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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
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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
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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
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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
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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
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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
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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).
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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,
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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)
=
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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
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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.
ˇ 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
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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 232
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){2tYil°g(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 233
233
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OCR for page 234
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 235
235
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OCR for page 236
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 237
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 238
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 239
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 240
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 241
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.
Representative terms from entire chapter:
breast cancer
