukemia
The committee’s model for estimating leukemia risks is based on analyses of LSS leukemia mortality data for the period 1950–2000. Recent LSS leukemia incidence data based on DS02 doses are not yet available. The quality of diagnostic information for non-type-specific leukemia mortality is thought to be much better than for most site-specific solid cancers. Although Preston and colleagues (1994) used incidence data to develop separate models for all types of leukemia—acute lymphocytic leukemia, acute myelogenous leukemia, chronic myelogenous leukemia, and other leukemias—in Hiroshima, the models in most past risk assessments (NRC 1990; ICRP 1991; UNSCEAR 2000b) have been based on leukemias of all types, and the BEIR VII committee has followed the same practice. Data on medically exposed cohorts indicate that CLL is not likely to be induced by radiation exposure (Boice and others 1987; Curtis and others 1994; Weiss and others 1995) but CLL is rare in Japan.
The committee began by considering the model used in a recent report on cancer mortality (Preston and others 2004). This model allows the EAR to vary as a linear-quadratic function of dose and allows both the overall level of risk and the dependence on time since exposure to vary by age at exposure:
(12B-9)
where D is dose in sieverts; s is sex; e is an index for three age-at-exposure categories: 0–19, 20–39, and 40+ years with γ20–39 fixed at 0; and t is time since exposure in years. The parameter θ indicates the degree of curvature, which does not depend on sex or age at exposure; βM and βF are the EAR at exposure ages 20–39 and 25 years following exposure (expressed as excess deaths per 104 PY-Sv for males and females, respectively); and δe indicates the dependence on time since exposure for each of the three age groups. Parameter estimates for this model are given by Preston and colleagues (2002b).
The committee also considered the UNSCEAR (2000) model, which was developed by Preston and colleagues (2004) and based on A-bomb survivor leukemia incidence data for the period 1950–1987. This model, which is described in Annex 12A, and is similar to the RERF model above except that t − 25 replaces log (t / 25) and the parameters δe are allowed to depend on sex.
Although the committee could have used the RERF or the UNSCEAR model, it was judged desirable to develop alternative models with the EAR and ERR expressed as continuous functions of age at exposure and without dependence of the modifying effect of time since exposure on sex (as in the UNSCEAR model). The committee thus analyzed the same leukemia mortality data (1950–2000) used by Preston and colleagues (2004), using the same model for baseline leukemia rates, and evaluated models of the following form:
(12B-10)
where e is age at exposure in years and t is time since exposure in years. The functions of age at exposure evaluated were f(e) = e; f(e) = e* = (e − 30) / 10 for e < 30, and 0 for e 0; and the RERF model in which f(e) was an indicator for one of the three categories: e < 20, 20 e < 40, and e 40. The functions of time since exposure evaluated were g(t) = log (t) and g(t) = t. The committee also fitted ERR models for leukemia of the form shown in Equation (12B-10).
Table 12B-6 shows the drop in deviance (compared to a model with no modification by e or t) for both the EAR and the ERR models. For comparisons among different models of the same type (EAR or ERR), the greater the drop in deviance, the better is the fit. Because it is not meaningful to compare the drop in deviance for an EAR model to that for an ERR model, the total deviances are also shown. In general, models in which age at exposure was treated as a continuous variable fitted the data nearly as well even though they have fewer parameters. Comparing the use of e and e* in models that are otherwise the same resulted in very similar fits, with slightly better fits with e*. The use of log (t) resulted in better fits that the use of t.
For the EAR models using e* and log (t) (models 5–7), the interaction term [e* × log (t)] was clearly needed (p < .001), but the main effect for log (t) was not (p > .5). With the main effect for log (t) in the model (model 5), the EAR decreases with time since exposure for those exposed under about age 25, but increases slightly with time since exposure at older exposure ages. Without the main effect (model 7), the EAR remains constant with time since exposure for those exposed over age 30 and decreases with time since exposure for those exposed under age 30, with a stronger decrease at the youngest ages. The latter model is the committee’s preferred EAR model for estimating leukemia risks. With this model, there was no need for an interaction of sex and time since exposure (p = .23), which was included in the UNSCEAR (2000b) leukemia model.
The committee’s preferred ERR leukemia model is model 5. With this model, the ERR decreases with time since exposure regardless of age at exposure, although the decrease is not as strong at older ages. Again, there was no strong evidence of a need for an interaction of sex and time since expo-
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TABLE 12B-6 Comparison of Fits of Several Models (as Measured by the Deviance) Expressing the Dependence of Risk of Leukemia Mortality on Age at Exposure (e) and Time Since Exposure (t)a
Model Number
Age at Exposure (e), f(e)
Time Since Exposure (t) or Attained Age (a), g(t) or g(a)
Difference in Deviance for This Model and Model with No Modification by e or t (degrees of freedom)
Deviance
EAR Model
ERR Model
EAR Model
ERR Model
1
Categoricalb
log (t): full model
21.3 (5)
21.4 (5)
2254.9
2258.7
2
e − 30
log (t): full model
20.1 (3)
22.5 (3)
2256.1
2257.6
3
e − 30
log (t): main effect only ( = 0)
9.4 (2)
20.2 (2)
2266.8
2259.8
4
e − 30
log (t): interaction only (δ = 0)
19.5 (2)
13.3 (2)
2256.7
2266.8
5
e*c
log (t): full model
21.1 (3)
24.9 (3)
2255.1
2255.1
6
e*
log (t): main effect only ( = 0)
9.4 (2)
21.9 (2)
2266.9
2258.2
7
e*
log (t): interaction only (δ = 0)
20.4 (2)
22.9 (2)
2255.8
2257.2
8
Categorical
t
17.7 (5)
19.9 (5)
2258.5
2260.2
9
e − 30
t: full model
15.9 (3)
21.0 (3)
2260.3
2259.1
10
e*
t: full model
18.2 (3)
23.9 (3)
2258.1
2256.1
aBased on analyses of leukemia mortality (1950–2000) using models in which the EAR or ERR is given by βs(d + θd2) exp [γ f(e) + δ g(t) + iconid=pphi f(e) g(t)].
bSeparate estimates for e < 20, 20 e < 40, e 40.
ce* is min[(e − 30) / 10, 0], where e is age at exposure in years.
sure (p = .15). The total deviances for the preferred EAR and ERR leukemia models were nearly identical.
Thus, the committee’s preferred models for the EAR and the ERR are as follows, with δ = 0 for the EAR model:
(12B-11)
The parameter estimates for the committee’s preferred leukemia models are listed in Table 12-3 in the main chapter. Figure 12-2 shows both the ERR and the EAR as a function of time since exposure for exposure ages of 10, 20, and 30+ years. The ERR model is similar to that used for all leukemia by NIH (2003), although its leukemia model was based on e instead of e*, and on t instead of log (t), and did not allow for the dependence of the ERR on sex. Although there was no indication that the ERR depended on sex, this was included for compatibility with models for site-specific solid cancers.
ANNEX 12C: DETAILS OF LAR UNCERTAINTY ANALYSIS
Uncertainty Due to Sampling Variability
The approximate variance of the estimated LAR due to the uncertainty in LSS estimated linear models can be derived with the “delta method” (Feinberg 1988). As an example, the estimated LAR based on relative risk transport for solid cancer (for males or females) is calculated as
(12C-1)
where e* = e − 30 if e (exposure age) is less than 30 years and 0 otherwise; B(a) is the age-specific baseline rate at age a for the cancer of interest; S(a) is the probability of survival (in the 1999 U.S. population) to age a; and the Greek letters with hats represent the estimated coefficients in the excess relative risk model. The logarithm of Equation (12C-1) gives
where .
The result of a first-order Taylor’s approximation about is
so that the estimate of log (LAR) is a constant plus , where
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and . Then var[log(LAR)] may be estimated by
(12-C2)
where V is the estimated variance-covariance matrix of , which is available as a component of the output from the computer program used to estimate the risk models. The standard error of the log of estimated LAR is the square root of the estimate of this variance. A 95% confidence interval for log (LAR) is obtained as the estimate of log (LAR) plus and minus 1.96 times the standard error, and the confidence interval for LAR is obtained by taking the antilogarithm of these end points.
The LAR based on absolute risk transport is
The issues and computations involve only slight modifications of what has been described above. For scenarios that involve a weighted average of different ages at exposure and for relative and absolute risk models for leukemia, which involve quadratic-in-dose terms and different modifiers including interactions, the computations differ but the ideas behind the delta method calculations are the same as above.
The confidence intervals in Tables 12-5A and 12-5B for risks of cancer incidence and mortality at specific sites were based on the same procedure as above, but without accounting for the uncertainty in γ and η, since, with a few exceptions, these quantities were fixed at their values estimated from all solid cancers combined (although the values of γ and η used in site-specific models were compatible with data for each site, the fixed values cannot be considered unbiased estimates of the correct values). For most sites, uncertainty in the estimated coefficient of dose (β) is quite large and is expected to dominate the uncertainty in the estimated LAR.
Combining Several Sources of Uncertainty
A single estimate of LAR is obtained from estimates based on ERR and EAR transport models as a combination on the log scale: log (LAR) = [p (log (LARERR) + (1 − p) log (LAREAR)], where LARERR and LAREAR are the estimates based on ERR and EAR transport, respectively, and p is a number between 0 and 1, reflecting the relative strength of belief in the two transport models. For most cancers, a value of .7 was taken for p. Exceptions were lung cancer, where p = .3, and thyroid cancer, where only an ERR model developed from data on Caucasian women was available. A further adjustment to the single estimate of LAR, due to the presumed curvature in the dose-response, is obtained by dividing this combined estimate by the presumed DDREF. A value of 1.5 was used for DDREF, which is an estimate of the median of the Bayesian posterior probability distribution for DDREF, as discussed in the chapter.
The uncertainty analysis here arrives at an approximate variance for log (LAR), emanating from the individual variances in LARERR and LAREAR (sampling variability from the LSS risk model estimation, as discussed above), p (uncertainty in the knowledge of whether absolute risk or excess risk is transportable from Japanese A-bomb survivors to the U.S. population), and DDREF (uncertainty in estimating dose-response curvature from animal studies and uncertainty with which the animal curvature applies to humans).
To accomplish this, the model above is written more formally as depending on four sets of unknown quantities: θR, the parameters in the relevant ERR model; θA, the parameters in the EAR model; IR, an indicator variable that takes on the value 1 if the ERR model is the correct one for transport and 0 if the EAR model is the correct one; and θDDREF, the unknown DDREF. The LAR associated with an acute radiation dose D at age e may be written as
where LARR(e, D; θR) and LARA(e, D; θA) are the LARs based on EAR and ERR transport, prior to DDREF adjustment, and θDDREF is the correct DDREF value. Notice that if the ERR model is the correct one for transport, then IR is 0 and the LAR expression above reduces to LARA(e, D; θA / θDDREF. Similarly, if the relative risk model is the correct one for transport, then the LAR expression reduces to the excess relative risk LAR with DDREF adjustment.
The estimated LAR can be expressed by the same formula, but with the known parameters replaced by their estimators: , where and are parameter estimates for the ERR and EAR models; is the (subjective) probability that the relative risk model is the correct one for transport; and is the (subjective) estimate of DDREF. Every quantity with a “hat” on it is an uncertain estimator and has a variance associated with it. The variance in the estimated LAR, consequently, is that which is propagated by the variances of these estimators.
Statistically, it is best to consider this propagation on the log scale:
With the simplifying approximation that the “hats” can be dropped from and in the middle term and the assumption that the uncertainties due to risk model estimation, subjective assessment of DDREF, and subjective as-
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Health Risks from Exposure to Low Levels of Ionizing Radiation: Beir VII Phase 2
sessment of transport model are independent of one another, the variance of the log of the estimated LAR is the sum of three pieces:
which are due, respectively, to the variability in the parameter estimators in the EAR model, the uncertainty in the transport model, and the uncertainty in the DDREF. It is a fairly simple matter to estimate the variance of the log (LAR) from these quantities. The variance of log (LAR), with a normal approximation to the sampling distribution of log (LAR), leads directly to the coefficient of variation in Table 12-10 and the subjective confidence intervals in Tables 12-6 and 12-7.
The simplifying approximation mentioned above amounts to assuming that log and log have equal variances and a correlation of 1 or, in other words, that the variance of an average of these two quantities is the same as the variance of either one individually. The effect of inaccuracies in this assumption is expected to be small relative to the overall variability. Furthermore, because the first term in the variance expression represents the variance of the estimated LAR for either transport model, a weighted average of and is used to estimate it (with the weight corresponding to the strength of belief in the relative risk transport model).
The approach for estimating the variances of the sampling distributions of the estimated LARs is discussed in the first section of this annex. The variance of is taken to be Bernoulli variance. If, for example, the probability that the relative risk transport is correct is taken to be .7, then the variance of is .7 × 0.3. The Bernoulli variance tends to be larger than a variance from a uniform distribution (for a model in which the correct transport is some completely unknown combination of relative and absolute risk) or from a beta distribution (for a model in which the correct transport is some unknown combination, but with more specific information about the possible combination). In the absence of any real knowledge about which of these is correct, the committee has elected to use the more conservative approach, which leads to somewhat wider confidence intervals.
As discussed in Annex 11B, the DDREF analysis is necessarily rough and the variance of the uncertainty distribution described there is, if anything, misleadingly small. For the uncertainty analysis considered here, therefore, the variance representing the uncertainty in log (DDREF) was inflated by 50%, using 0.09 as the variance of , rather than the derived posterior variance 0.06.
ANNEX 12D: ADDITIONAL EXAMPLES OF LIFETIME RISK ESTIMATES BASED ON BEIR VII PREFERRED MODELS
Tables 12D-1 and 12D-2 show lifetime risk estimates for cancer incidence and mortality resulting from a single dose of 0.1 Gy at several specific ages. Estimates are shown for all cancer, leukemia, all solid cancer, and cancer of several specific sites. Table 12D-3 shows analogous lifetime risk estimates for exposure to 1 mGy per year throughout life and to 10 mGy per year from ages 18 to 65. The examples below illustrate how these tables may be used to obtain estimates for other exposure scenarios. For clarity of presentation, the committee has generally shown more decimal places than are justified.
Example 1: A 10-year-old male receives a dose of 0.01 Gy (10 mGy) to the colon from a computed tomography (CT) scan. Table 12D-1 shows the estimated lifetime risk of being diagnosed with colon cancer for a male exposed to 0.1 Gy at age 10 as 241 per 100,000. The estimate for a male exposed at 0.01 Gy is obtained as (0.01 / 0.1) × 241 = 24.1 per 100,000 (about 1 in 4000). An estimate of the lifetime risk of dying of colon cancer can also be obtained using Table 12D-2, and is (0.01 / 0.1) × 117 = 11.7 per 100,000 (about 1 in 8500).
Example 2: A 45-year-old woman receives a dose of 0.001 Gy (1 mGy) to the breast from a mammogram. Table 12D-1 shows an estimated lifetime risk of being diagnosed with breast cancer for a female exposed to 0.1 Gy at age 40 as 141 per 100,000; the comparable estimate for exposure at age 50 is 70 per 100,000. Using linear interpolation, the risk from exposure to 0.1 Gy at age 45 is (141 + 70) / 2 = 105.5 per 100,000. The risk from exposure to 0.001 Gy is estimated as (0.001 / 0.1) × 105.5 = 1.055 per 100,000. A rough estimate of the risk from repeated annual mammograms could be obtained by adding estimates obtained from receiving a mammogram at ages 45, 46, 47, 48, and so forth. For most purposes, such an estimate will be reasonable, although this approach does not account for the possibility of dying before subsequent doses are received.
Example 3: A female is exposed to high natural background of 0.004 Gy (4 mGy) per year throughout life. Lifetime risk estimates for exposure to 0.001 Gy (1 mGy) per year throughout life are shown in columns 2 (incidence) and 4 (mortality) of Table 12D-3. To obtain estimates for exposure to 4 mGy throughout life, these estimates must be multiplied by 4. For example, the estimated risk of a female being diagnosed with a solid cancer would be 3872 (4 × 968), per 100,000 whereas the risk of being diagnosed with leukemia would be 204 (4 × 51) per 100,000, yielding a total risk of being diagnosed with cancer of 4076 per 100,000 (about 1 in 25). The risk of dying of cancer can be obtained in a similar manner and would be 1988 per 100,000 (about 1 in 50).
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TABLE 12D-1 Lifetime Attributable Risk of Cancer Incidencea
Cancer Site
Age at Exposure (years)
0
5
10
15
20
30
40
50
60
70
80
Males
Stomach
76
65
55
46
40
28
27
25
20
14
7
Colon
336
285
241
204
173
125
122
113
94
65
30
Liver
61
50
43
36
30
22
21
19
14
8
3
Lung
314
261
216
180
149
105
104
101
89
65
34
Prostate
93
80
67
57
48
35
35
33
26
14
5
Bladder
209
177
150
127
108
79
79
76
66
47
23
Other
1123
672
503
394
312
198
172
140
98
57
23
Thyroid
115
76
50
33
21
9
3
1
0.3
0.1
0.0
All solid
2326
1667
1325
1076
881
602
564
507
407
270
126
Leukemia
237
149
120
105
96
84
84
84
82
73
48
All cancers
2563
1816
1445
1182
977
686
648
591
489
343
174
Females
Stomach
101
85
72
61
52
36
35
32
27
19
11
Colon
220
187
158
134
114
82
79
73
62
45
23
Liver
28
23
20
16
14
10
10
9
7
5
2
Lung
733
608
504
417
346
242
240
230
201
147
77
Breast
1171
914
712
553
429
253
141
70
31
12
4
Uterus
50
42
36
30
26
18
16
13
9
5
2
Ovary
104
87
73
60
50
34
31
25
18
11
5
Bladder
212
180
152
129
109
79
78
74
64
47
24
Other
1339
719
523
409
323
207
181
148
109
68
30
Thyroid
634
419
275
178
113
41
14
4
1
0.3
0.0
All solid
4592
3265
2525
1988
1575
1002
824
678
529
358
177
Leukemia
185
112
86
76
71
63
62
62
57
51
37
All cancers
4777
3377
2611
2064
1646
1065
886
740
586
409
214
NOTE: Number of cases per 100,000 persons exposed to a single dose of 0.1 Gy.
aThese estimates are obtained as combined estimates based on relative and absolute risk transport and have been adjusted by a DDREF of 1.5, except for leukemia, which is based on a linear-quadratic model.
TABLE 12D-2 Lifetime Attributable Risk of Cancer Mortalitya
Cancer Site
Age at Exposure (years)
0
5
10
15
20
30
40
50
60
70
80
Males
Stomach
41
34
30
25
21
16
15
13
11
8
4
Colon
163
139
117
99
84
61
60
57
49
36
21
Liver
44
37
31
27
23
16
16
14
12
8
4
Lung
318
264
219
182
151
107
107
104
93
71
42
Prostate
17
15
12
10
9
7
6
7
7
7
5
Bladder
45
38
32
27
23
17
17
17
17
15
10
Other
400
255
200
162
134
94
88
77
58
36
17
All solid
1028
781
641
533
444
317
310
289
246
181
102
Leukemia
71
71
71
70
67
64
67
71
73
69
51
All cancers
1099
852
712
603
511
381
377
360
319
250
153
Females
Stomach
57
48
41
34
29
21
20
19
16
13
8
Colon
102
86
73
62
53
38
37
35
31
25
15
Liver
24
20
17
14
12
9
8
8
7
5
3
Lung
643
534
442
367
305
213
212
204
183
140
81
Breast
274
214
167
130
101
61
35
19
9
5
2
Uterus
11
10
8
7
6
4
4
3
3
2
1
Ovary
55
47
39
34
28
20
20
18
15
10
5
Bladder
59
51
43
36
31
23
23
22
22
19
13
Other
491
287
220
179
147
103
97
86
69
47
24
All solid
1717
1295
1051
862
711
491
455
415
354
265
152
Leukemia
53
52
53
52
51
51
52
54
55
52
38
All cancers
1770
1347
1104
914
762
542
507
469
409
317
190
NOTE: Number of deaths per 100,000 persons exposed to a single dose of 0.1 Gy.
aThese estimates are obtained as combined estimates based on relative and absolute risk transport and have been adjusted by a DDREF of 1.5, except for leukemia, which is based on a linear-quadratic model.
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TABLE 12D-3 Lifetime Attributable Risk of Solid Cancer Incidence and Mortalitya
Incidence: Exposure Scenario
Mortality: Exposure Scenario
Cancer site
1 mGy per Year throughout Life
10 mGy per Year from Ages 18 to 65
1 mGy per Year throughout Life
10 mGy per Year from Ages 18 to 65
Males
Stomach
24
123
13
66
Colon
107
551
53
273
Liver
18
93
14
72
Lung
96
581
99
492
Prostate
32
164
6.3
32
Bladder
69
358
16
80
Other
194
801
85
395
Thyroid
14
28
All solid
554
2699
285
1410
Leukemia
67
360
47
290
All cancers
621
3059
332
1700
Females
Stomach
32
163
19
94
Colon
72
368
34
174
Liver
8.7
44
8
40
Lung
229
1131
204
1002
Breast
223
795
53
193
Uterus
14
19
3.5
18
Ovary
29
140
18
91
Bladder
71
364
21
108
Other
213
861
98
449
Thyroid
75
139
All solid
968
4025
459
2169
Leukemia
51
270
38
220
All cancers
1019
4295
497
2389
NOTE: Number of cases or deaths per 100,000 persons exposed to 1 mGy per year throughout life or to 10 mGy per year from ages 18 to 64.
aThese estimates are obtained as combined estimates based on relative and absolute risk transport and have been adjusted by a DDREF of 1.5, except for leukemia, which is based on a linear-quadratic model.
Representative terms from entire chapter:
average dose
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