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CHAPTER 14
Shape of the Dose-Response Relationship,
and Low-Dose Cancer-Yields Based on the Best-Fit Curve
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This chapter is arranged in six parts:
1. Supra-Linear Shape of the Dose-Response Relationship, p.1
2. Basis for Ruling-Out a Concave-Upward Shape, p.2
3. Purely Low-LET Radiation versus Mixed (Gamma + Neutron), p.5
4. Basis for Generalizing from the A-Bomb Study, p.6
5. Low-Dose Cancer-Yields Derived from the Best-Fit Curve, p.6
6. The Bottom Line from Regression Analysis, p.8
Then tables.
Then figures.
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In the previous chapter, the Cancer Difference Method gives us
Minimum Fatal Cancer-Yields in both the T65DR and DS86
dosimetries, and the results indicate that the cancer-risk is more
severe per centi-sievert (rem) at low doses than at high doses. In
other words, the findings in the previous chapter strongly suggest
that shape of dose versus cancer-response is presently
supra-linear. (Other terms for supra-linear, including
"concave-downward," "upward convex," and even "sub-linear," are
discussed in Chapter 23, Part 4.)
In this chapter, we will use the technique of curvilinear
regression analysis for three purposes: (A) to depict the shape
of dose-response in the A-bomb survivors, (B) to determine whether
or not the supra-linear shape meets the test of statistical
significance, and (C) to calculate Cancer-Yields based on the
best-fit equation.
1. Supra-Linear Shape of the Dose-Response
===========================================
In Chapter 29, we have used the data from Table 13-A, Rows 1
through 6, to demonstrate the technique of curvilinear regression.
The steps of input, output, writing the best-fit equation,
plotting graphs, and statistical testing are all presented in
detail in that chapter. Readers who consult Chapter 29 will see
for themselves exactly how we obtain the findings which are
discussed in this chapter and elsewhere.
Findings from Chapter 29 are brought forward into this
chapter. For instance, the equation which best fits the
observations, in the T65DR dosimetry, is brought forward from
Table 29-B and is presented in the Upper Notes of Table 14-A of
this chapter.
Using the equation, we have calculated the predicted
cancer-rates in Table 14-A, Column C, for dose-intervals of 10 cSv
-- and for even smaller intervals at very low doses. In addition,
Column C includes best-fit cancer-rates calculated for the
specific organ-doses where we have the observed cancer-rates, so
that the observed rate (in Column D) and the rate predicted by the
curve (in Column C) can be compared. (Readers can ignore Columns
E, F, and G until Part 5 of this chapter.)
Since the best-fit equation can provide predicted cancer-rates
at any dose-level, of course Table 14-A includes estimates for 2,
5, and 10 cSv -- doses which lie between the mean doses received
by Dose-Group 2 and Dose-Group 3. These estimated rates are
interpolations between two actual observations; they are not
extrapolations in a direction beyond any observed datapoint.
Figures 14-E and 14-F :
-----------------------
The information in Columns A, C, and D is plotted in Figure
14-E, which shows the cumulative cancer death-rate per 10,000
initial persons versus T65DR dose. The boxes are the actual
observations, while the smooth curve says: This is what one
would most probably see if one had more observations and less
sampling variation.
Table 14-B and Figure 14-F provide the comparable information
for the DS86 dosimetry.
Figures 14-E and 14-F look very much alike. Indeed, in both
dosimetries, the equations which best fit the observations turn
out to have the same dose-exponent: Dose^0.75. From Figures 14-E
and F, it is self-evident that the dose-response curves are
presently concave-downward (supra-linear) in both dosimetries.
(Our analysis has been made in terms of cancer-deaths per
10,000 initial persons. Some readers may be curious about the
shape of dose-response if response is measured in cancers per
10,000 person-YEARS. The analysis is provided for them in Chapter
30.)
RERF's Treatment of Dose-Group 8 :
----------------------------------
The actual dose-response must be somewhat more supra-linear
than we can know. The basis for our statement is a fact found in
RERF's report TR-9-87 (p.7). In Dose-Group 8 (the highest
Dose-Group), " . . . the T65D total kerma is set equal to 6 Gy for
all survivors whose T65D total kerma estimate is greater than 6
Gy." With this sentence, RERF refers to both TR-1-86 and TR-12-80,
so apparently RERF has been throwing out some part of the dose not
only in the 1950-1982 follow-up, but also in the previous
1950-1978 follow-up.
It follows that, in our own analysis, the combined Dose-Group
6+7+8 must really have a somewhat higher mean organ-dose than we
can know. But, of course, the observed cancer death-rate would not
change. Therefore, in Figure 14-E, the uppermost datapoint really
needs some sliding to the right (toward higher dose), a move which
would operate in the direction of greater supra-linear curvature.
We are confident that the effect would be small. However, we do
not see how RERF's handling of Dose-Group 8 can IMPROVE anyone's
analysis of dose-response.
In Part 3 of this chapter, we identify another factor which
also will operate in the direction of underestimating the
supra-linearity of low-LET dose-response.
Males and Females Tested Separately :
-------------------------------------
By definition, the general public includes both sexes. It is
impossible to have "population exposure" without irradiating both
men and women. Therefore, if analysts are evaluating the
dose-response from exposure of a general population, what matters
is the NET dose-response. When they treat males and females as a
unit in their analyses, the shape they obtain for dose versus
cancer-response necessarily incorporates and reflects whatever
difference may exist in male versus female response.
For other purposes, however, we may want to know if males and
females are alike in the shape of dose-response. Of course, the
moment analysts start subdividing the database, they increase the
small-numbers problem, and findings are necessarily less reliable.
Using exactly the steps demonstrated in Chapter 29, we did
regression analyses for males and females separately. The input
data for cancer-rates and mean organ-doses were obtained from
Table 11-G. The results are summarized below, in the equations of
best fit. All the equations have supra-linear dose-exponents
(below 1.0).
o -- MALES :
T65DR: Ca-deaths per 10,000 initial persons = (5.986)(Dose^0.75)
+ 796.389
DS86: Ca-deaths per 10,000 initial persons =
(7.248)(Dose^0.70) + 792.248
o -- FEMALES :
T65DR: Ca-deaths per 10,000 initial persons =
(10.086)(Dose^0.70) + 540.838
DS86: Ca-deaths per 10,000 initial persons =
(9.463)(Dose^0.70) + 538.102
In other words, examined separately, males and females each
show a supra-linear dose-response. The values of R-Squared for
males are lower than for females, which means the finding is
statistically weaker for males.
2. Basis for Ruling-Out a Concave-Upward Dose-Response
=======================================================
Chapter 29 demonstrates the technique of achieving curvilinear
regression by raising a single dose-term, serially, to a variety
of dose-exponents. We vary the exponent from Dose^2 (the quadratic
dose-response), to Dose^1.4 and Dose^1.16 (linear-quadratic
shapes), to Dose^1.0 (the linear dose-response), to Dose^0.85 and
lower (supra-linear curves). Let us be explicit about the
cancer-risks associated with these terms.
Supra-Linear Dose-Response :
----------------------------
This model of dose-response predicts that, with increase in
total dose, the increase in cancer death-rate per cSv of dose will
decrease. Each additional cSv of exposure will be less hazardous
than the previous cSv. The plot of cancer-rate versus dose is
concave-DOWNWARD (illustrated by Figure 14-A), and the
dose-exponent is less than 1.0.
Linear Dose-Response :
----------------------
Here a plot of cancer death-rate versus dose yields a straight
line -- hence the name "linear." The increase in cancer-rate per
additional unit of dose is the same over the entire dose-range
(illustrated by Figure 14-B), and the dose-exponent is 1.0.
Linear-Quadratic Dose-Response :
--------------------------------
When the quadratic dose-term (Q) has a positive coefficient,
this model predicts that the increase in cancer-rate, per unit
increase in dose, will increase as total dose increases. Each
additional cSv of exposure will be more hazardous than the
previous cSv. The plot of cancer-rate versus dose is
concave-UPWARD (illustrated by Figure 14-C). When a single
dose-exponent is used, the exponent must be greater than 1.0, but
less than 2.0.
However, as emphasized elsewhere (Go89b; also Chapters 23
and 29 of this book), when the quadratic term has a negative
coefficient, the net result is a concave-DOWNWARD, supra-linear
dose-response (see Figure 23-H).
Pure Quadratic Dose-Response :
------------------------------
This model, whose plot is also concave-UPWARD, bends away even
more than the linear-quadratic dose-response from a straight line
(illustrated by Figure 14-D), and the dose-exponent is 2.0.
Figures 14-A, B, C, D, for males and females combined, come
from the input provided in Table 14-D. The four figures depict how
the ACTUAL observations in the T65DR dosimetry relate to the
values calculated by best-fit equations having the four shapes
described above. Comparable figures are not included for the DS86
dosimetry simply because Figure 14-F already reveals that they
would look like the T65DR figures.
Curve Fitting -- Supra-Linear Fit Is Significantly Better
---------------------------------------------------------
In a good fit, not only should the weightiest observations lie
close to the calculated curve, but their scatter (if any) should
fall to both sides of it. In addition, it is a sign of poor fit if
the observations on both ends lie on the same side of the curve
while the observations in the middle all lie on the opposite side.
Inspection of Figures 14-A, B, C, and D shows the greatly
inferior fit of both the linear-quadratic (Dose^1.4) and the pure
quadratic (Dose^2) models. Indeed, such inspection predicts the
results of the formal statistical testing in Tables 29-D and E.
The results in Tables 29-D and 29-E show that the supra-linear
dose-response in the A-Bomb Study (1950-1982), in both the T65DR
and the DS86 dosimetries, is significantly better than the linear
relationship (p = 0.01).
As for a concave-upward dose-response, statistical testing in
Tables 29-D and 29-E simply rules out such a relationship as the
plausible choice. Even in the absence of any formal statistical
testing, this conclusion is evident from inspection of Figures
14-C and 14-D, compared with Figures 14-A and 14-B.
As an independent check on the statistical significance of the
supra-linear fit, we also used the power polynomial method of
curve-fitting. It shows that there is both a statistically
significant linear dose-term (Dose^1.0) and a statistically
significant quadratic dose-term (Dose ^2.0), and that the
coefficient of the quadratic term is NEGATIVE. The equation of
best fit from the power polynomial method produces a plot of
cumulative cancer-rate versus dose which is virtually identical
with the plot produced by the best-fit equation containing the
Dose^0.75 term (Figures 14-E and 14-F).
Comparison with Statements from RERF :
--------------------------------------
Readers are in a position to evaluate our analysis of the
shape of dose-response, step-by-step, from start to finish. They
will not be able to compare it directly with RERF reports,
however. RERF analysts are determining dose-response from input
which is different from ours. For instance, in TR-5-88, Shimizu
and co-workers discard the evidence between 1950-1955, and use
only the observations from 1956 onwards. They are using only
75,991 of the initial 91,231 persons. For their 75,991 persons,
they have additional observations out to 1985. They are using
newly constructed cohorts, not a constant-cohort analysis. In
effect, they are using a different database.
Nonetheless, there is a key similarity between our analysis
and the analysis by Shimizu and co-workers: The RERF analysts do
not find a concave-upward dose-response either. They find the
following:
1. When they examine all cancers combined except leukemia as
we do, and when they include all the Dose-Groups as we do, they
find that their data fit linearity and supra-linearity equally
well (Shi87, pp.28-30, and Shi88, pp.50-51).
2. When they examine males and females separately and
include all the evidence, as we do, again they indicate that they
find a linear or supra-linear dose-response (Shi88, p.53, Table
19).
However, Shimizu and co-workers never use the term,
supra-linear. Their important points about the supra-linear shape
might even be missed by any readers who assume that LQ
(linear-quadratic) and LQ-L models are always concave-UPWARD. The
assumption would be mistaken. If the Q-coefficient for dose is
NEGATIVE in an LQ model, the net LQ curvature is concave-DOWNWARD
(Figure 23-H, again). Therefore readers of RERF reports need to
pay close attention to RERF statements and footnotes such as:
"For those sites other than leukemia and colon, the fitted curve
associated with the LQ model is invariably concave downwards, not
upwards . . . " (Shi87, top p.29).
" . . . since the curvature is invariably downwards when a
curvilinear model gives an acceptable fit, this would imply a
higher risk at low doses than that which obtains under a linear
model" (Shi87, p.30).
"Coefficient for the Q-term is negative" for the LQ model; this
is the footnote which applies to analysis of the full dose-range
in Table 19 of TR-5-88 (Shi88, p.53).
A Possible Route to Error :
---------------------------
Having found the dose-response to be linear or supra-linear
(concave-downward), Shimizu and co-workers propose an alternative
way to determine the dose-response. We quote:
"For all cancers except leukemia, although the L model fits
well for both the total dose range and the dose range excluding
high doses, the LQ model can not be shown to be inappropriate
statistically. It should be noted that Q term in the LQ model is
negative when the entire dose range is used, reflecting the level
off of the dose-response curve at the higher dose range. In order
to obtain useful risk estimates in the low-dose range with the LQ
model, we have estimated the risk limiting doses to under 2 Gy, so
as to obtain a positive Q term" (Shi88, p.50-51).
Although the paper (Shi88) is unclear on whether 2 Gy is kerma
dose or internal organ-dose unadjusted for RBE, the statement
quoted above means that they threw away the high Dose-Groups
(probably 6,7,8) because, in someone's opinion, supra-linearity
(the negative Q-coefficient) is not "useful." Not useful to whom?
And for what?
Where does such an approach to evidence end?
--------------------------------------------
It may easily end in error. For instance, it is self-evident
from Figures 13-A and 13-B in the previous chapter, that if one
discarded Dose-Group 5 as well as Dose-Group 6-8, one would end up
with the opposite result: The dose-response would be based on
the four residual datapoints, and it would be MORE supra-linear,
not less. (This statement is supported by regression analysis
which excludes Dose-Groups 5-8).
Moreover, if we look objectively at the entries in Table 13-A,
Column E, we see that the absolute number of cancer-deaths
observed in Dose-Group 4 is about the same as in Dose-Group 5, and
also in the combined Dose-Group 6+7+8. This means that the
statistical reliability of each of these three observations is
about the same. If analysts are willing to discard one, then on an
objective basis, why should they not discard all three?
Suppose the first discarding of data (Dose-Groups 6-8) would
result in DECREASING the study's supra-linear curvature, but
suppose the next, equally justifiable discarding of data
(Dose-Group 5) would result in EXAGGERATING its supra-linear
curvature. What is the appropriate choice?
In my opinion, the curvature which is most likely to be right
is the curvature which comes from using ALL the available
evidence. It would certainly not be science at all, if I were to
keep the evidence which leads to answers I may LIKE, while
throwing out the evidence which produces answers I may NOT like.
In my judgment, analysts will be most likely to obtain the
RIGHT answer about dose-response when they use all of the
observations. The reason is this. The jaggedness observed in
Figures 13-A and 13-B has virtually no chance of being
biologically meaningful. Such jaggedness is almost certainly the
result of sampling variation, which means that it would not be
there (the dose-response would be smooth) if the study had
included a BILLION persons instead of only 91,231. One of the
great scientific virtues of the A-Bomb Study is its inclusion of
such a vast range of doses. If we USE all the data in regression
analysis, the additional observations are likely to help "correct"
the jaggedness of sampling variation. But if we start throwing
away any of the valuable evidence without a very good reason
indeed, we will almost certainly increase the chance of mistaken
results.
Conclusion about Shape in the A-Bomb Study :
--------------------------------------------
Our analysis of dose-response is based on ALL the evidence. No
Dose-Groups (and no follow-up years) have been thrown out. Our
findings fit concavity-DOWNWARD (supra-linearity) provably better
than linearity, and fit concavity-downward enormously better than
concavity-UPWARD.
We are forced to conclude, not by preference but by the
evidence currently available to us, that concavity-upward is NOT
credible as the shape of dose-response in the A-Bomb Study. The
credible choice is presently supra-linearity.
Will supra-linearity persist to the end of the study, decades
from now? No one can know. (As we said in Chapter 12, no one can
rule out even remote possibilities -- like there being no EXCESS
cancer anymore at the end of the study, which would mean a flat
dose-response. Of course, in that unlikely case, the INTERIM
excess of cancer-deaths would represent a major misery for those
who died from the disease 10, 20, 30, 40 years earlier than
otherwise.)
Meanwhile, analysts must report whatever is ruled in and out
by the CURRENTLY available evidence. This chapter and Chapter 29
rule out the concave-upward shape as a good fit for the 1950-1982
observations. The data say that the dose-response curvature is
concave-DOWNWARD.
It should be emphasized that the findings about dose-response
-- like the findings for MINIMUM Fatal Cancer-Yields -- involve no
forward projections and no hypotheses about radiation
carcinogenesis. Our findings simply amount to an objective
description of what the present evidence IS on the shape of the
dose-response.
3. Purely Low-Let Radiation versus Mixed (Gamma + Neutron)
===========================================================
The dose-response curve which fits the observations best is
presently concave-downward or supra-linear (Figure 14-E for the
T65DR dosimetry; Figure 14-F for the DS86 dosimetry). In each
dosimetry, the equation which generates the best-fit has a
dose-exponent of 0.75.
The dose-input for the regression-analysis (Chapter 29) was
composed of two types of radiation: Gamma and neutron. (Tables
9-C and 10-E, Row 14, show the small fraction of the internal
organ-dose, in rems, which was contributed by neutrons.)
Therefore, the curves depict dose-response for a mixture of the
two radiations.
Nonetheless, one must conclude that the concave-downward
curvature is caused by the low-LET (gamma) component of the
exposure, not by the high-LET (neutron) component.
The basis for this conclusion is clear if we start by
imagining that the A-bomb survivors received ONLY
neutron-exposure, but no gamma exposure. For neutron-exposure, the
experimental observation is that dose-response is linear, at least
up to 10 rads of total neutron dose (Chapter 8, Part 5). And if we
adjust for the greater carcinogenic potency of neutrons, by
multiplying neutron doses (below 10 rads) by a constant RBE of 20
to obtain rems, a plot of cancer-rate versus pure neutron doses in
rems would still be linear. We have shown (page 8-8) that the
highest mean neutron organ-dose was about 4.369 rads in the DS86
dosimetry, where such doses are supposed to be correct; 4.369 is
a dose well below 10. Therefore, if the A-bomb survivors had
received ONLY neutron-exposure, our plots of cancer-rates versus
dose in rems would be LINEAR.
Now, we return to the real situation. The A-bomb survivors
ALSO received a gamma dose. And when cancer-rate is plotted versus
dose in rems, for the COMBINED neutron and gamma doses, the best
fit for the observations becomes supra-linear, even though it
would have been linear if only the neutrons had been present. It
follows that the curvature is caused by the gamma exposure, not by
the neutrons.
Underestimation of the Low-Let Curvature :
------------------------------------------
Our analyses must somewhat UNDERestimate the true degree of
supra-linearity for low-LET (gamma) dose-response. Table 10-E, Row
14, shows that the fraction of total dose, in cSv, contributed by
neutrons rises with rising total dose. The rising share from
neutrons (from 5.4 % in Dose-Group 2, up to 18 % in Dose-Group 8)
prevents the supra-linear curvature for gamma-exposure from being
fully seen.
The gamma's supra-linear dose-response means that the percent
increase in spontaneous cancer-rate, per average rem of gamma
dose, FALLS as gamma-dose rises. By contrast, the neutron's linear
dose-response means that the carcinogenicity of neutrons is
CONSTANT in all eight dose-groups. As the combined dose from
gammas and neutrons is rising, the average carcinogenicity of the
gamma rems is falling whereas the carcinogenicity of the neutron
rems is NOT falling.
Therefore, when neutrons contribute an "extra" share of the
combined dose as the combined dose is rising (Table 10-E, Rows 11
and 14), it means that the observed cancer-rates at the higher
doses are somewhat elevated above the rates which would have
occurred if the fraction contributed by neutrons had not risen.
The result is that the "extra" share from neutrons progressively
"lifts" the right-hand half of the curve of Cancer-Rate versus
Combined Dose, in the direction of linearity. In other words, the
supra-linear curvature would be MORE pronounced if the fraction of
combined dose coming from neutrons had not risen. Thus the
supra-linearity of low-LET dose-response is somewhat
underestimated in our DS86 analyses.
4. Basis for Generalizing from the A-Bomb Study
================================================
This chapter and Chapter 29 have confirmed what Table 13-B so
strongly suggested: The dose-response is presently supra-linear
throughout the dose-range. The result does not depend on high-dose
data. If analysts threw out Dose-Groups 5-8, the supra-linearity
would be even more pronounced. We would emphatically NOT approve
of throwing out data, however.
The finding, that dose-response for low-LET exposure is
concave-downward (supra-linear), is based on observation of all
fatal cancers COMBINED, with only leukemia excluded. In other
words, the finding does not rest on a small study involving just
leukemia or a few cancer-sites, or on a study resting on incidence
instead of mortality. And the finding is based on two dosimetries.
And the finding is not based on a single sex- or age-group. It is
broadly based on both sexes and all ages.
In other words, the finding of supra-linearity at low doses is
based on excellent human epidemiological evidence -- in our
judgment, the best which is available at this time anywhere.
Therefore, it is scientifically reasonable to generalize from
the A-Bomb Study, 1950-1982: In humans, the dose-response for
induction of fatal cancer by low-LET ionizing radiation is most
probably supra-linear in shape, even at low doses. The risk per
rem RISES as total dose falls.
This finding is directly at variance with the widely applied
presumption -- not based on human epidemiology -- that the human
cancer-hazard per centi-sievert of low-LET exposure would go DOWN
with decreasing total doses. Readers are referred to Un77, p.414,
para.318; Un86, p.191, para.153; Beir80, p.190; Ncrp80,
pp.5-9; Nih85, p.iv; Nrc85, p.II-101-103; Doe87, p.7.3, 7.4;
and others. Some of these sources use the presumption, while
also acknowledging that the available human epidemiological data
do not SUPPORT it (see Chapter 22).
The Past and Future of Supra-Linearity :
----------------------------------------
The supra-linear shape of dose-response has been showing up in
the A-Bomb Study for at least three consecutive follow-ups:
1950-1974, 1950-1978, and 1950-1982 (Go81; Go89a; Ncrp80 --
details in our Chapter 22, Part 2). In other words,
supra-linearity is not a characteristic which appeared only with
the addition of the 1978-1982 observations. And, according to RERF
analysts (Shi87; Shi88), it is still showing up in the revised
database when they add some observations through 1985 (see this
chapter, Part 2).
Although no one can be sure that supra-linearity will continue
its persistence through all future follow-ups, the only reasonable
forward projection is the one which rests on the best available
evidence. And the best available evidence, from at least three
consecutive follow-ups, suggests that supra-linearity will
persist.
On the other hand, if the A-Bomb Study itself does not persist
with a continuous "constant-cohort, dual-dosimetry" database, it
will be hard for anyone to sort out which future findings on
dose-response result from extension of the time-interval since the
exposure, and which future findings result from perpetual revision
of the DS86 doses and cohorts.
5. Low-Dose Cancer-Yields Based on the Best-Fit Curve
======================================================
When analysts seek to estimate the cancer-hazard from exposing
populations of mixed ages to ionizing radiation, the doses
received by Dose-Group 3 in the A-Bomb Study are considerably
higher than the relevant levels suggested by nuclear accidents
like Chernobyl, for example. We should be asking, what are the
likely Cancer-Yields if people receive total doses like 5 cSv (or
less)?
Tables 14-A and 14-B provide the probable values for the
MINIMUM Fatal Cancer-Yields, in Column G. We have starred the
entries calculated from 5 cSv of total exposure, because we think
those are the appropriate ones to use for low-dose exposures up to
5 cSv and for slow exposures. (We closely examine the issue of
slow dose-rates in Chapter 23, Parts 6 and 7.)
The notes of Tables 14-A and 14-B explain exactly how the
values were obtained. Readers will see that this is still the
Cancer Difference Method: A difference in cancer-rate is divided
by the corresponding difference in dose. However, in this version,
the cancer-rates are not the direct observations; instead, they
are the rates predicted after the actual observations have
produced an equation of best fit. In Tables 14-A and 14-B, the
division-step for the starred entries at 5 cSv amounts to the
approximation that every rem (cSv) between 0 and 5 rems is EQUALLY
potent.
Table 14-C assembles the low-dose Cancer-Yields from Table
13-B as well as from Tables 14-A and 14-B, so that they can be
easily compared with each other. The net effect of
regression-analysis is to reduce the T65DR risk-estimate below its
value in Table 13-B, and to render it almost identical with the
DS86 estimate.
The Basing of Values on a Total Dose of 5 Centi-Sieverts :
----------------------------------------------------------
Readers may wonder why we suggest using Cancer-Yields
calculated from a total dose of 5 cSv, even for use with
population-exposure which might be lower (say, one centi-sievert
or less). At first glance, it may look as if we are deliberately
underestimating the likely Minimum Fatal Cancer-Yields from very
low-dose exposure, since we are using linearity instead of
supra-linearity between 0 dose and 5 rems.
Our reasoning is as follows. The technique of curvilinear
regression provides the values of low-dose Cancer-Yield which are
most likely to be true, given the evidence at hand. And the
equation which has the highest R-Squared value in regression
analysis is the equation which is most likely to make the best
predictions. Therefore the equation which we should use, and which
we DO use, is the one in which the dose-exponent is 0.75.
Objectivity requires use of results from available evidence,
rather than use of preconceptions about how the curvature "ought"
to behave at low doses (see Chapter 23). Unlike the BEIR-3
Committee (see Chapter 22), we do not constrain any regression in
order to make it support a pre-judgment.
On the other hand, as we pointed out in Chapter 29, while we
know that 0.75 is significantly better than the dose-exponent 1.0,
we do not know that 0.75 is significantly better than 0.80, 0.85,
0.70, or 0.65. Yet the shape of the curve is such that small
changes in the dose-exponent have a big effect, at one or two cSv,
on the values for Cancer-Yield in Columns F and G of Tables 14-A
and 14-B. In view of this sensitivity, we want to avoid using any
values for Cancer-Yield derived directly from the curve at one or
two cSv.
We regard our decision as a scientifically reasonable judgment
which simultaneously (A) avoids the irresponsibility of throwing
away the low-dose results of regression analysis down to 5 cSv,
and (B) avoids the introduction of any unstable element into an
analysis which has been securely based in reality.
A Comment by RERF about BEIR Choices :
--------------------------------------
The shape of dose-response is central to obtaining
risk-estimates at low (and slow) doses. If analysts choose
unrealistic versions of the dose-response relationship, they will
provide unrealistic estimates of cancer-hazard. RERF analysts, in
trying to figure out why their own current risk-estimates are so
much higher than those of the BEIR-3 Committee, comment (TR-5-88,
p.51):
[Some of the disparity] " . . . may be ascribed to the fact
that in BEIR III, the curvature in dose response for leukemia was
used for all cancers except leukemia instead of the actual
curvature which probably is much closer to linearity, and this may
cause much smaller estimates to be produced than if the actual
dose-response curve were to be applied."
Venturing below 10 Rems :
-------------------------
Now that we have examined the logic and results of regression
analysis, as a tool for obtaining a smooth and probable
dose-response at all doses, we can discuss a matter which puzzles
us and may puzzle readers too.
In its 1980 report, the BEIR-3 Committee declined to make
risk-estimates for acute exposures lower than 10 rems (Beir80,
p.144). RERF analysts appear to be split on this issue. In TR-9-87
(Pr87b, p.35), Preston and Pierce present their estimates of
Lifetime Fatal Cancer-Yield as cancer deaths per 10 milli-sieverts
(per rem). By contrast, in TR-5-88 (Shi88, Table 19, p.53),
Shimizu and co-workers explicitly constrain their estimates of
Lifetime Fatal Cancer-Yields to acute exposures of 0.1 Sievert (10
rems).
It is puzzling to us that Shimizu and co-workers make a big
effort to determine what the dose-response relationship is,
starting at zero dose, and then they seem unwilling to USE it in
the low dose-range. As we pointed out in Part 1 of this chapter,
estimates below 10 rems are not extrapolations in a direction
beyond any actual observations. Such estimates are interpolations
BETWEEN actual observations in Dose-Group 3 and Dose-Group 2.
Indeed, Dose-Groups 1-3 provide the most reliable observations in
the whole study, in terms of cancer-cases (not necessarily in
dosimetry). If analysts will not use the section of the
dose-response BELOW Dose-Group 3, it would seem they should have
no reason to use it ABOVE Dose-Group 3 either, where the
datapoints are based on far fewer cancer-deaths.
By contrast, to us it seems highly reasonable -- almost
obligatory -- for analysts to presume that the dose-response which
derives from the dose-range as a whole ALSO characterizes the
little segment between zero dose and 10 rems.
On the other hand, refusal to make estimates below 10 rems
could be a way of suggesting that maybe the risk of
radiation-induced cancer just disappears somewhere between 10 rems
and zero dose.
The human evidence against any harmless dose of ionizing
radiation, with respect to carcinogenesis, is examined in detail
in the Threshold section of this book (Section 5). Here we shall
limit our comments to the A-Bomb Study (see also Chapter 35, Part
9).
The A-Bomb Study, properly handled, certainly offers no basis
for belief in a threshold, or a lesser hazard per rem either,
anywhere below 10 rems. On the contrary. Its present supra-linear
curvature indicates the risk per rem is growing steadily higher as
dose approaches zero. Even if its present dose-response were
linear (instead of supra-linear), this would be no basis for
belief either in a safe threshold somewhere below 10 rems, or a
lesser effect per rem.
In short, even if there were no additional evidence in Section
5 against a threshold, and even if the dose-response in the A-Bomb
Study were linear instead of supra-linear, we would consider the
basis for making risk-estimates below 10 rems to be scientifically
compelling.
6. The Bottom Line from Best-Fit Curves
========================================
1. This chapter and Chapter 29 show that the relationship
between dose and cancer-response per 10,000 initial persons is
presently supra-linear (concave-downward). Statistical testing
demonstrates that the evidence fits a concave-DOWNWARD curvature
significantly better than the evidence fits a linear
dose-response, and very much better than it fits a concave-UPWARD
shape. See Figures 14-A, B, C, and D. In short, the present
evidence from the A-bomb survivors is that cancer-risk is greater
per rem (centi-sievert) at low doses than at high doses, in both
dosimetries. (Chapter 30 shows the same finding in cancer-response
per 10,000 person-YEARS.)
2. The finding of supra-linearity is solidly based in the
existing evidence, and does not rely on any forward projections,
hypotheses, or models. We have simply presented an objective
description of what the available evidence is showing in a
database which covers all cancers (leukemia excluded), all doses,
all ages, and both sexes. This direct and comprehensive human
epidemiological evidence carries great scientific weight compared
with observations from other species, of course, or from
laboratory experiments.
3. The evidence is at variance with the assumption, almost
universally used by the radiation community, that the cancer-risk
should be less severe per rem at low acute doses than at high
acute doses. With regard to low doses delivered SLOWLY, we show in
Chapter 23, Part 7, that there is no reason to reduce the low-dose
Cancer-Yields in Table 14-C when exposure is slow instead of
acute.
4. Although no one can be certain that the supra-linear
curvature will persist through all future follow-ups, the only
reasonable forward projection is the one which rests on the best
available evidence. And the best available evidence, from at least
three consecutive follow-ups, is that supra-linearity is
persistent. However, if the A-Bomb Study ITSELF does not persist
with a continuous "constant-cohort, dual-dosimetry" database, it
will be hard for anyone to sort out which future findings on
dose-response result from extension of the time-interval since the
bombings, and which future findings result from perpetual revision
of the DS86 doses and cohorts.
5. Regression analysis provides the best-fit equation for
dose-response, and the equation can predict cancer-rates at any
dose-level, including doses like 2, 5, and 10 rems which lie
between the mean dose received by Dose-Group 2 and Dose-Group 3.
The estimated cancer-rates at these doses are interpolations
between two actual observations -- they are not extrapolations in
a direction beyond any observed data-point.
6. Unlike some current analysis at RERF, our analysis of
dose-response uses ALL of the observations, high-dose and
low-dose, and ALL of the follow-up years, in order to obtain the
most reliable results. We do not approve of throwing away evidence
without a very good reason indeed. It should be noted that the
supra-linear curvature of dose versus cancer-response occurs
throughout the dose-range. In fact, if the high-dose evidence from
Dose-Groups 5-8 were discarded, the low-dose evidence from
Dose-Groups 1-4 would produce greater supra-linearity -- not less.
7. The best-fit equation from our regression analysis is
used to obtain another set of Minimum and Lifetime Fatal
Cancer-Yields by the Cancer Difference Method, for low-dose
exposure. Table 14-C compares the new set with the first set, in
both T65DR and DS86 dosimetries. The net effect of regression
analysis is to REDUCE the estimate in the T65DR dosimetry. In the
new set of estimates, the Lifetime Cancer-Yields remain probable
underestimates, as they were in Table 13-B. The Lifetime Fatal
Cancer-Yield from the best-fit curve is 12.90 in the T65DR
dosimetry, and 12.03 in the current version of the DS86 dosimetry.
By contrast, the lifetime values commonly used by the radiation
community for statements about low-dose exposure are between 1.0
and 2.0 (see Chapter 24, Part 7, and Chapter 34, Wolfe).
------------------------------------------------------------------
----------------------------------------------------------------------------
----------------------------------------------------------------------------
Table 14-A
T65DR Dosimetry (RBE = 2): Comparison of Calculated Cancer-Rates
with Observed Cancer-Rates.
T65DR Dosimetry (RBE = 2): Minimum Fatal Cancer-Yields
per Centi-Sievert Among 10,000 Persons.
|=============================================================================================|
| Col.A Col.B Col.C Col.D | Col.E Col.F Col.G |
| | |
| Dose Dose^0.75 Cancer-Rate Cancer-Rate | Calculated Ca-Rate Avg.Incr. MINIMUM |
| cSv per 10,000 per 10,000 | MINUS the Calculated in Ca-Rate FATAL |
| T65DR Calculated Observed | Spontaneous Ca-Rate per cSv CA-YIELD |
|========================================================================================== |
| 0 0.00000 649.5440 649.31 | |
| 1 1.00000 656.5968 | 7.053 7.053 8.675 |
| 1.511 1.36260 659.1542 651.89 | 9.610 6.362 7.825 |
| 2 1.68179 661.4053 | 11.861 5.931 7.295 |
| 5 3.34370 673.1265 | 23.582 4.716 5.801 * |
| 10 5.62341 689.2048 | 39.661 3.966 4.878 |
| 10.994 6.03762 692.1261 712.02 | 42.582 3.873 4.764 |
| 20 9.45742 716.2453 | 66.701 3.335 4.102 |
| 30 12.81861 739.9511 | 90.407 3.014 3.707 |
| 35.361 14.50098 751.8165 723.72 | 102.273 2.892 3.557 |
| 40 15.90541 761.7217 | 112.178 2.804 3.449 |
| 50 18.80302 782.1579 | 132.614 2.652 3.262 |
| 60 21.55825 801.5900 | 152.046 2.534 3.117 |
| 70 24.20045 820.2250 | 170.681 2.438 2.999 |
| 71.308 24.53891 822.6120 836.27 | 173.068 2.427 2.985 |
| 80 26.74961 838.2037 | 188.660 2.358 2.901 |
| 90 29.22011 855.6276 | 206.084 2.290 2.816 |
| 100 31.62278 872.5731 | 223.029 2.230 2.743 |
| 110 33.96601 889.0995 | 239.555 2.178 2.679 |
| 120 36.25650 905.2539 | 255.710 2.131 2.621 |
| 130 38.49971 921.0748 | 271.531 2.089 2.569 |
| 140 40.70015 936.5940 | 287.050 2.050 2.522 |
| 150 42.86161 951.8383 | 302.294 2.015 2.479 |
| 160 44.98731 966.8305 | 317.286 1.983 2.439 |
| 170 47.08003 981.5900 | 332.046 1.953 2.402 |
|176.662 48.45714 991.3025 988.45 | 341.759 1.935 2.379 |
| 180 49.14218 996.1339 | 346.590 1.925 2.368 |
| 190 51.17587 1010.477 | 360.933 1.900 2.337 |
| 200 53.18296 1024.633 | 375.089 1.875 2.307 |
|=============================================================================================|
UPPER NOTES: -----
Entries in Col.A come from Table 13-A, with many doses added between
observations.
Entries in Col.C for the predicted rates are calculated, both for
observed doses and interpolated doses, with the equation derived from Table
29-D:
Cancer-Rate = (7.0528)(Dose^0.75) + 649.544.
Values for the term (Dose^0.75) are obtained from Col.B above. Entries
in Col.D come from Table 13-A, and lie near the calculated values. Columns
A, C, and D are plotted in Figure 14-E.
-------------------- Right-Hand Side of Table --------------------
FATAL CANCER-YIELD = NUMBER OF RADIATION-INDUCED CANCER-DEATHS AMONG 10,000
INITIAL PERSONS OF MIXED AGES, PER CENTI-SIEVERT OF WHOLE-BODY INTERNAL
ORGAN-DOSE.
Entries in Col.E are Col.C minus 649.544 (which is the calculated
spontaneous rate / 10,000).
Entries in Col.F are Col.E / Col.A. The entries correspond to the Min.
Fatal Cancer Yield calculated by the Cancer Difference Method, before the
1.23-fold correction used by RERF for underascertainment of cancer-deaths
(see Chapter 11). The progressive decline of Col.F entries with rising dose
reflects the supra-linearity of dose-response.
Entries in Col.G are Col.F entries times 1.23, the underascertainment
correction. The starred value is the one which we use for low-dose exposure.
In subsequent chapters also, we use values per cSv based on best-fit at 5
cSv.
----------------------------------------------------------------------------
----------------------------------------------------------------------------
----------------------------------------------------------------------------
----------------------------------------------------------------------------
Table 14-B
DS86 Dosimetry: Comparison of Calculated Cancer-Rates With ObservedD
Cancer-Rates.
DS86 Dosimetry: Minimum Fatal Cancer-Yields per CentiI-Sievert Among
10,000 Persons.
|==============================================================================================|
| Col.A Col.B Col.C Col.D | Col.E Col.F Col.G |
| | |
| Dose Dose^0.75 Cancer-Rate Cancer-Rate | Calculated Ca-Rate Avg.Incr. MINIMUM |
| cSv per 10,000 per 10,000 | MINUS the Calculated in Ca-Rate FATAL |
| DS86 Calculated Observed | Spontaneous Ca-Rate per cSv CA-YIELD |
|=========================================================================================== |
| 0 0.0000 647.693 | |
| 0.089 0.1634 648.768 649.31 | |
| 1 1.0000 654.272 | 6.579 6.579 8.093 |
| 1.890 1.6121 658.299 651.89 | 10.606 5.611 6.902 |
| 2 1.6818 658.758 | 11.065 5.533 6.805 |
| 5 3.3437 669.692 | 21.999 4.400 5.412 * |
| 10 5.6234 684.691 | 36.998 3.700 4.551 |
| 14.564 7.4553 696.744 712.02 | 49.051 3.368 4.143 |
| 20 9.4574 709.916 | 62.223 3.111 3.827 |
| 30 12.8186 732.030 | 84.337 2.811 3.458 |
| 40 15.9054 752.339 | 104.646 2.616 3.218 |
| 40.625 16.0915 753.564 723.72 | 105.871 2.606 3.205 |
| 50 18.8030 771.404 | 123.711 2.474 3.043 |
| 60 21.5582 789.531 | 141.838 2.364 2.908 |
| 70 24.2005 806.915 | 159.222 2.275 2.798 |
| 74.238 25.2911 814.091 836.27 | 166.398 2.241 2.757 |
| 80 26.7496 823.687 | 175.994 2.200 2.706 |
| 90 29.2201 839.941 | 192.248 2.136 2.627 |
| 100 31.6228 855.749 | 208.056 2.081 2.559 |
| 110 33.9660 871.166 | 223.473 2.032 2.499 |
| 120 36.2565 886.235 | 238.542 1.988 2.445 |
| 130 38.4997 900.994 | 253.301 1.948 2.397 |
| 140 40.7002 915.472 | 267.779 1.913 2.353 |
| 150 42.8616 929.692 | 281.999 1.880 2.312 |
| 160 44.9873 943.678 | 295.985 1.850 2.275 |
| 170 47.0800 957.447 | 309.754 1.822 2.241 |
| 180 49.1422 971.014 | 323.321 1.796 2.209 |
|197.054 52.5943 993.727 988.45 | 346.034 1.756 2.160 |
| 200 53.1830 997.600 | 349.907 1.750 2.152 |
|==============================================================================================|
UPPER NOTES: -----
Entries in Col.A come from Table 13-A, with many doses added between
observations.
Entries in Col.C for the predicted rates are calculated, both for
observed doses and interpolated doses, with the equation derived from Table
29-C:
Cancer-Rate = (6.5793)(Dose^0.75) + 647.693.
Values for the term (Dose^0.75) are obtained from Col.B above. Entries
in Col.D come from Table 13-A, and lie near the calculated values. Columns
A, C, and D are plotted in Figure 14-F.
-------------------- Right-Hand Side of Table --------------------
FATAL CANCER YIELD = NUMBER OF RADIATION-INDUCED CANCER-DEATHS AMONG
10,000 PERSONS OF MIXED AGES, PER CENTI-SIEVERT OF WHOLE-BODY INTERNAL
ORGAN-DOSE.
Entries in Col.E are Col.C minus 647.693 (which is the calculated
spontaneous rate / 10,000).
Entries in Col.F are Col.E / Col.A. The entries correspond to the Min.
Fatal Cancer Yield calculated by the Cancer Difference Method, before the
1.23-fold correction used by RERF for underascertainment of cancer-deaths
(see Chapter 11). The progressive decline of Col.F entries with rising dose
reflects the supra-linearity of dose-response.
Entries in Col.G are Col.F entries times 1.23, the underascertainment
correction. The starred value is the one which we use for low-dose exposure.
In subsequent chapters also, we use values per cSv based on best-fit at 5
cSv.
----------------------------------------------------------------------------
----------------------------------------------------------------------------
----------------------------------------------------------------------------
----------------------------------------------------------------------------
Table 14-C
Cancer-Yields at the Low Doses, by the Cancer Difference Method,
with and without Curvilinear Regression.
----------------------------------------------------------------------------
Basis: A-bomb survivors, all ages combined, 1950-1982. Both T65DR and DS86
dosimetries.
Cancer-hazard from X-rays may be underestimated by the A-Bomb Study. See
Chapter 13, Part 4.
Cancer-Yields are radiation-induced cancer-deaths among 10,000 persons
of mixed ages, per cSv of whole-body internal organ-dose.
All Cancer-Yields below are corrected for underascertainment of
cancer-deaths.
|==================================================================================|
| || || |
| || --Fatal Cancer-Yield-- || --Fatal Cancer-Yield-- |
| || T65DR Dosimetry || DS86 Dosimetry |
| || Neutron RBE = 2.0 || Neutron RBE = 20 |
| || || |
|==================================================================================|
| Col.A || Col.B Col.C || Col.D Col.E |
| || || |
| || MINIMUM LIFETIME || MINIMUM LIFETIME |
| Source of Estimate || FATAL FATAL || FATAL FATAL |
| for Minimum Fatal || CANCER- CANCER- || CANCER- CANCER- |
| Cancer-Yields || YIELD YIELD || YIELD YIELD |
|==================================================================================|
| Row || || |
| Dose-Group 3 || || |
| versus Ref. Group || || |
| 1 Table 13-B. || 7.29 16.20 || 5.50 12.23 |
| || || |
| || || |
| Best-Fit Curve || || |
| Tables 14-A and || || |
| 2 14-B. || 5.80 12.90 || 5.41 12.03 |
| || || |
|==================================================================================|
NOTES -----
1. The MINIMUM values above in Row 1 come from Table 13-B, Columns B and
H. If there had been no dose-groups higher than Dose-Group 3 in the
A-bomb experience, these are the only values which would exist in Table
13-B. The entries in Row 1 above are the values before regression
analysis provides a smooth best-fit curve.
-----------------------------------------------------------------------
2. The MINIMUM values in Row 2 above come from the best-fit curves
provided by regression analysis, using all dose-groups.
The MINIMUM value in Row 2, Column B, comes from Table 14-A, Column G
(the starred value).
The MINIMUM value in Row 2, Column D, comes from Table 14-B, Column G
(the starred value).
-----------------------------------------------------------------------
3. LIFETIME values ( Columns C and E ) are always the MINIMUM value times
2.223, in the Cancer Difference Method. These LIFETIME entries are
probably underestimates (see text and subsequent chapters). The factor
2.223 comes from Table 28-D, Row 14.
----------------------------------------------------------------------------
----------------------------------------------------------------------------
----------------------------------------------------------------------------
----------------------------------------------------------------------------
Table 14-D
Input Values for Figures 14-A, 14-B, 14-C, and 14-D.
T65DR Dosimetry with Neutron RBE = 2.
|=====================================================================================|
| Input for Figure 14-A | Input for Figure 14-B |
| ======================== | ======================== |
| Equation for Dose^0.75 from Table 29-B: | Equation for Dose^1 from Table 29-B: |
| Ca-Rate = (7.0528)(Dose^0.75) + 649.544 | Ca-Rate = (1.947)(Dose^1) + 661.153 |
| | |
| Dose Dose Ca-Rate Ca-Rate | Dose Dose Ca-Rate Ca-Rate |
| cSv cSv^0.75 Calc. Observed | cSv cSv^1 Calc. Observed |
| | |
| 0.000 0.0000 649.544 649.31 | 0.000 0.000 661.153 649.31 |
| 1.511 1.3626 659.154 651.89 | 1.511 1.511 664.094 651.89 |
| 10.994 6.0376 692.126 712.02 | 10.994 10.994 682.558 712.02 |
| 35.361 14.5010 751.817 723.72 | 35.361 35.361 730.002 723.72 |
| 71.308 24.5388 822.611 836.27 | 71.308 71.308 799.990 836.27 |
| 130.000 38.4997 921.075 | 130.000 130.000 914.263 |
| 176.662 48.4571 991.303 988.45 | 176.662 176.662 1005.114 988.45 |
|=====================================================================================|
| | |
| Input for Figure 14-C | Input for Figure 14-D |
| ======================== | ======================== |
| Equation for Dose^1.4 from Table 29-B: | Equation for Dose^2 from Table 29-B: |
| Ca-Rate = (0.242)(Dose^1.4) + 671.922 | Ca-Rate = (0.01047)(Dose^2) + 680.048 |
| | |
| Dose Dose Ca-Rate Ca-Rate | Dose Dose Ca-Rate Ca-Rate |
| cSv cSv^1.4 Calc. Observed | cSv cSv^2 Calc. Observed |
| | |
| 0.000 0.000 671.922 649.31 | 0.000 0.00 680.048 649.31 |
| 1.511 1.782 672.353 651.89 | 1.511 2.28 680.072 651.89 |
| 10.994 28.682 678.863 712.02 | 10.994 120.87 681.313 712.02 |
| 35.361 147.212 707.547 723.72 | 35.361 1250.43 693.140 723.72 |
| 71.308 393.001 767.028 836.27 | 71.308 5084.83 733.286 836.27 |
| 130.000 911.005 892.385 | 130.000 6900.00 856.991 |
| 176.662 1399.591 1010.623 988.45 | 176.662 31209.54 1006.812 988.45 |
|=====================================================================================|
The construction of Table 14-D is described, step by step, in Chapter 29.
When the above values are plotted for dose (cSv), calculated cancer-rate,
and observed cancer-rate, they demonstrate graphically how closely or how
distantly the observed points lie to the corresponding curve calculated by
regression analysis.
In a good fit, not only should the weightiest observations lie close to the
calculated curve, but their scatter (if any) should fall to both sides of
it. In addition, it is a sign of poor fit if the observations on both ends
lie on the same side of the curve while the observations in the middle all
lie on the opposite side.
Because the dose-response is so similar in T65DR and DS86 (compare Figure
14-E with Figure 14-F), we have not shown graphs comparable to 14-B, 14-C,
and 14-D for the DS86 analysis.
----------------------------------------------------------------------------
----------------------------------------------------------------------------
----------------------------------------------------------------------------
----------------------------------------------------------------------------
Figures 14-A,B,C,D
Distribution of Datapoints Relative to Four Dose-Response Curves. T65DR
Dosimetry: Cumulative Cancer-Deaths versus Dose.
----------------------------------------------------------------------------
Input for the four figures below is provided by Table 14-D. Each figure
depicts the SAME observations (indicated by the boxy symbol):
Cancer-mortality versus dose in the A-Bomb Study, 1950-1982. What differs is
the dose-response curve in each figure.
o -- In Figure 14-A, the "fit" between the observations and the
supra-linear curve is good, with datapoints either lying on the curve or
falling to both sides of it.
o -- In Figure 14-B, the fit between the observations and the linear
"curve" is inferior to the fit in Figure 14-A.
o -- In Figure 14-C, the fit between the observations and the
linear-quadratic (Q-positive) curve is very poor, with the observations at
both ends lying on the same side of the curve, and the observations in the
middle all lying on the opposite side.
o -- In Figure 14-D, the fit between observations and the quadratic
dose-response curve is even worse than in Figure 14-C.
o -- Statistical testing (Chapter 29) establishes that the supra-linear
dose-response fits the evidence significantly better than the linear
dose-response.
Figure 14-A, below: Fit Relative to Supra-Linear (Dose^0.75)
[fig 14-A]
Figure 14-B, below: Fit Relative to Linear (Dose^1.0)
[fig 14-B]
Figure 14-C, below: Fit Relative to Linear-Quadratic (Dose^1.4)
[fig 14-C]
Figure 14-D, below: Fit Relative to Quadratic (Dose^2.0).
[fig 14-D]
----------------------------------------------------------------------------
----------------------------------------------------------------------------
----------------------------------------------------------------------------
----------------------------------------------------------------------------
Figure 14-E
T65DR Dosimetry: Best-Fit Curve for Cumulative Cancer-Deaths versus Dose.
----------------------------------------------------------------------------
For the atomic-bomb survivors, this plot shows cumulative cancer-deaths
(1950-1982) per 10,000 initial persons, versus mean whole-body internal
organ-dose in the T65DR dosimetry (RBE = 2). Input for this figure comes
from Table 14-A, Columns A, C, and D.
o -- The boxy symbols, which show the observed cancer death-rate per
10,000 initial persons versus dose, come from Columns A and D of Table 14-A.
o -- Points along the best-fit curve come from Column C of Table 14-A,
and show calculated cancer death-rates per 10,000 initial persons versus
dose, based on the equation of best fit, shown below. This curve is the same
as the curve in Figure 14-A, of course.
Figure 14-F will show the best-fit curve for the SAME cohorts of
survivors in the supplemental DS86 dosimetry.
[fig 14-E]
----------------------------------------------------------------------------
----------------------------------------------------------------------------
----------------------------------------------------------------------------
----------------------------------------------------------------------------
Figure 14-F
DS86 Dosimetry: Best-Fit Curve for Cumulative Cancer-Deaths versus Dose.
----------------------------------------------------------------------------
For the atomic-bomb survivors, this plot shows cumulative cancer-deaths
(1950-1982) per 10,000 initial persons, versus mean whole-body internal
organ-dose in the DS86 dosimetry (RBE = 20). Input for this figure comes
from Table 14-B, Columns A, C, and D.
o -- The boxy symbols, which show the observed cancer death-rate per
10,000 initial persons versus dose, come from Columns A and D of Table 14-B.
o -- Points along the best-fit curve come from Column C of Table 14-B,
and show calculated cancer death-rates per 10,000 initial persons versus
dose, based on the equation of best fit.
With our "constant-cohort, dual dosimetry" approach to the DS86
dosimetry, the T65DR cohorts of survivors remain undisturbed, and merely
receive a second dose-estimate. Super-imposition of Figures 14-F and 14-E
would show that the DS86 dosimetry shifts the boxy symbols somewhat to the
right (higher dose) -- as predictable from comparing Column A in Tables 14-A
and 14-B. Consequently, the equations of best fit for the T65DR and DS86
dosimetries are somewhat different.
[fig 14-F]
----------------------------------------------------------------------------
----------------------------------------------------------------------------