Click for next page ( 162


The National Academies | 500 Fifth St. N.W. | Washington, D.C. 20001
Copyright © National Academy of Sciences. All rights reserved.
Terms of Use and Privacy Statement



Below are the first 10 and last 10 pages of uncorrected machine-read text (when available) of this chapter, followed by the top 30 algorithmically extracted key phrases from the chapter as a whole.
Intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text on the opening pages of each chapter. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.

Do not use for reproduction, copying, pasting, or reading; exclusively for search engines.

OCR for page 161
4 Risks of Cancer All 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 promoters 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 161

OCR for page 161
162 EFFECTS OF EXPOSURE TO TOW LE~LS OF IONIZING MOTION 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 red) 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 (Sham. But 34,272 of those survivors were so far from the hypocenters that their radiation doses were negligible- less than 0.005 Gy (0.5 red) and 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 UN- SCEAR in its latest report (UNTO. 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

OCR for page 161
RISKS OF CANCER ALL 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. 1b 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. i] While this approach limits the application of these results for calculat- ng 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 (IJN88), 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

OCR for page 161
164 EFFECTS OF EXPOSURE TOOLS OFlONIZING~MTION TABLE 4-1 Fitting Major Characteristics of the Data Sets Used for Model Incidence Cancer Study Population Reference or Mortality Sites Total Total Cases Person Years Atomic bomb survivors Sh87 Mortality All5,9362,185~335 To87 Incidence Breast376940,000 Ankylosing spondylitis patients Da87 Mortality Leukemia36104,000 All except leukemia and colon563104,000 Canadian fluoroscope patients Mi89 Mortality Breast482867,541 Mass. fluoroscope Hr89 Mortality Breast7430,932 N.Y. postpartum mastitis Sh86 Incidence Breast11545,000 Israel tinea capitis Ro84 Incidence Thyroid55712,000 Rochester thymus Sh85 Incidence Thyroid28138,000 from which these various data sets derive are described in Annex 4A to this chapter. Able 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. 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 commit- tee'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 de- graded neutron spectrum at the survivors locations (see Annex 4B) and the potential low bias in the DS86 estimates of neutron kerma (Romp. The analysis of the sensitivity of the results to this assumption in Annex 4D

OCR for page 161
RISk:;S OF CANCER ALL SITES 165 shows that the estimated risks for A-bomb survivors change insignificantly for a neutron RBE of 10 vis ~ 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 (Howl. 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 mis- specification 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 (Leafy. Second, since there were no unexposed comparison sub- jects, 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

OCR for page 161
166 EFFECTS OF EXPOSURE TO LOW LE~LS OF IONIZING EDITION 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 anlylosing 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 ye 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 Aide as :(d) = ~ot1 + f (d~g(~. (4-1) Letf (d) represent a function of the dose d which in the committee's models is always a linear or linear-quadratic function, i.e., fade = Ovid or fade = clod + cx3d2. In general, the excess risk function, gads 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 :(d) = :0 + f (`d~g(`fB). (4-2) These models give similar results (see Annex 4D) as expected since the function gall is allowed to depend on age, time, etc. This would not be the case if gall 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 rise The committee chose not to model it, but rather

OCR for page 161
RlSk:;S OF CANCER ALL 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, Kaput. 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 con- structed 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 (Comb. 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).

OCR for page 161
168 EFFECTS OF EXPOSURE TO LOW LE~LS OF IONIZING MOTION The leukemia model mathematically is as follows (see the general equation 4.1~: f (d) = a2d + a3d2 `~' _ ~ expert I(T < 15) + ,B2 It 15 < T < 25~] if E < 20 g~exptp3I(T 20, (4-3) where the indicator function I(T < 15) is defined as 1 if T < 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: 0~2 = 0.243~0.291), or3 = 0.271~0.314), p: = 4.885~1.349), p2 = 2.380~1.311),,03 = 2.367~1.121), 34= 1.638~1.321~. 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: f~d) = aid 9~) = expt,0~ln(T/20) + 32I(S)], (4-4) where T = years after exposure and I(S) = 1 if female, O if male with cat = 0.636~0.291), p~ = -1.437~0.910), p2 = 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, - 1.437,

OCR for page 161
RISKS OF CANCER ALL 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 de- creasing relative risk observed in the Ankylosing Spondylitis study (Da87) which influenced the committee's choice of parameters. While the inclu- sion 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 feds = aid `~' ~ expel, + p21n(T/20) + p31n2(T/20~] if E < 15 9 ll expt~321n(T/20) ~ p31n2(T/20) + p4(E - 15~] if E > 15, where E is age at exposure and T is years after exposure with a (4-5) =

OCR for page 161
170 EFFECTS OF EXPOSURE TO LOW LE~LS OF IONIZING MOTION 1.220~0.610), p: = 1.385~0.554), 32 = -0.104 (0.8~), p3 = -2.212 (1.376), p4 = -0.~28 (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: fade = aid 9(,3) = exp[~I(S) + ~E] where I (S) equals 1 for females and 0 for males and (0 if E < 25 HE = p2(E-25) if 25 < E < 35 t 1032 if E > 35 (4-6) with E = age at exposure. The estimated parameter values are cot = 0.809~9.327),,B~ = 0.553~0.462), g2 = -0.198~0.06281. 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 fade = orid `4 7' gaff= 1 if E< 10andexp BANE-10~] if ED 10, where E = age at exposure and a~ = 1.220~0.519), p~ = - 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

OCR for page 161
RlSk:;S OF CANCER ALL 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. . Instantaneous exposure causing a dose equivalent to all body organs of 0.1Sv (10 red 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. Continuous lifetime exposure causing a dose equivalent in all body organs of 1 mSv (0.1 red of low-LET radiation) per year. Continuous exposure from age 18 to age 65 causing a dose equiv- alent to all body organs of 10 mSv (1 red 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 eRectiveness 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

OCR for page 161
RISKS OF CANCER-ALL SITES 2000 1 500 7 1 000 500 2000 1 500 z 1 O0O G 500 o - Respiratory System n _-EM By;  I\= 2`,`; ]h 2 LiF ~ ~ ~ ~ TO ~ L'-j;~''~[-,'1 ~ ~ ~l''l~ ~ ~ 453O ~ ooze ~0~ ~ ~0 ~ 00 ~ ~0~ ~ ~0 ~ 00~ ~0 lo' ,~' in' ~ lo' lo' lo' ,0' ,0' ,0' O O' O' O' a' a' a' a' lo' A' A' FREEMAN-TUKEY RESIDUAL, 9; Other Cancers ` 4, `1,, 0.0 0.5 ~ ., ,, ~,1 1.0 1.5 2.0 2.5 -2.5 -2.0 -1.5 -1.0 231 FREEMAN-TUKEY RESIDUAL, 9;

OCR for page 161
232 EFFECTS OF EXPOSURE TO LOW LEVELS OF IONIZING RADIATION TABLE 4F-2 Summary of Residual Analysis for BEIR V Models Tumors d(Min) d(Max) x(Min) x(Max) g(Min) "(Max) Leukemia -1.375 2.389 - 0.973 5.853 - 1.187 1.812 Digestive -2.739 3.309 - 1.937 25.418 - 3.001 2.393 Respiratory -2.143 3.197 - 1.515 10.&62 -2.191 2.074 Other -2.220 3.127 - 1.685 12.091 -2.295 2.301 No. of No. of No. of No. of No. of No. of di' - 2 di > 2 Xi' -2 xi > 2 gi' - 2 gi > 2 Leukemia 0 ~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 Id2 EX, ~g' 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 = sgntyi - ili){2tYilg(Y'/lli) - (Yi - 1li)~} b) Pearson chi-squared residual: Xi = (pi - Dimly c) Freeman-Tukey residual: gi = ~ + >/~- I. Pi = observed cases. Hi = fitted cases. Hi = Aci. ci = person years at risk for ith record. n,, Deviance= Ida. n,, Chi-squared = ~X' n" = number of records for which Hi > 0. See Table 4F-3. n >,g2 = sum of squared Freeman-Tukey residuals. n = total number of records. See Table 4F-3. respective sample as listed in Table 4F-3. These are (1) the n Freeman- nlkey residuals, pi, 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. Note in Figure 4F-1 there is an excess (with respect to the Normal) Of pi in the vicinity of gi = 0. This is evidence of the extreme sparseness of these pi data, where there are many records for which yi = 0. Since EYi = Epi, it follows that there are, as well, many small residuals, pi = >/~ ~ i/=-~pi + 1. The respective distributions of Freeman-~key residuals are described more precisely in Table 4F-4.

OCR for page 161
233 Lit V) a' Ct Cal o au o V) a' i_ Ct so Ct ct 1 To a' CD m ~ ~ O ~I ~o - - ~ - - 3 G S ~ ~ ~ ~ 50 ~ 0< S X ~ ~ X Up ~ ~ Via A* ~ rid ~ a_ a' Cal - U ON V) so a) _` V) o Cal an S `_ Via ~ ~ So Via ~C rimrr ~ cry x ~ ~ 0 00 0 Cal O ~ ~ ~ r ~ ~ O O O 0 It) ~ It) UP O .> ~ ~ V, ~ ~ ~ a, au ~ . ~ ~ Al A 1 ' - < - ~C s 1 ._ _ s 3 3 11 o o ~ ~ o o o o~ 11 11 -s ~5 11 < - 5 .= _ ~ S a' - Ct - V) V) o O ~ a' _ ~ ~ LL~ Ct a' ~ ~_ '~ a ~ _ ~ x 3 X a' 0 ~ 11 5 _ cn < ~ ._ ~ O ~ O Ct ~ s~ ~4 ~ S ~ _ O ct a ~ _ ~ X a V) ~ = ~ V) ~ . . ~ 4_ LL O (u - 0 A C Z '- ~ o ._

OCR for page 161
234 EFFECTS OF EXPOSURE TO LOW LE~LS OF IONIZING ORATION It should be noted in Bible 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-~key residuals (Mc83), the BEIR V models are not inconsistent with the LSS (DS86) data: the number of pi exceeding ~2.0~ is very small compared to the number of records, n, and there is no strong pattern (suggestive of model mix-specification) in plots of gi against either the response or predictor variables (Gimpy. The Bias and Variance of the Sample Estimate of the Cross-Over Dose O and Dose-Rate Effectiveness Factor 02 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 (3, of two regression parameters. These ratios are the cross-over dose, Hi, and the dose-rate-effectiveness factor, 02. 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, G) = g~/~2, where p~ is the coefficient of the dose, D, and g2 is the coefficient of D2 in the LO model. It should be noted that for the BEIR V LQ model of leukemia mortality the precision of the respective estimates, p~ and 32 is quite low: A I ~ A / ~ - pl/~/Var(pl) = 0.864 and ,02/~/Var(32) = 0.865. 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 (Nancy: p~ /~ = 1 .065; 32/ ~ =1.518. 2. The ratio C'2 = p~(L)//3~(LQ) where p~ (L) is the coefficient of dose, D, in the linear model, and i3~(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 mortal- ity the precision of the respective estimates, 43~(L) and /3~`LQ) is quite A I A A / A low: pl(L)/~/Var(pl(L)) = 0.878 and,Bl(LQ)/;Var(gl(LQ)) = 0.834. Note also that these are rather less than the cognate precisions of the BEIR III models of leukemia incidence: pl(L)/~/Var(~(L)) = 3.647 and /3~ (LQ)/ ~/Var(~ (LQ) ~ = 1.065.

OCR for page 161
235 Cal oo Can _' U: o - o m o - C~ ._ V) a' LLI o o ._ 4 - lo _ m V7 ~7 at 3 a' Can `_ , C . ~ a., Con o ~ Cal r-, X - c - , - - 1 . . .. _ _ __ _ _ __ 1 1 1 1 X - 3 _ - _ ~ . . .. - r - , rid cad 1 1 1 1 _ ~= ~ ~ r - , ~ lo, ~1 _ _ _ 1 1 1 1 .= ~ O is.> Q ~ _ au ~- ~ ~ ~ O

OCR for page 161
236 EFFECTS OF EXPOSURE TO LOW LE~LS OF IONIZING EDITION Since these ratios, E), are non-linear functions of the regression param- eters, say As and pk. the maximum likelihood (ML) estimates, ~ = Fj/gk, are biased: E(~(~)-C) it 0 (Co74, Ef82, Hi7?, Weeks. If the respective Recisions of the sample estimates, Hi and pk. are quite poor and the correlation, say p, between ,dj and ink is negative (p ~ 0), then the bias, as well as the variance of the sample estimate, ~ = /3j/~3k of 0, may be quite large. Estimates of the bias and variance of ~ can be obtained by several methods: the delta method (Co74, Hi77) and the weighted jack- knife method (Hi77, We83) are two. Estimates of the bias can also be obtained by the MELO method (Ze78~. All three methods yield compa- rable estimates of (3 for which the bias is less than for the ML estimate, A i A 07 when ~j/;Var(pj) > 1.0. However, only the weighted jackknife meth ods (Hi73, We83) provide useful estimates of ~ when ,Cj // < 1.0 A I ~ and/or pk/~/Var(,Bk) < 1.0. Table 4F-S presents estimates of the bias and variance of (3~ and 02 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, Hemp. The sample estimate of the parameter variance-covariance matrix, Var(,B), 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), ~2 = X2/df = 0.358, is not included in the estimates given in Table 4F-S. However, a dispersion factor is included in the estimates given by Table V-8 in the BEIR III report (NRC80, Hemp. 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 (1-a) confidence regions on the parameters of non-linear models differ considerably in both size and symmetry from the familiar ellipsoids of linear models as ax - ~ 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; Guest. However, these measures have been developed only for non-linear models of observed responses in which

OCR for page 161
RISKS OF CANCER ALL SITES 237 TABLE 4F-5 Maximum Likelihood and Reduced Bias Estimates of the Ratios ED and e2 for Poisson Regression Models of Leukemia Standard Error (Delta Est.) ej (ML Est.) ej* (Delta Est.)a Ratio A emit Al, Cross-over dose (Gy) BEIR V 0.89 1.12 0.86 1.04 (p > 0) BEIR III 1.18 0.31 1.82 0.6 (p ~ O) e2, DREF BEIR V 1.99 1.92 2.33 0.85 BEIR III 2.24 1.51 1.92 1.17 aML estimate with a first-order correction for bias. NOTE: The estimates of e2 were based on an assumed value of the correlation coefficient, p*, for GIL) and p~(LQ). This value is p* = 0.50. This value of p* was obtained from the observed correlation of p~(L)(i) in the set of n row-deleted estimates p(i), 1 c i c n (Be80, Co82) of the respective parameter vectors, A, of the BEIR III L - L and LQ - L models of the BEIR III leukemia incidence data. The estimate of e2 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. the random part has a Normal distribution, and hence are not directly applicable to the non-linear Poisson models in the BEIR V report. 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 a, 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 act = 0.50) on the parameters of a non-linear (Normal theory) model often are nearly coincident with the cognate ellipsoids of linear theory (Beam. Therefore, the comparison of the estimates of non-linear functions of parameters, such as DREF = 6)2 = /31(L)//31(LQj, 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 LO 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: At // ~ 1.0

OCR for page 161
238 EFFECTS OF EXPOSURE TO LOW LEVELS OF IONIZING RADIATION for j = 1, 2. This is consistent with the precision of the estimates of the A I ~ numerator and denominator: ~j/~/Var(3j) ~ 1.0 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 A A (3j,pk) or to the present of the covariates ~ time, age, etc. which, of course, also inflates Var(,0~. References Ba80 Be60 Be77 Be80 Bi75 Br65 Br85 Co74 Ef82 FrS0 Fr83a Fr83b Gi84 Gu65 He86 He89 Bates, D. M., and D. G. Watts. 1980. Relative eu~vature measures of non-linearity. J. Royal Statist. Soe. B. 42~1~:1-25. Beale, E. M. L. 1%0. Confidence regions in non-linear estimation. J. Royal Statist. Soe. 22~1~:41~8. Beck, J. V., and K. J. Arnold. 1977. Parameter Estimation in Engineering and Science. New York: John Wiley & Sons. Belsley, D. A., E. Kuh, and R. E. Welsch. 1980. Regression diagnostics. New York: John Wiley & Sons. Bishop, Y. M. M., S. E. Fienberg, and P. W. Holland. 1974. Discrete Multivariate Analysis: Theory and Practice. Cambridge, Mass.: MIT Press. Brownlee, H. 1965. Statistical Theory and Methodology in Science and Engineering. New York: John Wiley & Sons. Breslow, N. E., and B. E. Storer. 1985. General relative risk functions for core control studies. Am. J. Epidemiol. 122~1~:149-162. Cox, D. R., and D. ~ Hinkley. 1974. Theoretical Statistics. New York: Chapman and Hall. Efron, B. 1982. The Jackknife, The Bootstrap and Other Resampling Plans. Philadelphia, Pa.: SIAM. Freeman, M. F., and J. W. ~key. 1950. Transformations related to the angular and the square root. Ann. Math. Statist. 21:607-611. Frome, E. L. 1983. The analysis of rates using Poisson regression models. Biometrics 39:665-674. 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. Gilchrist, W. 1984. Statistical Modelling. New York: John Alley & Sons. Guttman, I., and D. A. Meeter. 1965. On Beale's measures of non-linearity. Technometrics 7:623-637. Herbert, D. E. 1986. Clinical Radiocareinogenesis. 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. Herbert, D. E. 1989. Dose response models: construction, criticism, diserim- ination, 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.

OCR for page 161
RISKS OF CANCER ALL SITES Hi77 Ho85 IC86 McS3 Pi89 Ro86 We83 Ze78 239 Hinkley, D. V. 19 77. Jackknifing in unbalanced situations. Technometrics. 19~3~:285-292. Hoaglin, D. C., F. Mosteller, and J. W. Pokey. 1985. Exploring Data. Ibbles, ~ends, and Shapes. New York: John Wiley & Sons. 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. 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 Radioopidemiological Bibles. NIH Publication 85-2748. Washington, D.C.: U.S. Government Printing Office. 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 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. Velleman, P. F., and D. C. Hoaglin. 1981. Applications, Basics, and Computing Exploratory Data Analysis. Boston: Duxbu~y Press. Weber, N.C., and A. H. Welsh. 1983. Jackknifing the general linear model. Austral. J. Statist. 24~3~:425-436. Zellner, ~ 1978. Estimations of functions of population means and regression coefficients including structural coefficients: a minimum expected loss (MELD) approach. J. Econometrics 8:127-158. ANNEX 4G: 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 read is the age specific lung cancer mortality rate. Ryan = rO(a)~1 + 0.025-y~a)(W~ + 0.5W2~], where rO(a) is the age specific ambient lung cancer rate for persons of a given sex and smoking status; blat 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. We 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.

OCR for page 161
240 EFFECTS OF EXPOSURE TO LOW LE^LS OF IONIZING MOTION TABLE 4G-1 Ratio of Lifetime Risksa (RelRo), Lifetime Risk of Lung Cancer Mortality (Red, and Years of Life Lost (Lo - LeJb for Lifetime Exposure at Various Rates of Annual Exposure (NAS88)C Males Exposure Nonsmokers Smokers Rate (WLM/yr) RelRo Re Lo - Le RelRo Re Lo - Le 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 ().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, rfa), 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 Bible 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

OCR for page 161
RISKS OF CANCER ALL SITES TABLE 4G-1 Continued 241 Females Exposure ~ 1 Nonsmokers Smokers Rate WLM/yr) RelRo Re L - L RelRo Re L - L 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 ().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. bLo 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. 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.