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RISKS OF CANCERâALL SITES 161 4 Risks of CancerâAll Sites INTRODUCTION This report seeks to present the best description that can be provided at this time of the risk of cancer resulting from a specified dose of ionizing radiation. However, this description is bound to be inexact since the etiology of radiation- induced cancer is complex and incompletely understood. The risk depends on the particular kind of cancer; on the age and sex of the person exposed; on the magnitude of the dose to a particular organ; on the quality of the radiation; on the nature of the exposure, whether brief or chronic; on the presence of factors such as exposure to other carcinogens and promotors that may interact with the radiation; and on individual characteristics that cannot be specified but which may help to explain why some persons do and others do not develop cancers when similarly exposed. Although scientists understand some of the intra-cellular processes that are initiated or stimulated by radiation and which may eventually result in a cancer, the level of understanding is insufficient at present to enable prediction of the exact outcome in irradiated cells. Estimates of the risk of cancer, therefore, must rely largely on observations of the numbers of cancers of different kinds that arise in irradiated groups. Since nearly 20% of all deaths in the United States result from cancer, the estimated number of cancers attributable to low- level radiation is only a small fraction of the total number that occur. Furthermore, the cancers that result from radiation have no special features by which they can be distinguished from those produced by other causes. Thus the probability that cancer will result from a small dose can be estimated only by extrapolation from the

RISKS OF CANCERâALL SITES 162 increased rates of cancer that have been observed after larger doses, based on assumptions about the dose-incidence relationship at low doses. In this report it is estimated that if 100,000 persons of all ages received a whole body dose of 0.1 Gy (10 rad) of gamma radiation in a single brief exposure, about 800 extra cancer deaths would be expected to occur during their remaining lifetimes in addition to the nearly 20,000 cancer deaths that would occur in the absence of the radiation. Because the extra cancer deaths would be indistinguishable from those that occurred naturally, even to obtain a measure of how many extra deaths occurred is a difficult statistical estimation problem. Like all such problems, the answers obtained are subject to statistical errors which can be exacerbated by a limited sample size. The largest series of humans exposed to radiation for whom estimates of individual doses are available consists of the populations of Hiroshima and Nagasaki who were exposed to atomic bomb detonations in 1945. There were 75,991 A-bomb survivors in the two cities for whom dose estimates are available and who have been traced through 1985 to learn the health effects of exposure (Sh87). But 34,272 of those survivors were so far from the hypocenters that their radiation doses were negligibleâless than 0.005 Gy (0.5 rad)âand thus they serve as a comparison, or ''control" group, leaving 41,719 whose doses are estimated at 0.005 Gy or more. Of these, 3,435 died from some form of cancer between 1950 and 1985. This cohort is not only the largest available, but it has been followed through 1985, that is, for forty years after irradiation, and is the most important source of data for analysis in this report. Even so, there are large statistical uncertainties as to the number of cancer deaths that were induced by radiation and (relatively) even larger uncertainties in the number of radiation- related cancers of particular kinds. The Committee has taken special care to quantify these uncertainties to the extent possible. Nevertheless, the limitations of the data bases on which the Committee's risk estimates are based have conditioned the kinds of estimates that can be developed. Heretofore, cancer risk estimates for low-LET radiations have been made by BEIR committees on the basis of constant additive risk and constant relative risk models (NRC80), an approach followed also by UNSCEAR in its latest report (UN88). That is, after a minimum latent period, risks were assumed to be relatively independent of time after exposure. The continued follow up of the A- bomb survivors and persons in the ankylosing spondylitis study indicates that temporal variations in risk are too important to be ignored. Consequently, it is necessary to model, not only how the risk increases with dose, but also how it varies as a function of time for persons exposed at various ages. This puts a heavy burden on available data. Only the A-bomb survivor cohort contains persons of all ages at exposure. Those survivors who were young when exposed are just now

RISKS OF CANCERâALL SITES 163 entering the age range at which cancer becomes an appreciable cause of death in the general population. Consequently, the number of excess cancer deaths that have occurred among them to date is small, and estimates of how the radiation- induced excess changes over time for those exposed as children introduce a large uncertainty into any attempt to project lifetime risks for the population as a whole. Moreover, the estimated risk is largest for this age group, so that final results are sensitive to the way in which the risk from childhood exposures is accounted for in the risk model. Although the number of excess cases has increased as exposed groups have been followed for longer periods, the data are not strong when stratified into different dose, age, and time categories. Even though modern statistical methodologies facilitate the analysis of highly stratified data, the fact remains that the number of cases in a given dose, age, and time interval is small and often zero. In situations such as this, one cannot differentiate between various competing risk models because of large statistical uncertainties. This problem is particularly acute when using models which take into account time dependence, age at exposure, etc. and applying them to cancers at a specific site. Because of these limitations, it was not possible for the committee to provide risk estimates for cancers at all of the specific sites of interest. Rather, attention was focused on estimating the risk for leukemia, breast cancer, thyroid cancer, and cancers of the respiratory and digestive systems, where the numbers of excess cases are substantial. To obtain an estimate of the total risk of mortality from all cancers, the committee also modeled cancers other than those listed above as a group. While this approach limits the application of these results for calculating the probability of causation of cancers at specific sites, the Committee judges it is preferable to aggregating data over age and time on the basis of simple risk models that do not adequately reflect the observational data. In this respect, the report differs from that of the United Nations Scientific Committee on the Effects of Radiation (UN88), which presented two life-time risk estimates from fatal cancer at each of 10 individual organ sites, one estimate based on a simple additive risk model and the other based on a simple multiplicative risk model. MODEL FITTING Methods The Committee's estimates of cancer risks rely most heavily on data from the Life Span Study (LSS) of the Japanese atomic bomb survivors at Hiroshima and Nagasaki, although other studies also were used for estimation of incidence or mortality risks for specific sites. The cohorts

RISKS OF CANCERâALL SITES 164 from which these various data sets derive are described in Annex 4A to this chapter. Table 4-1 provides a summary of the various data sets that the committee used in developing its risk estimates. All of the data sets were provided in grouped form, consisting of the numbers of cases at each cancer site, the number of person-years, and mean dose. These data were stratified by sex and time-related variables, e.g., age at exposure. TABLE 4-1 Major Characteristics of the Data Sets Used for Model Fitting Study Reference Incidence Cancer Total Total Population or Sites Cases Person Mortality Years Atomic Sh87 Mortality All 5,936 2,185,335 bomb survivors To87 Incidence Breast 376 940,000 Ankylosing Da87 Mortality Leukemia 36 104,000 spondylitis patients All except 563 104,000 leukemia and colon Canadian Mi89 Mortality Breast 482 867,541 fluoroscopy patients Mass. Hr89 Mortality Breast 74 30,932 fluoroscopy N.Y. Sh86 Incidence Breast 115 45,000 postpartum mastitis Israel tinea Ro84 Incidence Thyroid 55 712,000 capitis Rochester Sh85 Incidence Thyroid 28 138,000 thymus The Japanese LSS data consisted of 8714 records, stratified by sex, city, ten exposure groups (based on the kerma at a survivors' location using DS86), and five-year intervals of attained age, age at exposure, and time since exposure. Most analyses used a reduced data set of 3399 records obtained by collapsing over attained age. As outlined in Annex 4B, where the new dosimetry system (DS86) for A-bomb survivors is discussed, survivors exposures are stratified into ten groups and organ doses calculated by multiplying the neutron and gamma kermas for each stratum by city-specific and age-specific body transmission factors. As the estimate of the neutron component under DS86 is quite small and not very different between the two cities, there is virtually no prospect for estimating the RBE for neutrons from the available data. The committee's analyses are based on an assumed RBE of 20. This is a comparatively large value for high dose rate neutrons relative to high dose and dose rate gamma ray exposures, but is necessarily prudent in view of the degraded neutron spectrum at the survivors locations (see Annex 4B) and the potential low bias in the DS86 estimates of neutron kerma (Ro87). The analysis of the sensitivity of the results to this assumption in Annex 4D

RISKS OF CANCERâALL SITES 165 shows that the estimated risks for A-bomb survivors change insignificantly for a neutron RBE of 10 vis Ã vis 20. Under DS86, the dose response exhibited by A-bomb survivors levels off at high exposure levels. Therefore, to avoid errors in dose estimation at high doses, the records with organ dose equivalents greater than 4 Sv (based on RBE = 20) were eliminated from all analyses. The effect of excluding the observations at dose equivalents greater than 4 Sv is discussed in Annex 4D. Records of cancer mortality at attained ages greater than 75 years were omitted because of the lesser reliability of death certificate information in such cases, as outlined in Annex 4F. Except for breast and thyroid cancers, the committee did not find cancer from tumor registries of sufficient quality to justify model fitting and estimating the incidence of radiogenic cancer. However, the effects of radiation on cancer incidence can be estimated from mortality data (Ho89). Mortality among A-bomb survivors due to leukemia, cancer of the respiratory tract, cancer of the digestive tract, breast cancer, and as a group, all "other" cancers was analyzed in detail for the lifetime risk projections described below. In making this selection, the committee fitted models for ten sites or groups of sites, with the number of cancer deaths ranging from 2034 to 34. Clearly the larger groups produced more stable estimates of the model parameters. In developing estimates of lifetime risks, it was necessary for the Committee to weigh the consequences of model misspecification in using a single model for all non-leukemia cancers (since some of the sites clearly behaved quite differently across time) against the larger random errors if each of the subsite models were used. If one were not extrapolating in time, these two options would probably give quite similar answers, since larger relative variability of the estimates for the rarer sites would be offset by their lower overall risks. However, it was noticed that the lifetime risk estimates for some sites which had strong time-related modifiers seemed to be unreasonably large, and the reason was inferred to be the instability of the model in regions where the data were too sparse. Faced with this trade-off between precision and possible bias, the Committee opted for a compromise, treating only cancers of the respiratory tract, breast, digestive tract, and thyroid separately. The only other cohort study that provided data on all cancers was the ankylosing spondylitis series (ASS). Its data set was similarly structured, with two important differences. First, no dose information at the level of the individual was available, so the cohort was fitted as a single exposed group and risk coefficients were derived by dividing the excess estimates by the estimated mean dose, e.g., 1.92 Gy for whole body, 3.83 for bone marrow (Le88). Second, since there were no unexposed comparison subjects, national rates were used to derive an expected number of events in each cell of the cross tabulation. A total of 250 strata by sex and 2 1/2 year

RISKS OF CANCERâALL SITES 166 intervals of age at exposure and time after exposure were used in these analyses. Because the numbers of cases of cancer were relatively small, and because the risk of colon cancer may be related to ankylosing spondylitis itself, analyses were restricted to leukemia and, as a group, all other cancers except colon cancer. Statistical Methods The program AMFIT, described in Annex 4C, was used to fit various exposure-time-response models to these data sets. This program fits a general form of "Poisson regression" model, in which the observed number of events in each cell of the cross-tabulation is treated as a Poisson variate with parameters given by the predicted number of events under the model, the product of the person-years in that cell times the fitted rate. The specific models used can be formally expressed as follows. Let Î³Âº denote the age-specific background risk of death due to a specific cancer for an individual at a given age. This background risk will also depend upon the individual's sex and birth cohort (that is year of birth). For a given radiation dose equivalent d in sievert (Sv) we write the individual's age-specific cancer risk Î³(d) as Let f(d) represent a function of the dose d which in the committee's models is always a linear or linear-quadratic function, i.e., f(d) = Î±1d or f(d) = Î±2d + Î±3d2. In general, the excess risk function, g(Î²) will depend upon a number of parameters, for example, sex, attained age, age-at-exposure, and time-since- exposure. One can also write the age-specific risk as an additive risk model These models give similar results (see Annex 4D) as expected since the function g(Î²) is allowed to depend on age, time, etc. This would not be the case if g(Î²) were restricted to having a constant value other than for sex and age at exposure. The models were fitted using maximum likelihood, i.e., the values of the unknown parameters which maximize the probability of the observed number of cases (the "likelihood function") are taken as the best estimates, and, where applicable, confidence limits and significance tests are derived from standard large-sample statistical theory. It was expected that the form of the background term might vary considerably between populations at risk and is not of particular interest in terms of radiation risk. The committee chose not to model it, but rather

RISKS OF CANCERâALL SITES 167 to estimate the baseline rate nonparametrically by allowing for a large number of multiplicative rate parameters as is often done when fitting hazard models to ungrouped data (Co72, Ka80). Annex 4D provides some comparisons of the results with parametric and stratified background rates. Parametric models for breast cancer are described in Annex 4E. To summarize, each model considered can be described in terms of the "point" estimates of the various parameters, their respective standard errors and significance tests, and an overall "deviance" for the model as a whole (see Annex 4D). Because of the extreme sparseness of the data, comparison of deviance to its degrees of freedom should not be used as a test of fit of the model. However, differences in deviance between nested alternative models (pairs of models for which all terms in one model are included in the other) have an asymptotic chi squared distribution with degrees of freedom equal to the difference in the degrees of freedom between the models being compared. Therefore, this test can be used to assess the improvement in fit as a result of adding terms to the dose response function. This test was used repeatedly by the committee to minimize potential over-specification of the risk models. Annex 4D provides some comparisons of the many alternative models that were considered. Approximate confidence limits on parameter estimates can be constructed in the usual way by adding and subtracting the standard error times 1.65 (for 90% confidence) or 1.96 (for 95% confidence). However, in cases where the committee had reason to believe that the use of a normal distribution to estimate confidence limits is not valid, it reports "likelihood based" limits found by iteratively searching for the parameter values which led to a corresponding increase in the deviance (Co74). The Committee's Preferred Risk Models The committee's models for each site are discussed in the respective sections on site specific cancers in Chapter 5. Only a brief summary and the equations for dose response are presented here. Leukemia (ICD 204-207): The final model for leukemia is a relative risk model with terms for dose, dose squared, age at exposure, time after exposure, and interaction effects. A minimum latency of 2 years is assumed. There is a distinct difference between the risks exhibited by individuals exposed before age 20 and those exposed later in life. Within these two groups, there does not appear to be any effect of age at exposure but simply a different time pattern within each group. A simple step function with two steps fit both groups rather well. As indicated in Chapter 5, splines can be used to smooth these transitions when desired (e.g., in the calculation of probability of causation).

RISKS OF CANCERâALL SITES 168 The leukemia model mathematically is as follows (see the general equation 4.1): where the indicator function I (T â¤ 15) is defined as 1 if T â¤ 15 and 0 if T > 15, T is years after exposure, and E is age at exposure. The estimated parameter values and their standard errors, in parentheses, are: The standard errors for the dose effect coefficients were estimated by means of the likelihood method mentioned above and are both imprecise and highly skewed (see Annex 4F). The Monte Carlo analysis of the statistical uncertainty in the risk estimates for leukemia, described below in the section on uncertainty in point estimates, provides a better measure of the precision. Cancers other than leukemia: In fitting the data for cancers other than breast cancer and leukemia, a 10-year minimum latency was assumed; this was done simply by excluding all the observations (cases and person-years) less than 10 years after exposure. As for leukemia, similar fits could be obtained with either additive or relative risk models, but with different modifying effects (see Annex 4D). As was the case for leukemia, relative risk models were more parsimonious or required weaker modifiers. The committee subdivided solid tumors into cancers of the respiratory tract, breast, digestive tract, and other sites as described in the 8th revision of the International Classification of Diseases (ICD) (ICD67). Respiratory cancer (ICD 160-163): The committee's preferred model is as follows: where T = years after exposure and I (S) = 1 if female, 0 if male with Î±1 = 0.636(0.291), Î²1 = â1.437(0.910), Î²2 = 0.711(0.610). Under the committee's model, the relative risk for this site decreases with time after exposure. The coefficient for time after exposure, â1.437,

RISKS OF CANCERâALL SITES 169 means that the relative risk will decrease by a factor of about 5 over the period of 10 to 30 years post-exposure. The committee notes that few data are available, as yet, on respiratory cancer among those exposed as children. Finally, the relative risk is 2 times higher for females (owing to their much lower baseline rates) than for males, although the observed excess risks are similar. The fit of a constant relative risk model to the data on respiratory cancer is not statistically different from that for the committee's preferred model. When testing departures from a constant relative risk model, the addition of a parameter for time after exposure resulted in the greatest improvement in describing the data. This finding is consistent with the decreasing relative risk observed in the Ankylosing Spondylitis study (Da87) which influenced the committee's choice of parameters. While the inclusion of a parameter for sex did not improve the model's fit to the data significantly, there was some improvement, and the committee felt that it was appropriate to include a parameter for sex. Although it had been used in other risk models for respiratory cancer, there was no improvement whatever when a term for age-at- exposure was added to the regression model. When in fact such a term was estimated, its value was sufficiently close to zero as to have no influence on the estimated risk. Breast cancer (ICD 174): The breast cancer models are based on a parallel analysis of several cohorts. The important modifying factors found were age at exposure and time after exposure. The dependence of risk on age at exposure is complex, doubtless being heavily influenced by the woman's hormonal and reproductive status at that time. Lacking any data on these biological variables, the committee found that the best fit was obtained with the use of an indicator variable for age-at-exposure less than 16, together with additional indicator or trend variables depending on the data set. Both incidence and mortality models were developed. Although these differ, the highest risks are seen in women under 15-20 years of age at exposure. Risks are very low in women exposed at ages greater than 40. This suggests that risks decrease with age at exposure. Finally, risks decrease with time after exposure in all age groups. These issues are discussed in some detail in Annex 4E and the section on breast cancer, in Chapter 5. The model for breast cancer age specific mortality (female only) is where E is age at exposure and T is years after exposure with Î±1 =

RISKS OF CANCERâALL SITES 170 1.220(0.610), Î²1 = 1.385(0.554), Î²2 = -0.104 (0.804), Î²3 = -2.212 (1.376), Î²4 = -0.0628 (0.0321). Digestive cancer (ICD 150-159): The most significant aspect of the LSS data is the greatly increased risk (factor of 7) for those exposed under the age of 30. Although the committee has no explanation for this observation, the LSS data strongly support this effect. There is no evidence of a significant change in the relative risk with time after exposure. The committee's preferred model is: where I (S) equals 1 for females and 0 for males and with E = age at exposure. The estimated parameter values are Î±1 = 0.809 (9.327), Î²1 = 0.553(0.462), Î²2 = -0.198(0.0628). Other cancers (ICD 140-209 less those listed above): This group of miscellaneous cancers contributes significantly to the total radiation-induced cancer burden. Finer subdivision of the group did not, however, provide sufficient cases for modeling individual substituent sites. When attempted, the models were quite unstable, resulting in risk estimates for which there was little confidence. The general group of "other cancers" was reasonably fit by a simple model with only a negative linear effect by age-at-exposure at ages greater than 10. There was no evidence of either an effect by sex or by time after exposure. The preferred model is where E = age at exposure and Î±1 = 1.220(0.519), Î²1 = -0.0464(0.0234). Nonleukemia: For risk estimation, the committee simply chose to sum the risks of the components of the nonleukemia cancer group (i.e. respiratory cancer, digestive cancer, etc.). Alternatively, modeling the risk for all nonleukemia cancers directly yielded models which are linear in dose with additional variables for sex and time. These models provided a significantly poorer fit than other reasonable models and also project greater estimated risks (see Annex 4D). Analysis of the ankylosing spondylitis study (ASS) data for all cancers other than leukemia and colon gave a somewhat different picture. Here

RISKS OF CANCERâALL SITES 171 the fit was significantly improved by the addition of linear and quadratic terms for time after exposure, so that the risk essentially decreases to zero after about 20 years post-exposure. Part of the difference between the LSS and ASS data may be due to differences in the proportions of cancers of different sites. The most common cancers in the ASS series are lung cancer and breast cancer, the frequency of which declined with time after exposure in both data sets. On the other hand, cancers of the digestive system were very common in the LSS and showed no variation with time after exposure. RISK ASSESSMENT Point Estimates of Lifetime Risk Methods: The committee used standard lifetable methods as outlined in Chapter 1. Vital Statistics of the United States 1980 was used as the source of baseline data on cancer mortality (PHS84). The fitted risk models described above were applied to a stationary population having United States death rates for 1979-81 (NCHS85) and lifetime risks calculated for the following patterns of exposure. â¢ Instantaneous exposure causing a dose equivalent to all body organs of 0.1Sv (10 rad of low-LET radiation), varying the age at exposure by 10-year intervals and taking the population-weighted average of the resulting estimates, weighted by the probability of surviving to a specified age in an exposed stationary population. â¢ Continuous lifetime exposure causing a dose equivalent in all body organs of 1 mSv (0.1 rad of low-LET radiation) per year. â¢ Continuous exposure from age 18 to age 65 causing a dose equivalent to all body organs of 10 mSv (1 rad of low-LET radiation) per year. Application to low dose rates: Since the risk models were derived primarily from data on acute exposures (a single instantaneous exposure in the case of the LSS data, or fractionated but still high dose rate exposures in the case of most of the medical exposures), the application of these models to continuous low dose-rate exposures requires consideration of the dose rate effectiveness factor (DREF), as discussed in Chapter 1. For linear-quadratic models, there is an implicit dose-rate effect, since the quadratic contribution vanishes at low doses and, presumably, low dose-rates leaving only the linear term which is generally taken to reflect one-hit kinetics. The magnitude of this reduction is expressed by the DREF values. For the leukemia data, a linear extrapolation indicates that the lifetime risks per unit bone marrow dose may be half as large for continuous low dose rate as for instantaneous high dose rate exposures. For most other cancers in the

TABLE 4-2 Excess Cancer Mortality Estimates and Their Statistical UncertaintyâLifetime Risks per 100,000 Exposed Personsa Male Female Total Nonleukemia b Leukemiac Total Nonleukemia Leukemia Single exposure to 0.1 Sv (10 rem) 770 660 110 810 730 80 90% confidence limitsd 540â1,240 420â1,040 50â280 630â1,160 550â1,020 30â190 Normal expectation 20,510 19,750 760 16,150 15,540 610 % of normal 3.7 3.3 15 5 4.7 14 Total years of life lost 12,000 14,500 Average years of life lost per excess death 16 18 Continuous lifetime exposure e to 1 mSv/y (0.1 remly) 520 450 70 600 540 60 90% confidence limitsd 410â980 320â830 20â260 500â930 430â800 20â200 RISKS OF CANCERâALL SITES Normal expectation 20,560 19,760 790 17,520 16,850 660 % of normal 2.5 2.3 8.9 3.4 3.2 8.6 Total years of life lost 8,100 10,500 Average years of life lost per excess death 16 18 172

Continuous exposure e to 0.01 Svly (1 remly) from age 18 2,880 2,480 400 3,070 2,760 310 until age 65 90% confidence limitsd 2,150-5,460 1,670â4,560 130â1,160 2,510â4,580 2,120â4,190 110â910 Normal expectation 20,910 20,140 780 17,710 17,050 650 % of normal 14 12 52 17 16 48 Total years of life lost 42,200 51,600 Average years of life lost per excess death 15 17 a Based on an equal dose to all organs and the committee's preferred risk modelsâestimates rounded to nearest 10. b Sum of respiratory, breast, digestive, and other cancers. c Estimates for leukemia contain an implicit dose rate reduction factor. d Additional sources of uncertainty are discussed in Annex 4F. RISKS OF CANCERâALL SITES e A dose rate reduction factor has not been applied to the risk estimates for solid cancers. 173

RISKS OF CANCERâALL SITES 174 LSS, the quadratic contribution is nearly zero, and the estimated DREFs are near unity. Nevertheless, the committee judged that some account should be taken of dose rate effects and in Chapter 1 suggests a range of dose rate reduction factors that may be applicable. It must be emphasized, however, that such reductions should be applied only to the non-leukemia risks, as the leukemia risks already contain an implicit DREF owing to the use of the linear- quadratic model. For this reason, the tables which follow report excess risks for leukemia and all other cancers separately even though the quadratic term for leukemia is numerically negligible at 0.1 Sv. Faced with a similar situation, the BEIR III Committee chose to estimate a DREF from the leukemia data and apply it to the nonleukemia data as a fixed constant. After considerable discussion, this committee concluded that it could not justify assuming the same dose-response model for all cancer sites and, therefore, fitted separate dose- response models, with no DREF. The method of lifetime excess risk estimation used in this report differs slightly from that used in BEIR III (NRC80) and UNSCEAR (UN77,UN88) reports. In this report, separate lifetime risks are estimated for exposed and unexposed populations, and the excess risk is simply the difference between the two lifetime risk estimates. Competing risks due to other radiogenic cancers are included in the population decrement. In the other reports, the differences in age-specific rates between exposed and unexposed populations were multiplied by the survival probabilities for an exposed population and summed. Because an exposed population will have smaller survival probabilities, the method used here produces lower excess risk estimates, which more correctly reflect the difference in the lifetime risk of cancer mortality. Vaeth and Pierce (Va89) have shown that the ratio of the two estimates is approximately the lifetime probability of not dying of cancer, or in this case, about 0.8. Results: Table 4-2 summarizes the estimates of lifetime risks for leukemia and all other cancers resulting from two continuous exposure situations (lifetime and ages 18-65) and a population-weighted instantaneous exposure to persons of all ages. These results were obtained using the committee's preferred relative risk models for each site and a lifetable analysis that accounts for all competing risks including those due to radiation-induced cancer. Stratification of these results by age at exposure and by cancer site, for the case of instantaneous exposure, is provided in Table 4-3. Results from alternative risk models are considered in Annex 4D to this chapter. Table 4-4 provides a comparison of the risk projections under the preferred relative risk models from this report and the relative and absolute risk models in the BEIR III report. Overall, the risk estimates in this report are consistently higher than in the BEIR III report. This is due, in part,

RISKS OF CANCERâALL SITES 175 to this Committee's use of a linear dose response model for cancers other than leukemia rather than a linear quadratic one with an implicit DREF of nearly 2.5, as was the case in the BEIR III Committee's report. However, there are several other reasons for the differences between the two sets of results. These include the new dosimetry for the LSS data (Annex 4B), the additional years of follow- up, and the changes in the structure of the fitted models. In their work on the comparison of T65D and DS86 risk estimates using linear dose response models, Preston and Pierce (Pr88) concluded that while the changes in leukemia risk estimates were largely attributable to changes in dose estimates, the other two factors were more important for solid cancers; so that only 35-40% of the increase in their risk estimates was due to the use of the DS86 dose estimates.

RISKS OF CANCERâALL SITES 176 TABLE 4-4 Comparison of Lifetime Excess Cancer Risk Estimates from the BEIR III and BEIR V Reports Continuous Lifetime Instantaneous Exposure, 0.1 Exposure, 1 mGy/y (deaths Gy (deaths per 100,000) per 100,000) Males Females Males Females Leukemia BEIR IIIa 15.9 12.1 27.4 18.6 BEIR V 70 60 110 80 Ratio BEIR V/ 4.4 5.0 4.0 4.3 BEIR III Nonleukemia BEIR III Additive risk 24.6 42.4 42.1 65.2 model Relative risk 92.9 118.5 192 213 model BEIR V 450 540 660 730 Ratio BEIR V/ 4.8â18.3 4.6â12.7 3.4â15.7 3.4â11.2 BEIR III a Based on Table V-16, page 203, and Table V-19, page 206 model for nonleukemia) (NAS80). The major differences between the two sets of estimates in Table 4-4 are for the BEIR III Committee's additive risk models. It is the opinion of this committee that the assumption of a constant additive excess risk is no longer tenable in the face of the data now available and that the risk estimates from this model provided in the BEIR III report are therefore too low. The estimates presented in this report are also higher than those based on a simple additive risk model in the latest UNSCEAR report (UN88) but are not quite as high as those based on the simple multiplicative risk model in that report. UNCERTAINTY IN POINT ESTIMATES OF LIFETIME RISK The total uncertainty in the Committee's risk models is discussed in Annex 4F. In this section, the discussion is largely limited to the statistical uncertainty in the risk estimates made with the Committee's preferred models. Lifetime risk projections are subject to three types of uncertainty. The first is simply random error owing to sampling variation in the fitted coefficients of the final models; this is thought to be the largest component of uncertainty and is expressed in terms of confidence intervals on the fitted model parameters and the estimated lifetime risks. Second, there is

RISKS OF CANCERâALL SITES FIGURE 4-1 Excess mortality due to solid cancers per 104 person Sv (million person rem). Results of 1,000 Monte Carlo simulations and lifetable analyses of the excess mortality from all solid cancers following an acute total body dose of 0.1 Sv. The populations at risk are 100,000 males and 100,000 females. The Committee's preferred models yield a point estimate for males of 660 excess deaths; for females, 730. In 50% of the trials, the excess mortality for males was between 590 and 820 deaths; for females, between 670 and 860 deaths. 177

RISKS OF CANCERâALL SITES 178 FIGURE 4-2 Excess leukemia fatalities per 104 person Sv (million person rem). Results of 1,000 Monte Carlo simulations and lifetable analyses of the excess mortality from leukemia following an acute total body dose of 0.1 Sv. The populations at risk are 100,000 males and 100,000 females. The point estimate for males is 111 excess deaths; for females, 82. In 50 percent of the trials the excess mortality for males was between 60 and 135 deaths; for females, between 55 and 115 deaths. EXCESS LEUKEMIA DEATHS per 104 PERSON Sv

RISKS OF CANCERâALL SITES 179

RISKS OF CANCERâALL SITES 180 uncertainty as to the correct form of the exposure-time-response model, since the true model could be misspecified in a number of ways. It is more difficult to assess this component of the uncertainty, but a sense of its importance can be obtained by considering the range of lifetime risks resulting from alternative well-fitting models as discussed in Annex 4D and 4F. In addition, there are various potential biases in the data themselves; while these cannot be quantified precisely, they are discussed in Annex 4F along with the Committee's judgment concerning their magnitude. Since the lifetime risk is a complex function of the parameters of the fitted models, it is not a simple matter to translate the standard errors in risk coefficients into uncertainties in lifetime risk. This overall uncertainty depends not just on the uncertainty in the coefficient of dose, but also on the uncertainty in the coefficients of the modifying factors and their correlations. Furthermore, the distributions of the estimates of the coefficients are often quite skewed, leading to skewness in the resulting distribution of lifetime risks. For these reasons, the Committee undertook an uncertainty analysis by means of Monte Carlo simulation. In this approach, parameter vectors for each cancer site were randomly sampled from multivariate normal distributions with means and covariant matrices given by their maximum likelihood estimates. Any components that showed marked skewness were adjusted by multiplying the deviations of the sampled value from their means by the ratio of the likelihood- based to asymptotic confidence intervals for the corresponding 90% upper or lower tail. Lifetable calculations of risk were repeated for each randomly selected set of parameters, and in this way a distribution of lifetime risk estimates was produced. Figure 4-1 presents results for each sex based on 1,000 Monte Carlo simulations and lifetable analyses of the excess mortality risk for all solid cancers following a 0.1 Sv acute total body dose to a stationary population. Figure 4-2 presents the same results for leukemia. These histograms give a good idea of the statistical uncertainty in the Committee's risk models. Table 4-2 summarizes the resulting 90% confidence limits due to statistical uncertainty on the lifetime risk estimates for each of three exposure patterns. The intervals are wide indicating sparseness of data. For the most part, risk estimates derived from the alternative models described in Annex 4D are within these confidence intervals. Not included in Table 4-2 are several additional sources of uncertainty external to model parameters that are discussed in Annex 4F. The effect of these external sources of uncertainty on the risk estimates is not as well quantified as the uncertainty due to sampling variation shown in Figures 4-1 and 4-2; however, they probably contribute comparable uncertainty. The Committee's analysis in Annex 4F indicates these external factors increase the confidence intervals due to sampling variation in Table 4-2 by about a factor of 1.4.

RISKS OF CANCERâALL SITES 181 Finally, it must be recognized that derivation of risk estimates for low doses and dose rates through the use of any type of risk model involves assumptions that remain to be validated. At low doses, a model dependent interpolation is involved between the spontaneous incidence and the incidence at the lowest doses for which data are available. Since the committee's preferred risk models are a linear function of dose, little uncertainty should be introduced on this account, but departure from linearity cannot be excluded at low doses below the range of observation. Such departures could be in the direction of either an increased or decreased risk. Moreover, epidemiologic data cannot rigorously exclude the existence of a threshold in the millisievert dose range. Thus the possibility that there may be no risks from exposures comparable to external natural background radiation cannot be ruled out. At such low doses and dose rates, it must be acknowledged that the lower limit of the range of uncertainty in the risk estimates extends to zero. REFERENCES Co72 Cox, D. R. 1972. Regresson models and lifetables (with discussion). J. R. Stat. Soc. B 34:187-200. Co74 Cox, D. R., and D. V. Hinkley. 1974. Theoretical Statistics. London: Chapman and Hall. Da87 Darby, S. C., R. Doll, S. K. Gill, and P. G. Smith. 1987. Long-term mortality after a single treatment course with X-rays in patients treated for ankylosing spondylitis. Br. J. Cancer 55:179-190. Ho89 Hoel, D. G., and G. E. Dinse, 1989. Using mortality data to estimate radiation effects on breast cancer incidence. In press. Environ. Health Perspectives. Hr89 Hrubec, Z., J. Boice, R. Monson, and M. Rosenstein. 1989. Breast cancer after multiple chest fluoroscopies: Second follow-up of Massachusetts women with tuberculosis. Cancer Res. 49:229-234. ICD67 Eighth Revision International Classification of Diseases, Vol. 1. Public Health Service Publication No. 1639, Washington, D.C. Government Printing Office. Ka80 Kalbfleisch J., and R. Prentice 1980. The Statistical Analysis of Failure Time Data, New York: John Wiley & Sons. Le88 Lewis, C. A., P. G. Smith, I. M. Stratton, S. C. Darby, and R. Doll. 1988. Estimated Radiation Doses to Different Organs Among Patients Treated for Ankylosing Spondylitis with a Single Course of X-rays. Br. J. Radiol. 61:212-220. Mi89 Miller, A., P. Dinner, G. Howe, G. Sherman, J. Lindsay, M. Yaffe, H. Risch, and D. Preston. 1989. Breast cancer mortality following irradiation in a cohort of Canadian Tuberculosis Patients. New England Journal Medicine (in press). NCHS85 U.S. Decennial Life Tables for 1979-1981, Vol 1 No. 1, 1985. DHHS publication (PHS) 85-1150-1, Hyattsville, Md.: National Center for Health Statistics. NRC80 National Research Council. 1980. Committee on the Biological Effects of Ionizing Radiations. The Effects on Populations of Exposure to Low Levels of Ionizing Radiation (BEIR III). Washington, D.C.: National Academy Press. Pp. 524.

RISKS OF CANCERâALL SITES 182 PHS84 Vital Statistics of the United States 1980, Public Health Service, Hyattsville, Md.: National Center for Health Statistics. Pr87 Preston, D. L., H. Kato, K. J. Kopecky, and S. Fujita. 1987. Life Span Study Report 10. Part 1. Cancer mortality among a-bomb survivors in Hiroshima and Nagasaki, 1950-82. Radiat. Res. 111:151-178. Pr88 Preston, D., and D. Pierce. 1988. The effect of changes in dosimetry on cancer mortality risk estimates in atomic bomb survivors. Radiat. Res. 114:437-466. Ro84 Ron, E., and B. Modan 1984. Thyroid and other neoplasms following childhood scalp irradiation Pp. 139-151 in Radiation Cancergenesic: Epidemiology and Biological Significance. J. D. Boice and J. F. Fraumeni, Jr., eds. New York: Raven Press. Sh85 Shore, R. E., E. Woodard, N. Hildreth, P. Dvoretsky, L. Hempelmann, and B. Pasternack. 1985. Thyroid tumors following thymus irradiation. J. Natl. Cancer Inst. 74:1177-1184. Sh87 Shimizu, Y., H. Kato, W. J. Schull, D. L. Preston, S. Fujita, and D. A. Pierce. 1987. Life Span Study Report 11, Part 1. Comparison of Risk Coefficients for Site-Specific Cancer Mortality Based on the DS86 and T65DR Shielded Kerma and Organ Doses. Technical Report RERF TR 12-87. Hiroshima Radiation Effects Research Foundation. Sh86 Shore, R., N. Hildreth, E. Woodward, P. Dvoretsky, L. Hempelmann, and B. Pasternack. 1986. Breast cancer among women given x-ray therapy for acute postpartum mastitis. J. Natl. Cancer Inst. 77:689-696. To87 Tokunaga, M., C. Land, T. Yamamoto, M. Asano, S. Tokuoka, H. Ezaki, and I. Nishimori. 1987. Incidence of female breast cancer among atomic bomb survivors, Hiroshima and Nagasaki, 1950-1985 Radiat. Res. 112:243-272. UN77 United Nations Scientific Committee on the Effects of Atomic Radiation (UNSCEAR). 1977. Sources and Effects of Ionizing Radiation. Report E. 77. IX. 1. New York: United Nations. Pp. 725. UN88 United Nations Scientific Committee on the Effects of Atomic Radiation. 1988. Sources, Effects, and Risks of Ionizing Radiations. U.N. Publication E.88.IX.7.647. New York: United Nations. Pp. 647. Va89 Vaeth, M., and D. Pierce. 1989. Calculating excess lifetime risk in relative risk models. Environ. Health Persect. (in press). ANNEX 4Aâ SUMMARY OF MAJOR EPIDEMIOLOGIC STUDIES USED IN BEIR V The Life Span Study of A-Bomb Survivors Cohort Source and Exposure A mortality study (Sh87) of 120,321 individuals resident in Hiroshima or Nagasaki in 1950 make up the cohort. Among these there are 91,228 individuals who were exposed at the time of the bombing. This cohort continues to be followed up with deaths routinely determined through the Japanese household registries where ascertainment is essentially complete. Mortality data for the cohort has been completed for the period 1950-1985. As discussed in Annex 4B, new dose estimates are now available for the A- bomb survivors of Hiroshima and Nagasaki. The main difference

RISKS OF CANCERâALL SITES 183 between the old and new dosimetry is that the estimated level of neutron kerma has been decreased by approximately an order of magnitude in Hiroshima and by a factor of two in Nagasaki. The result is that the neutrons are no longer a significant component of the dose in either of the two cities. Mean organ doses have been calculated for twelve organs. For most high dose survivors, these doses are determined on an individual basis which includes a consideration of local shielding and orientation. The number of survivors in the life span study with new dose estimates, stratified by the kerma at the location where they were exposed, is as follows: Kerma 0 0.01-0.05 0.06-0.09 0.10-0.99 1.00-1.99 2.00+ (Gray) Cohort 34,272 19,192 4,129 15,346 1,946 1,106 size Follow-up The subcohort of approximately 76,000 subjects for which there are new dose estimates represents over two million person-years-at-risk. A total of 5,936 cancer deaths have been observed in the subcohort through 1985 The number of deaths due to cancer at sites showing a statistically significant excess are listed below. Number of Cancer Deaths (Sh87) leukemia 202 colon 232 ovary 82 esophagus 176 multiple myeloma 36 bladder 133 stomach 2007 female breast 155 lung 638 Incidence data are also being gathered and studied, the most prominent being data on breast cancer (To87). Strengths and Limitations This is the most important single cohort for estimating cancer risk from gamma radiation. The population is large and there is a wide range of doses. With these data it is possible to make determinations of dose-response and the effects of modifying factors such as age and time on the major cancer sites. The data are, however, limited at the high doses by the uncertainty in the dose estimates for highly exposed individuals. With this in mind, analyses in this report are carried out using only individuals with estimated doses to internal organs of less than 4 Gy. The cohort of Japanese survivors is not a normal Japanese population, apart from their radiation exposures. Many young adult males were not present at the time of the bombing, but away in military service. It must be presumed that those who were still in the cities included persons whose

RISKS OF CANCERâALL SITES 184 physical condition barred them from active service. Children of both sexes and the elderly perished, in consequence of the bombing, at a greater rate than did young adults. While exact location and shielding situations played an important role in determining who survived and who did not, the possibility must be allowed for that the survivors were, in some sense, harder than those who did not. It has been hypothesized by Stewart (St84, St85, St88) that increased deaths, due to infections from suppressed immune function, resulted in a dose related survival-of-the-fittest plus permanent bone marrow damage at higher doses. The dose response for noncancer deaths does, in fact, have a U shaped behavior, as described by Stewart. However, there does not seem to be evidence of infectious disease; instead the lower mortality rates in the moderately exposed individuals result from lower rates of death from a variety of causes (Da85). It does not appear, at this point, that these differences in mortality contribute in any substantial way to cancer mortality risk estimates based upon data from this cohort. Ankylosing Spondylitis Source of Cohort and Exposure The cohort consists of 14,106 patients treated with radiotherapy to the spine for ankylosing spondylitis in 87 centers in the United Kingdom between 1935 and 1954. Of this cohort, 7,431 individuals contributed an average of only 3.5 years of follow-up before they received a second course of radiotherapy and were then excluded from the study. Because the radiotherapy treatment was aimed at the spine, a large fraction of the body received substantial doses of radiation. Dosimetry Individual dose estimates are not available for the whole cohort, but radiotherapy records have been extracted for a random sample of 1 in 15 and Monte Carlo methods used to estimate individual organ doses for 30 organs or regions of the body and 12 bone marrow sites (Le88). Comparison of the mean marrow dose with earlier estimates based on phantom dosimetry are in good agreement. Follow-up The mortality of the cohort has been monitored using searches in the National Health Service central registry for death certificates. Mortality has been reported to the end of 1982, at which point 727 cancer deaths and 104,146 person-years of follow-up had been observed (Da88). Results have

RISKS OF CANCERâALL SITES 185 been reported for a number of sites, but colon cancer has been excluded because of its suspected association with ankylosing spondylitis. Strengths and Limitations This is a large irradiated series with a substantial number of organs, including the bone marrow, receiving fairly high doses. The underlying population is likely to be genetically similar to that of the U.S. but the applicability to a general population of the results from such patients, who have a condition that affects several causes of mortality, remains an issue. Comparisons of the cohort to date have mainly been made with general population rates, though it should be noted that a follow-up of ankylosing spondylitis patients not treated with radiotherapy has indicated that the comparison to the general population is not likely to be biased by the presence of the disease (Sm77). Doses were largely unfractionated, and no individual doses for all cohort members are available. Only cancer mortality, and not cancer incidence data are available for the cohort. Study of Women Treated for Cancer of the Cervix Cohort Source and Exposure The cohort consists of approximately 150,000 women treated for cancer of the uterine cervix who were either registered in one of 19 population-based cancer registries or treated at one of 20 clinics in a number of countries. A substantial proportion of these women (approximately 70%) were treated with radium implants or external radiotherapy, which resulted in substantial radiation doses to a number of organs close to the cervix and moderate doses to organs located more distantly in the body. Dosimetry The original radiotherapy treatment records of the 4,188 women in the cohort who subsequently developed a second primary cancer were used to estimate individual organ doses for the organs of interest. Similar estimates were made for a control series consisting of 6,880 women who did not develop a second primary. Follow-up Follow-up of the cohort was carried out using the population-based cancer registries to identify second primaries occurring in the cohort. As indicated above, a total of 4,188 such cases have been identified, and their prior radiation experience has been compared to that of the 6,880

RISKS OF CANCERâALL SITES 186 age-matched controls in order to estimate the relative risk for the various second cancers. The results of this analysis have been reported (Bo88). Strengths and Limitations This is a very large follow-up study with a substantial number of cancers for a number of organs of interest. Substantial doses were received by a number of organs, and moderate doses by a number of others, and these doses have been estimated with a good deal of care on an individual patient basis. The choice of a case-control analysis in order to make such dose estimates computationally feasible, however, means that absolute risk estimates can be made only by imputation. The most serious limitation of this study arises from the fact that the subjects had all developed cancer of the cervix, with its many associated risk factors, particularly those relating to socioeconomic status. Although an internal control group has been used in the analysis, extrapolation of the results to the general population must be made with some caution. Canadian Fluoroscopy Study This cohort consists of 31,710 women, first treated for tuberculosis in Canadian sanatoria between 1930 and 1952. A substantial proportion of these women were exposed to multiple fluoroscopies in conjunction with artificial pneumothorax treatment for tuberculosis, and 8,380 (26.4%) received breast tissue doses of 10 rads or more. The maximum dose received was over 2000 rads. That part of the cohort which was treated in the province of Nova Scotia was generally treated in the anterior-posterior (AP) position, in contrast to the more usual PA orientation in the rest of Canada, and this sub-cohort was therefore exposed to particularly high doses to the breast. A similar number of men have also been included in this cohort, but to date, no analyses have been reported for the males. Dosimetry Individual breast tissue doses have been estimated for the 31,710 women. These estimates are based on a count of the number of fluoroscopies recorded in the medical records, interviews with a number of physicians using fluoroscopy during the relevant time period, and on phantom measurements and Monte Carlo simulations (Sh78). Although counts are based on individual records, the dose per fluoroscopy is an average figure which is a function only of the province where most exposures were received (Nova Scotia vs. the others), and the year the exposure was received (after 1945 or before). Doses to other organs have not been reported for this cohort.

RISKS OF CANCERâALL SITES 187 Follow-up The cohort has been monitored for mortality between 1950 and 1980 using computerized record linkage to the Canadian National Mortality Data Base. By 1980, 482 breast cancer deaths and 867,541 women years of follow-up had been observed. Analyses of these results have been reported (Mi88). No cancer incidence data have yet been obtained for this cohort. Strengths and Limitations This cohort has reported the largest number of breast cancer deaths observed to date in a single cohort, and the exposure is highly fractionated, and in a North American population. However, these subjects all had tuberculosis, and although comparisons are made internally within the cohort, extrapolations to the general population may require caution. Only organs in the direct beam (notably breast and lung) are likely to have received doses leading to any measurable increase in risk, and the averaging involved in the dose estimation procedure will inevitably lead to some misclassification of dose. To date, only cancer mortality and not incidence is available for this cohort. New York State Postpartum Mastitis Study Cohort Source and Exposure The cohort consists of 601 women treated with radiotherapy for postpartum acute mastitis in New York State during the 1940's and 1950's, together with 1,239 non-exposed women consisting of women with mastitis not treated by radiotherapy, and siblings of both groups of women with mastitis. Doses were received in a small number of series, with breast tissue dose ranging from 60 to about 1,400 rads. The age range at first exposure was limited, with few under age 20 or over age 40 at entry. Dosimetry Individual breast tissue doses have been estimated for all 601 women from the original radiotherapy records. Follow-up Follow-up to ascertain breast cancer incidence has been carried out using mailed questionnaires, and results for such incidence have been reported for up to 45 years of follow-up (Sh86). During this period 115 breast cancer cases were observed.

RISKS OF CANCERâALL SITES 188 Strengths and Limitations This is a fairly small cohort, with most exposure limited to the breasts. The exposure was largely unfractionated, and estimates of breast tissue dose are probably accurate. However, the interpretation of possible differences in response of breast tissue with an inflammatory condition and subject to the hormonal changes due to pregnancy compared to the response of breast tissue unaffected by these factors is not clear. Massachusetts Fluoroscopy Study Sample Source and Exposure The cohort consists of 1,742 women first treated between 1930 and 1956 in two Massachusetts sanatoria, one of which treated only those under the age of 17. Of these women, 1,044 were subjected to regular fluoroscopy in conjunction with treatment by artificial pneumothorax, and consequently received substantial doses of low-LET radiation to the breast. Dosimetry Individual breast tissue doses have been estimated from the original patient records, by interviews with physicians conducting the treatment during the time period of interest, measurements on fluoroscopes of the relevant vintage, and by Monte Carlo simulations (Bo78, Bo81). Follow-up The vital status of 97% of the cohort through 1980 has been determined from hospital records, death certificates, and mailed questionnaires (Hr88). A total of 74 breast cancer cases have been observed in this cohort, with a total accumulation of 30,932 women-years at risk. Advantages and Limitations The exposure in this study was highly fractionated, and the population is a U.S. one. Dosimetry has been carefully reconstructed and complete follow-up carried out. The major disadvantage of this cohort is its size, which is small, thus limiting the interpretation of results within subgroups of the cohort. Extrapolation of the results from a cohort with tuberculosis to the general population, however, requires cautious interpretation.

RISKS OF CANCERâALL SITES 189 References Bo78 Boice, J. D. Jr., M. Rosenstein, and D. E. Trout. 1978. Estimation of breast cancer doses and breast cancer risk associated with repeated fluoroscopic chest examinations of women with tuberculosis. Radiat. Res. 73:373-390. Bo81 Boice, J. D. Jr., R. R. Monson, and M. Rosenstein. 1981. Cancer mortality in women after repeated fluoroscopic examinations of the chest. J. Natl. Cancer Inst. 66:863-867. Bo88 Boice, J. D. Jr., G. Engholm, R. A. Kleinerman et al. 1988. Radiation dose and second cancer risk in patients treated for cancer of the cervix. Radiat. Res 116:3-55. Da85 Darby, S. C., R. Doll, and M. C. Pike. 1985. Detection of late effects of ionizing radiation: why deaths of a-bomb survivors are a valuable resource. Letters to the Editor. Int. J. Epidemiol. 14:637-638. Da88 Darby, S. G , R. Doll, and P. G. Smith. 1988. Paper 9. Trends in long term mortality in ankylosing spondylitis treated with a single course of x-rays. Health effects of low dose ionising radiation. BNES, London. DS86 US-Japan Joint Reassessment of Atomic Bomb Radiation Dosimetry in Hiroshima and Nagasaki, Dosimetry System 1986 (DS86), Final Report. Radiation Effects Research Foundation, Volume 1. Hr88 Hrubec, Z., J. D. Boice Jr., R. R. Monson, and M. Rosenstein. 1988. Breast cancer after multiple chest fluoroscopies: second follow-up of Massachusetts women with tuberculosis. Cancer Res. (in press). Le88 Lewis, C. A., P. G. Smith, I. M. Stratton, S. C. Darby, and R. Doll. 1988. Estimated radiation doses to different organs among patients treated for ankylosing spondylitis with a single course of x-rays. Br. J. Radiol. 61:212-220. Mi88 Miller, A. B., G. R. Howe, G. J. Sherman, J. P. Lindsay, and M. J. Yaffe. 1988. Breast cancer risk in relation to low-LET radiation: the Canadian study of cancer following multiple fluoroscopies. N. Engl. J. Med. (submitted). Sh78 Sherman, G. J., G. R. Howe, A. B. Miller, and M. Rosenstein. 1978. Organ dose per unit exposure resulting from fluoroscopy for artificial pneumothorax. Health Phys. 35:259-269. Sh87 Shimizu, Y., H. Kato, W. Schull, D. Preston, S. Fujita, and D. Pierce. 1987. Comparison of risk coefficients for site-specific cancer mortality based on the DS86 and T65DR shielded kerma and organ doses. Technical Report TR 12-87. Radiation Effects Research Foundation. Sh86 Shore, R. E., N. Hildreth, E. Woodard, P. Dvoretsky, L. Hempelmann, and B. Pasternack. 1986. Breast cancer among women given x-ray therapy for acute postpartum mastitis. JNOI 77(3):689-696. Sm77 Smith, P. G., R. Doll, and E. P. Radford. 1977. Cancer mortality among patients with ankylosing spondylitis not given x-ray therapy. Br. J. Radiol. 50:728. St84 Stewart, A. M., and G. W. Kneale. 1984. Non-cancer effects of exposure to a-bomb radiation. J. Epidemiol. Comm. Health 38:108-112. St85 Stewart, A. M. 1985. Detection of late effects of ionizing radiation: why deaths of a-bomb survivors are so misleading Int. J. Epidemiol. 14:52-56. St88 Stewart, A. M., and G. W. Kneale. 1988. A-bomb survivors as a source of cancer risk estimates: confirmation of suspected bias. Proceedings of the 14th Gray Conference. Radiat. Prot. Dosimetry. In Press. To87 Tokunaga, M., C. E. Land, T. Yamamoto, M. Asano, S. Tokuoka, H. Ezaki, and I. Nishimori. 1987. Incidence of female breast cancer among atomic bomb survivors, Hiroshima and Nagasaki, 1950-1980. Radiat. Res. 112:243-272.

RISKS OF CANCERâALL SITES 190 ANNEX 4Bâ CHANGES IN THE ESTIMATED DOSE FOR A- BOMB SURVIVORS The New Dosimetry, DS86 The analyses of radiation effects among the Japanese A-bomb survivors in this report make use of new dose estimates developed in a five-year study by Japanese and American scientists. This binational study resulted in a new dosimetry system, designated DS86, which is documented in two recent Radiation Effects Research Foundation (RERF) reports (RERF87, RERF88). The reassessment of A-bomb dosimetry consisted of a careful review of information on the number of fissions that occurred in the A-bomb explosions and detailed calculations of neutron and gamma ray transport through weapons materials and the intervening air. This was followed by Monte Carlo calculations of the radiation field within Japanese houses, which also take into account the shielding provided by neighboring houses, and finally, the organ doses received by survivors having various shielding circumstances, location, orientation, and size. The calculational program was supported by new measurements of gamma- ray kerma to roof tiles by means of thermal luminescence and a reevaluation of the measurements of neutron-induced radioactivity that were made after the bombings by Japanese scientists. The dose reassessment was reviewed by a National Research Council (NRC) panel which concluded that the new dose estimates are more accurate and more soundly based than those used previously, and that they should be used in the assessment of radiation risks (NRC87). Nevertheless, investigations to determine the precision of the estimated doses and to account for differences between measured and calculated thermal neutron influences are continuing. A Comparison of DS86 and T65D Doses estimated with DS86 differ from the tentative 1965 dosimetry (T65D) system estimates (Au77, Mi68) used by RERF before 1987 and by previous BEIR Committees (NRC72, NRC80). Before outlining these differences, it is necessary to identify the various ways dose estimates for the A- bomb survivors have been specified, as this can be a source of confusion when comparing results obtained with the new and older dosimetries. In RERF reports, particularly those on the Life Span Study, individual survivors are categorized in terms of the incident radiation, i.e., the kerma, at the location where a survivor was exposed. If a survivor was outside and not near buildings or other structures, the kerma at this location is the ''free field tissue kerma in air" (FIA kerma), but more often survivors were in houses or otherwise shielded. In such cases, the kerma is smaller than the FIA kerma at the same location.

RISKS OF CANCERâALL SITES 191 For risk estimation, the mean dose within a given organ is the governing dosimetric parameter. This organ dose is smaller than the kerma due to the self- shielding provided by the body itself. How much smaller depends on the location of a particular organ within the body and the orientation of the survivor in the radiation field. In this report, as in the BEIR III report, risk estimates are based on organ doses, not the kerma at a survivor's location. This is in contrast to RERF reports on the Life Span Study in which results are often reported in terms of kerma. Because neutrons have a larger effect per unit dose than gamma rays, the quantity dose equivalent is used to express the organ dose due to both radiations in combination. As indicated in Chapter 1, organ dose equivalents are calculated by multiplying the organ dose due to neutrons by an appropriate value of the neutron RBE and adding this product to the organ dose due to gamma radiation. Therefore, the difference between the new and old dosimetries, in terms of organ dose equivalent, also depends on what RBE value is assigned to neutrons. This point is particularly important when considering organ dose equivalents under T65D for the Hiroshima survivors. Because of the dissimilarity between the atomic weapons used at Hiroshima and Nagasaki, it was assumed under the T65D dosimetry system that neutrons made a major contribution to the doses at Hiroshima but not at Nagasaki. The new dosimetry indicates that the neutron doses in both cities were quite small compared to the organ dose from gamma rays. Although differences between the two dosimetries vary somewhat with distance, the following generalities hold. At Hiroshima, neutron FIA kerma is about a factor of ten smaller under DS86 than under T65D. Conversely, the gamma ray FIA kerma at Hiroshima is greater under DS86 than under T65D. At Nagasaki, the newly estimated gamma ray and neutron FIA kermas are somewhat smaller than for T65D. These results are illustrated in the first panels of Figure 4B-1, Hiroshima, and 4B-2, Nagasaki. The results shown for Hiroshima are for a distance from ground zero of 1,150 meters; those for Nagasaki for 1,275 meters. These are "average" ranges in that approximately one-half of the collective dose (person rad) was delivered within these distances in the respective cities. Although the estimated FIA gamma kerma at Hiroshima is greater under DS86 than T65D, the gamma kerma to house shielded survivors is smaller since the shielding provided by a house was underestimated under T65D (Figure 4B-1) This is important since most of the survivors who received appreciable doses were shielded from blast and thermal effects. Under DS86, the gamma ray kerma incident on survivors at Nagasaki is about a factor of two less than under T65D (Figure 4B-2). Conversely, the amount of shielding provided by the body was overestimated under T65D, so that in spite of the smaller shielded kerma at Hiroshima, organ doses are

RISKS OF CANCERâALL SITES 192 slightly higher under DS86 than T65D (Figure 4B-1); at Nagasaki, organ doses are smaller under DS86 than T65D (Figure 4B-2). FIGURE 4B-1 Comparison of T65D and DS86 dose estimates for gamma rays and neutrons in Hiroshima. At first glance, the near equality in organ rad under both the old and new dosimetries would indicate little net change with the introduction of the new dosimetry, DS86. This is not always the case. Where neutrons have been assigned a large RBE, such as in the BEIR III report (NRC80), they make a substantial contribution to the dose equivalent under T65D but not under DS86. For a neutron RBE of 20, the dose equivalents in bone marrow at Hiroshima becomes a factor of two smaller with the new dosimetry than with T65D (Figure 4B-1). Similar results are found for other internal organs. For survivors at Nagasaki, the estimated neutron doses under T65D are so small that RBE has little effect on the estimated

RISKS OF CANCERâALL SITES 193 dose equivalent (Figure 4B-2). It is important to note that, compared to T65D, organ dose equivalents at Nagasaki are somewhat smaller with the new dosimetry. Historically, risks have been lower per estimated unit dose or per unit dose equivalent in Nagasaki than in Hiroshima, a difference that was attributed to the neutrons in Hiroshima. Under DS86, observed risks per unit dose or per unit dose equivalent are still somewhat lower in Nagasaki than in Hiroshima, but the difference is small and not statistically significant. Moreover, neutron doses are so low in both cities that the FIGURE 4B-2 Comparison of T65D and DS86 dose estimates for gamma rays and neutrons in Nagasaki.

RISKS OF CANCERâALL SITES 194 A-bomb survivor data contain no information on the RBE of neutrons for human carcinogenesis (Pr87). The Committee's Use of DS86 The A-bomb survivor data made available to the Committee by RERF pertain to the DS86 subcohort used to prepare Life Span Study Report 11 (Sh87). This subcohort is composed of 75,991 survivors for whom sufficient information was available in 1987 to calculate DS86 dose estimates. This subcohort is somewhat smaller than the exposed population covered by T65D dosimetry, because more data on shielding are required under DS86 protocols to compute a survivor's dose. Little information is lost by this restriction, since those excluded were mainly distal survivors whose shielding circumstances are poorly defined or unknown. The sex-and city-specific mortality data used by the Committee were stratified in terms of both the gamma and neutron kerma at the survivor's location in one of ten categories. The lower bounds of these categories are 0, 0.006, 0.05, 0.10, 0.20, 0.50, 1.0, 2.0, 3.0, and 4.0 Gy. The gamma and neutron kerma in each strata is a person-years weighted average for the survivors at risk in a specified age and city category. Organ doses were calculated by RERF for each survivor but were not used directly. Instead, average age-specific and city-specific body transmission factors are being used to estimate organ doses. Organ-specific transmission factors averaged over survivors of all ages are listed in Table 4B-1. Although there is some variation in the transmission factors for neutrons, the high energy gamma radiation from the bombs resulted in an uncommon degree of uniformity in the dose to internal organs due to low-LET radiation (Table 4B-1). Application of the transmission factors was straightforward. The stomach was used for the category cancers of the digestive system and as surrogate for all organs in the category all solid cancers. For the category other cancers, the transmission factor for the large intestine was used to estimate the neutron and gamma-ray dose. As discussed in Chapter 4, an organ specific dose equivalent for each strata in the dose-response regressions was calculated using an RBE of 20 for neutrons. In this regard, it should be noted that the bomb neutron spectrum at distances where survivorship frequently occurred is considerably less energetic than an unattenuated spectrum of fission neutrons. Because of neutron scattering in bomb materials and well over a kilometer of air, a large fraction of the neutron kerma is below 1 MEV. For example at 1200 meters in Hiroshima, 50 percent of the incident kerma was between 0.1 and 1 MEV (Ka89). In such circumstances, the recoil protons in tissue have energies of a few hundred keV and are near the LET for maximum biological effectiveness (see Figure 3.3).

RISKS OF CANCERâALL SITES 195 TABLE 4B-1 Averages of the Body Transmission Factors Under DS86a (Sh87) Organ Gamma Neutron n,Î³b Bone marrow 0.81 0.37 0.42 Stomach 0.75 0.28 0.40 Colon 0.74 0.19 0.41 Lung 0.80 0.33 0.37 Bladder 0.76 0.22 0.40 Liver 0.76 0.29 0.39 Pancreas 0.72 0.18 0.42 Breast 0.85 0.61 0.32 Ovary 0.74 0.16 0.39 Uterus 0.73 0.14 0.40 Testis 0.78 0.32 0.38 Thyroid 0.85 0.41 0.43 a The body transmission factor is the ratio of the organ dose in a male survivor to the kerma at his location. The values in the table are averages for 19,113 survivors and are largely independent of city and distance but do depend on age (body size). b Gamma radiation following neutron capture within the body. The Committee deliberated on whether risk estimates in terms of the kerma at a survivor's location would be a worthwhile addition to this report but decided against such an approach because the radiation field from the A-bombs is not representative of exposure situations that are often encountered in radiation protection practice. Because the gamma radiation from the bombs is so energetic, the degree of self-shielding provided by the body is small. Moreover, the A-bomb radiation had a substantial vertical component which leads to a rather atypical exposure geometry. Effective application of the Committee's risk estimates to other exposure situations are dependent therefore on a careful consideration of the dose distribution within the body and the resultant organ doses, as illustrated in Table 4B-1 for the A-bomb survivors. References Au77 Auxier, J. A. 1977. Ichiban. Technical Information Center, Energy Research and Development Administration, TID-27080, National Technical Information Service, U.S. Department of Commerce, Springfield, VA 22161. Ka89 Kaul, D. C., and S. D. Egbert. 1989. Cumulative Fraction of Neutron Dose. Communication to RERF Office at NAS, SAIC, San Diego, Calif.

RISKS OF CANCERâALL SITES 196 Mi68 Milton, R., and T. Shohoji. 1968. Tentative 1965 Radiation Dose Estimation for Atomic Bomb Survivors, Hiroshima and Nagasaki, 1968. ABCC TR 1-68. Hiroshima, Japan: ABCC. NRC72 National Academy of Sciences. 1972. The Effects on Populations of Exposure to Low levels of Ionizing Radiation. Advisory Committee on the Biological Effects of Ionizing Radiation. Washington, D.C. NRC80 National Academy of Sciences. 1980. The Effects of Populations of Exposure to Low levels of Ionizing Radiation. Advisory Committee on the Biological Effects of Ionizing Radiation. Washington, D.C. NRC87 National Research Council. 1987. An Assessment of the New Dosimetry for A-bomb Survivors. Panel on the Reassessment of A-bomb Dosimetry. W. H. Ellett, ed. Washington, D.C.: National Academy Press, Pr87 Preston, D., and D. Pierce. 1987. The Effect of Change in Dosimetry on Cancer Mortality Risk Estimates in the Atomic Bomb Survivors. TR 9-87. Hiroshima, Japan. RERF. Sh87 Shimizu, Y., H. Kato, W. Schull, D. Preston, S. Fujita, and D. Pierce. 1987. Life Span Study Report 11, Part 1. Comparison of Risk Coefficients for Site-Specific Cancer Mortality Based on the DS86 and T 65R Shielded Kerma and Organ Doses TR 12-87. Hiroshima, Japan: RERF RERF87 Radiation Effects Research Foundation. 1987. U.S.-Japan Joint Reassessment of Atomic Bomb Radiation Dosimetry in Hiroshima and NagasakiâFinal Report, Vol. 1. Hiroshima, Japan. RERF88 Radiation Effects Research Foundation. 1988. U.S.-Japan Joint Reassessment of Atomic Bomb Radiation Dosimetry in Hiroshima and NagasakiâFinal Report, Vol. 2. Hiroshima, Japan. ANNEX 4Câ AMFIT Parameter estimates for the relative and excess risk models used for risk projections in this report were obtained using AMFIT, a program for the analysis of cohort survival data which was written by Dale Preston and Donald Pierce. The detailed cross-tabulations of person-years and cases used as input to AMFIT were generally constructed using PYTAB, which was written by Dale Preston. Both programs were originally developed for analyses of mortality and incidence in the RERF Life Span Study. These programs have been used extensively in recent analyses of the RERF data, including the two most recent Life Span Study reports (Pr87, Sh87, Sh88), and the comparison of DS86 and T65D risk estimates (pr88). The programs were also used by the BEIR IV Committee in their analyses of lung cancer risks among miners exposed to radon (NRC88). AMFIT makes use of Poisson regression methods for the analysis of cohort survival data stratified on time and other factors (Fr83, Ho76, Ra86, Pi87, Br87). AMFIT computes maximum likelihood estimates of parameters in a general class of hazard function models, which includes both excess and relative risk (proportional hazards) models, using a Newton-Raphson algorithm which is equivalent, for fully parametric models, to the iteratively weighted least squares algorithm used for Poisson regression

RISKS OF CANCERâALL SITES 197 as in the systems, GLIM (Ba78) and PREG (Fr83, Fr85). Some of the simpler relative risk models available in AMFIT can be fit using GLIM or PREG, and these three programs produce identical estimates in such cases. The committee chose to use AMFIT in the development of risk projection models because of its ease of use and the broad range of models available in the program. AMFIT can be used to fit relative risk models in which the background is a function of a large number (possibly several hundred) of stratum parameters. In order to avoid the inversion of a (potentially) large matrix in such cases, AMFIT uses a Gauss-Seidel iteration (Th88). Upon convergence for stratified models, the covariance matrix of the non-strata parameters is adjusted to take into account the stratum parameter estimates. The fitting of stratified Poisson regression models for grouped survival data in which time is one of the stratification variables is closely related to partial likelihood methods for ungrouped survival data (Co72, Ka80). The models used by the committee were generally fully parametric models, i.e., they did not contain stratum parameters. For fully-specified parametric models, AMFIT can be used to produce residuals and other components for generalized regression diagnostics (Mc83, Pr81). These statistics were used in some of the goodness-of-fit evaluations carried out by the committee. Current PC versions of AMFIT and PYTAB can be obtained from the Radiation Epidemiology Branch of the National Cancer Institute. References Ba78 Baker, R. J., and J. A. Nelder. 1978. The GLIM System: Release 3 Numerical Analysis Group, Oxford. Br87 Breslow, N. J., and N. E. Day. 1987. Statistical Methods in Cancer Research Volume IIâThe Design and Analysis of Cohort Studies. IARC Scientific Publication 82. Lyon: International Agency for Research on Cancer. Co72 Cox, D. R. 1972. Regression models and life tables (with discussion). J. R. Stat. Soc. Ser. B. 34:187-220. Fr83 Frome, E. L. 1983. The analysis of rates using Poisson regression models, Biometrics 39:665-674. Fr85 Frome, E. L., and H. Checkoway. 1985. Use of Poisson regression models in estimating incidence ratios and rates. Am. J. Epidemiol. 121:309-323. Ho76 Holford, T. 1976. Life tables with concomitant information. Biometrics 32:587-597. Ka80 Kalbfleisch, J. D., and R. A. Prentice. 1980. The analysis of failure time data. New York: Wiley. Mc83 McCullagh, P., and J. A. Nelder. 1983. Generalized Linear Models. New York: Chapman and Hall. NRC88 National Research Council, Committee on the Biological Effects of Ionizing Radiations (BEIR IV). 1988. Health Risks of Radon and Other Internally

RISKS OF CANCERâALL SITES 198 Deposited Alpha Emmitters. Washington, D.C.: National Academy Press. 602 pp. Pi87 Pierce, D. A., and D. L. Preston. 1987. Developments in cohort analysis with application 46th Session of the International Statistics Institute 31.2, 557-569. Pr81 Pregibon, D. 1981. Logistic regression diagnostics. Ann. Stat. 9:705-724. Pr87 Preston, D. L., H. Kato, K. Kopecky, and S. Fujita. 1987. Life span study Report 10 Part 1. Cancer mortality among A-bomb survivors in Hiroshima and Nagasaki, 1950-82. Pr88 Preston, D. L., and D. A. Pierce. 1988. The effect of changes in dosimetry on the risk of cancer mortality among A-bomb survivors. Rad. Res. 114:151-178. Ra86 Radford, E. P., D. L. Preston, and K. J. Kopecky. 1986. Methods for the study of delayed health effects of A-bomb radiation in cancer in atomic bomb survivors. GANN monograph on Cancer Research No. 32. I. Shigematsu and A. Kagan, eds. New York: Plenum Press. Sh87 Shimizu, Y., H. Kato, W. J. Schull, D. L. Preston, S. Fujita, and D. A. Pierce. 1987. Life Span Study Report 11, Part 1, Comparison of risk coefficients for site specific cancer mortality based on the DW86 and T65 Dr shielded kerma and organ doses. RERF TR 12-87. Hiroshima: Radiation Effects Research Foundation. Sh88 Shimizu Y, H. Kato, and W. J. Schull. 1988. Life Span Study Report 11, Part 2, Cancer mortality in the years 1950-1985, based on the recently revised doses. RERF TR 5-88. Hiroshima: Radiation Effects Research Foundation. Th88 Thisted R. 1988. Elements of Statistical Computing: Numerical Computation. New York: Chapman and Hall. ANNEX 4Dâ THE COMMITTEE'S ANALYSIS OF A-BOMB SURVIVOR DATA Data Used As outlined in Annex 4A, the RERF LSS data comprise the primary data set used by the committee for risk modeling. The data supplied to the committee by RERF covered follow-up through 1985 and were the same stratified data as used by RERF to prepare LSS Report 11. Two RERF reports have compared risk estimates under the new DS86 and old T65D dosimetries (Pr87, Sh87). As the aim of this report is to provide risk estimates based on the best available data, the committee confined itself to analyses using just the DS86 data. The primary data file used by the Committee contained a total of 3,399 strata, compartmentalized by cancer mortality at a specific site, person years at risk, age at exposure, time after exposure, dose, city, and sex. The committee combined the cancer deaths into five categories: leukemia, breast, respiratory, digestive and "other" cancers. These broad categories were chosen to ensure adequate numbers for detailed modeling of modifying effects without combining cancers that showed distinctly different epidemiologic patterns. In addition, studies of the accuracy of death certificates by specific cause showed that for some sites errors in

RISKS OF CANCERâALL SITES 199 certification were numerous; this was especially true for cancers of the liver and pancreas which were often assigned to stomach cancer on the death certificates. This provided an additional reason for modelling all cancers of the digestive system as a group. TABLE 4D-1 Effects of Varying RBE on Relative Risk Models for Radiation- Induced Cancer Dose Coefficients (Std. Dev.) Leukemiaa Î±2 Î±3 RBE (Per. Sv) (Per. Sv) Deviance 1 0.257(0.313) 0.310(0.349) 498.46 5 0.254(0.309) 0.301(0.341) 498.37 10 0.251(0.303) 0.290(0.331) 498.27 20 0.243(0.292) 0.271(0.314) 498.08 50 0.219(0.258) 0.225(0.276) 497.65 Nonleukemiab Î±1 RBE (Per. Sv) Deviance 1 1.158(0.381) 1,453.34 5 1.113(0.366) 1,452.95 10 1.061(0.349) 1,452.54 20 0.969(0.320) 1,451.95 50 0.763(0.253) 1,451.15 a Linear. Î± , and quadratic, Î± , coefficients for dose response using the committee's preferred 2 3 model, Equation 4.3; observations for organ dose greater than 4 Sv are excluded. b Linear coefficient Î± , for dose response for all solid cancers using age at exposure and sex as 1 risk factors with 10-year minimum latency. The kerma categories were replaced with the corresponding organ doses, based on age-, city-, and organ-specific transfer coefficients and an RBE for neutrons of 20. Table 4D-1 describes the results of varying the RBE in relative risk models for nonleukemia cancers and leukemia. Although the slope of the dose-response curve decreased with increasing RBE, the fit of the model (as judged by the column "Deviance") was unaffected and there was no change in the estimate of any of the parameters for modifying variables. The RERF data show a tendency toward decreased risk per Gy in the highest dose groups, which may reflect either cell-killing or overestimation of the doses in this group. The committee considered various ways of dealing with this problem, including adding terms to the dose-response part of the model and adjusting the highest doses downward. In the end, it was decided simply to exclude the two highest dose groups. Table 4D-2

RISKS OF CANCERâALL SITES 200 illustrates the results of this exclusion on fitted linear models for nonleukemia and leukemia. For both outcomes, the slope of the linear dose-response relation is highest when doses over 4 Gy (using an RBE of 20) are excluded. For nonleukemia cancers, there is no sign of a positive quadratic component at any restriction, but as shown in Table 4D-2 for leukemia, the evidence for a positive quadratic component is strongest upon restriction to under 4 Gy. With further restriction, the standard errors of all model parameters begin to increase to unacceptable levels. Hence it was decided to restrict all further analyses to the subgroup under 4 Gy. TABLE 4D-2 Effect of Excluding High-Dose Groups on Fitted Dose-Response Relationships Exclusion (Sv) Linear Dose Coefficient Per Sv Score for Adding Quadratic (Std. Dev.) Term Leukemiaa None 0.575(0.503) 0.08 >5 0.763(0.625) 1.76 >4 0.482(0.550) 2.14 >3 0.254(0.520) 1.45 >2 0.050(0.556) 1.49 Nonleukemiab None 0.781(0.248) â2.04 >5 0.823(0.274) â1.88 >4 0.969(0.320) â0.41 >3 0.980(0.331) â0.31 >2 1.136(0.448) 0.66 aLinear fit using the risk modifiers in the preferred model with an RBE of 20. bLinear fit using age at exposure and sex as risk modifier with a 10-year minimum latency and an RBE of 20. Model Selection While the BEIR III report used both additive and relative risk models, this committee prefers relative risk models. The relative risk models provide not only a more parsimonious description of the data but also have additional advantages. For example, relative risks are less affected by losses of cause of death assignments due to data arising from errors in certification by site, unless the errors are correlated with radiation dose. In contrast, absolute risks are strongly affected by losses due to erroneous

RISKS OF CANCERâALL SITES 201 certification. Investigation of the RERF autopsy data base shows that erroneous certifications are essentially unrelated to the dose estimates for A-bomb survivors. One can show mathematically that the additive risk model and the relative risk model can be made equivalent if the variables used in the excess risk terms are also the ones used for estimating the background. Therefore, this committee does not make a distinction between additive risk and relative risk models. In BEIR III, however, the excess risk functions for the additive and relative risk models were either constant or approximately constant and as such, there needed to be a definite distinction between additive risk and relative risk. It is clear from the present analyses that such simple additive or relative risk models do not provide an adequate description of the data. Therefore, the committee choose to estimate risk with inclusion of several explanatory variables in the excess risk term. Functionally, the committee chose to use the relative risk formulation with a stratified or nonparametrically estimated background. The reason is simply that this avoids using the necessary but complicated functions to estimate the background. Three modeling approaches are illustrated in Table 4D-3: additive risk with its necessarily modeled background; relative risk model with a modeled background; and the relative risk with the stratified background, which the committee chose to use. Three sets of parameters were used in these illustrated models. They all provide a fairly reasonable fit, although some of them are statistically superior, based on the values of deviance. The average risks for these various models do vary as one might suspect. However, they are reasonably close to one another, generally within a factor of 2 and, for the most part, are well within the statistical confidence intervals given for the committee's preferred models, which differentiate between cancer types. Previous risk analyses (e.g., UNSCEAR), for the group of all nonleukemia cancers, have used a constant relative risk model with adjustments for sex and age-at-exposure. The second model, #5 in the relative risk-stratified background group in Table 4D-3, is essentially this model since the coefficient for time since exposure (0.0775) is effectively zero. This model, however, provides a significantly poorer fit than the other two models (#4, #6) as measured by deviance. Secondly, the risk estimates are considerably larger than for the other two models. In Table 4D-3 we have included the risk estimates for acute exposure at age 5. These values can be quite large and tend to vary to a much greater degree than the all-age average. This is not surprising when it is realized that there are few data for survivors exposed at the early ages, because they are only now reaching the age at which cancer rates are measurable.

TABLE 4D-3 Three Illustrative Models for all Cancers Other Than Leukemia Risk/104 Person Sv Males Females Model No. Î±1 Î²1 Î²2 Î²3 Î²4 DEV AVE AGE 5 AVE AGE 5 Relative RiskâModeled Background 1 0.4054 â2.451 0.8062 0.4134 1,723.6 426 801 529 1,080 2 0.3246 â0.1466 â0.6688 0.5709 1,731.1 557 1,483 817 2,362 3 0.4054 â1.570 â0.2855 0.5062 1,726.6 371 697 503 1,031 Relative RiskâStratified Background 4 0.3933 â2.463 0.9199 0.4770 1,449.7 448 877 592 1,259 5 0.3251 0.0775 â0.6688 0.5446 1,456.6 669 1,923 960 2,991 RISKS OF CANCERâALL SITES 6 0.4322 â1.592 â0.2866 0.4671 1,443.3 393 1,052 513 1,052 Additive RiskâModeled Background 7 7.222 2.334 0.5466 0.2309 1,725.2 350 600 630 1,108 8 8.145 1.772 0.8784 0.1015 1,723.3 315 313 490 476 9 7.548 2.697 â0.0930 0.2829 1,727.0 302 453 566 863 where f(d) = Î±1d g(Î²) = exp[Î²1ln(A/50) + Î²2ln(T/20) + Î²3ln (E/30) + Î²4I(S)] with A = attained age, T = time since exposure, E = age at exposure. 202

RISKS OF CANCERâALL SITES 203 TABLE 4D-4 Excess Risk Estimates and 90% Confidence Intervals with the Preferred Models (0.1 Sv Acute Exposure to 100,000 Males of Each Age) Age at Exposure Leukemia Nonleukemia 5 111 (20â455)a 1,165 (673â1,956) 15 109 (21â450) 1,035 (642â1,775) 25 36 (8â87) 885 (534â1,442) 35 62 (21â134) 504 (272â947) 45 108 (43â223) 492 (257â883) 55 166 (59â338) 450 (217â815) 65 191 (65â369) 290 (137â572) 75 165 (56â316) 93 (38â233) 85 96 (33â183) 14 (5â44) a (5%, 95%) 200 replications. Therefore estimates for the young are, in a sense, a model dependent extrapolation from the data for older ages. The degree of precision in the projections for the cancer risk at young ages is illustrated further in Table 4D-4. In that table for leukemia, the estimated excess risk is 111 cases for exposure at age 5, with a 90% confidence interval extending from 20 to 455, i.e., the upper bound is about 4 times the point estimate. On the other hand, for ages 35, 45, etc., the upper bound of the 90% confidence limit is within about a factor of 2 of the point estimate. Confidence limits do not vary as much with age at exposure for nonleukemia mortality (Table 4D-4). Nevertheless, the risks for nonleukemia are relatively high and imprecise for early ages at exposure, so that considerably more experience will be needed before there are sufficient data to estimate more precisely the lifetime risks for those exposed at early ages. Alternative Models The committee considered a variety of models before selecting the preferred models described in Chapter 4. Some of these alternative models and their deviance are described in Table 4D-5 for the various types of cancer considered in the chapter. In each case, model 0 is the committee's preferred model described in Chapter 4. In general, the preferred models fit the data as well as the alternatives and have fewer terms. This was not the sole criterion for model selection. The committee paid particular attention to how risks were proportioned between various age groups. Lifetime risks following an acute exposure of 0.1 Sv under these models

RISKS OF CANCERâALL SITES 204 TABLE 4D-5 Alternative Models

RISKS OF CANCERâALL SITES 205 TABLE 4D-6 Alternative ModelsâLifetime Cancer Mortality Risk per 10,000 Person Sv Acute Dose Equivalent (106 person rem) Male Female Age at Exposure 5 45 Avg. 5 45 Avg. Leukemia Model 0a 111 108 111 75 73 82 1 66 75 66 42 51 48 2 41 65 57 27 45 42 3 44 69 57 29 47 43 Respiratory Model 0 17 353 188 48 277 150 1 249 246 207 226 207 171 2 65 492 276 26 186 100 3 370 379 316 146 141 113 Digestive Model 0 361 22 167 655 71 288 1 367 23 164 508 56 222 2 234 12 122 403 60 206 3 412 22 184 637 63 274

RISKS OF CANCERâALL SITES 206 are shown in Table 4D-6 for ages of exposure 5 and 45 and averaged over all ages. Although the averaged risks generated by the various models are comparable, this is less true for risks at specified age of exposure. Other Cancers Model 0 787 117 300 625 100 222 1 64 642 310 46 602 253 2 639 85 241 509 86 184 3 219 121 165 185 109 131 Nonleukemia Model 0 1,165 492 655 1,457 468 730 1 680 912 681 920 886 717 2 939 590 638 1,078 356 563 3 1,000 522 655 1,105 339 592 a Model 0 is the committee's preferred model. References Pr87 Preston, D. L., and D. A. Pierce. 1987. The effect of changes in dosimetry on cancer mortality risk estimates in the atomic bomb survivors. RERF TR 9-87. Radiation Effects Research Foundation. Sh87 Shimizu, Y., H. Kato, W. J. Schull, D. L. Preston, S. Fujita, and D. A. Pierce. 1987. Life Span Study Report 11. Part 1. Comparison of risk coefficients for site-specific cancer mortality based on the DS86 and T65DR shielded kerma and organ doses. RERF TR 12-87. Radiation Effects Research Foundation. ANNEX 4Eâ MODELING BREAST CANCER Introduction A general description of the Committee's final models for radiation induced breast cancer incidence and mortality risks was given in Chapter 4. This annex contains additional information on these models and on issues considered in their development. The topics to be considered herein include: summary information on the cohorts used; background rate models; relative versus absolute time-dependent risk models; cohort effects; the shape of the dose-response relationship; and effects due to age-at-exposure and time-after- exposure. This annex concludes with a summary of the parameter estimates in the Committee's preferred risk models.

RISKS OF CANCERâALL SITES 207 Description of the Cohorts The Committee's parallel analyses made use of mortality data from two cohorts: the Canadian TB Fluoroscopy Study (CAN-TB) (Mi89) and the subcohort of the RERF Life Span Study (LSS) for which DS86 doses are available (Sh87). Data from three cohorts were used in the incidence analyses. These cohorts included: a subset of women in the 1950 to 1980 LSS incidence series (To87) for whom DS86 dose estimates were available (LSS-I); data on women in the New York Acute Postpartum Mastitis study (NY-APM) (Sh86); and data on women in the Massachusetts TB Fluoroscopy (MASS-TB) cohort (Hr89). In all of the Committee's analyses, data on the first five-years of follow- up and, as described below, data on women with the highest exposures have been omitted. Tables 4E-1 and 4E-2 summarize the follow-up and exposure information for the mortality and incidence cohorts used in these analyses. Background Rate Models For the LSS, and CAN-TB cohorts there were enough deaths in the zero dose group to allow the use of internal estimates of the base line rate for breast cancer mortality. For each of these series the background rates were modelled as a log-linear spline of attained age with a single inflection point at age 50 and a log-linear trend in the age-specific rates with time (years since 1945). Table 4E-3 contains the parameter estimates for these models as estimated in the Committee's preferred mortality and incidence models. Because the MASS-TB and NY-APM data did not include enough information on the evidence of breast cancer among unexposed women to allow internal estimation baseline rates, they were described using cohort-specific standardized incidence ratios (SIRs) relative to age-and time-specific breast cancer rates in Connecticut obtained from the SEER registry (NCI86). The estimated SIR for the MASS-TB series was 0.75 (90% confidence interval 0.59-0.94) while that for the NY-APM series was 1.6 (90% confidence interval 1.3 to 1.9). The difference between these SIRs was highly significant (p < .001). In order to compare Connecticut and Japanese background incidence rates, a model of the form used for the LSS data was fitted to the Connecticut rates. Figure 4E-1 compares the fitted rates for several birth cohorts. The fitted age- specific breast-cancer incidence rates in Connecticut are 2.5 to 6 times the corresponding fitted rates in the LSS. The largest differences are seen in the earlier birth cohorts. Figure 4E-2 presents a similar comparison of the fitted background mortality rates for the LSS and CAN-TB cohorts.

RISKS OF CANCERâALL SITES 208 Cohort Effects under Relative Risk and Additive Risks The excess relative risk for the incidence of breast cancer in the LSS was estimated to be about 50% greater than that in the two U.S. cohorts, but this difference was not statistically significant (p = 0.4). There was no evidence of differences in the relative risk between the NY-APM and MASS-TB cohorts. The additive excess incidence rates per unit dose in the LSS were about half of the average for the two U.S. cohorts. This difference was statistically significant (p = 0.01). On the basis of the Committee's analyses of these data it was decided to use a relative risk model in which the excess relative risk was estimated using the pooled data from all three incidence series, with allowance for

RISKS OF CANCERâALL SITES 209 TABLE 4E-2 Summary of Cohorts Used for BEIR V Breast Cancer Mortality Analyses Cohorta Subcohort Person Cases Mean Crude Years Dose Rate per (1,000's) (Sv)b 1,000 Person Years CAN-TB TOTAL 774.3 473 0.61 (1950-1980) Nova Scotia Dose â¥ 23.9 58 2.46 2.43 0.005 Gy Dose < 0.005 29.3 13 0.44 Non-Nova Scotia Dose â¥ 287.9 156 0.25 0.54 0.005 Gy Dose < 0.005 433.2 246 0.57 RERF TOTAL 1,163.2 153 0.13 (1950-1985) Hiroshima 804.4 112 0.14 Dose â¥ 490.0 75 0.32 0.15 0.005 Sv Dose < 0.005 314.4 37 0.12 Nagasaki 358.8 41 0.11 Dose â¥ 163.4 21 0.22 0.13 0.005 Sv Dose < 0.005 195.4 20 0.10 GRAND 1,937.5 626.0 0.32 TOTAL a In both studies only women with at least five years of follow-up have been included. In the RERF cohort women with doses greater than 4 Sv have been excluded. b Mean doses are weighted by person years. TABLE 4E-3 BEIR V Breast Cancer ModelsâLog Rate Parameter Estimates for the Background Models Incidence LSS Effect Estimate S.E. Connecticut Estimate Constant 0.97 0.18 2.46 Log(age/50) 3.35 0.41 3.41 Log(age/50) if (age 50) â4.50 0.67 â2.51 Years since 1945 0.038 0.006 0.020 Mortality LSS Effect Estimate S.E. Canadian TB Estimate S.E. Constant 0.58 0.07 1.39 0.17 Log(age/50) 4.38 0.48 4.38 0.48 Log(age/50) if (age 50) â4.71 0.82 â3.57 0.69 Years since 1945 â0.003 0.009 0.021 0.006

RISKS OF CANCERâALL SITES 210 FIGURE 4E-1 Breast cancer incidence in the U.S. (Connecticut) and Japan by attained age for women who were 15 and 40 years old in 1945. FIGURE 4E-2 Breast cancer mortality in the Japanese RERF Life Span and Canadian TB Studies by attained age for 15- and 40-year-old cohorts in 1945.

RISKS OF CANCERâALL SITES 211 analysis of the breast cancer incidence in these cohorts (La80) had suggested that, while relative risk models provide a better fit within each cohort than do constant excess additive risk models, the additive excess risks averaged over the (then current) follow-up periods were roughly comparable for the different cohorts. In contrast, the Committee's analyses indicate that constant additive excess risk models do not adequately describe either the mortality or incidence data. In addition, the Committee's analyses suggest that if one allows the additive risks to depend on time, the excess risk of breast cancer seen in the LSS data is lower than the excess risks in the U.S. data while the relative risks are roughly comparable. Differences between the present findings and those of the earlier parallel analyses can be attributed to various factors, including additional follow-up for the U.S. cohorts, the introduction of the DS86 doses along with the consequent changes in the makeup of the LSS cohort, and the use of time-variable excess risk models. For the case of breast cancer mortality, striking and highly significant (p < 0.001) differences were seen in both the estimated relative and additive excess risks within the Canadian cohort. In particular, the estimated risks per unit dose for the Nova Scotia women were about six times those for women in other provinces. It was suggested that this difference could be attributed to nonlinearities in the dose-response since the estimated doses for the women treated in Nova Scotia were much higher than those for women treated in other Canadian provinces. However, it was found that the differences in risk between Nova Scotia and the other provinces remain significant in a linear-quadratic dose-response model. This topic will be discussed further below. The estimated excess relative risk per unit dose for women in the LSS was two to three times that for Canadian women from provinces other than Nova Scotia and about half that seen for Nova Scotia women. Neither of these differences were statistically significant (p = 0.12 for the LSS-non-Nova Scotia comparison and p = 0.2 for the LSS-Nova Scotia contrast). Since Japanese background rates are considerably lower than those in Canada, the LSS additive excess risks per unit dose were significantly less than those for Nova Scotia women (p < .001), but were not significantly lower than those for other Canadian women (p > .5). The large, if not always statistically significant, differences in the magnitude of risk between and within the mortality cohorts complicate the choice of a preferred model for use in lifetime risk projections. The Committee's final choice was to estimate the level of risk per Gy using the pooled LSS and non-Nova Scotia CAN-TB data, but to use data on all women in both cohorts in describing temporal factors affecting the dose response. This choice was based upon an assumption that relative risks for breast cancer mortality and incidence should be roughly similar across

RISKS OF CANCERâALL SITES 212 cohorts and a judgment that the estimated relative risks for mortality due to breast cancer in the Nova Scotia subcohort of the CAN-TB series were larger than one might reasonably expect on the basis of estimated relative risks obtained from the incidence data. In theory, the excess risk of breast cancer mortality or incidence following irradiation can be described equally well by suitably rich time-dependent relative or additive risk models. Indeed, for the mortality data, models of either type with similar numbers of parameters were found to fit the data equally well. However, for the incidence data, the relative risk models considered by the Committee had fewer parameters and, on the basis of deviance comparisons, fit better than did the additive risk models considered. Based upon these results and the fact that relative risks are less subject to bias as a result of incomplete (non-dose related) ascertainment, the Committee decided to use time-dependent relative risk models for their lifetime risk estimates for both breast cancer incidence and mortality. Dose-Response Relationships There is strong evidence for a flattening of the dose-response curve at high doses in all of the cohorts except the CAN-TB series, in which the curvature appears to be in the opposite direction, i.e., concave upward. It has been suggested that the flattening in the dose-response function at doses in excess of 4 Gy or so is the result of cell-killing effects. However it is unlikely that this curvature is solely a result of cell-killing since: 1. For the fluoroscopy cohorts (MASS-TB and CAN-TB) the doses were highly fractionated and it is unlikely that any single exposure involved doses which were high enough to cause appreciable cell- killing. 2. While it is likely that some survivors in the LSS received doses large enough to cause cell-killing, there is a large positive bias in the highest dose estimates as a result of the combination of: (a) random errors in the dosimetry; (b) the fact that only survivors are included in the cohort. Since the emphasis in this report is on low dose effects, the committee decided to restrict the dose range in order to eliminate the need to consider the shape of the dose response at high doses. Even when the women who received the highest doses are excluded, it is difficult to reach firm conclusions about the shape of the dose-response function at low doses. The incidence data provide weak evidence for a negative quadratic response (p = 0.1), while the Canadian mortality data indicate evidence for a positive quadratic component when the Nova Scotia data are included in the analyses. However, after allowing for this nonlinearity, a significant difference between the risk per unit dose in the two Canadian subcohorts remains. In contrast, if one allows for

RISKS OF CANCERâALL SITES 213 in the two Canadian subcohorts remains. In contrast, if one allows for this subcohort difference, the quadratic component of the dose response is not statistically significant (p = 0.5). Based upon these analyses the Committee's preferred models for breast cancer incidence and mortality are linear dose- response models. Effects Due to Age at Exposure Effects For both incidence and mortality there is a strong association between age- at-exposure and the subsequent risk of breast cancer following exposure to low- LET radiation. The general pattern is for the relative risks to decrease with increasing age at exposure. It is clear that relative risks for women who are over age 40 at exposure are quite small. There remains considerable uncertainty about the excess risk among women exposed under the age of 10, since these women are just now reaching ages at which baseline breast cancer incidence rates become appreciable. In the incidence data, it was found that the estimated relative risks for women between 15 and 19 years old at the time of exposure in the NY-APM cohort were significantly lower than the risks for women initially exposed at the same ages in the other two cohorts (p = 0.05). Except for this effect, there were little variability and no significant differences in the relative risk estimates between the 0-9, 10-14, and 15-19 age-at-exposure categories. The estimated relative risk in the combined 0- to 19-year-old category (allowing for the reduced effect among the NY-APM 15-19 group) was significantly higher than that for the women in the 20-40 year age-at-exposure group. For women over age 40 at exposure, the excess relative risk estimate is about half of that for women who were between 20 and 40 when first exposed; however, this estimate is neither significantly lower than that for 20- to 40-year-olds nor significantly greater than 0. If one looks at the estimated excess relative risks for women under the age of 10 at exposure, a similarly ambiguous result is seen. As noted above, the point estimate of the excess relative risk for this group differs little from that for the non NY-APM 10- to 19-year-olds, but, because of the small number of cases (23) among women in this age-at- exposure group, their estimated relative risk is also not significantly greater than 0. Although attempts were made to model the age-at-exposure effects on incidence as a log-linear trend or log-linear spline, it was found that these models did not fit the incidence data as well as step functions with discontinuities at age of exposure 20 and 40. Thus, in the committee's preferred model, the age-at-exposure effect on the excess relative risk is modelled as a step function with steps at ages 20 and 40. In the case of breast cancer mortality, the highest estimated relative risks were seen among women aged 10 to 14 at exposure. The excess

RISKS OF CANCERâALL SITES 214 relative risk in this age group appeared to be significantly greater than that for women aged 15-19 at exposure. In contrast to the incidence data, there is as yet little evidence of any excess risk of breast cancer mortality among those exposed under the age of 10. However, the risk in this group was also not significantly lower than that seen among 10- to 14-year-olds. Because the total number of breast cancer deaths in the youngest age-at-exposure group is low (7), and because of the suggestion of an elevated risk in the incidence data, it was decided to pool the 0-9 and 10-14 age-at-exposure categories in the final model. The excess relative risk of breast cancer mortality for women over age 40 at exposure was lower than that seen for women who were between 20 and 40 years of age when exposed (p < 0.1); in fact, the point estimate of the relative risk for this group was slightly, but not significantly, less than one. It was found that the variability in the excess relative risk as a function of age-at-exposure for women who were 15 or over at the time of exposure was best described by a decreasing log-linear trend in risk with age-at-exposure. As described in Chapter 4, the committee's final model for breast cancer mortality allows for this age-at-exposure trend together with an elevated risk for women who were under age 15 at exposure. The function is not constrained to be continuous at age 15. The Effect of Time-after-Exposure The Committee's analyses suggest that for both the incidence and mortality data the relative risks of breast cancer following exposure to low-LET radiation are not constant in time. The pattern that emerges from these analyses is that the relative risk for breast cancer incidence increases with time until about 15 years after exposure then begins to decrease. Similarly, the mortality data suggest that risks increase for about 20 years and then begin to decline. The decreases in the relative risk 15 to 20 years after exposure are of sufficient magnitude to result in predictions of decreases in the additive excess risks by the age of 50 for women who were exposed more than 20 years before. For the case of breast cancer incidence, a log-quadratic model in log time- after-exposure was found to fit the data marginally better than a time-constant relative risk model. However, when the temporal pattern of risk was modeled as a log-linear spline in log time-after-exposure with a knot at 15 years after exposure, the fit was improved significantly (p = 0.01) relative to the time- constant model. The primary difference between the spline and quadratic models is that the spline yields a sharper peak and a less rapid decline in the risks following the peak than does a quadratic model. In order to assess the significance of the decrease in the excess relative risk after the peak, the committee considered a model in which

RISKS OF CANCERâALL SITES 215 and then remain constant thereafter. The unconstrained spline fit the data significantly better than this constrained model (p = 0.02). On the basis of these analyses the Committee's preferred breast cancer incidence model is a log-linear spline with a single knot at 15 years after exposure. In the case of breast cancer mortality there is a suggestion (p = 0.1) of a temporal pattern similar to that seen in the incidence data. In particular, the risk appears to reach a peak at about 20 years after exposure. A log quadratic function of log time-since-exposure fit the data slightly better than a log-linear spline with a single inflection point knot. The Committee has chosen to use a log-quadratic model for the variation in the excess relative risk with time in its preferred risk model for breast cancer mortality. TABLE 4E-4 BEIR V Breast Cancer Incidence AnalysisâPreferred Model Effect Estimate S.E. Z RR Constant â0.73 0.28 â2.61 1.48 Cohort effects NY-APM [â0.80] MASS-TB [â0.62] LSS [1.13] Age-at-exposure effects <20 1.49 0.30 4.97 3.14 0-9 [â0.19] 10-14 [0.31] 15-19 [â0.17] NY-APM and 15-19 â2.26 1.65 â1.37 1.22 20-30 [â0.34] 30-40 [0.34] 40+ â0.90 1.06 â0.85 1.20 Time-since-exposure (T) effects Log(T/30) â1.28 0.54 â2.37 Log(T/15) if (T < 15) 6.67 3.92 1.70 NOTES: RR is the relative risk at 1 Gy 30 years after exposure. For the constant term this is the risk for a woman exposed at age 20. For the other estimates RR is the relative risk in the corresponding subgroup. In the fitted model the estimated excess relative risk at 1 Gy is a loglinear function of the parameters. Thus the estimated relative risk at dose d is RR = 1 + dexp(BZ), where B is the vector of parameter estimates and Z is a vector of covariates. The dose response is assumed to be linear. Values in []'s are the signed square roots of score statistics for a test of the null hypothesis that the corresponding parameter has no effect. These statistics are asymptotically distributed as standard normal deviates.

RISKS OF CANCERâALL SITES 216 TABLE 4E-5 BEIR V Breast Cancer Mortality Analysis Preferred Model Effect Estimate S.E. Z RR Constant â0.21 0.50 â0.41 1.81 Cohort effects CAN-TB Nova Scotia 1.14 0.42 2.72 3.54 CAN-TB Non-Nova Scotia [â1.35] LSS [1.35] Age-at-exposure (E) effects <15 1.39 0.55 2.50 4.25 (Eâ15) if (E > 15) â0.06 0.03 â1.95 0-9 [â1.29] 10-14 [1.28] 15-19 [â0.34] 20-30 [0.43] 30-40 [0.75] 40+ [â0.87] Time-since-exposure (T) effects Log(T/30) â1.90 0.84 â2.28 Log(T/30)**2 â2.22 1.38 â1.61 NOTES: RR is the relative risk at 1 Gy 30 years after exposure. For the constant term this is the risk for a woman exposed at age 15. For the other estimates RR is the relative risk in the corresponding subgroup. In the fitted model the estimated excess relative risk at 1 Gy is a loglinear function of the parameters. Thus the estimated relative risk at dose d is RR = 1 + dexp (BZ), where B is the vector of parameter estimates and Z is a vector of covariates. The dose response is assumed to be linear. Values in []'s are the signed square roots of score statistics for a test of the null hypothesis that the corresponding parameter has no effect. These statistics are asymptotically distributed as standard normal deviates. Assuming that the risk of radiation-induced breast cancer does not appear until at least the age of 25, i.e., until the earliest ages at which naturally occurring breast cancer appears, and allowing a minimal latency period of five years for women over the age of 20 at exposure, the committee found no evidence that the temporal pattern of risk was affected by dose or age-at- exposure. It should be noted that although a 5-year minimum latency was used in the development of the preferred model, no excess breast cancer risk was observed within ten years of exposure. Therefore, in the calculations of lifetime risk for various patterns of exposure presented in Chapter 4, a 10-year minimum latency was assumed in life table calculations.

RISKS OF CANCERâALL SITES 217 Final Models The analyses which led to the Committee's preferred models have been discussed in the earlier sections of this annex. Tables 4E-4 and 4E-5 contain the estimates and standard errors for all of the parameters in the excess relative risk models used as a basis for the breast cancer risk estimates and lifetime risk projections presented in Chapter 4. These tables also include score test statistics for some of the other parameters considered in the modeling. For parameters included in the final models, Wald statistics (ratios of the parameter estimate to its standard error) are given (in the column labeled Z). The p-values reported in this annex were based upon likelihood ratio statistics which provide a better guide to the statistical significance of an effect. References Hr89 Hrubec, F., J. Boice, R. Monson, and M. Rosenstein. 1989. Breast cancer after multiple chest fluoroscopies: Second follow-up of Massachusetts women with tuberculosis. Cancer Res. 40:229-234. La80 Land, C. E., J. D. Boice, Jr., R. E. Shore, J. E. Norman, and M. Tokunaga. 1980. Breast cancer risk from low-dose exposure to ionizing radiation: Results of parallel analysis of three exposed populations of women. J. Natl. Cancer Inst. 65:353-365. Mi89 Miller, A., P. Dinner, H. Risch, and D. Preston. 1989. Breast cancer mortality following irradiation in a cohort of Canadian tuberculosis patients. N. Engl. J. Med. (in press). NCI86 National Cancer Institute. 1986. Forty-Five Years of Cancer Incidence in Connecticut: 1935-1979. NCI Monograph 70. Bethesda, Md.: National Cancer Institute. Sh87 Shimizu, Y., H. Kato, W. J. Schull, D. L Preston, S. Fujita, and D. A. Pierce. 1987. Life Span Study Report 11, Part 1. Comparison of risk coefficients for site-specific cancer mortality based on the DS86 and T65DR shielded kerma and organ doses. RERF TR 12-87. Radiation Effects Research Foundation. Sh86 Shore, R. E., N. Hildreth, E. Woodard, P. Dvoretsky, L. Hempelmann, and B. Pasternack. 1986. Breast cancer among women given X-ray therapy for acute postpartum mastitis. J. Natl. Cancer Inst. 77:689-696. To87 Tokunaga, M., C. E. Land, T. Yamomoto, M. Asano, S. Tokuoka, H. Ezaki, and I. Nishimori. 1987. Incidence of female breast cancer among atomic bomb survivors, Hiroshima and Nagasaki, 1950-1980. Radiat. Res. 112:243-272. ANNEX 4Fâ UNCERTAINTY, PROBABILITY OF CAUSATION, AND DIAGNOSTICS Uncertainty Estimates of radiation risks formulated on the basis of epidemiological data are far from precise. The data show, as expected, considerable

RISKS OF CANCERâALL SITES 218 sample variation due to the relatively small number of cases in a given category. Such statistical uncertainties are additional to those arising from other sources which are not readily evaluated. These include uncertainties inherent in dose estimates, in the selection of an appropriate risk model, and in the applicability of risk estimates measured in one population to other exposed groups. Population Effects A Japanese population is the most important source of data for this report, and for some types of cancer the only source. Since baseline (naturally occurring) cancer rates are different in the U.S. from those in Japan for many kinds of cancer, it is not clear whether cancer risks derived in one population are applicable to the other, and if so, whether relative or absolute risks should be used. The answer to this question may vary from cancer site to site; in fact, it may be that neither absolute nor relative risks can be extrapolated with assurance. The general applicability of the experience of the Japanese A-bomb survivors is uncertain on additional grounds. Most human exposures to low- LET ionizing radiation are to x rays, while the A-bomb survivors received low- LET radiation in the form of high energy gamma rays. These are reported to be only about half as effective as ortho-voltage x rays (ICRU86). While that is not a conclusion of this Committee, which did not consider this question in detail, it could be argued that since the risk estimates that are presented in this report are derived chiefly (or exclusively) from the Japanese experience they should be doubled as they may be applied to medical, industrial, or other x-ray exposures. Certification of Cause of Death An additional source of uncertainty that affects the estimates of risk of death from specific cancers is the fact that specification of cause of death on death certificates (the source of data for almost all analyses of mortality) is not always accurate. The Committee has been provided with data by the RERF leading to the conclusion that great specificity as to cancer site cannot be justified on the basis of certificate-based data (e.g., cancer of the uterus is reasonably well reported, but not cancer of the uterine corpus). A further conclusion is that, at least in that body of data, the accuracy of diagnosis from death certificates declines rather sharply beyond age 75, to the point that little reliance can be placed on the data for specific sites. The Committee has refrained from basing analyses on data that it considers unreliable.

RISKS OF CANCERâALL SITES 219 Sex Differences Baseline cancer rates differ markedly between the sexes for most forms of cancer. The effect of radiation may, then, also be different for males and females. Sex was included specifically in all of the models that were fitted except for the group ''other" cancers and for leukemia, where the effect was small and not statistically significant. Where sex is included in the models, uncertainties associated with sex differences are taken into account explicitly. Because sex does not appear in the final models for leukemia and "other" cancers, a residual uncertainty of 10% is assessed in the risk estimates for these cancers. Time-Related Effects It is difficult enough to determine the cancer risk over a lifetime; if one asks what is the risk at a particular time following exposure, the number of cases available for analysis becomes so small as to frustrate attempts at direct estimation of risks. This problem is avoided by estimating instead a mathematical function that describes the time-course, but that function is subject to uncertainties of two kinds: the proper functional form to use in the first place, and the values of the parameters that enter into it. Age-Related Effects How does radiation sensitivity vary with the age of the person exposed? Is it true that very young children are at greater risk than older persons? Is there some age after which sensitivity disappears and there is no risk? The Committee has addressed these questions explicitly in devising mathematical models for cancer risk as functions of kinds of cancer, sex, age at exposure, and time after exposure (latency). All of these factors were considered for each site for which models were fitted. For some cancers, not all of these factors were influential. For example, the leukemia model does not vary by sex, and the model for respiratory cancer does not depend upon age at exposure. An especially difficult problem is encountered at the very youngest and oldest ages; since there were few cases of breast cancer in women more than 55 years of age at the time of exposure, the risk of breast cancer in such women is poorly estimated. Similarly, since there is no follow-up information from the Life-Span Study until 5 years after exposure, the risk of death from leukemia after a latent period of 5 years or less are rather uncertain. It will be noticed, however, from the accompanying table of uncertainty that large geometric standard deviations usually apply to quite small estimates of risk, so that although the uncertainties may be large as proportions of the risk estimates, their absolute values are not large.

RISKS OF CANCERâALL SITES 220 Shape of the Dose-Response Curve Is the cancer risk from a given dose of radiation strictly proportional to the dose? Are larger doses more effective than linear extrapolation of low dose risks would imply? Are the effects of repeated doses, separated in time, the same as if the entire dose had been delivered at once? Are the effects of a given total dose received at very low dose rates the same as those from the same dose at high dose rates? Are there doses so small that they have no effect? Specifically, since the effects are measured in populations that have had rather large doses delivered at a very high dose rate, how shall we use that information to assess the effects of small doses, received at low dose rates? The latter problem is faced by those who must establish limitations for occupational and general population exposures. As is suggested in Chapter 1 of this report, it may be desirable to reduce the estimates derived here by a "Dose Rate Effectiveness Factor" (DREF) of about 2 for application to populations or persons exposed to small doses at low dose rates. On the other hand, as mentioned above, the estimates could be too small by a factor of about 2 for application to the consequences of x-ray exposures. It may be that these two factors (DREF and the relative biological effectiveness of gamma rays) could, in some cases, simply offset each other. Procedures Employed The approach taken here follows that used by the NIH Committee in its report on the Radioepidemiological Tables (NIH85). In brief, that approach is to assess the magnitude of the error that may be attributable to each independent component of an estimate and then to combine the individual estimates into an overall estimate. Some of the components of error, such as the statistical variability in the number of deaths in a population group, can be evaluated in a conventional way; others, however, like the uncertainty associated with the application of risks in a Japanese population to a U.S. population, cannot be evaluated objectively. Instead, we resort to a consensus of expert opinion as to the uncertainty, expressed in a number on a scale commensurate with ordinary statistical measures of variability. Uncertainty is expressed as the "Geometric Standard Deviation," (or GSD), that is in ratio terms; by an uncertainty of 1.2 (20%) it is meant that the range of uncertainty of the estimate is from its value divided by 1.2 to the value multiplied by 1.2. If, for example, some excess relative risk is estimated to be 0.3 per Gy, with an uncertainty (exp Ï) of 1.4 (Ï = 0.336), we would mean that it is believed that the chance is 68% that the value lies in the range from 0.3 divided by 1.4 = 0.21 to 0.3 times 1.4 = 0.42. We call such an interval a "68% credibility interval." We use the

RISKS OF CANCERâALL SITES 221 term "credibility interval," instead of the commonly used statistical term "confidence interval" because the values are obtained, at least in part, by judgment, not calculation. A basic assumption is that the error in the final estimate of risk is distributed lognormally, that is, that the logarithms of the errors are normally distributed. This assumption gains credibility from the fact that the logarithm of the total error is the sum of the logarithms of the individual components of error. There is a well-known mathematical result that the distribution of a sum of variables will be approximately normal, so the assumption is unlikely to be seriously wrong. In order to obtain an interval with any desired credibility coefficient, say 90%, the factor exp (1.645 Ã Ï) would be used. In the example above, Ï was assumed to be 0.336, so a 90% interval would require division and multiplication by exp (1.645 Ã 0.336) = 1.74. The 90% interval on the estimated risk of 0.3 would be from 0.17 to 0.52. The value of the error attributable to all of the independent sources is obtained by the usual method of calculation for the logarithmic errors. That is, if ÏT denotes the standard deviation of the logarithm of the total error, and Ï1, Ï2, etc. denote the standard deviations of the logarithms of the individual components, then Models used in this report are, generally, of the form: Excess Relative Risk = D exp {Î²0 + Î²1X1 + Î²2X2 + â¦}. where D represents the organ dose equivalent in sievert and the X's are covariates such as age at exposure, etc., and the Î²'s are their respective coefficients. If we denote the logarithm of the excess relative risk by In(R), we have, then, ln(R) = ln(D) + Î²0 + Î²1X1 + Î²2X2 + â¦ We suppose that the covariates are known without error, only their coefficients, which have been calculated from the available data, will have statistical error. Then the variance of In(R), which we call V will be: V = V(Î²0) + 2X1 Cov(Î²0, Î²1) +â¦ The maximum-likelihood fitting procedures employed supply the variance- covariance matrix applicable to the coefficients, and these values have been used to obtain the variance of V and its standard error.

RISKS OF CANCERâALL SITES 222 Uncertainties External to the Parametric Model Although it can be assumed that such factors as age and time of death are known without error, there can be no such assurance concerning the estimates of radiation dose. Dose estimates for medical exposures are based upon recorded parameters of the x-ray exposure; such estimates cannot be exact, but the uncertainty to be attributed to them is not known. Dose estimates for the Japanese A-bomb survivors are based upon statements by the survivors concerning their location at the time of the bombing, their shielding situation, and estimates of the air dose curves, the exact location of the hypocenters, shielding characteristics of building materials and, for doses to specific organs, the attenuation of external dose by tissues overlaying the organ of interest. For breast cancer, especially, the orientation of the survivor with respect to the direction of the bomb is of importance, but cannot be known with any precision. The magnitude of the uncertainty in the new DS86 dose estimates for A-bomb survivors is still being evaluated. Preliminary assessments indicate that bias in the risk estimates resulting from random errors in the dose estimates is about 10% when organ doses are limited to 4 Sv, as is the case here (Pi89). Further review of this issue, including the role of bias in the estimated neutron kerma, is required. Although the magnitude of some of the sources of uncertainty (such as the effect of statistical variability on risk estimates) can be evaluated explicitly, others, like the error of "transportation" (application of risks determined in one population to another population) cannot be. In such cases we rely on consensus judgment; we judge what is the range within which it is believed that the variable lies with 95 percent "credibility." A "standard deviation" can be obtained by dividing the width of that range by 3.92. All of the standard deviations, both those actually calculated and those estimated as just explained, can be combined by the methods described above to obtain a combined measure of uncertainty which we call a "standard error" and used to obtain "credibility intervals'' by the same procedure that would be used to obtain "confidence intervals" were the uncertainty measures really statistically determined standard errors. The sources of uncertainty that can be evaluated in a straightforward way, using conventional statistical theory, are those that derive from sampling variability as it affects the fitting of specific models for the excess risk of particular cancers that result from radiation exposure. Such models have been fit for cancer mortality from leukemia, and for cancers of the respiratory system, the digestive system, the female breast and other sites. Most of the models have used the data on the Japanese A-bomb survivors, for whom 40- year follow-up data have been made available by the Radiation

RISKS OF CANCERâALL SITES 223 Effects Research Foundation. As discussed in Annex 4E, several additional sources of epidemiologic data have been used for breast cancer. Our task has been somewhat simplified by the fact that several of the factors that contribute to uncertainty, mentioned above, were considered explicitly in the model-fitting procedures, and their uncertainties are incorporated in the model uncertainties. These include age at exposure, time from exposure (latent period), sex, and the possible contribution of the square of dose in addition to radiation dose itself. Only for leukemia was the dose- squared factor significant. In any case, the statistical variability of the models includes the contributions from all of these factors. The most important element that is not accounted for in the models themselves is the population factor, that is, the applicability of risks determined in a Japanese population to populations of different ethnic composition, having different diets, industrial exposures, and, generally, different life styles. For cancer of the breast, however, data were available for mortality not only in Japanese but also in Canadian and U.S. women. Interestingly, for reasons that have not yet been elucidated, the only important differences were within the Canadian series, where it appeared that women in Nova Scotia had significantly different risks from those in other parts of Canada and from the other series. Apart from the Nova Scotia series there were no significant differences among the other series. We evaluate the population uncertainty at 20%, that is, the GSD corresponds to an uncertainty factor of 1.2. Another source of uncertainty, which cannot be captured by usual statistical methods, is possible mis-specification of the model finally fitted to the data. Many variables (factors) were considered as candidates for inclusion in the final models; those selected were often the "best" in the statistical sense. Nevertheless, there can be no assurance that the models finally chosen were "correct" in that the factors included were just the right ones. The importance of possible mis-specification was evaluated by considering the variations in estimated risk for the fitted different models described in Annex 4D, weighting the risks from the various models by the reciprocals of their deviancies. By this test, model mis-specification for males (1.16) was larger than for females (1.08). For children aged 5 at exposure, the mis-specification uncertainty is about 1.55 for both sexes. Results Uncertainties that result from the model fitting are displayed in Table 4F-1. Unlike the Monte Carlo generated estimates of uncertainties in lifetime risk given in Chapter 4 and Annex 4D, the uncertainties in Table 4F-1 are shown explicitly as functions of age at exposure, latency and sex when these factors are significant. This level of detail is not practical with

RISKS OF CANCERâALL SITES 224 Monte Carlo techniques. It will be seen that the models for respiratory and digestive cancers do not show risk variation by age at exposure, so that the uncertainty factor for each sex varies only by time after exposure. For leukemia and the group "other cancers" there is significant variation by age and latency, but sex seems not to play an important role. The possible effect of sex on the uncertainty in these two cases is considered below. In general, where data are relatively sparse, as is true for leukemia, the uncertainties are large, varying from nearly 2 to 8 for different ages and latencies. Uncertainties are usually not large for respiratory or digestive cancers or for breast cancer except for a short latency of 10 years. Uncertainties not accounted for in the model themselves (referred to as non-model) derive from population differences (e.g., Japanese vs. Caucasians vs. Blacks) and uncertainty in the dosimetry estimates. The Committee's assessment of the magnitude of their contributions in terms of geometric standard deviations (GSD) are: (A) Model mis-specification Males :1.16 Females :1.08 (B) Population differences :1.20 (C) Dosimetry system :1.10 (D) Sex (leukemia and "other" cancers) :1.10 TOTAL GSD All Except Leukemia and "Other" "Other" Cancers and Leukemia Males Females Males Females 1.29 1.25 1.31 1.27 Comparison with Table 4F-1 indicates that the uncertainties in the Committee's preferred model due to sampling variation are usually much larger than those due to the factors considered above. Where required, the non-model component shown above, can be added in quadrature to the model-based component shown in the tables using the methods outlined above. Probability of Causation In the Report of the National Institutes of Health Ad Hoc Working Group to Develop Epidemiological Tables (NIH85), the formula for the PC (probability of causation) is given as: PC = R/(1 + R), where R, really R(D,X), is the excess relative risk that results from the dose D to a person with characteristics X. The PC is an estimate of the probability

RISKS OF CANCERâALL SITES 225 TABLE 4F-1 Estimates of the Excess Relative Cancer Risk from 0.1-Sv Acute Dose and Their Geometric Standard Deviations (GSD) due to Sampling Variation Male Female Cancer Type Age at Time After GSD Risk GSD Risk Exposure Exposure Breast cancer 5 15 â â 1.90 0.418 mortality 25 â â 1.60 0.427 35 â â 1.57 0.230 45 â â 1.89 0.105 15 15 â â 1.90 0.418 25 â â 1.60 0.427 35 â â 1.57 0.230 45 â â 1.89 0.105 25 15 â â 1.77 0.056 25 â â 1.54 0.057 35 â â 1.60 0.031 45 â â 1.99 0.014 35 15 â â 1.90 0.030 25 â â 1.76 0.030 35 â â 1.85 0.016 45 15 â â 2.31 0.016 25 â â 2.25 0.016 55 15 â â 2.99 0.008 Breast cancer <20 15 â â 1.45 0.52 incidence 25 â â 1.24 0.27 35 â â 1.30 0.18 45 â â 1.44 0.13 20 to 39 15 â â 1.35 0.12 25 â â 1.26 0.06 35 â â 1.40 0.04 45 â â 1.57 0.03 â¥40 15 â â 2.90 0.05 25 â â 2.88 0.02 35 â â 2.99 0.02 Respiratory All ages 15 1.59 0.096 1.47 0.196 cancer mortality 25 2.03 0.046 1.76 0.094 35 2.63 0.028 2.27 0.058 45 3.23 0.020 2.80 0.040 Digestive All ages All times 1.50 0.081 1.33 0.141 cancer mortality >10 yr 1.50 0.081 1.33 0.141 1.88 0.011 1.77 0.019 1.88 0.011 1.77 0.019 that a given radiation dose in the history of a patient was the cause, in some sense, of a subsequent malignant neoplasm that has actually occurred. The value of R in any given case can be obtained from the formulas provided in Chapter 4. Since the formulas for R for the malignancies other than leukemia are linear functions of the dose, D, Table 4F-1, can be used to obtain, not only the value of R but also its Geometric Standard Deviation, which leads

RISKS OF CANCERâALL SITES 226 immediately to an estimate of the associated uncertainty in the PC. These formulas do not, of course, take into account any lack of precision in the estimate of the radiation dose to the relevant organ; often this uncertainty will be comparable in magnitude to the uncertainty inherent in the models. Male or Female Cancer Type Age at Exposure Time After GSD Risk Exposure Leukemia mortality â¤20 <15 2.80 3.63 16 to 25 2.53 0.291 â¥26 3.32 0.027 >21 â¤25 1.83 0.287 26 to 30 2.52 0.139 â¥31 3.32 0.027 Other cancer 5 All times 1.53 0.123 mortality 15 >10 yr 1.40 0.097 25 1.31 0.061 35 1.45 0.038 45 1.75 0.024 55 2.17 0.015 65 2.71 0.009 The data for breast cancer incidence in Table 4F-1 shows that the excess relative risk for breast cancer in a woman aged 20 through 39, 25 years after exposure, is 0.06 per 0.1 Gy (10 rads). The GSD (uncertainty) is 1.26. Assume that a woman who had an exposure that gave a dose of 2 rads to the breast at age 25 developed a breast cancer 25 years later, at age 50. Then the excess relative risk ( R) would be 2/10 Ã (0.06) = 0.012. A 68% "credibility interval" for R would be from 0.01 to 0.015 (dividing and multiplying by the GSD, 1.26) and the PC would then be calculated as: Lower limit :0.010 Ã· (1+0.0010) = 0.010, or 1% Best estimate :0.012 Ã· (1+0.012) = 0.0118, or 1.2% Upper limit :0.015 Ã· (1+0.015) = 0.0147, or 1.5% If a 90% or 95% credibility interval is desired, the GSD (1.26) must be raised to the power 1.64 or 1.96, respectively; the values turn out to be 1.46 and 1.57 and the intervals become:

RISKS OF CANCERâALL SITES 227 90% :0.8% to 1.7% 95% :0.8% to 1.8% Similar calculations can be made for any of the models presented in Chapter 4. Values for the GSD can be obtained by interpolation in Table 4F-1 with sufficient accuracy. Diagnostic Examination of the Committee's Risk Models Throughout its development of analytical models of cancer risk as a function of dose and other variables, the committee used a number of diagnostic tests to examine the degree of correspondence between a given model and the data on which it is based (Be80, Mc83). As noted in Chapter 4, decrements of deviance were used as a measure of the improvement in model "fit" gained by adding additional terms. This is, however, not a test of concordance between the data and the model as it is obvious that while the difference between the respective deviancies can perhaps discriminate with an acceptable fineness between two rival nested models, this procedure does not guarantee that either rival "fits" very well. It is important to know how well a given model fits, or describes, a given set of data, not just that it describes the data "better" than an alternative model. There are several aspects to the issue of concordance. A "good fit" does not prove that the model is correct; it simply suggests that, at a chosen level of significance, the sample at hand does not provide any empirical evidence against the model in question. A "poor fit" suggests that there are problems with either the model or with the data. In either case, however, the issue of fit, if based solely on the the criterion of a goodness of fit statistic, such as Pearson's chi-squared Ï2, may lead to errors of inference simply because the assumptions required for the validity of the chi-squared approximation to the sampling distribution of the selected measure of concordance are not satisfied. A measure of whether a model "fits" a given set of Poisson distributed data is the difference between observed and fitted values. The concordance, or goodness-of-fit, of a model of size k with a set of data of size n can be described by the "distance" between the vector of observations, y = (y1, y2, â¦, yn) and the vector of expectations, Here yi is the observed number of cancer cases in the ith cell of the cross-classification of the data, is the number of cases expected if the estimated model is correct and n is the number of cells, or records, in the cross-classification. The components, or more properly, functions thereof, are described as the residuals. There are two forms of residuals that are most commonly deployed for Poisson regression models. These are the deviance, di, and the Pearson chi- squared, Ïi, these are defined as, â

RISKS OF CANCERâALL SITES 228 Note that di includes the ratio and Ïi includes the ratio Thus, it is obvious that as approaches zero when yi > 0, both di and Ïi become quite large. On the null hypothesis, H0, that the model is correct, the respective sums of squares of di and Ïi are, for "large" Âµi, distributed as chi-squared variates on (n â k) degrees of freedom where n is the sample size and k is the size of the model; for a model with s strata and p free parameters, k = s + p. The sums of squared residuals are the aggregate statistics of goodness-of-fit: In general, for a model that "fits" the data and for which the set of are acceptably "large", There is another form of residual that is quite useful to Poisson regression models of "sparse" data. This is the Freeman-Tukey residual, gi, defined as (Bi75, Fr50, Fr83a, Fr83b, Ho85): gi is a standardized residual, that is, it is distributed as N(0, 1). Thus, is distributed approximately as chi-squared on (n â k) degrees of freedom. It is immediately evident that the gi residuals will be "well-behaved" at both yi = 0 and This behavior is quite different from that of the di and Ïi residuals. That is, gi is a more robust measure of discrepancy, between the observed and expected numbers of cases when Âµ i â 0, than are the di and Ïi residuals, in sparse data. In using the aggregate statistics, as measures of overall fit, it is common practice to combine, or pool, the sparse observations in the cells of the cross-classification until This maneuver "adjusts" the number of degrees of freedom (df) by reducing the number, n, of cells. Then, are distributed asymptotically as chi-squared on (n' â k) degrees of freedom where n' < n. But for the sum of squares of Freeman-Tukey residuals, , an alternative and more satisfactory adjustment to the degrees of freedom, can be achieved (Fr83b, Ve81) by subtracting (Tukey correction) the sum, from the usual measure of degrees of freedom to give the adjusted degrees of freedom: df* = (n â k) â c. The sum is over all n* cells for which Âµ i < 1. Then, is distributed as chi-squared on df* degrees of freedom and the pth quantile, up, of the cognate chi-squared distribution can be obtained from the fact that

RISKS OF CANCERâALL SITES 229 is distributed approximately Normally with expected value and variance 1 (Br65): When the data are "sparse," then many of the < 1, and In particular, are inflated, as each is a function of . In general, is inflated more than Î£di2 since Ïi is a stronger function of than di. Moreover, di and Ïi are not defined for although gi is. Thus, as Breslow (Br85) has cautioned, for sparse data neither the deviance, Î£di2 nor Pearson chi-squared, statistic, is suitable as an aggregate measure of the concordance of model and data. If data are not too sparse, Tukey has pointed out that is still a useful aggregate statistic of goodness-of-fit (Fr83, Ve81). Tests of the Committee's Preferred Models When stratified by dose, age and time, the LSS data for leukemia, digestive, respiratory and the group "other cancers" are very sparse. The proportions of records for which there are one or more cases, yi â¥ 1, are 0.061, 0.336, 0.155, and 0.259, respectively. This results, of course, in an excessive number of records for which for any model. Therefore, the committee found the analysis of Freeman-Tukey residuals to be the most useful measure of goodness of fit. It is well-known that, on occasion, aggregate statistics of concordance such as the deviance, , may indicate that a model "fits the data" but examination of the set of component residuals, di, 1 â¤ i â¤ n, may disclose that the model is, "grossly inconsistent with the data" (Ro86). However, on other occasions, especially if the data are sparse, the selected aggregate statistic of fit, say may lead to the opposite inference, indicating that a model does not fit the data when in fact, more sensitive tests that are based on the distributions of the gi residuals rather than on the (sampling) distribution of their sum of squares may, as shown below, disclose a quite acceptable degree of concordance with the data. Some of the results of analyses of the residuals of the respective BEIR V models of the LSS (DS86) data are presented in Table 4F-2. It will be noted that the deviance, di, and chi-squared, Ïi, residuals are greatly inflated; moreover, their respective distributions are decidedly skewed. However, the cognate Freeman-Tukey residuals, gi, are much smaller and more "well-behaved," with rather symmetric distributions in each case, and with means more nearly equal to zero than is the case for the di and Ïi residuals, as shown in Figure 4F-1 for cancers at specified sites. The figure presents the superpositions of the histograms for two samples of random variates, both of sizes n, where n is the number of records in the

RISKS OF CANCERâALL SITES 230 FIGURE 4F-1 Distribution of Freeman-Tukey residuals under the committee's models for leukemia, cancers of the respiratory and digestive systems, and the group "other cancers" (stippled) compared to a normal distribution with the same mean, variance, and sample size.

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RISKS OF CANCERâALL SITES 232 respective sample as listed in Table 4F-3. These are (1) the n Freeman- Tukey residuals, gi, of the BEIR V models of the sample (stippled); and (2) the n random variates drawn from a Normal population with the mean and variance equal to those of the sample of Freeman-Tukey residuals. TABLE 4F-2 Summary of Residual Analysis for BEIR V Models Tumors d(Min) d(Max) Ï(Min) Ï(Max) g(Min) g(Max) Leukemia â1.375 2.389 â0.973 5.853 â1.187 1.812 Digestive â2.739 3.309 â1.937 25.418 â3.001 2.393 Respiratory â2.143 3.197 â1.515 10.862 â2.191 2.074 Other â2.220 3.127 â1.685 12.091 â2.295 2.301 No. of No. of No. of No. of Ïi No. of No. of di â¤ â2 di > 2 Ïi â¤ â2 >2 gi â¤ â2 gi > 2 Leukemia 0 8 0 56 0 0 Digestive 5 21 0 69 5 7 Respiratory 2 18 0 54 2 2 Other 2 29 0 86 2 5 Sum of Squared Residuals df Leukemia 2,266 498 811 244 Digestive 1,909 1,191 2,159 806 Respiratory 1,888 710 1,203 432 Other 1,904 1,124 1,774 712 NOTE: a) Deviance residual: di = sign b) Pearson chi-squared residual: c) Freeman-Tukey residual: gi = yi = observed cases. = fitted cases. = person years at risk for ith record. Deviance = Chi-squared = n" = number of records for which > 0. See Table 4F-3. = sum of squared Freeman-Tukey residuals. n = total number of records. See Table 4F-3. Note in Figure 4F-1 there is an excess (with respect to the Normal) of gi in the vicinity of gi = 0. This is evidence of the extreme sparseness of these Âµ i data, where there are many records for which yi = 0. Since it follows that there are, as well, many small residuals, gi = The respective distributions of Freeman-Tukey residuals are described more precisely in Table 4F-4.

TABLE 4F-3 Records, Strata, Parameters, Degrees of Freedom, and Cases for BEIR V Models Tumor n (Records) s (Strata) p (Parameters) dfa Total yi (Cases) Total n'b n''c Leukemia 2,575 302 7 2,266 173 158 1,010 Digestive 2,162 250 3 1,909 2,193 726 1,789 Respiratory 2,141 250 3 1,888 555 331 1,181 Other 2,156 250 2 1,904 1,162 558 1,741 TOTAL 4,083 a df = degrees of freedom = n â s â p. b n' = number of records for which yi â¥ 1. c n" = number of records for which . NOTE: Deviance, , and Pearson chi-squared, , are calculated from those records, n" in number, for which = 0. RISKS OF CANCERâALL SITES , since di and Ïi are not defined at However, the Freeman-Tukey residuals are defined at = 0 and hence the sum is over all n records. 233

RISKS OF CANCERâALL SITES 234 It should be noted in Table 4F-2 that for Leukemia, no value of gi exceeds | 2|. For Digestive tumors, only 12 gi exceed |2|. For Respiratory and Other tumors, the respective numbers having gi > 2 are also acceptably small, see Frome (Fr83a). Thus, on the evidence of the distributions of the Freeman-Tukey residuals (Mc83), the BEIR V models are not inconsistent with the LSS (DS86) data: the number of gi exceeding |2.0| is very small compared to the number of records, n, and there is no strong pattern (suggestive of model mis- specification) in plots of gi against either the response or predictor variables (Gi84). The Bias and Variance of the Sample Estimate of the Cross- Over Dose Î¸1 and Dose-Rate Effectiveness Factor Î¸2 for Leukemia Dose-Response There are two important classes of problems in the study of somatic responses to low doses of low-LET radiation for which the solutions devolve into inferences on a ratio, say Î¸, of two regression parameters. These ratios are the cross-over dose, Î¸1, and the dose-rate effectiveness factor, Î¸2. 1. The dose at which the linear and quadratic terms in a linear quadratic (LQ) dose-response function are equal is called the cross- over dose. This dose is defined by the ratio, Î¸ = Î²1/Î²2, where Î²1 is the coefficient of the dose, D, and Î²2 is the coefficient of D2 in the LQ model. It should be noted that for the BEIR V LQ model of leukemia mortality the precision of the respective estimates, and is quite low: Note also that these are rather less than are the cognate precisions of the LQ-L model of leukemia incidence described in Table V-8 of the BEIR III Report (Na80): 2. The ratio Î¸2 = Î²1(L)/Î²1(LQ) where Î²1 (L) is the coefficient of dose, D, in the linear model, and Î²1(LQ) is the coefficient of dose in the linear-quadratic model (of the same set of observations) is taken to be a measure of the dose-rate effectiveness factor (DREF). It should be noted that for the BEIR V models of leukemia mortality the precision of the respective estimates, (L) and (LQ) is quite low: Note also that these are rather less than the cognate precisions of the BEIR III models of leukemia incidence: and

TABLE 4F-4 Distribution of Freeman-Tukey Residuals for BEIR V Models of LSS (DS86) Data Quantiles Tumor n Mean Standard Deviation Skewness Kurtosis 0a 0.25 0.50 0.75 1.00b Leukemia 2,575 â0.02 0.31 2.20 8.75 â1.18 â0.10 0 0 1.81 Digestive 2,162 â0.03 0.61 0.36 1.71 â3.00 â0.32 â0.07 0.05 2.39 Respiratory 2,141 â0.02 0.45 0.66 4.31 â2.19 â0.13 0 0 2.07 Other 2,156 â0.03 0.57 0.57 1.87 â2.29 â0.28 â0.07 0 2.30 a Minimum. b Maximum. RISKS OF CANCERâALL SITES 235

RISKS OF CANCERâALL SITES 236 Since these ratios, Î¸, are non-linear functions of the regression parameters, say Î²j, and Î²k, the maximum likelihood (ML) estimates, are biased: (Co74, Ef82, Hi77, We83). If the respective precisions of the sample estimates , are quite poor and the correlation, say Ï, between is negative (Ï < 0), then the bias, as well as the variance of the sample estimate, of Î¸, may be quite large. Estimates of the bias and variance of Î¸ can be obtained by several methods: the delta method (Co74, Hi77) and the weighted jackknife method (Hi77, We83) are two. Estimates of the bias can also be obtained by the MELO method (Ze78). All three methods yield comparable estimates of Î¸ for which the bias is less than for the ML estimate, when However, only the weighted jackknife methods (Hi73, We83) provide useful estimates of Î¸ when < 1.0 and/or Table 4F-5 presents estimates of the bias and variance of and for the preferred (non-linear) Poisson models of leukemia mortality. Cognate estimates for the Poisson (linear) models of leukemia incidence in the BEIR III report, (Table V-8; NRC80) are included for comparison (He86, He89). The sample estimate of the parameter variance-covariance matrix, Var( ) for the BEIR V model is conservative and hence the confidence limits are wide. In this regard it should be noted that the dispersion factor (Mc83), Ï2 = Ï2/df = 0.358, is not included in the estimates given in Table 4F-5. However, a dispersion factor is included in the estimates given by Table V-8 in the BEIR III report (NRC80, He86). It is well-known that the statistical theory and measures for assessing the adequacy (e.g., goodness-of-fit) of a regression model and the precision of the parameter estimates that are adequate for models that are linear in the parameter vectors (e.g., the Poisson regression models of the BEIR III data) are only approximately valid for models that are non-linear in the parameters (e.g., the Poisson regression models of the BEIR V data). For instance, the exact likelihood (1âÎ±) confidence regions on the parameters of non-linear models differ considerably in both size and symmetry from the familiar ellipsoids of linear models as Î± â 0. There has been some work in the development of indices of the degree of non-linearity that would identify those combinations of model and data in which the measures (e.g., confidence regions) for linear models provided adequate approximations for non-linear models (Ba80; Be60; Gu65). However, these measures have been developed only for non-linear models of observed responses in which

RISKS OF CANCERâALL SITES 237 the random part has a Normal distribution, and hence are not directly applicable to the non-linear Poisson models in the BEIR V report. TABLE 4F-5 Maximum Likelihood and Reduced Bias Estimates of the Ratios Î¸1 and Î¸2 for Poisson Regression Models of Leukemia (ML (Delta Standard Error Ratio Est.) Est.)a (Delta Est.) Î¸1, Cross- over dose (Gy) BEIR V 0.89 1.12 0.86 1.04 (Ï > 0) BEIR III 1.18 0.31 1.82 0.6 (Ï < 0) Î¸2, DREF BEIR V 1.99 1.92 2.33 0.85 BEIR III 2.24 1.51 1.92 1.17 a ML estimate with a first-order correction for bias. NOTE: The estimates of Î¸2 were based on an assumed value of the correlation coefficient, p*, for This value is p* = 0.50. This value of p* was obtained from the observed correlation of (i) in the set of n row-deleted estimates (Be80, Co82) of the respective parameter vectors, Î², of the BEIR III L â L and LQ â L models of the BEIR III leukemia incidence data. The estimate of Î¸2 is much more sensitive to the size and sign of p* for the models of the BEIR V data than for those of the BEIR III data. The estimates of bias and variance obtained by the delta method are conservative. Cognate estimates obtained by the jackknife method will be larger. Nonetheless, the comparison of the estimated parameters of non-linear models with their respective standard errors provides a useful appreciation of the precision of the estimates. And indeed, for small values of Î±, the exact confidence regions on the parameters of a non-linear model are frequently well- approximated by those obtained from linear theory. For example, the exact 50% confidence regions (Î± = 0.50) on the parameters of a non-linear (Normal theory) model often are nearly coincident with the cognate ellipsoids of linear theory (Be77). Therefore, the comparison of the estimates of non-linear functions of parameters, such as DREF = with their respective standard errors will provide a useful appreciation of the precision (or, perhaps more precisely, the lack thereof) with which estimates of these important ratios can be obtained from the L and LQ regression models of a given set of data. Such comparisons disclose that the respective standard errors of the two ratios are about equal to the ML point estimates:

RISKS OF CANCERâALL SITES 238 for j = 1, 2. This is consistent with the precision of the estimates of the numerator and denominator: for j = 1, 2. The bias in the ML point estimates varies from about 5% to about 50% of the size of the respective standard errors in each case. The negative sign of the bias in the BEIR V models may be due to the presence of large random errors in the sample estimates of the respective covariances, Cov or to the presence of the covariates in time, age, etc. which, of course, also inflates References Ba80 Bates, D. M., and D. G. Watts. 1980. Relative curvature measures of non-linearity. J. Royal Statist. Soc. B. 42(1):1-25. Be60 Beale, E. M. L. 1960. Confidence regions in non-linear estimation. J. Royal Statist. Soc. 22 (1):41-88. Be77 Beck, J. V., and K. J. Arnold. 1977. Parameter Estimation in Engineering and Science. New York: John Wiley & Sons. Be80 Belsley, D. A., E. Kuh, and R. E. Welsch. 1980. Regression diagnostics. New York: John Wiley & Sons. Bi75 Bishop, Y. M. M., S. E. Fienberg, and P. W. Holland. 1974. Discrete Multivariate Analysis: Theory and Practice. Cambridge, Mass.: MIT Press. Br65 Brownlee, H. 1965. Statistical Theory and Methodology in Science and Engineering. New York: John Wiley & Sons. Br85 Breslow, N. E., and B. E. Storer. 1985. General relative risk functions for core control studies. Am. J. Epidemiol. 122(1):149-162. Co74 Cox, D. R., and D. V. Hinkley. 1974. Theoretical Statistics. New York: Chapman and Hall. Ef82 Efron, B. 1982. The Jackknife, The Bootstrap and Other Resampling Plans. Philadelphia, Pa.: SIAM. Fr50 Freeman, M. F., and J. W. Tukey. 1950. Transformations related to the angular and the square root. Ann. Math. Statist. 21:607-611. Fr83a Frome, E. L. 1983. The analysis of rates using Poisson regression models. Biometrics 39:665-674. Fr83b Frome, E. L., and R. J. DuFrain. 1983. Maximum likelihood estimation for cytogenetic dose- response curves. ORNL/CSD-123. Office of Health and Environ. Research and U.S. Dept. of Energy and Oak Ridge Assoc. Univ. Gi84 Gilchrist, W. 1984. Statistical Modelling. New York: John Wiley & Sons. Gu65 Guttman, I., and D. A. Meeter. 1965. On Beale's measures of non-linearity. Technometrics 7:623-637. He86 Herbert, D. E. 1986. Clinical Radiocarcinogenesis. Applications of regression diagnostics and Bayesian methods to Poisson regression models. Pp. 307-364 in Multiple Regression Analysis: 2 Applications in the Health Sciences, D. E. Herbert and R. H. Myers, eds. AAPM Med. Phys. Monograph No. 13. New York: AIP. He89 Herbert, D. E. 1989. Dose response models: construction, criticism, discrimination, validation and deployment. Pp. 534-630 in Prediction of Response in Radiation Therapy: Analytical Models and Modelling, B. R. Paliwal, J. F. Fowler, D. E. Herbert, T. J. Kinsella, and C. G. Orton, eds. AAPM Symposium Proceedings No.7, Part 2. New York: AIP. In press.

RISKS OF CANCERâALL SITES 239 Hi77 Hinkley, D. V. 1977. Jackknifing in unbalanced situations. Technometrics. 19(3):285-292. Ho85 Hoaglin, D. C., F. Mosteller, and J. W. Tukey. 1985. Exploring Data. Tables, Trends, and Shapes. New York: John Wiley & Sons. IC86 International Commission on Radiation Units and Measurements. 1986. The Quality Factor in Radiation Protection. ICRU Report 40. Report to the ICRP and ICRU of a joint task group. Bethesda, Md.: International Commission on Radiation Units and Measurements. Mc83 McCullagh, P., and J. A. Nelder. 1983. Generalized Linear Models. New York: Chapman and Hall. NRC80 National Academy of Sciences/National Research Council. 1980. The Effects on Populations of Exposure to Low Levels of Ionizing Radiation: 1980 (BEIR III). Washington, D.C.: National Academy Press. NIH85 National Institutes of Health. 1985. Report of the Ad Hoc Working Group to Develop Radioepidemiological Tables. NIH Publication 85-2748. Washington, D.C.: U.S. Government Printing Office. Pi89 Pierce, D.A., D.O. Stram, and M. Vaeth. 1989. Allowing for random errors in radiation exposure estimates for the atomic bombs RERF TR 2-89. Hiroshima: RERF Ro86 Robins, J. M., and S. Greenland. 1986. The role of model selection in causal inference from nonexperimental data. Am. J. Epidemiol. 123(3):392-402. Ve81 Velleman, P. F., and D. C. Hoaglin. 1981. Applications, Basics, and Computing Exploratory Data Analysis. Boston: Duxbury Press. We83 Weber, N.C., and A. H. Welsh. 1983. Jackknifing the general linear model. Austral. J. Statist. 24(3):425-436. Ze78 Zellner, A. 1978. Estimations of functions of population means and regression coefficients including structural coefficients: a minimum expected loss (MELO) approach. J. Econometrics 8:127-158. ANNEX 4Gâ THE BEIR IV COMMITTEE'S MODEL AND RISK ESTIMATES FOR LUNG CANCER DUE TO RADON PROGENY The BEIR IV Committee's risk model is based on analyses of the lung cancer mortality experience of four cohorts of underground miners. These analyses indicated a decline in the excess relative risk with both attained age and time since exposure. The Committee modeled these temporal parameters as step functions as indicated in the equation below, where r (a) is the age specific lung cancer mortality rate. r(a) = ro(a)[1 + 0.025Î³(a)(W1 + 0.5W2)], where ro(a) is the age specific ambient lung cancer rate for persons of a given sex and smoking status; Î³(a) is 1.2 when age a is less than 55 yr, 1.0 when a is 55-64 yr, and 0.4 when a is 65 yr or more. W1 is the cumulative exposure in Working Level Month (WLM) incurred between 5 and 15 yr before this age and W2 is the WLM incurred 15 or more years before this age.

RISKS OF CANCERâALL SITES 240 TABLE 4G-1 Ratio of Lifetime Risksa (Re/Ro), Lifetime Risk of Lung Cancer Mortality (Re), and Years of Life Lost (Lo â Le)b for Lifetime Exposure at Various Rates of Annual Exposure (NAS88)c Males Nonsmokers Smokers Exposure Rate (WLM/ Re/Ro Re Lo â Le Re/Ro Re Lo â Le yr) 0 1.0 0.0112 0 1.0 0.123 1.50 0.1 1.06 0.0118 0.00907 1.05 0.129 1.59 0.2 1.11 0.0124 0.0181 1.10 0.135 1.69 0.3 1.16 0.0131 0.0272 1.15 0.141 1.79 0.4 1.22 0.0137 0.0362 1.20 0.147 1.88 0.5 1.27 0.0143 0.0453 1.24 0.153 1.98 0.6 1.33 0.0149 0.0544 1.29 0.159 2.07 0.8 1.44 0.0161 0.0724 1.39 0.170 2.26 1.0 1.54 0.0173 0.0905 1.48 0.182 2.44 1.5 1.82 0.0204 0.136 1.70 0.209 2.89 2.0 2.08 0.0234 0.180 1.91 0.235 3.33 2.5 2.35 0.0264 0.225 2.12 0.260 3.75 3.0 2.62 0.0294 0.270 2.31 0.284 4.16 3.5 2.89 0.0324 0.314 2.49 0.306 4.56 4.0 3.15 0.0354 0.359 2.66 0.328 4.95 4.5 3.41 0.0383 0.403 2.83 0.348 5.32 5.0 3.68 0.0413 0.447 2.99 0.368 5.68 10.0 6.24 0.0700 0.883 4.24 0.521 8.77 This model is applied as follows. First, exposures are separated into two intervals as indicated above for each year in the period of interest, and then the total annual risk is calculated, using the appropriate age specific ambient rate. This age-specific mortality rate for lung cancer, r(a), is multiplied by the chance of surviving all causes of death to that age, including the risk due to exposure, and these products are summed over successive ages of interest. Lifetime risks of lung cancer mortality due to radon exposure over a full lifetime are presented in Table 4G-1. Three measures of risk are listed: Re/Ro, the ratio of lifetime risk relative to that of an unexposed person of the same sex and smoking status; Re, the lifetime risk of lung cancer; and the average years of life lost compared to the longevity of a nonsmoker of the same sex. The BEIR IV Committee pointed out a number of uncertainties in these risk estimates. These include the model for the effect of smoking used by the committee, the statistical uncertainty and possible biases in the

RISKS OF CANCERâALL SITES 241 cohort data, the modeling uncertainty, and the uncertainty introduced by using data for occupationally exposed males to project the risks to persons in the general population having a wide range of ages and differing exposure situations. All of these factors are discussed at some length in the BEIR IV Committee's Report (NRC 88). References NRC88 National Research Council, Committee on the Biological Effects of Ionizing Radiations. Health Risks of Radon and Other Internally Deposited Alpha-Emitters (BEIR IV). Washington, D.C.: National Academy Press. 602 pp. Females Nonsmokers Smokers Exposure Rate Re/Ro Re Lo â Le Re/Ro Re Lo â Le (WLM/yr) 0 1.0 0.00603 0 1.0 0.582 0.809 0.1 1.06 0.00637 0.00606 1.06 0.0614 0.867 0.2 1.11 0.00672 0.0121 1.11 0.0646 0.925 0.3 1.17 0.00706 0.0182 1.16 0.0678 0.983 0.4 1.23 0.00741 0.0242 1.22 0.0710 1.04 0.5 1.28 0.00775 0.0303 1.27 0.0742 1.10 0.6 1.34 0.00809 0.0363 1.33 0.0773 1.16 0.8 1.46 0.00878 0.0484 1.44 0.0836 1.27 1.0 1.57 0.00946 0.0605 1.54 0.0898 1.38 1.5 1.85 0.0112 0.0907 1.80 0.105 1.67 2.0 2.14 0.0129 0.121 2.06 0.120 1.95 2.5 2.42 0.0146 0.151 2.32 0.135 2.22 3.0 2.70 0.0163 0.181 2.56 0.149 2.49 3.5 2.98 0.0180 0.211 2.81 0.163 2.76 4.0 3.26 0.0197 0.241 3.04 0.177 3.03 4.5 3.55 0.0214 0.271 3.28 0.191 3.29 5.0 3.83 0.0231 0.301 3.51 0.204 3.55 10.0 6.59 0.0398 0.598 5.56 0.324 5.98 a Relative to persons of the same sex and smoking status. b Lo is the average lifetime of nonsmokers of the same sex. c Estimated with the committee's TSE model and a multiplicative interaction between smoking and exposure to radon progeny.