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12 Estimating Cancer Risk INTRODUCTION from exposure to low levels of low-LET ionizing radiation. These include the work of the BEIR V committee (NRC This chapter presents models that allow one to estimate 1990), the International Commission on Radiological Pro- the lifetime risk of cancer resulting from any specified dose tection (ICRP 1991), the National Council on Radiation Pro- of ionizing radiation and applies these models to example tection and Measurements (NCRP 1993), the Environmental exposure scenarios for the U.S. population. Models are de- Protection Agency (EPA 1994, 1999), the United Nations veloped for estimating lifetime risks of cancer incidence and Scientific Committee on the Effects of Atomic Radiation mortality and take account of sex, age at exposure, dose rate, (UNSCEAR 2000b), and the National Institutes of Health and other factors. Estimates are given for all solid cancers, (NIH 2003). The approaches used in these past assessments leukemia, and cancers of several specific sites. Like previ- are described in Annex 12A. ous BEIR reports addressing low-LET (linear energy trans- fer) radiation, risk models are based primarily from data on Japanese atomic bomb survivors. However, the vast litera- DATA EVALUATED FOR BEIR VII MODELS ture on both medically exposed persons and nuclear workers As in earlier BEIR reports addressing health effects from exposed at relatively low doses has been reviewed to evalu- exposure to low-LET radiation, the committee’s models for ate whether findings from these studies are compatible with risk estimation are based primarily on the Life Span Study A-bomb survivor-based models. In many cases, results of (LSS) cohort of survivors of the atomic bombings in fitting models similar to those in this chapter have been Hiroshima and Nagasaki. As discussed in Chapter 6, the LSS published. cohort offers several advantages for developing quantitative Risk estimates are subject to several sources of uncer- estimates of risk from exposure to ionizing radiation. These tainty due to inherent limitations in epidemiologic data and include its large size, the inclusion of both sexes and all ages, in our understanding of exactly how radiation exposure in- a wide range of doses that have been estimated for individual creases the risk of cancer. In addition to statistical uncer- subjects, and high-quality mortality and cancer incidence tainty, the populations and exposures for which risk esti- data. In addition, because the exposure was to the whole mates are needed nearly always differ from those for whom body, the LSS cohort offers the opportunity to assess risks epidemiologic data are available. This means that assump- for cancers of a large number of specific sites and to evaluate tions are required, many of which involve considerable un- the comparability of site-specific risks. certainty. Risk may depend on the type of cancer, the magni- Another consideration in the choice of data was that it tude of the dose, the quality of the radiation, the dose-rate, was considered essential that the data used by the committee the age and sex of the person exposed, exposure to other eventually be available to other investigators. The Radiation carcinogens such as tobacco, and other characteristics of the Effects Research Foundation (RERF) has developed a policy exposed individual. Despite the abundance of epidemiologic of making summarized data available to those who request and experimental data on the health effects of exposure to it, thus enabling other investigators to analyze data used by radiation, data are not adequate to quantify these dependen- the BEIR VII committee. This is not the case for data sets on cies precisely. Uncertainties in the BEIR VII risk models are most other radiation-exposed cohorts. discussed, and a quantitative assessment of selected sources Although the committee’s models have been developed of uncertainty is made. from A-bomb survivor data, attention has been given to their In recent years, several national and international organi- compatibility with data from other cohorts. Fortunately, for zations have developed models for estimating cancer risk 267

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268 BEIR VII most cohorts with suitable data for developing quantitative risk with time since exposure and other variables, and also risk models, analyses based on models similar to those used because the excess relative risk for leukemia is clearly by the committee have been conducted and published. This greater than that for solid cancers, all recent risk assessments facilitated the committee’s evaluation of data from other have provided separate models and estimates for leukemia. studies. Pooled analyses of thyroid cancer risks (Ron and For exposure scenarios in which various tissues of the others 1995a) and of breast cancer risks (Preston and others body receive substantially different doses, estimates of risks 2002a) were especially helpful in this regard, as were sev- for cancers of specific sites are needed. Adjudication of com- eral meta-analyses by Little and colleagues. In addition, the pensation claims for possible radiation-related cancer, which many published analyses based on A-bomb survivor data is usually specific to organ site, also requires site-specific have guided and facilitated the committee’s efforts in its estimates. Furthermore, site-specific cancers vary in their choice of models. The committee notes particularly the main causes and baseline risks, and it might thus be expected that publications on mortality (Preston and others 2003) and in- models for estimating excess risks from radiation exposure cidence data (Thompson and others 1994) and the models could also vary by site. For this reason, even for estimating developed by UNSCEAR (2000b) and NIH (2003). total cancer risk, it is desirable to estimate risks for each of The use of data on persons exposed at low doses and low several specific cancer sites and then sum the results. dose rates merits special mention. Of these studies, the most The development of site-specific models is limited by data promising for quantitative risk assessment are the studies of characteristics. For A-bomb survivor data on solid cancers, nuclear workers who have been monitored for radiation ex- parameter estimates based on site-specific data are less pre- posure through the use of personal dosimeters. These stud- cise than those based on all solid cancers analyzed as a group, ies, which are reviewed in Chapter 8, were not used as the particularly for less common cancers. It is especially diffi- primary source of data for risk modeling principally because cult to detect and quantify the modifying effects of variables of the imprecision of the risk estimates obtained. For ex- such as sex, age at exposure, and attained age for site-specific ample, in a large combined study of nuclear workers in three cancers. It was for these reasons that the BEIR V committee countries, the estimated relative risk per gray (ERR/Gy) for provided estimates for only five broad cancer categories. all cancers other than leukemia was negative, and the confi- In addition to statistical uncertainties, it has recently been dence interval included negative values and values larger recognized that estimates of the modifying effects of age at than estimates based on A-bomb survivors (Cardis and oth- exposure based on A-bomb survivor data can be influenced ers 1995). strongly by secular trends in Japanese baseline rates (Pierce Since the publication of BEIR V, data on cancer inci- 2002; Preston and others 2003). This occurs because age at dence in the LSS cohort from the Hiroshima Tumor Registry exposure in the LSS cohort is confounded with birth cohort, have become available, whereas previously only data from making it impossible to estimate their separate effects with- the Nagasaki Tumor Registry were available. Thus, the com- out additional information on the relation of baseline and mittee could use both incidence and mortality data to de- radiation-related risks. (See Annex 12B for further discus- velop its models. The incidence data offer the advantages of sion of this issue.) Japanese rates for several cancer sites including nonfatal cancers and of better diagnostic accuracy. changed over the period 1950–1998 as Japan became more However, the mortality data offer the advantages of cover- Westernized, including rates for cancers of the stomach, co- ing a longer period (1950–2000) than the incidence data lon, lung, and female breast. A related problem is that (1958–1998) and of including deaths of LSS members who baseline risks for the United States and Japan differ substan- migrated from Hiroshima and Nagasaki to other parts of tially for many cancer sites, and it is unclear how to account Japan. 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 MEASURES OF RISK AND CHOICE OF CANCER END and colleagues (2003) found little evidence of heterogeneity POINTS among excess relative risk (ERR)1 models developed for To express the health impact of whole-body exposures to several specific cancer sites. Although these authors caution radiation, the lifetime risk of total cancer, without distinc- that this finding should be taken mainly as a warning against tion as to site, is usually of primary concern. Estimates of overinterpreting apparent differences in sites, some group- risk for both mortality and incidence are of interest, the ing of cancers seems justified. In developing its models, the former because it is the most serious consequence of expo- committee has tried to strike a balance between allowing for sure to radiation and the latter because it reflects public differences among cancer sites and statistical precision. As health impact more fully. The time or age of cancer occur- discussed later in this chapter, most of the committee’s mod- rence is also of interest, and for this reason, estimates of cancer mortality risks are sometimes accompanied by esti- mates of the years of life lost or years of life lost per death. 1ERR is the rate of disease in an exposed population divided by the rate Because leukemia exhibits markedly different patterns of of disease in an unexposed population minus 1.0.

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ESTIMATING CANCER RISK 269 els for site-specific cancers make use of data on all solid on deaths occurring in the period 1950–1997 (Preston and cancers to estimate the modifying effects of age at exposure others 2003). Both excess relative risk models and excess and attained age, but make use only of data for the site of absolute risk (EAR)2 models were evaluated. Methods were interest to estimate the overall level of risk. generally similar to those that have been used in recent re- Considerations in deciding on the sites for which indi- ports by RERF investigators (Pierce and others 1996; Preston vidual estimates should be provided are whether or not the and others 2003) and were based on Poisson regression us- cancer has been linked clearly with radiation exposure and ing the AMFIT module of the software package EPICURE the adequacy of the data for developing reliable risk esti- (Preston and others 1991). Additional detail is given in An- mates. On the first point, it can be argued that the range of nex 12B. uncertainty for risk of a particular cancer is of interest re- All analyses were based on the newly implemented DS02 gardless of whether or not a statistically significant dose- dose estimates. Doses were expressed in sieverts, with a con- response had been observed, a position taken by NIH (2003). stant weighting factor of 10 for the neutron dose; that is, the Cancers of the salivary glands, stomach, colon, liver, lung, doses were calculated as γ-ray absorbed dose (Gy) + 10 × breast, bladder, ovary, and thyroid and nonmelanoma skin neutron absorbed dose (Gy). The DS02 system provides cancer have all been linked clearly with radiation exposure estimates of doses to several organs of the body. For site- in A-bomb survivor data, with evidence somewhat more specific estimates, the committee used dose to the organ equivocal for a few additional sites such as esophagus, gall being evaluated, with colon dose used for the residual bladder, and kidney. Other studies support many of these category of “other” cancers. The weighted dose, d, to the associations, and bone cancer has been linked with exposure colon was used for the combined category of all solid cancer to α-irradiation from 224Ra. Leukemia has been strongly or all solid cancers excluding thyroid and nonmelanoma skin linked with radiation exposure in several studies including cancer. Additional discussion of the doses used in the those of atomic bomb survivors. analyses is given in Annex 12B. Another consideration in selecting sites for evaluation is the likelihood of exposure scenarios that will irradiate the Models for All Solid Cancers site selectively. Here it is noted that inhalation exposures will selectively irradiate the lung, exposures from ingestion Risk estimates for all solid cancers were obtained by sum- will selectively irradiate the digestive organs, exposure to ming the estimates for cancers of specific sites. However, strontium selectively irradiates the bone marrow, and expo- the general form of the model and the estimates of the pa- sure to uranium selectively irradiates the kidney. rameters that quantify the modifying effects of age at expo- Based on these considerations, the committee has pro- sure and attained age were (with some exceptions) based on vided models and mortality and incidence estimates for can- analyses of data on all solid cancers. Such analyses offer the cers of the stomach, colon, liver, lung, female breast, pros- advantage of larger numbers of cancer cases and deaths, tate, uterus, ovary, bladder, and all other solid cancers. which increases statistical precision. Incidence estimates are also provided for thyroid cancer. As discussed in Chapter 6, most recent analyses of data The inclusion of cancers of the prostate and uterus merits on the LSS cohort have been based on either ERR models, in comment because these cancers are not usually thought to be which the excess risk is expressed relative to the background radiation-induced and have not been evaluated separately in risk, or EAR models, in which the excess risk is expressed as previous risk assessments. However, the committee did not the difference in the total risk and the background risk. With want to include these cancers in the residual category of “all linear dose-response functions, the general models for the other solid cancers,” particularly since prostate cancer is ERR and EAR are given below: much more common in the United States than in Japan. λ(c, s, a, b, d) = λ(c, s, a, b) [1 + βs ERR(e, a)d] or THE BEIR VII COMMITTEE’S PREFERRED MODELS λ(c, s, a, b, d) = λ(c, s, a, b) + βs EAR(e, a)d, Approach to Analyses where λ(c, s, a, b) denotes the background rate at zero dose, This section describes the results of analyses of data on and depends on city (c), sex (s), attained age (a), and birth cancer incidence and mortality in the LSS cohort that were cohort (b). The terms βs ERR(e, a) and βs EAR(e, a) are, conducted by the committee with the help of RERF person- respectively, the ERR and the EAR per unit of dose ex- nel acting as agents of the National Academies. Analyses of pressed in sieverts, which may depend on sex (s), age at cancer incidence were based on cases diagnosed in the pe- exposure (e), and attained age (a). riod 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 2EAR is the rate of disease in an exposed population minus the rate of analyses of mortality from cancer of specific sites were based disease in an unexposed population.

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270 BEIR VII 2.4 2.2 70 2.0 Age at exposure 10 Age at exposure 10 Excess cases per 10,000 PY-Sv 60 Excess Relative Risk (1 Sv) 1.8 Age at exposure 20 Age at exposure 20 Age at exposure 30+ 50 Age at exposure 30+ 1.6 1.4 40 1.2 1.0 30 0.8 20 0.6 10 0.4 0.2 0 30 40 50 60 70 80 90 30 40 50 60 70 80 90 Attained age Attained age FIGURE 12-1 A 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. 40 Age at exposure 10 Excess deaths per 10,000 PY-Sv Age at exposure 10 Excess Relative Risk (1 Sv) Age at exposure 20 Age at exposure 20 30 Age at exposure 30+ Age at exposure 30+ 20 10 0 30 40 50 60 70 80 90 Attained age Attained age 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 in- difficulties in distinguishing the fits of models with only one cidence and mortality data (e.g., Preston and others 2003, of those variables and because, with the incidence data, 2004) are based on models in which ERR (e, a) and EAR (e, analyses of all solid cancers indicated dependence on both a) are of the form below: variables. The committee’s models were developed from analyses RERF model: of both LSS incidence and LSS mortality data. Analyses of ERR(e, a) or EAR(e, a) = exp (γe) aη. (12-1) incidence data were based on the category consisting of all solid cancers excluding thyroid and nonmelanoma skin can- The parameters γ and η quantify the dependence of the ERR cers. These exclusions were made because both thyroid can- or EAR on e and a. These models, with dependence on both cer and nonmelanoma skin cancer exhibit exceptionally age at exposure and attained age, were chosen because of strong age-at-exposure dependencies that do not seem typi-

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ESTIMATING CANCER RISK 271 cal of cancer of other sites (Thompson and others 1994). The committee chose the model shown in Equation (12- Because the most recent mortality data (1950–2000) avail- 2) because it fitted both incidence and mortality data on all able to the committee did not include site-specific solid can- solid cancers excluding thyroid cancer and nonmelanoma cers and because thyroid cancer and nonmelanoma skin can- skin cancer slightly better than the RERF model shown in cer are rarely fatal, analyses of mortality data were based on Equation (12-1). There was no indication of a continued de- the category of all solid cancers. The committee’s preferred crease with exposure age in the ERR or EAR after exposure models for estimating solid cancer risks are similar to the age 30, and there was even a suggestion of an increase at RERF model, except that the ERR and EAR depend on age older ages. Further discussion of the rationale for choosing at exposure only for exposure ages under 30 years and are the Equation (12-2) model, including a detailed description constant for exposure ages over 30. That is, of analyses that were conducted by the committee, can be found in Annex 12B. In that annex, the committee evaluates BEIR VII model: several alternative model choices, including models that al- ERR(e, a) or EAR(e, a) = exp (γ e*) aη, (12-2) low for dependence on age at exposure alone, on attained where e is age at exposure in years, e* is equal to e – 30 age alone, and on time since exposure instead of attained when e < 30, and equal to zero when e 30, and a is attained age. Also evaluated are models that use different functional age in years. forms to express the dependence on exposure age, attained Figure 12-1A shows plots of the ERR and EAR for inci- age, or time since exposure. Although several alternative dence of all solid cancers excluding thyroid cancer and models provided reasonable descriptions of the data, the nonmelanoma skin cancer as a function of exposure age and BEIR VII preferred model shown in Equation (12-2) pro- attained age using the BEIR VII model. Figure 12-1B shows vided the best fit. similar plots for mortality from all solid cancers. Although Table 12-1 shows estimates of the parameters of the ERR the ERR and EAR models have the same form, the values and EAR models obtained from analyses of LSS incidence and interpretation of the parameters are different. In particu- data (1958–1998) for all solid cancers excluding thyroid and lar, the ERR shows a decrease with attained age, whereas the nonmelanoma skin cancers and of LSS mortality data (1950– EAR shows a strong increase with attained age. Both the 2000) for all solid cancers. Further description of these ERR and the EAR decrease with increasing age at exposure results and how they were obtained can be found in for those exposed under age 30. 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/Sv (95% CI) at Age 30 and Attained Age 60 Per-Decade Increase in Age at Exposure Exponent of No. of Cases Over the Range Attained Age ERR Models or Deaths Males (βM) Females (βF) 0–30 Yearsc (95% CI), γ (95% CI), η 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 per 104 PY-Sv (95% CI) EAR Models 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 β 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 s 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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272 BEIR VII Models for Site-Specific Solid Cancers Other Than Breast excluding thyroid and nonmelanoma skin cancers (shown in and Thyroid Table 12-1) unless site-specific analyses indicated significant departure from these estimates. This approach is similar to Although the committee provides risk estimates for both that used by UNSCEAR (2000b) except that the committee cancer incidence and mortality, models for site-specific estimated the parameters βM and βF separately for each site cancers were based on cancer incidence data. This was done of interest. primarily because site-specific cancer incidence data are The committee’s preferred ERR and EAR models for site- based on diagnostic information that is more detailed and specific cancer incidence and mortality are shown in Table accurate than death certificate data and because, for several 12-2. The estimates of βM and βF are for a person exposed at sites, the number of incident cases is considerably larger than age 30 or older at an attained age of 60. Models for breast the number of deaths (see annex Table 12B-2). However, and thyroid cancer were based on published analyses that models developed from incidence data were checked for included data on medically exposed persons as discussed consistency with mortality data. Since there is little evidence in the next two sections. For other sites, common values of that radiation-induced cancers are more rapidly fatal than the parameter γ indicating dependence on age at exposure cancer that occurs for other reasons, ERR models based could be used in all cases. With the ERR models, common on incidence data can be used directly to estimate risks of values of the parameter indicating the dependence of risks cancer mortality, whereas EAR models require adjustment. on attained age (η) could be used in all cases except the (See “Method of Calculating Lifetime Risks” for a descrip- category “all other solid cancers.” With the EAR models, tion of how the models are used to estimate risks of cancer it was necessary to estimate the attained-age parameter, η, incidence and mortality.) separately for cancers of the liver, lung, and bladder, which Models for estimating risks of solid cancers of specific may reflect variation in the pattern of increase with age for sites other than breast and thyroid were also of the form site-specific baseline rates. shown in Equation (12-2). The committee’s approach to The committee emphasizes that there is considerable quantifying the parameters γ and η was to use the estimates uncertainty in models for site-specific cancers. Statistical obtained from analyzing incidence data on all solid cancers uncertainty in the estimates of the main effect parameter βs TABLE 12-2  Committee’s Preferred ERR and EAR Models for Estimating Site-Specific Solid Cancer Incidence and Mortalitya ERR Models EAR Models Cancer Site No. of Cases βFb (95% CI) βMb (95% CI) γ c η d βMe (95% CI) βFe (95% CI) γ c 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) Breast 952 — 0.51 (0.28, 0.83) 0 –2.0 — 9.9f (7.1, 14) –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. a The 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. b ERR/Sv for exposure at age 30+ at attained age 60. c Per-decade increase in age at exposure over the range 0–30 years (γ). d Exponent of attained age (η). e EAR 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. f Based on a pooled analysis by Preston and others (2002a). See text for details. Unlike other EAR (βF) shown in this table, the estimate of 9.9 is for exposure at age 25 and attained age 50. The ERR estimate of 0.51, however, is for an attained age of 60 and applies to all exposure ages since γ=0. g The first number is for attained ages less than 50; the second number is for attained ages 50 or greater. h Based 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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ESTIMATING CANCER RISK 273 is often large. Although the common values of the param- modifying factors and is thus more comparable to models eters γ and η that have been used to quantify the modifying used for other sites. effects of age at exposure and attained age are compatible with site-specific data, estimates of these parameters based Model for Thyroid Cancer on site-specific data are often quite different from the com- mon values. Annex 12B shows the site-specific estimates of The committee’s preferred model for estimating thyroid γ and η. 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 Models for Female Breast Cancer data from five cohorts of persons exposed under age 15 to The committee’s preferred models for estimating breast develop a thyroid cancer incidence model. The five studies cancer incidence and mortality are those developed by Pres- were the A-bomb survivors (including only those exposed ton and colleagues (2002a) from analyses of combined data under age 15; Thompson and others 1994), the Rochester on breast cancer incidence in several cohorts including the thymus study (Shore and others 1993b), the Israel tinea LSS. The LSS data used in these analyses were for the period capitis study (Ron and others 1989), children treated for 1958–1993, whereas the committee’s analyses included data enlarged tonsils and other conditions (Pottern and others through 1998. Although these models were developed for 1990; Schneider and others 1993), and an international estimating breast cancer incidence, they may also be used childhood cancer study (Tucker and others 1991). Ron and to estimate breast cancer mortality using the same approach colleagues found that the ERR/Gy for females was about as that for other site-specific solid cancers. twice that for males although the difference was not statisti- Preston and colleagues (2002a) found that common mod- cally significant. Although the NIH (2003) used a non-sex- els could be used to describe data from the LSS cohort, the specific model, for consistency with the treatment of cancers original Massachusetts tuberculosis fluoroscopy cohort and of other sites, the committee has used a sex-specific model. an extension of this cohort (Boice and others 1991b), and From data presented in NIH (2003, Table IV.D.8), it can be the Rochester infant thymus irradiation cohort (Hildreth and determined that the model takes the form ERR/Gy = 0.79 exp others 1989). Models for both the ERR and the EAR were [–0.083 (e – 30)], where e is exposure age in years. The BEIR developed for these cohorts. The ERR model was as follows: VII model is as follows: ERR/Sv = β (a / 60)–2, ERR/Gy = 0.53 exp [– 0.083 (e – 30)] for males, and where a is attained age. With this model, it was necessary ERR/Gy = 1.05 exp [– 0.083 (e – 30)] for females. to estimate β separately for the LSS and the remaining U.S. women. Parameter estimates were β = 1.46 for the LSS The estimate of the ERR per Gy given by Ron and col- and 0.51 for the remaining U.S. cohorts. The committee’s leagues was 7.7 (95% CI 2.1, 29) in a model without modi- preferred ERR model for estimating risks for U.S. women fication by age at exposure. With the committee’s model, uses β = 0.51. In the formulation above, the committee has this would be the ERR/Gy, averaged over the two sexes, for parameterized the model so that β indicates the ERR at an exposure at about 2.5 years of age, which was about the aver- attained age of 60 instead of 50 as given in Preston and col- age exposure age in the data analyzed by Ron and colleagues. leagues. The pooled EAR model from Preston and colleagues Ron and colleagues (1995a) did not present results for (2002b) was as follows: ERR or EAR models that allowed for modification by both EAR per 104 woman-years per gray = age at exposure and attained age. 9.9 exp [–0.05 (e – 25)] (a / 50)η, Model for Leukemia 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 The committee’s models for estimating leukemia risks value of the overall level of risk (9.9) could be used for all were based on analyses of LSS leukemia mortality data for four cohorts. the period 1950–2000 (Preston and others 2004). The quality Although the committee calculates lifetime risk estimates of diagnostic information for the non-type-specific leukemia based on both the ERR and the EAR models described above, mortality used in these analyses is thought to be high. Data its preferred estimates are based on the EAR model. With on medically exposed cohorts have indicated that chronic this model the estimated main effect is more stable because lymphocytic leukemia (CLL) is not likely to be induced by it is based on both LSS and U.S. women. In addition, this radiation exposure (Boice and others 1987; Curtis and oth- model includes both age at exposure and attained age as ers 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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274 BEIR VII Models used for estimating leukemia risks in the past have categorical treatment of age at exposure. It was also found to expressed the ERR (NRC 1990; NIH 2003) or EAR (ICRP be necessary to allow the dependence on time since expo- 1991; UNSCEAR 2000b) as a linear-quadratic function of sure to vary by age at exposure by including the term e* log dose and have allowed for dependence on sex, age at expo- (t / 25). For the EAR model, there was no need to include a sure, and time since exposure. Both categorical and continu- term for the main effect of time since exposure; note that ous treatments of age at exposure and time since exposure with this parameterization, there is no decrease with time have been used. The BEIR VII committee models also ex- since exposure for those exposed at age 30 or more. For ap- press the ERR or EAR as a linear-quadratic function of dose plication of these models, the reader should consult the sec- with allowance for dependencies on sex, age at exposure, tion “Use of the Committee’s Preferred Models to Estimate and time since exposure. The committee’s preferred models Risks for the U.S. Population.” are of the following form: BEIR VII leukemia model: USE OF THE COMMITTEE’S PREFERRED MODELS TO EAR(D, s, e, t) or ERR(D, s, e, t) = ESTIMATE RISKS FOR THE U.S. POPULATION βsD (1 + θD) exp [γ e* + δ log (t / 25) + φe* log (t / 25)], To use models developed primarily from Japanese A- (12-3) bomb survivor data for the estimation of lifetime risks for where D is dose (Sv), s is sex, and e* is (e – 30) / 10 for the U.S. population, several issues must be addressed. These e < 30 and 0 for e 30 ( e is age at exposure in years). include determining approaches for estimating risks at low Table 12-3 shows the parameter estimates, and Figure 12-2 doses and low dose rates, projecting risks over time, trans- depicts the dependence of the ERR or EAR on age at expo- porting risks from the Japanese to the U.S. population, and sure and time since exposure. The parameter θ indicates the estimating risks from exposure to X-rays. This section de- degree of curvature, which does not depend on sex, age at scribes the approach for addressing each of these issues, as exposure, or time since exposure; βM and βF represent the well as the methodology used to estimate lifetime risk. More ERR/Sv or the EAR (expressed as excess deaths per 104 PY-Sv, detailed discussion of some of the issues is given in Chap- where PY = person-years), for exposure at age 30 or more at ter 10, and the approach for quantifying the uncertainties 25 years following exposure. This model was found to fit the associated with some of these issues is discussed later in this data better than analogous models using e instead of e*, or chapter. using t instead of log (t), and nearly as well as models with a Estimating Risks from Exposure to Low Doses and Low Dose Rates TABLE 12-3 Committee’s Preferred ERR and EAR The BEIR VII risk models have been developed prima- Models for Estimating Leukemia Incidence and rily from analyses of data on the LSS cohort of Japanese Mortalitya,b,c A-bomb survivors. Although more than 60% of the exposed members of this cohort were exposed to relatively low doses Parameter ERR Model EAR Model (0.005–0.1 Sv), survivors who were exposed to doses exceed- ing 0.5 Gy are still influential in estimating the ERR/Sv. In βM 1.1 per Sv (0.1, 2.6) 1.62 deaths per 104 PY-Sv (0.1, 3.6) addition, exposure of A-bomb survivors was at high dose βF 1.2 per Sv (0.1, 2.9) 0.93 deaths per 104 PY-Sv (0.1, 2.0) rates, whereas exposure at low dose rates is of primary con- γ –0.40 per decade 0.29 per decade (0.0, 0.62) cern for risk assessment. Based on evidence from experi- (–0.78, 0.0) mental data, ICRP (1991), NCRP (1993), EPA (1999), and δ –0.48 (–1.1, 0.2) 0.0 UNSCEAR (2000b) recommended reducing linear estimates based on A-bomb survivor (or other high-dose-rate) exposure φ 0.42 (0.0, 0.96) 0.56 (0.31, 0.85) by a dose and dose-rate reduction factor (DDREF) of 2.0. θ 0.87 per Sv (0.16, 15) 0.88 Sv–1 (0.16, 15) In Chapter 10, both data on solid cancer risks in the LSS cohort and experimental data pertinent to this issue are evalu- NOTE: Estimated parameters with 95% CIsd based on likelihood ratio profile. ated by the committee. Based on this evaluation, the com- mittee found a believable range of DDREF values (for ad- aThe ERR or EAR is of the form β (D + θ D2) exp [γ e* + δ log (t / 25) + s justing linear risk estimates based on the LSS cohort) to be φ 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 1.1 to 2.3. When a single value is needed, 1.5 (the median of time since exposure (years). the subjective probability distribution for the LSS DDREF) bBased on analyses of LSS mortality data (1950–2000), with 296 deaths is used to estimate risk for solid tumors. To estimate the risk from leukemia. of leukemia, the BEIR VII model is linear-quadratic, since cThese models apply only to the period 5 or more years following expo- this model fitted the data substantially better than the linear sure. dConfidence intervals based on likelihood ratio profile. model.

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ESTIMATING CANCER RISK 275 5 20 4 Age at exposure 10 Age at exposure 10 Excess deaths per 10,000 PY-Sv Age at exposure 20 Excess relative risk per Sv Age at exposure 20 15 Age at exposure 30+ Age at exposure 30+ 3 10 2 5 1 0 0 0 10 20 30 40 50 60 0 10 20 30 40 50 60 Time since exposure Time since exposure 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 Transport of Risks from a Japanese to a U.S. Population The LSS cohort has now been followed for more than 50 Baseline risks for many site-specific cancers are different years, so that lifetime follow-up is nearly complete for all for the United States and Japan. For example, baseline risks but the youngest survivors (under age 20 at exposure). Al- for cancers of the colon, lung, and female breast are higher though the extrapolation involved in estimating lifetime risks in the United States, whereas baseline risks for cancers of based on limited follow-up has been a major source of un- the stomach and liver are much higher in Japan. The BEIR V certainty in past risk assessments, it is now much less so. committee based its estimates on relative risk transport, The BEIR VII models allow for dependencies of both the where it is assumed that the excess risk due to radiation is ERR and the EAR on attained age, and it is assumed that the proportional to baseline risks; that is, the ERR is the same identified patterns persist until the end of life for the young- for the United States and Japan. However, the BEIR III com- est survivors. Additional discussion of this issue is found in mittee based its estimates on absolute risk transport, where it Chapter 10. is assumed that the excess risk does not depend on baseline For leukemia, the early years of follow-up also must be risks; that is, the EAR is the same for the United States and addressed. Ascertainment of leukemia cases for the LSS co- Japan. The EPA (1994) used the geometric mean of the two hort did not begin until 1950, while data on medically ex- estimates, whereas UNSCEAR (2000b) presented estimates posed cohorts have demonstrated that excess leukemia cases based on both approaches without indicating a preference. can occur as early as a year or two after exposure (Boice and Estimates based on relative and absolute risk can differ sub- others 1987; Curtis and others 1992, 1994; Inskip and others stantially. For example, the UNSCEAR stomach cancer esti- 1993; Weiss and others 1994, 1995). In several of these stud- mates for the U.S. population based on absolute risk trans- ies, relative risks were highest in the period 1–5 years after port are nearly an order of magnitude larger than those based exposure. In addition, a recent analysis of data on Mayak on relative risk transport. workers found that leukemia risks 3–5 years following ex- For breast and thyroid cancer, the committee’s models ternal radiation exposure were more than an order of magni- are based on combined analyses that include Caucasian sub- tude higher than risks for later periods (Shilnikova and oth- jects. For other solid cancer sites including leukemia, the ers 2003). The UNSCEAR (2000b) committee addressed this committee has calculated risks using both relative and abso- problem by assuming that excess risks for the first 5 years lute risk transport, which provides an indication of the un- after exposure were half those observed 5 years after expo- certainty from this source. The recommended point estimates sure. The BEIR VII committee has instead assumed that ex- are weighted means of estimates obtained under the two cess absolute risk in the period 2–5 years following exposure models (adjusted by a DDREF of 1.5 as discussed above). is equal to that observed 5 years after exposure. Clearly there For sites other than breast, thyroid, and lung, a weight of 0.7 is uncertainty in the magnitude of the risk during the initial is used for the estimate obtained using relative risk transport years following exposure. and a weight of 0.3 for the estimate obtained using absolute

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276 BEIR VII risk transport, with the weighting done on a logarithmic effectiveness between different photon radiations are not scale. This choice was made because, as discussed in Chap- considered of sufficient consequence to require explicit ac- ter 10, there is somewhat greater support for relative risk counting in radiation protection regulations. However, the than for absolute risk transport. In addition, the ERR models significant difference between the (dose average) unre- used to obtain relative risk transport estimates may be less stricted LET of 60Co (about 0.4keV / µm) or 137Cs γ-rays vulnerable to possible bias from underascertainment of (about 0.8keV / µm) and that of 200 kVp X-rays (about cases. For lung cancer, the weighting scheme is reversed, 3.5keV / µm) makes it clear that the relative biological ef- and a weight of 0.7 is used for the absolute risk transport fectiveness (RBE) at low doses can differ appreciably for γ- estimate and a weight of 0.3 for the relative risk transport rays and X-rays. For actual risk estimates it is, therefore, estimate. This departure was made because of evidence that necessary to consider these differences in terms of the radio- the interaction of radiation and smoking in A-bomb survi- biological findings, the dosimetric and microdosimetric pa- vors is additive (Pierce and others 2003). Although it is likely rameters of radiation quality, and the radioepidemiologic that the correct transport model varies by cancer site, for evidence. sites other than breast, thyroid, and lung the committee As discussed in ICRP (2004) and in Chapters 1 and 3 of judged that current knowledge was insufficient to allow the this report, there is evidence based on chromosomal aberra- approach to vary by cancer site. tion data and on biophysical considerations that, at low Transport has not generally been considered an important doses, the effectiveness per unit absorbed dose of standard source of uncertainty for estimating leukemia risks. The X-rays may be about twice that of high-energy photons. The committee has nevertheless developed both ERR and EAR effectiveness of lower-energy X-rays may be even higher. models for leukemia and obtained estimates based on both How this translates into risks of late effects in man is an relative and absolute risk transport. As shown later, the EAR open question. Estimates based on studies of persons ex- model leads to substantially lower lifetime risks than the posed to X-rays for medical reasons tend to be lower than ERR model (Table 12-7). Since there is no reason to suspect those based on A-bomb survivors (Little 2001; ICRP 2004), underascertainment of leukemia deaths, apparently this but a number of other differences may confound these com- comes about because baseline risks in the LSS cohort are parisons. In addition, doses in many medically exposed different than those for a modern U.S. population. Because populations are higher than those at which the energy of the of the small number of deaths in the early period among radiation (based on biophysical considerations) would be those who were unexposed, it might be thought that the un- expected to be important. certainty in the estimated ERR/Sv would be large; however Because of the lack of adequate epidemiologic data on in fact, it is only slightly larger than that for the EAR model this issue, the committee makes no specific recommendation (Table 12-3). 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 Relative Effectiveness of X-Rays and γ-Rays purpose of estimating risks from low-dose X-ray exposure. Risk estimates in this report have been developed prima- rily from data on A-bomb survivors and are thus directly Relative Effectiveness of Internal Exposure relevant to exposure from high-energy photons. However, the report is concerned with low-LET radiation generally, Internal exposure through inhalation or ingestion is also which includes γ-rays, X-rays, and fast electrons. There is no of interest. For example, internal exposure to 131I, strontium, principal difference between the action of these different and cesium may occur from atmospheric fallout from nuclear types of radiation, because they all work through fast elec- weapons testing. Epidemiologic studies involving these ex- trons that either are incident on the body or are released posures are reviewed in Chapter 9. Studies of thyroid cancer within the body by electrons or photons. The various types in relation to 131I include those of persons exposed to atmo- of low-LET radiation vary in their ability to penetrate to spheric fallout in Utah, to releases from the Hanford plant, greater depths in the body. The more penetrating, high-en- and as a result of the Chernobyl accident. There are also ergy radiation tends to produce electrons with linear energy studies of persons exposed to cesium and strontium from transfer less than 1 keV / µm, while the softer X-rays release releases from the Mayak nuclear facility in Russia into the slower electrons with linear energy transfer up to several Techa River. To date, these studies are not adequate to quan- kiloelectronvolts per micrometer. tify carcinogenic risk reliably as a function of dose. Although With regard to setting dose limits in radiation protection, there are no strong reasons to think that the dose-response γ-rays, fast electrons, and X-rays are all given the radiation from internal low-LET exposure would differ from that for weighting factor 1; that is, an absorbed dose of 1 Gy of these external exposure, there is additional uncertainty in applying radiations is taken to be equal to the effective dose 1 Sv the BEIR VII risk models to estimate risks from internal (ICRP 1991), which expresses the fact that the differences of exposure.

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ESTIMATING CANCER RISK 277 Method of Calculating Lifetime Risks 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) Several measures of lifetime risk have been used to ex- represents sex- and age-specific 1995–1999 U.S. cancer in- press radiation risks and are discussed by Vaeth and Pierce cidence rates from Surveillance Epidemiology, and End Re- (1990), Thomas and colleagues (1992), UNSCEAR (2000b), sults (SEER) registries, whereas the λMc (a) are sex- and and Kellerer and colleagues (2001). The BEIR VII commit- age-specific 1995–1999 U.S. cancer mortality rates (http:// tee has chosen to use what Kellerer and coworkers refer to as seer.cancer.gov/csr/1975_2000), where c designates the can- the lifetime attributable risk (LAR), which was earlier called cer site or category. These rates were available for each 5- the risk of untimely death by Vaeth and Pierce (1990). The year age group with linear interpolation used to develop es- LAR is an approximation of the risk of exposure-induced timates for single years of age. With the exception of the death (REID), the measure used by UNSCEAR (2000b), category “all solid cancers,” the same ERR models were used which estimates the probability that an individual will die to estimate both cancer incidence and mortality. from (or develop) cancer associated with the exposure. Al- Lifetime risk estimates using absolute risk transport were though the nomenclature is recent, the LAR was used by the based on EAR models (see “Transport of Risks from a Japa- BEIR III committee (1980b) and by the EPA (1994). nese to a U.S. Population”). For estimating cancer incidence, The LAR and the REID both differ from the excess life- M(D, e, a) is taken to be the EAR(D, e, a) based on the time risk (ELR) used by the BEIR V committee in that the models shown in Tables 12-1, 12-2, and 12-3. For estimat- former include deaths or incident cases of cancer that would ing mortality from all solid cancers, the EAR mortality model have occurred without exposure but occurred at a younger shown in Table 12-1 was used directly. For estimating site- age because of the exposure. As noted by Thomas and col- specific cancer mortality, it was necessary to adjust the leagues (1992) and earlier by Pierce and Vaeth (1989), the EAR(D, e, a) from Tables 12-2 and 12-3 by multiplying by ratio of ELR to REID is approximately 1 – Qc where Qc is λMc (a) / λIc (a), the ratio of the sex- and age-specific mortal- the lifetime risk of dying from the cause of interest. For ex- ity and incidence rates for the U.S. population. That is, for ample, the ELR for all cancer mortality would be about 20% site-specific mortality, lower than the REID. The LAR differs from the REID in that the survival function used in calculating the LAR does not M(D, e, a) = EAR(D, e, a) λMc (a) / λIc (s, a). take account of persons dying of radiation-induced disease, Leukemia merits special comment. The approach for de- thus simplifying the computations. This difference may be riving incidence and mortality estimates based on relative important for estimating risks at higher doses (1+ Sv), but and absolute risk transport is the same for leukemia as for not at the low doses of interest for this report. Kellerer and other site-specific cancers, despite the fact that leukemia colleagues show that the REID and the LAR are nearly iden- models were developed from LSS mortality data rather than tical at low doses and discuss other aspects of the LAR com- incidence data as for other sites. This is because LSS leuke- pared to the REID. mia data were obtained at a time when this disease was nearly The LAR for a person exposed to dose D at age e is calcu- always rapidly fatal, so that estimates of leukemia mortality lated as follows: should closely approximate those for leukemia incidence. In LAR(D, e) = the last few decades, however, marked progress has been aM(D, e, a) S(a) / S(e), (12-4) made in treating leukemia, and the disease is not always fa- where the summation is from a = e + L to l00, where a de- tal. Thus, the committee has used the EAR model shown in notes attained age (years) and L is a risk-free latent period (L Table 12-3 to estimate leukemia incidence, but has adjusted = 5 for solid cancers; L = 2 for leukemia). The M(D, e, a) is the EAR(D, s, e, a) from Table 12-3 in the manner described the EAR, S(a) is the probability of surviving until age a, and above to obtain estimates of leukemia mortality. In all cases, S(a) / S(e) is the probability of surviving to age a conditional the U.S. leukemia baseline rates were for all leukemias ex- on survival to age e. All calculations are sex-specific; thus, cluding CLL. the dependence of all quantities on sex is suppressed. Models for leukemia differ from those for solid cancers The quantities S(a) were obtained from a 1999 unabridged in that risk is expressed as a function of age at exposure (e) life table for the U.S. population (Anderson and DeTurk and time since exposure (t) instead of age at exposure and 2002). Lifetime risk estimates using relative risk transport attained age (a). Since t = a – e, ERR(D, e, a) or EAR(D, e, were based on ERR models. For these calculations, a) is obtained by substituting a – e for t in the models pre- sented in Table 12-3. Note further that for the period 2–5 M(D, e, a) = ERR(D, e, a) λIc (a) 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, for cancer incidence, and M(D, e, a) = M(D, e, e + 5). The approach described above for obtaining estimates M(D, e, a) = ERR(D, e, a) λMc (a) based on absolute transport differs from that used by UNSCEAR (2000b) and NIH (2003), where M(D, e, a) for

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302 BEIR VII were more than eight times those for the 45–60 exposure age Based on the analyses of A-bomb survivor data described group (p = .02), while for the remaining solid cancers this above, the committee has selected the model shown in Equa- ratio was less than 2 and did not differ significantly from tion (12B-6) as its preferred model for estimating solid can- unity (p > .5). cer risks. However, several alternative choices, including the The increased ERR/Sv and EAR per 104 PY-Sv for the RERF model shown in Equation (12B-3), fitted the data oldest age-at-exposure group was one of the reasons the com- nearly as well and would also have been reasonable choices. mittee selected the BEIR VII model with no decline with Both ERR and EAR models are evaluated. Table 12B-4 exposure age after age 30 in preference to the RERF model shows the estimated parameters (with 95% confidence inter- with a decline throughout the entire range of exposure age. vals) for ERR and EAR models obtained from both inci- The committee notes particularly that stomach and liver can- dence and mortality data. With the ERR models, the effect cers, for which this effect was strongest, are far more preva- of exposure age is stronger for mortality than for incidence lent in Japan than in the United States. With the incidence data, while the effect of attained age is weaker. The two data, about 37% of the cancers in the solid cancer category EAR models show similar exposure age effects, but the rate that the committee analyzed were cancers of the stomach of increase with attained age is greater for the mortality data and liver; by contrast, SEER data for the United States (see than for the incidence data. Table 12-3) indicate that only about 3% of incident cancers The committee also evaluated mortality data on all solid are of these types. Furthermore, risks for stomach and liver cancers to compare the use of 5- and 10-year minimal latent cancers may be affected by infectious agents such as periods. This was done by fitting the BEIR VII ERR model, Helicobacter pylori for stomach cancer and the hepatitis vi- and estimating the ERR/Sv separately for the period 5–9 rus for liver cancer (Parsonnet and others 1994; Aromaa and years following exposure and for the period 10 or more years others 1996; Goldstone and others 1996). Infection rates following exposure. Although the estimate for the 5–9-year might differ by birth cohort (and thus exposure age), which period was not quite statistically significant with a two-sided could affect risks due to radiation in ways that are not cur- test (p = .10), there was no evidence that it differed from the rently understood. Although the reason for the relatively high estimate for the later follow-up period (p = .44). The com- ERR/Sv among those exposed at older ages is not fully mittee accordingly has used a minimal latent period of 5 understood the committee does not think that this effect is years in its calculations of lifetime risks. likely to generalize to a modern U.S. population. 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/Sv (95% CI) at Age 30 and Attained Age 60 Per-Decade Increase in Age No. of Cases at Exposure Over the Range Exponent of Attained ERR Models or Deaths Males (βM) Females (βF) 0–30 Yearsc (95% CI), γ Age (95% CI), η 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 per 104 PY-Sv (95% CI) EAR models 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 β 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 s 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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ESTIMATING CANCER RISK 303 Analyses of Incidence and Mortality Data on Site-Specific cers unless site-specific analyses indicated significant Solid Cancers departure from these estimates. Table 12B-5A shows the re- sults of fitting ERR site-specific models to the incidence Although the committee provides risk estimates for both data. Results are shown for a model in which all four of the cancer incidence and mortality, models for site-specific can- parameters βM, βF, γ, and η were estimated and are also cers were based mainly on cancer incidence data. This was shown for a model in which the parameters quantifying the done primarily because site-specific cancer incidence data modifying effects of age of exposure and attained age γ and are based on diagnostic information that is more detailed and η were set equal to the values obtained from analysis of the accurate than death certificate data and because, for several category all solid cancers excluding thyroid and non- sites, the number of incident cases is considerably larger than melanoma skin cancers; these values are referred to subse- the number of deaths. For cancers of the colon, breast, pros- quently as the “common values.” The final column gives the tate, and bladder, the number of cases in the LSS cohort is deviance difference between the two models and the result- more than double the number of deaths (Table 12B-1B). In ing p-value based on a two-degree-of-freedom test compar- addition, mortality data may be more subject than incidence ing the fits of the two models. This test does not take account data to changes over time brought about because of improved of uncertainty in the estimates of the common values of γ survival. Models developed from incidence data were how- and η. In addition, the committee fitted models in which just ever evaluated for consistency with mortality data. Since one of the parameters γ and η was fixed, with the other esti- there is little evidence that radiation-induced cancers are mated allowing a one-degree-of-freedom test for each of the more rapidly fatal than cancer that occurs for other reasons, parameters. ERR models based on incidence data can be used directly to The only sites with even modest evidence (p < .10) of estimate risks of cancer mortality. EAR models require ad- departure from the fixed values of γ and η were cancer of the justment as discussed in the chapter. uterus and the category “all other solid cancers.” For cancer Models for site-specific cancers were based on the BEIR of the uterus, the estimated ERR/Sv was very small and non- VII model indicated by Equation (12B-6). The committee’s significant so that it was not possible to obtain stable esti- approach to quantifying the parameters γ and η was to use mates of the modifying parameters; thus the common values the estimates obtained from analyzing incidence data on all were used. For other solid cancers, a test for the parameter η solid cancers excluding thyroid and nonmelanoma skin can- 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 Fixed Parameters: All Parameters Estimated γ = –0.30; η = –1.4 Deviance Differenceb Cancer Site No. of Cases βM βF γ η βM βF (p-value) 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 2969 0.27 0.45 Fixed at –2.8 0.003e (>0 .5) (alternative) –0.30 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). β and β are the ERR/Sv M F 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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304 BEIR VII shown for an alternative model with η estimated separately Table 12B-5C shows results of fitting EAR models to the for this category. cancer incidence data and is analogous to Table 12B-5A for Table 12B-5B shows results based on mortality data on the ERR models. There is clear evidence that common val- site-specific cancers. As in Table 12B-5A, columns 3–6 ues of the parameters γ and η are not appropriate for cancers show results with all four of the parameters βM, βF, γ, and η of lung, breast, and bladder. For all three of these sites, and estimated using data on that site alone. Columns 7 and 8 also for liver cancer (see below), alternative models in which show the results of testing the compatibility of these models η was estimated and γ was set at the common value (–0.41) with models developed from the incidence data with γ and η provided acceptable fits. fixed as indicated in columns 7 and 8 of Table 12B-5A. Col- For breast cancer, the committee fitted additional EAR umn 7 is based on analyses in which γ was set equal to –0.30 models with separate parameters for attained ages under 50 per decade and η was set equal to –1.4, and the parameters and over 50, similar to the model used by Preston and col- βM and βF were estimated, and thus tests whether the fixed leagues (2002a) in a pooled analysis of breast cancer inci- values of data γ and η are compatible with the mortality data. dence data from several cohorts including the LSS data. This Column 8 is based on analyses in which all four of the pa- model (labeled alternative 2) provided a significantly better rameters βM, βF, γ and η were set equal to the values esti- fit (p < .001) than did the model with a single parameter for mated from the incidence data (Table 12B-5A). The alterna- attained age. As discussed in this chapter, the committee’s tive model for “all other solid cancers,” based on the preferred models for breast cancer were based on pooled incidence data, was also evaluated. Because of difficulties in analyses by Preston and colleagues (2002a). However, it was fitting four-parameter models for cancers of the prostate and of interest to compare these results with those obtained from uterus, these sites are not shown in Table 12B-4B. Only for models based on the same approach as most other cancer colon cancer and for all other solid cancers was there a sug- sites. gestion (p < .10) that the models based on incidence data did Table 12B-5D shows results of fitting EAR models to the not fit the mortality data. Because there was no evidence mortality data. All but the last column are analogous to those against using the common values of η and γ for colon cancer in Table 12B-4C for the ERR models. The last column of based on the incidence data, the committee chose to use the Table 12B-5D shows the deviance differences for models common values for this site. For all other solid cancers, the based on the mortality data and the alternative models shown alternative model developed from the incidence data was in Table 12B-5C. Only for cancers of the liver, lung, breast, also more compatible with the mortality data, and this was and bladder was there evidence (p < .10) of departure from chosen as the preferred model. 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 All Parameters Estimated Fixed Parameters γ = –0.30; η = –1.4 Deviance Difference Deviance Difference Cancer Site No. of for Testing γ and for Testing βM, βF, γ, Deaths βM βF γ η βM βF ηb (p-value) 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 2,211 0.24 0.30 –0.68 –1.7 0.35 0.53 5.1 (0.079) 5.1 (0.28) cancers All other solid Fixed at Fixed at 0.32 0.44 3.3 (0.20) 3.5 (0.48) cancer –0.30 –2.8 (alternative) 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). β and β are the ERR/Sv M F 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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ESTIMATING CANCER RISK 305 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 Fixed Parameters: All Parameters Estimated γ = –4.1; η = 2.8 Deviance Differenceb Cancer Site No. of Cases βM βF γ η βM βF (p-value) 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 4.1 0.3e (> 0.5) –0.41 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 5.2 2.0e (0.16) –0.41 Breast 847 — 5.6 –0.51 1.5 — 6.3 16.5 (<0.001) Breast (alternative 1) 847 — 6.1 Fixed at 1.3 0.42e (> 0.5) –0.41 Breast (alternative 2) 847 — 5.9 Fixed at 3.4, –13.9g (<0.001) –0.41 –2.4f 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 6.0 0.1e (>0.5) –0.41 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. β and β are the number M F 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 tained age, but do not address the possibility of common models. In fact, the alternative liver cancer model was devel- parameters for the overall level of the ERR or EAR (βM and oped because of the large attained age effect identified in the βF). Because at least some of the variation among cancer mortality data. In general, the numbers of excess deaths per sites in these estimated parameters is due to sampling varia- 104 PY-Sv would be expected to be less than the numbers of tion, one might consider using common parameters for sites excess cases; thus, it was not sensible to evaluate the com- where there is no evidence of statistical differences. The patibility of the estimated βM and βF as was done for the committee chose not to use such an approach because it ERR models. However, for sites common to both sexes, the seems likely that there are true differences among the sites committee tested whether or not the ratio βF / βM estimated and because it was considered desirable to use site-specific from the mortality data was compatible with that estimated data to reflect the uncertainty in site-specific estimates. A from the incidence data (with the latter treated as a fixed promising approach for the future is to use methods that draw value). The p-values for the sites tested, based on a single- both on data for individual sites and on data for the com- degree-of-freedom test, were as follows: stomach (p = .19), bined category of all solid cancers. With this approach, the colon (p = .35), liver (p > .5), lung (p = .28), and all other variance of the site-specific estimate and the degree of de- solid cancers (p > .5). viation from the all-solid-cancer estimate are considered in The analyses of site-specific cancer presented in the last developing site-specific estimates that draw both on data for few paragraphs address the use of common parameters to the specific individual site and on data for all solid cancers. quantify the modifying effects of age at exposure and at- The National Research Council (2000) gives a simple il-

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306 BEIR VII 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 All Parameters Estimated Fixed Parameters: γ = –4.1; η = 2.8 Deviance Differenceb Cancer Site No. of Deaths βM βF γ η βM βF (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). β and β are the number of excess M F 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 mortality from site-specific data were the better diagnostic DerSimonian and Laird (1986) for estimating site-specific quality and the larger number of cases for several cancer excess relative risks for the purpose of developing radio- sites. These considerations do not apply when evaluating epidemiologic tables. risks for the broad category of all solid cancers. In addition, The committee’s preferred models for estimating site-spe- the mix of cancers is different for incidence and mortality cific cancer incidence and mortality are summarized in Table data so that one might expect greater differences than for 12-2. With the exception of the category of all other solid site-specific data as evidenced from the parameter estimates cancers, the ERR models are based on common values of the shown in Table 12B-4. Nevertheless, the committee con- parameters γ and η that quantify the modifying effects of age ducted analyses of the solid cancer mortality data with pa- at exposure and attained age. For the EAR models, the pre- rameters set equal to the estimates obtained from the inci- ferred models are based on site-specific estimates of η for dence data (as in columns 7 and 8 of Tables 12B-5B and cancers of the liver, lung, and bladder; for the remaining 12B-5D). With the solid cancer ERR model, a joint test of γ sites (other than breast), common values of γ and η were = –0.30 per decade and η = –1.4 (the values from the inci- used. For breast and thyroid cancers, models developed by dence data) resulted in a p-value of .06. However, there was Preston and colleagues (2002a) and by Ron and coworkers no evidence of further differences when main effects param- (1995a) are used as discussed in this chapter. The EAR coef- eters βM and βF were set equal to those for the incidence data ficients βM and βF shown in Table 12-2 can be used directly (βM = 0.33; βF = 0.57). only for cancer incidence and must be adjusted as described With EAR models, the estimated main effects (βM and in this chapter for cancer mortality. βF) based on the incidence data were about twice those based As stated earlier, the committee’s models for mortality on mortality data, reflecting the fact that not all cancers are from all solid cancers were based on mortality data. An al- fatal. The estimates of γ, the parameter quantifying the ef- ternative might have been to use incidence data for this pur- fects of age at exposure, were similar, whereas the increase pose as was done for site-specific cancers. However, the two with attained age (quantified by η) was stronger for the mor- main reasons for using incidence data for estimating tality data than for the incidence data. When mortality data

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ESTIMATING CANCER RISK 307 were analyzed with the parameters γ and η set equal to the Although the committee could have used the RERF or the values estimated from incidence data, the joint test resulted UNSCEAR model, it was judged desirable to develop alter- in a p-value of .041; the evidence for differences came about native models with the EAR and ERR expressed as continu- mainly from differences in the attained age parameter η (p = ous functions of age at exposure and without dependence of .047) with little evidence of differences in the exposure age the modifying effect of time since exposure on sex (as in the parameter γ (p > .5). 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 leuke- Analyses of Data on Leukemia mia rates, and evaluated models of the following form: The committee’s model for estimating leukemia risks is based on analyses of LSS leukemia mortality data for the ERR(D, s, e, t) or EAR(D, s, e, t) = period 1950–2000. Recent LSS leukemia incidence data βs(D + θD2) exp [γ f (e) + based on DS02 doses are not yet available. The quality of δ g(t) + φ f (e) g(t)], (12B-10) diagnostic information for non-type-specific leukemia mor- tality is thought to be much better than for most site-specific where e is age at exposure in years and t is time since expo- solid cancers. Although Preston and colleagues (1994) used sure in years. The functions of age at exposure evaluated incidence data to develop separate models for all types of were f(e) = e; f(e) = e* = (e – 30) / 10 for e < 30, and 0 for e leukemia—acute lymphocytic leukemia, acute myelogenous 0; and the RERF model in which f(e) was an indicator for leukemia, chronic myelogenous leukemia, and other leuke- one of the three categories: e < 20, 20 e < 40, and e 40. mias—in Hiroshima, the models in most past risk assess- The functions of time since exposure evaluated were g(t) = ments (NRC 1990; ICRP 1991; UNSCEAR 2000b) have log (t) and g(t) = t. The committee also fitted ERR models been based on leukemias of all types, and the BEIR VII com- for leukemia of the form shown in Equation (12B-10). mittee has followed the same practice. Data on medically Table 12B-6 shows the drop in deviance (compared to a exposed cohorts indicate that CLL is not likely to be induced model with no modification by e or t) for both the EAR and by radiation exposure (Boice and others 1987; Curtis and the ERR models. For comparisons among different models others 1994; Weiss and others 1995) but CLL is rare in of the same type (EAR or ERR), the greater the drop in devi- Japan. ance, the better is the fit. Because it is not meaningful to The committee began by considering the model used in a compare the drop in deviance for an EAR model to that for recent report on cancer mortality (Preston and others 2004). an ERR model, the total deviances are also shown. In gen- This model allows the EAR to vary as a linear-quadratic eral, models in which age at exposure was treated as a con- function of dose and allows both the overall level of risk and tinuous variable fitted the data nearly as well even though the dependence on time since exposure to vary by age at they have fewer parameters. Comparing the use of e and e* exposure: in models that are otherwise the same resulted in very simi- lar fits, with slightly better fits with e*. The use of log (t) RERF leukemia model: EAR(d, s, e, t) = resulted in better fits that the use of t. βs (D + θD2) exp [γe + δe log (t / 25)], (12B-9) For the EAR models using e* and log (t) (models 5–7), the interaction term [e* × log (t)] was clearly needed (p < where D is dose in sieverts; s is sex; e is an index for three .001), but the main effect for log (t) was not (p > .5). With age-at-exposure categories: 0–19, 20–39, and 40+ years with the main effect for log (t) in the model (model 5), the EAR γ20–39 fixed at 0; and t is time since exposure in years. The decreases with time since exposure for those exposed under parameter θ indicates the degree of curvature, which does about age 25, but increases slightly with time since exposure not depend on sex or age at exposure; βM and βF are the EAR at older exposure ages. Without the main effect (model 7), at exposure ages 20–39 and 25 years following exposure (ex- the EAR remains constant with time since exposure for those pressed as excess deaths per 104 PY-Sv for males and exposed over age 30 and decreases with time since exposure females, respectively); and δe indicates the dependence on for those exposed under age 30, with a stronger decrease at time since exposure for each of the three age groups. the youngest ages. The latter model is the committee’s pre- Parameter estimates for this model are given by Preston and ferred EAR model for estimating leukemia risks. With this colleagues (2002b). model, there was no need for an interaction of sex and time The committee also considered the UNSCEAR (2000) since exposure (p = .23), which was included in the UNSCEAR model, which was developed by Preston and colleagues (2000b) leukemia model. (2004) and based on A-bomb survivor leukemia incidence The committee’s preferred ERR leukemia model is model data for the period 1950–1987. This model, which is de- 5. With this model, the ERR decreases with time since expo- scribed in Annex 12A, and is similar to the RERF model sure regardless of age at exposure, although the decrease is above except that t – 25 replaces log (t / 25) and the param- not as strong at older ages. Again, there was no strong evi- eters δe are allowed to depend on sex. dence of a need for an interaction of sex and time since expo-

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308 BEIR VII 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 Difference in Deviance for This Model and Model with No Modification by e or t (degrees of freedom) Deviance Model Age at Exposure Time Since Exposure (t) or EAR ERR EAR ERR Number (e), f(e) Attained Age (a), g(t) or g(a) Model Model Model 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 (φ = 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 (φ = 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) + φ 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. 100 sure (p = .15). The total deviances for the preferred EAR and LAR = βD × exp[ γe* ] ∑ exp[ η log( a / 60)]B( a)S( a) / S(e), ˆ ˆ ˆ a=e+5 ERR leukemia models were nearly identical. Thus, the committee’s preferred models for the EAR and (12C-1) the ERR are as follows, with δ = 0 for the EAR model: where e* = e – 30 if e (exposure age) is less than 30 years BEIR VII leukemia model: EAR(d, s, e, t) or and 0 otherwise; B(a) is the age-specific baseline rate at age ERR(d, s, e, t) = βs(D + θD2) exp [γe* + a for the cancer of interest; S(a) is the probability of survival δ log (t / 25) + φ e* log (t / 25)]. (12B-11) (in the 1999 U.S. population) to age a; and the Greek letters with hats represent the estimated coefficients in the excess The parameter estimates for the committee’s preferred relative risk model. The logarithm of Equation (12C-1) gives leukemia models are listed in Table 12-3 in the main chap- ˆ log( LAR) = log( D) + β* + γe* + ˆ ter. Figure 12-2 shows both the ERR and the EAR as a func- tion of time since exposure for exposure ages of 10, 20, and  100  log  ∑ exp[ η log( a / 60)]B( a)S( a) / S(e),, , ˆ 30+ years. The ERR model is similar to that used for all a = e + 5  leukemia by NIH (2003), although its leukemia model was based on e instead of e*, and on t instead of log (t), and did ˆ ˆ where β* = log(β). not allow for the dependence of the ERR on sex. Although The result of a first-order Taylor’s approximation about there was no indication that the ERR depended on sex, this η = η is ˆ was included for compatibility with models for site-specific solid cancers. ˆ log( LAR) ≈ log( D) + β* + γe* + ˆ  100  ANNEX 12C: DETAILS OF LAR UNCERTAINTY log  ∑ exp[ η log( a / 60)]B( a)S( a) / S(e) + ANALYSIS a = e + 5  100 Uncertainty Due to Sampling Variability ∑ exp[η log(a / 60)][ B(a)S(a) / S(e)]log(a / 60) a=e+5 100 The approximate variance of the estimated LAR due to the uncertainty in LSS estimated linear models can be de- ∑ exp[η log(a / 60)][ B(a)S(a) / S(e)] a=e+5 rived with the “delta method” (Feinberg 1988). As an ex- Tˆ ample, the estimated LAR based on relative risk transport so that the estimate of log (LAR) is a constant plus A θ, for solid cancer (for males or females) is calculated as where

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ESTIMATING CANCER RISK 309 adjustment to the single estimate of LAR, due to the pre- AT = sumed curvature in the dose-response, is obtained by divid-  100  ing this combined estimate by the presumed DDREF. A  ∑ exp[η log(a / 60)][ B(a)S(a) / S(e)]log(a / 60)  ˆ value of 1.5 was used for DDREF, which is an estimate of a=e+5 1, e*, 100  , the median of the Bayesian posterior probability distribution    ∑ exp[ η log( a / 60)][ B( a)S( a) / S(e)] ˆ    for DDREF, as discussed in the chapter. a=e+5 The uncertainty analysis here arrives at an approximate ˆT ˆ* ˆ ˆ and θ = (β , γ , η) . Then var[log(LAR)] may be estimated by variance for log (LAR), emanating from the individual vari- ances in LARERR and LAREAR (sampling variability from var[log(LAR)] = ATVA, (12-C2) the LSS risk model estimation, as discussed above), p (un- certainty in the knowledge of whether absolute risk or ex- where V is the estimated variance-covariance matrix of cess risk is transportable from Japanese A-bomb survivors ˆ ˆ ˆ (β*, γ , η), which is available as a component of the output to the U.S. population), and DDREF (uncertainty in estimat- from the computer program used to estimate the risk models. ing dose-response curvature from animal studies and uncer- The standard error of the log of estimated LAR is the square tainty with which the animal curvature applies to humans). root of the estimate of this variance. A 95% confidence in- To accomplish this, the model above is written more for- terval for log (LAR) is obtained as the estimate of log (LAR) mally as depending on four sets of unknown quantities: θR, plus and minus 1.96 times the standard error, and the confi- the parameters in the relevant ERR model; θA, the param- dence interval for LAR is obtained by taking the antiloga- eters in the EAR model; IR, an indicator variable that takes rithm of these end points. on the value 1 if the ERR model is the correct one for trans- The LAR based on absolute risk transport is port and 0 if the EAR model is the correct one; and θDDREF, 100 the unknown DDREF. The LAR associated with an acute LAR = βD × exp[ γe* ] ∑ exp[ η log( a / 60)]S( a) / S(e). ˆ ˆ ˆ radiation dose D at age e may be written as a=e+5 The issues and computations involve only slight modifica- LAR(e, D; θ R , θ A , I R , θ DDREF ) = tions of what has been described above. For scenarios that LAR R (e, D; θ R ) I R LAR A (e, D; θ A )1− I R / θ DDREF , involve a weighted average of different ages at exposure and for relative and absolute risk models for leukemia, which where LARR(e, D; θR) and LARA(e, D; θA) are the LARs involve quadratic-in-dose terms and different modifiers in- based on EAR and ERR transport, prior to DDREF adjust- cluding interactions, the computations differ but the ideas ment, and θDDREF is the correct DDREF value. Notice that if behind the delta method calculations are the same as above. the ERR model is the correct one for transport, then IR is 0 The confidence intervals in Tables 12-5A and 12-5B for and the LAR expression above reduces to LARA(e, D; θA / risks of cancer incidence and mortality at specific sites were θDDREF. Similarly, if the relative risk model is the correct based on the same procedure as above, but without account- one for transport, then the LAR expression reduces to the ing for the uncertainty in γ and η, since, with a few excep- excess relative risk LAR with DDREF adjustment. tions, these quantities were fixed at their values estimated The estimated LAR can be expressed by the same from all solid cancers combined (although the values of γ formula, but with the known parameters replaced by their and η used in site-specific models were compatible with data ˆ ˆ ˆ ˆ ˆ estimators: LAR(e, D; θ R , θ A , I E , θ DDREF ), where θ R and are for each site, the fixed values cannot be considered unbiased parameter estimates for the ERR and EAR models; I R is the ˆ estimates of the correct values). For most sites, uncertainty (subjective) probability that the relative risk model is the in the estimated coefficient of dose (β) is quite large and is ˆ correct one for transport; and θ DDREF is the (subjective) esti- expected to dominate the uncertainty in the estimated LAR. mate of DDREF. Every quantity with a “hat” on it is an uncertain estimator and has a variance associated with it. Combining Several Sources of Uncertainty The variance in the estimated LAR, consequently, is that which is propagated by the variances of these estimators. A single estimate of LAR is obtained from estimates Statistically, it is best to consider this propagation on the based on ERR and EAR transport models as a combination log scale: on the log scale: log (LAR) = [p (log (LARERR) + (1 – p) log ˆ ˆ ˆ ˆ ˆ log LAR(e, D; θ R , θ A , I R , θ DDREF ) = log LAR A (e, D; θ A ) + (LAREAR)], where LARERR and LAREAR are the estimates based on ERR and EAR transport, respectively, and p is a ˆ ˆ ˆ ˆ I A log[LAR R (e, D; θ R ) / LAR A (e, D; θ A )] − log θ DDREF . number between 0 and 1, reflecting the relative strength of belief in the two transport models. For most cancers, a value With the simplifying approximation that the “hats” can of .7 was taken for p. Exceptions were lung cancer, where ˆ ˆ be dropped from θ A and θ R in the middle term and the p = .3, and thyroid cancer, where only an ERR model devel- assumption that the uncertainties due to risk model estima- oped from data on Caucasian women was available. A further tion, subjective assessment of DDREF, and subjective as-

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310 BEIR VII sessment of transport model are independent of one another, ANNEX 12D: ADDITIONAL EXAMPLES OF LIFETIME the variance of the log of the estimated LAR is the sum of RISK ESTIMATES BASED ON BEIR VII PREFERRED three pieces: MODELS ˆ ˆ ˆ ˆ var[log LAR(e, D; θ A , θ R , I A , θ DDREF )] = Tables 12D-1 and 12D-2 show lifetime risk estimates for cancer incidence and mortality resulting from a single dose ˆ ˆ var[log LAR A (e, D; θ A ) + {log[LAR R (e, D; θ R ) / of 0.1 Gy at several specific ages. Estimates are shown for ˆ ˆ ˆ LAR A (e, D; θ A )]}2 var( I R ) + var(log θ DDREF ), all cancer, leukemia, all solid cancer, and cancer of several specific sites. Table 12D-3 shows analogous lifetime risk which are due, respectively, to the variability in the param- estimates for exposure to 1 mGy per year throughout life eter estimators in the EAR model, the uncertainty in the and to 10 mGy per year from ages 18 to 65. The examples transport model, and the uncertainty in the DDREF. It is a below illustrate how these tables may be used to obtain esti- fairly simple matter to estimate the variance of the log (LAR) mates for other exposure scenarios. For clarity of presenta- from these quantities. The variance of log (LAR), with a tion, the committee has generally shown more decimal places normal approximation to the sampling distribution of log than are justified. (LAR), leads directly to the coefficient of variation in Table 12-10 and the subjective confidence intervals in Tables 12-6 Example 1: A 10-year-old male receives a dose of 0.01 Gy and 12-7. (10 mGy) to the colon from a computed tomography (CT) The simplifying approximation mentioned above scan. Table 12D-1 shows the estimated lifetime risk of being ˆ amounts to assuming that log [ LAR A (e, D; θ A )] and log diagnosed with colon cancer for a male exposed to 0.1 Gy at ˆ )] have equal variances and a correlation of 1 [ LAR E (e, D; θ R age 10 as 241 per 100,000. The estimate for a male exposed or, in other words, that the variance of an average of these at 0.01 Gy is obtained as (0.01 / 0.1) × 241 = 24.1 per two quantities is the same as the variance of either one indi- 100,000 (about 1 in 4000). An estimate of the lifetime risk of vidually. The effect of inaccuracies in this assumption is ex- dying of colon cancer can also be obtained using Table 12D-2, pected to be small relative to the overall variability. Further- and is (0.01 / 0.1) × 117 = 11.7 per 100,000 (about 1 in 8500). more, because the first term in the variance expression represents the variance of the estimated LAR for either trans- Example 2: A 45-year-old woman receives a dose of port model, a weighted average of var[log LARR(e, D; θ R )] ˆ 0.001 Gy (1 mGy) to the breast from a mammogram. Table and var[log LARR(e, D; θ A ˆ )] is used to estimate it (with the 12D-1 shows an estimated lifetime risk of being diagnosed weight corresponding to the strength of belief in the relative with breast cancer for a female exposed to 0.1 Gy at age 40 risk transport model). as 141 per 100,000; the comparable estimate for exposure at The approach for estimating the variances of the sam- age 50 is 70 per 100,000. Using linear interpolation, the risk pling distributions of the estimated LARs is discussed in the from exposure to 0.1 Gy at age 45 is (141 + 70) / 2 = 105.5 ˆ first section of this annex. The variance of I R is taken to be per 100,000. The risk from exposure to 0.001 Gy is esti- Bernoulli variance. If, for example, the probability that the mated as (0.001 / 0.1) × 105.5 = 1.055 per 100,000. A rough relative risk transport is correct is taken to be .7, then the estimate of the risk from repeated annual mammograms ˆ variance of I R is .7 × 0.3. The Bernoulli variance tends to be could be obtained by adding estimates obtained from receiv- larger than a variance from a uniform distribution (for a ing a mammogram at ages 45, 46, 47, 48, and so forth. For model in which the correct transport is some completely un- most purposes, such an estimate will be reasonable, although known combination of relative and absolute risk) or from a this approach does not account for the possibility of dying beta distribution (for a model in which the correct transport before subsequent doses are received. is some unknown combination, but with more specific infor- mation about the possible combination). In the absence of Example 3: A female is exposed to high natural background any real knowledge about which of these is correct, the com- of 0.004 Gy (4 mGy) per year throughout life. Lifetime risk mittee has elected to use the more conservative approach, estimates for exposure to 0.001 Gy (1 mGy) per year which leads to somewhat wider confidence intervals. throughout life are shown in columns 2 (incidence) and 4 As discussed in Annex 11B, the DDREF analysis is nec- (mortality) of Table 12D-3. To obtain estimates for exposure essarily rough and the variance of the uncertainty distribu- to 4 mGy throughout life, these estimates must be multiplied tion described there is, if anything, misleadingly small. For by 4. For example, the estimated risk of a female being diag- the uncertainty analysis considered here, therefore, the vari- nosed with a solid cancer would be 3872 (4 × 968), per ance representing the uncertainty in log (DDREF) was in- 100,000 whereas the risk of being diagnosed with leukemia ˆ flated by 50%, using 0.09 as the variance of var(log θ DDREF), would be 204 (4 × 51) per 100,000, yielding a total risk of rather than the derived posterior variance 0.06. 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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ESTIMATING CANCER RISK 311 TABLE 12D-1 Lifetime Attributable Risk of Cancer Incidencea Age at Exposure (years) Cancer Site 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 Age at Exposure (years) Cancer Site 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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312 BEIR VII TABLE 12D-3 Lifetime Attributable Risk of Solid Cancer Incidence and Mortalitya Incidence: Mortality: Exposure Scenario Exposure Scenario 1 mGy 10 mGy 1 mGy 10 mGy per Year per Year per Year per Year throughout from Ages throughout from Ages Cancer site Life 18 to 65 Life 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.