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CHAPTER 15
Radiation Risk by Age and Sex, from the Cancer-Rate Ratio Method
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This chapter is arranged in eight parts:
1. Overview and Definitions, p.1
2. Origin of the Key Equation, p.2
3. Obtaining Raw K-Values for Each Age and Sex, p.2
4. Discussion of the Raw K-Values, p.3
5. Obtaining K-Values for Low-Dose Exposure, p.4
6. Discussion of Low-Dose K-Values, p.6
7. Some Ties between K-Values, Supra-Linearity, Duration, p.7
8. Bottom Line on Radiation Risk by Age and Sex, p.9
Then tables.
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1. Overview and Definitions
============================
Unlike the Cancer Difference Method, the Cancer-Rate Ratio
Method will obtain Minimum and Lifetime Fatal Cancer-Yields, for a
population of mixed ages, by summing the SEPARATE contributions
made by distinct age-sex subsets of the population.
This chapter evaluates the risk of radiation-induced cancer
observed so far in each of the five age-bands of the A-bomb
survivors, males and females separately. The risks are expressed
in terms of ten different "K-values" (defined below). The next
chapter will use the K-values from this chapter to obtain the
Minimum and Lifetime Fatal Cancer-Yields.
The Definition of K-Value :
---------------------------
K is defined here as the fractional increase in the
spontaneous cancer death-rate per centi-sievert of whole-body
internal organ-dose. (Multiplied by 100, K would be the PERCENT
increase in the spontaneous cancer death-rate per cSv.) The
definition of K needs comparison with the definition of Fatal
Cancer-Yield.
Fatal Cancer-Yield is defined as the number of
radiation-induced fatal cancers among 10,000 initial persons per
cSv average whole-body internal organ-dose.
Therefore, if the observed K-values are applied to the
spontaneous cancer-deaths observed so far in the Reference Group
per 10,000 initial persons, the result is the MINIMUM Fatal
Cancer-Yield. If these observed K-values are applied to the
estimated ULTIMATE spontaneous cancer-deaths per 10,000 initial
persons in the Reference Group, the result is the LIFETIME Fatal
Cancer-Yield. Readers who look ahead to Tables 16-A and 16-B, in
the next chapter, can see immediately how K-values and spontaneous
cancer-rates are used to estimate Cancer-Yields (the "per 10,000"
step occurs at the end).
That is the easy part. The work comes beforehand, in obtaining
the proper K-values to use in the range of common low-dose
exposures, up to 5 cSv.
Raw versus Low-Dose K-Values :
------------------------------
The evidence in Chapters 14 and 29 shows that the
dose-response relationship is presently concave-downward
(supra-linear), and that the dose-exponent which produces the
best-fit is Dose^0.75. Therefore it would be inexcusable --
indeed, a sign of bias -- if we ignored this information in
deriving the best estimates we can of K-values.
Our method for taking supra-linearity into account, however,
uses a series of linear equations. The analysis begins in Part 2
by developing the simple linear equations which yield Equation
(7), which is the key one.
We shall use Equation (7) first to obtain a set of "raw
K-values" which do NOT take supra-linearity into account, and then
a set of "low-dose K-values" which DO take supra-linearity into
account. It is not necessary to obtain the raw K-values in order
to obtain the low-dose K-values, but we do it so that everyone
(ourselves included) can know how raw and low-dose K-values
compare in magnitude.
The input data which are assembled and consolidated in Tables
15-B through 15-K are needed equally for obtaining raw and
low-dose K-values.
2. Origin of the Key Equation
==============================
We will use the following symbols; when a digit follows a
letter, the digit is serving as a subscript.
D2 = some dose of ionizing radiation greater than zero-dose.
R2 = cancer death-rate (1950-1982) at D2, per 10,000 exposed
persons.
D1 = some dose less than D2.
R1 = cancer death-rate (1950-1982) at D1, per 10,000 exposed
persons.
Ro = spontaneous cancer death-rate (1950-1982) when dose is zero.
K = fractional increase in Ro per cSv of dose.
When the dose-response relationship in a set of observations
is linear, then the fractional increase in the spontaneous cancer
death-rate per cSv of dose is the the same everywhere in the
dose-range, high-dose and low-dose alike. Of course, this is
definitely not true when dose-response is either concave-downward
or concave-upward. But in a linear dose-response, K is a constant.
Equations (1) and (4) below are nothing other than the
equation for a straight line, where Ro is the intercept on the
y-axis, where the quantity (KRo) is the slope of the straight
line, and where the intercept and points (D2,R2) and (D1,R1) all
lie along the SAME straight line. Since Equation (7) below is
derived from Equations (1) and (4), Equation (7) produces K-values
which are valid if the dose-response relationship is LINEAR.
o -- Equation (1) :
R2 = Ro + (K)(Ro)(D2)
Factoring-out Ro, and then re-arranging, we have
o -- Equation (2) :
R2 = Ro (1 + KD2) , then
R2/Ro = 1 + KD2 , then
o -- Equation (3) :
(R2/Ro) - 1
K = ---------------
D2
And also for the lower dose, D1, we can write
o -- Equation (4) :
R1 = Ro + (K)(Ro)(D1)
o -- Then Equation (5) :
R1 = Ro (1 + KD1)
If we need to solve for K without using Ro at all, it can be
done without using Equation (3), if we simply divide Equation (2)
by Equation (5) -- which causes Ro to cancel out in Equation (6).
o -- Equation (6) :
(1 + KD2)
(R2/R1) = -----------
(1 + KD1)
And, as we begin to isolate K, we have:
(R2/R1)(1 + KD1) = (1 + KD2) , then
(R2/R1) + (R2/R1)(KD1) = 1 + KD2
Transposing terms and factoring-out K, we have:
(KD2) - (R2/R1)(KD1) = (R2/R1) - 1 , then
K [ D2 - (R2/R1)(D1) ] = (R2/R1) - 1 , then
o -- Equation (7) :
(R2/R1) - 1
K = ------------------
(D2) - (R2/R1)(D1)
So K can be evaluated with Equation (7) from ANY two
observations, since R2, D2, R1, and D1 are all known from two
observations. Equation (7) is the one which we will use repeatedly
in this chapter. Indeed, its term (R2/R1) is the basis for calling
this the Cancer-Rate Ratio Method.
3. Obtaining Raw K-Values for Each Age and Sex
===============================================
In Part 1 of this chapter, we drew a distinction between two
sets of K-values: "Low-dose K-values" which take account of
supra-linearity, and "raw K-values" which do NOT take account of
supra-linearity. Before this new use of the word "raw" causes any
confusion, we must point out that BOTH the low-dose and the raw
K-values are derived from the raw (pre-normalized) A-bomb data.
The work in this chapter uses only the raw data. It is
completely unnecessary to use age-normalized data when we are
keeping each age-band separate, and completely unnecessary to use
sex-normalized data when we are keeping males and females
separate. Therefore, we are using the raw data from Tables 11-B
(males) and 11-D (females). In addition, we use Master Tables
26-A,B,C,D in order to show the data for Dose-Groups 6, 7, and 8
separately.
Elsewhere, we established that WITHIN a single age-band, the
slight age-differences ATB across Dose-Groups are appropriately
disregarded (see Chapter 11).
Dose-Increment for Small Body-Size :
------------------------------------
As indicated by Table 4-B, the average age of the 0-9
year-olds ATB was only 4.1 years. The organ-doses in Master Tables
26-A,B,C,D, and in Tables 11-B and 11-D, do not include any
correction for the small body-size of this age-band. Chapter 31
presents the method used for making the adjustment, and the
findings are presented in Table 15-A.
In the Cancer-Rate Ratio Method, which examines each age-band
separately, the 4-year-olds ATB take on importance in the
estimates of LIFETIME Fatal Cancer-Yield for a population of
mixed-ages. Therefore, the work in Chapter 31 is worthwhile, in
order to avoid preventable error.
The effect of the adjustment is to increase dose by about
13-20 percent for this age-band, without changing the
cancer-observations of course. The result is to REDUCE the
K-values for the very young children ATB, and thus to REDUCE the
Lifetime Fatal Cancer-Yield for the overall population, compared
with estimates calculated without this dose-adjustment, in the
Cancer-Rate Ratio Method.
The Small-Numbers Problem :
---------------------------
All analysts who begin to subdivide the Dose-Groups of the
A-Bomb Study are immediately confronted with the small-numbers
problem, especially for RERF's two age-bands who were youngest ATB
(0-9 years and 10-19 years).
For example, inspection of Tables 11-B and 11-D, Column N,
shows that it would be scientifically meaningless, at this stage
of the follow-up, to base K-values on comparing observations in
Dose-Group 3 with the Reference Group (1+2) AFTER the database has
been subdivided into ten age-sex groups. After subdivision,
analysts are confronted in Dose-Group 3 with statistically
unstable numbers of cancer-deaths like 1 cancer for males 0-9
years ATB, 19 cancers for males 10-19 years ATB, 9 cancers for
females 0-9 years ATB, and 23 cancers for females 10-19 years ATB.
Therefore the comparison of Dose-Group 3 with the Reference
Group, which was statistically strong in the Cancer Difference
Method when observations were not subdivided, is ruled out by the
small-numbers problem after subdivision. To reduce the instability
of small numbers, all good analysts must decide on some
combination of age-bands, sexes, or dose-groups (see for instance
RERF TR-9-87, Table 7, p.21; and TR-5-88, Table 2-4, p.64).
The Consolidation of Dose-Groups :
----------------------------------
This chapter lessens the small-numbers problem by
consolidating the observations within each age-sex group into two
classes: Low-dose and high-dose. The low-dose class is composed
of RERF Dose-Groups 1 + 2 + 3, and represents an average
organ-dose in the neighborhood of 3 cSv (specifics are in Tables
15-B through 15-K). The high-dose class is composed of Dose-Groups
4 + 5 + 6 + 7 + 8, and represents an average organ-dose in the
neighborhood of 70-100 cSv (specifics are in Tables 15-B through
15-K).
This consolidation provides real-world observations to use for
D2, R2, D1, and R1 in Equation (7), and provides them for each of
the ten age-sex groups separately.
Calculation of Raw K-Values :
-----------------------------
Tables 15-B through 15-K show the derivation of twenty raw
K-values (ten in each dosimetry), step-by- step, from the input
data to the result. Each calculation amounts to having a two-point
dose-response at about 3 cSv and at about 85 cSv. One can imagine
a straight line connecting these two points. By using Equation
(7), the K-value which applies to this straight line is
determined.
4. Discussion of the Raw K-Values
==================================
The raw K-values derived in Tables 15-B through 15-K are
assembled for convenience at the bottom of Table 15-L (Note 2).
Higher Hazard for Those Who Are Young at Exposure :
---------------------------------------------------
The raw K-values reflect a greater sensitivity to radiation
carcinogenesis in those who are young at exposure (the two
youngest age-bands ATB) than in those who are older. This is seen
in both sexes independently. It is even seen for each sex in the
age-band 0-9 years ATB, in spite of the severe small-numbers
problem in those groups.
In the females, sensitivity falls with advancing age in a
remarkably regular way. In the males, there is an irregularity in
the age-band 20-34 years ATB. We regard this as more likely to be
an artifact from sampling than to be biologically meaningful, but
only time will tell with certainty. Meanwhile, we shall not use
any smoothing operation for either the raw K-values or (later) the
low-dose K-values.
Male versus Female K-Values :
-----------------------------
When we compare K-values for males and females, we find that
the males seem generally less radio-sensitive than the females. In
the one age-band (50+) where these are the final results --
because almost everyone has died -- this is what we see. On the
other hand, the age-band 35-49 years ATB is the age-band which
accounts for the most cancer-deaths in the study by far (Table
4-B), which makes it the most reliable to date. In this age-band,
radio-sensitivity is about the SAME in males and females.
Independence from Hypotheses and Models :
-----------------------------------------
It is self-evident that there necessarily exists some ratio
between two cancer-rates (R2 and R1) observed at two different
doses (D2 and D1). The ratio may be greater than 1.0, equal to
1.0, or less than 1.0, but whatever its value, it exists. Equation
(7) simply uses the observed ratio and the doses to calculate the
value of K: The fractional increase in the spontaneous
cancer-rate per cSv of dose.
Thus the raw K-values in Table 15-L are independent from any
forward projection, hypothesis, or model of radiation
carcinogenesis. They are "in-the-box" observations with respect to
the follow-up through 1982. Whether or not they will keep the same
value during the remaining follow-up periods is a separate
question, which no one can answer with certainty, of course.
Raw K-Values Not Applicable for Low-Doses :
-------------------------------------------
Because dose-response is concave-downward instead of linear,
and because raw K-values are derived from a D2 in the range of
70-100 cSv of average organ-dose, the raw K-values would (if used)
necessarily underestimate the Cancer-Yield -- the radiation hazard
-- from low-dose exposure. In Part 6, we will determine the size
of the underestimate.
5. Obtaining K-Values for Low-Dose Exposure
============================================
The Key Assumption, and Overview of the Method :
------------------------------------------------
In Chapters 14 and 29, it was demonstrated that (A) the
dose-response relationship in the A-Bomb Study -- for both cities,
both sexes, and all five age-bands combined -- is concave-downward
in shape (supra-linear), and (B) the best fit to the data is
obtained by using Dose^0.75 in the equation of cancer death-rate
versus dose. Indeed, the fit is excellent, with R-Squared values
of 0.9831 for the T65DR dosimetry (Table 29-B) and 0.9825 for the
DS86 dosimetry (Table 29-C).
Since the ten age-sex subsets examined here, by the
Cancer-Rate Ratio Method, represent the entire substrate which
generated that dose-exponent, it is a reasonable expectation that
approximately the same dose-exponent characterizes the ten age-sex
groups individually.
Because of the small-numbers problem, this expectation cannot
yet be tested; another decade or more of follow-up will perhaps
produce adequate numbers to do curvilinear regression analysis for
the ten groups separately. Meanwhile, the assumption that they DO
share a similar dose-response curve seems far more reasonable than
a speculative claim that they do NOT. Therefore, we will make the
approximation that the dose-exponent of 0.75, which characterizes
dose-response for the overall population, also applies
individually to each of the population's ten subsets.
With this single assumption, we can write individual equations
of best fit for each subset, based on the real-world observations
belonging to that particular age-sex group (from Tables 15-B
through 15-K), and then we can use the equations to determine the
corresponding LOW-DOSE K-values for each age-sex group.
Before demonstrating the two-step procedure, first we will
show the origin of the additional equations to be used. In the
end, we also use Equation (7) again.
Equations (8) Through (12) :
----------------------------
With our combined dose-groups, we can refer to two categories:
The "L" Group is the Lower Group
(Dose-Groups 1 + 2 + 3).
The "H" Group is the Higher Group
(Dose-Groups 4 + 5 + 6 + 7 + 8).
In Group L, we have a dose, D1, where the
observed cancer-rate is R1.
In Group H, we have a dose, D2, where the
observed cancer-rate is R2.
Equation (8) below states the general dose-response relationship
which, as noted in Chapter 29, is an equation which produces a
straight line if dose is plotted in units of cSv^0.75 instead of
cSv:
o -- Equation (8) :
Cancer-Rate
= (Coefficient)(Dose^0.75) + (Constant)
Readers will recognize that the format of Equation (8) is the
analytic expression of a straight line: y = mx + b. Since b is
the line's y-intercept, the Constant in Equation (8) is the
cancer-rate when dose is zero (the spontaneous cancer-rate).
We can write Equation (9) for Group L, and Equation (10) for Group
H.
o -- Equation (9) :
R1 = (Coefficient)(D1^0.75) + (Constant)
o -- Equation (10) :
R2 = (Coefficient)(D2^0.75) + (Constant)
Since these linear equations necessarily share the same
Coefficient and Constant, and since Tables 15-B through 15-K
provide the values of R1, R2, D1, and D2, we will be able to solve
these two equations for both the Coefficient and the Constant.
Solving for the Coefficient first, we subtract Equation (9) from
Equation (10), to obtain:
R2-R1 = (Coefficient)(D2^0.75 - D1^0.75) , and then
o -- Equation (11) :
(Coefficient) = (R2-R1) / (D2^0.75 - D1^0.75)
For the Constant, we re-arrange Equation (9).
o -- Equation (12) :
Constant = (R1) - (Coefficient)(D1^0.75)
Since we evaluated the Coefficient in Equation (11), and since
R1 and D1^0.75 are knowns, we now have the value of the Constant
-- or would, if we had been using actual observations. In Step 1
below, we shall apply these equations to some real numbers from
the tables.
Step 1 -- o
Obtaining the Equation of Best Fit
----------------------------------
The procedure to be demonstrated is general, and has been
applied to all ten age-sex groups under study here. It will be
illustrated below by using the input from Table 15-B for the males
age 0-9 years ATB, in the T65DR dosimetry. Any other set of data
(Tables 15-C through 15-K) would serve just as well. The results
become entries in Table 15-L.
D1 = 2.90 cSv
D2 = 96.64 cSv
R1 = 31.08 cancers per 10,000 persons, 1950-82
R2 = 105.26 cancers per 10,000 persons, 1950-82
D1^0.75 = (2.9)^0.75 = 2.2222
D2^0.75 = (96.64)^0.75 = 30.822
Applying Equation (11), we solve for Coefficient:
Coefficient = (R2-R1) / (D2^0.75 - D1^0.75)
Coefficient = (105.26-31.08) / (30.82248-2.222278)
Coefficient = 2.593687
Applying Equation (12), we solve for Constant:
Constant = R1 - (Coefficient)(D1^0.75)
Constant = 31.08 - (2.593687)(2.222278)
Constant = 25.31610
And now, with Equation (8) as the model, we can write the
entire Equation of Best Fit for this particular age- and
sex-group:
Cancer-Rate = (2.5937)(Dose^0.75) + (25.3161)
Precisely this entry is to be found in Table 15-L for the
Equation of Best Fit for males, 0-9 years of age ATB, in the T65DR
dosimetry.
Step 2 -- o
Obtaining (R2/R1) & Solving for Low-Dose K :
--------------------------------------------
In order to calculate the appropriate K-value for a total dose
up to 5 cSv, we now need to use this Equation of Best Fit to
obtain the predicted cancer-rates at zero-dose and at 5 cSv.
For 5 cSv :
Cancer-rate = (2.5937)(5^0.75) + (25.3161)
Since 5^0.75 = 3.343701
Cancer-rate = (2.5937)(3.343701) + (25.3161)
= 33.98865
For Zero cSv :
Cancer-rate = (2.5937)(0^0.75) + (25.3161)
Since 0^0.75 = 0,
Cancer-rate = 25.3161
Thus, for these two doses and cancer-rates :
D1 = 0 cSv
D2 = 5 cSv
R1 = 25.3161
R2 = 33.98865
R2/R1 = 33.98865 / 25.3161 = 1.3425
Now, going back to Equation (7) and making the approximation
that dose-response is linear between 0 and 5 cSv, we can calculate
the K-value which is appropriate for low-dose exposure:
o -- Equation (7) :
(R2/R1) - 1
K = ------------------
(D2) - (R2/R1)(D1)
Substituting our values, we have for the average K-value up to
5 cSv of total dose:
1.34257 - 1
K = --------------------
5 - (1.34257)(0)
K = 0.34257 / 5 = 0.06851
In Table 15-L of low-dose K-values, exactly this K-value of
0.06851 is entered for males 0-9 years of age ATB, in the T65DR
dosimetry. All twenty low-dose K-values in Table 15-L are derived
in the same way.
6. Discussion of Low-Dose K-Values
===================================
There are two checks which confirm that the method is correct
for obtaining low-dose K-values from the evidence at hand.
Checking the Constants :
------------------------
First, since the constants in the Equations of Best Fit in
Table 15-L are the predicted spontaneous cancer-rates when the
dose is zero, those constants should be consistent with the rates
observed in the Reference Group, whose exposure was not far above
zero. Since Tables 15-B through 15-K include the cancer-rate per
10,000 initial persons in the Reference Group, such comparisons
are easily made with the constants in Table 15-L. The
correspondence between predicted and observed rates is very good,
especially for the older age-bands where the number of
cancer-cases is statistically the most stable.
Checking the Ratio (Low-Dose K / Raw K) :
-----------------------------------------
Second, the ratio between the low-dose K-values and the raw
K-values for each of the ten subsets should be about the same
magnitude as it would be, if the comparable ratio were determined
for the COMBINATION of all age-bands and both sexes. We made this
check by using Equation (7) with appropriate entries from Tables
14-A and 14-B.
Because raw K-values for the subsets were calculated with D2
equal to about 85 cSv, and D1 equal to about 3 cSv, in making a
calculation of the corresponding K-value with all ages and both
sexes combined, we chose the closest values available in Tables
14-A and 14-B. We used D2 = 80 cSv and D1 = 2 cSv. For the
low-dose K-value, of course we used D2 = 5 cSv and D1 = 0 cSv. The
resulting ratios are below:
T65DR without age-sex subdivision:
RATIO, LOW-DOSE K TO RAW K = 2.104 .
DS86 without age-sex subdivision:
RATIO, LOW-DOSE K TO RAW K = 2.103 .
This assures us that the overall ratio is, indeed, about the
same magnitude as the individual ratios shown in the tabulations
which follow. Moreover, everything here is consistent with the
ratios of low-dose and higher-dose Minimum Fatal Cancer-Yields in
Table 13-B, Row 1.
-------------------- T65DR ----------------------
| Sex & Raw Low-Dose Ratio, Low-Dose K |
| Age ATB K-Value K-Value over Raw K |
| (Years) |
| M 0-9 0.02749 0.068510 2.49 |
| M 10-19 0.00677 0.015190 2.24 |
| M 20-34 0.00157 0.003426 2.18 |
| M 35-49 0.00228 0.004936 2.16 |
| M 50+ 0.00162 0.003454 2.13 |
| |
| F 0-9 0.01922 0.046150 2.40 |
| F 10-19 0.01097 0.024570 2.24 |
| F 20-34 0.00492 0.010730 2.18 |
| F 35-49 0.00289 0.006152 2.13 |
| F 50+ 0.00288 0.005945 2.06 |
|--------------------------------------------------
-------------------- DS86 ----------------------
| Sex & Raw Low-Dose Ratio, Low-Dose K |
| Age ATB K-Value K-Value over Raw K |
| (Years) |
| M 0-9 0.02565 0.066170 2.58 |
| M 10-19 0.00647 0.014840 2.29 |
| M 20-34 0.00150 0.003344 2.23 |
| M 35-49 0.00207 0.004634 2.24 |
| M 50+ 0.00140 0.003114 2.22 |
| |
| F 0-9 0.01771 0.043880 2.48 |
| F 10-19 0.01081 0.024700 2.28 |
| F 20-34 0.00442 0.010000 2.26 |
| F 35-49 0.00250 0.005565 2.23 |
| F 50+ 0.00252 0.005425 2.15 |
--------------------------------------------------
It deserves emphasis, however, that correctness of method and
computation can never overcome inherent sampling variation and the
small-numbers problem in a set of observations. It is self-evident
from the raw data in Tables 15-B through 15-K that every analyst
who subdivides A-bomb data is dealing with some small and unstable
numbers. Even if K-values are biologically constant for the
lifespan which follows irradiation, future follow-ups may cause a
K-value to rise or fall due to the random variation of sampling.
(However, the values for the oldest age-band ATB are as stable as
they will ever become, since almost all of this age-band had died
before the end of the 1950-1982 follow-up.)
Effect of Extrapolation from High Doses :
-----------------------------------------
The ratios between low-dose K-values, and their corresponding
raw K-values, range from 2.1 to 2.5. Like Tables 13-B, 14-A, and
14-B, this indicates that failure to appreciate the
supra-linearity of the dose-response relationship accounts for
more than a 2-fold underestimate of fatal cancer-risk when high
doses and the linear dose-response are used to evaluate the hazard
from low-dose exposure.
This finding is in great contrast to the "old refrain" that
extrapolation from high doses would exaggerate the cancer-risk at
low doses from ionizing radiation. However, we repeat that it is
not necessary for anyone to extrapolate at all. One should use the
findings which are based DIRECTLY upon human exposure in the low
dose-range.
Free from Speculation :
-----------------------
Low-dose K-values, like the raw K-values, are "in-the-box."
Readers have seen for themselves that low-dose K-values are
derived from the actual observations (1950-1982) of D1, R1, D2,
R2, in Tables 15-B through 15-K, without any reliance on
speculation, hypotheses, or models of radiation carcinogenesis. As
shown in Chapter 14, the dose-exponent of 0.75 (used in Steps 1
and 2) ALSO comes from the evidence itself, not from speculation,
hypothesis, or pre-judgment.
Low-dose K-values vary with age ATB, as do the raw K-values.
Comments in Part 4 of this chapter regarding age and sex apply
equally to raw and low-dose K-values.
7. Some Ties between K-Values, Supra-Linearity, Duration
=========================================================
K-Values and Supra-Linearity :
------------------------------
For the sake of exploration, we are going to use the RAW
K-values at the bottom of Table 15-L, to predict the consequences
of radiation exposure, regardless of dose-level.
Let us say that the raw K-values at the bottom of Table 15-L,
for the children who were age 0-9 years old ATB, are "good" -- by
which we mean, if there were a billion such children in the study
instead of 18402 children, we would still observe a raw K-value of
about 0.02, or 2 % per rem, from the 1950-1982 follow-up. In other
words, suppose there is no basis for thinking 0.02 is spuriously
high or low, due to sampling variation.
If we use the approximation for this exploration that, in
populations with a long lifespan, some 20 % of people die from
SPONTANEOUS cancer, and if we make the presumption that the
magnitude of the raw K-value neither rises nor falls with further
follow-up, then what would we expect for children irradiated
between 0-9 years of age?
SCENARIO 1 : Among every 10,000 children who receive one rem
(cSv) of whole-body internal organ-dose, we would expect that
2,000 would die eventually from spontaneous cancer, and from the
definition of K -- which is the fractional increase in the
spontaneous rate per rem -- we would also expect (2000 spontaneous
cancers x 0.02 per rem x 1 rem), or 40 radiation-induced cancers.
Combined lifelong cancer-deaths expected for this group = 2,040
per 10,000 initial persons.
SCENARIO 2 : Among every 10,000 children who receive 25 rems
(cSv) of whole-body internal organ-dose, we would expect that
2,000 would die eventually from spontaneous cancer, and from using
the raw K-value of 0.02, we would also expect (2000 spontaneous
cancers x 0.02 per rem x 25 rems), or 1,000 radiation-induced
cancers. Combined lifelong cancer-deaths expected for this group =
3,000 per 10,000 initial persons.
SCENARIO 3 : Among every 10,000 children who receive 200
rems of whole-body internal organ-dose, we would expect that 2,000
would die eventually from spontaneous cancer, and still using the
raw K-value of 0.02, we would also expect (2000 spontaneous
cancers x 0.02 per rem x 200 rems), or 8,000 radiation-induced
cancers. Combined lifelong cancer-deaths expected for this group =
10,000 per 10,000 initial persons.
Thus, use of the same K-value at high doses and low doses
would, in certain circumstances, lead to absurd predictions at
HIGH doses.
In the A-Bomb Study, there are about 200 children who survived
the acute effects of 200 rems or more of whole-body internal
organ-dose (see Dose-Groups 7 and 8, in Tables 15-B and 15-G). If
a single raw K-value were applicable at every dose-level and if it
persisted lifelong, then all of these 200 persons would be
expected to die of cancer. (The expectation would be 40
spontaneous fatal cancers, plus 160 radiation-induced cases.)
But in reality, it would NOT happen that way, because
non-cancer causes of death would "compete" with cancer in this
group. As a result, the ultimate observation would be fewer than
200 cancers per 200 initial persons. Therefore, under these
circumstances, the single raw K-value of 0.02 could NOT
characterize all dose-levels. The K-value at 200 rems would have
to be LOWER than 0.02 -- and that would be consistent with
SUPRA-linearity of dose-response.
A recurrent finding in this field is that K-values are high
for children. Unless dose-response is supra-linear (meaning lower
K-values at high doses than at low doses), predictions based on
high doses and on high, lifelong K-values will "require" lifetime
cancer death-rates which exceed 100 percent. In contrast to such
an absurdity, high and lifelong K-values at LOW doses are
consistent with predictions which are credible.
K-Values and Duration of Magnitude :
------------------------------------
Absurd predictions for high-dose consequences, illustrated in
Scenario 3 above, could be avoided by acceptance of different
K-values for different dose-levels (in accordance with the current
evidence from the A-bomb survivors), but there is also another
route to credible high-dose estimates. One could speculate that
K-values, though truly observed and reported for a given follow-up
period, will not remain constant for the full remainder of a
lifespan follow-up.
For instance, if one observed a very high K-value like 0.5 per
rem (not 0.05 or 0.005 per rem) in some sample of irradiated
children during an incomplete lifespan follow-up, then K = 0.5 per
rem would mean that a dose of only 8 rems would cause everyone in
that sample to die from cancer, if the K-value remained at the
SAME magnitude of 0.5 for the remaining lifespan:
(2,000 spontaneous cancers per 10,000 initial persons) x (0.5
per rem) x (8 rems) = 8,000 radiation-induced cancers. When the
expected 2,000 spontaneous cancer-deaths are added, cancer would
claim 10,000 out of every 10,000 initial persons in such a sample.
Nonetheless, the observation of K = 0.5 may be exactly right
for the time-period which has passed. One cannot presently rule
out the possibility that K-values vary with time -- as well as
with dose-level. On the other hand, one cannot rule out
predictions which come fairly close to 100 % cancer-mortality
either. For instance, among persons with chronic hepatitis-B
infection, the lifetime incidence of a SINGLE TYPE of cancer alone
(hepatocellular carcinoma) has been reported as high as 50 %
(Ober89).
Supra-Linearity in the Absence of High K-Values :
-------------------------------------------------
Table 4-B is a reminder that the supra-linearity presently
observed in the A-bomb survivors is overwhelmingly generated by
the cancer-response of those who were already adults at the time
of bombing, because fully 92.7 percent of all the cancers observed
during the 1950-1982 follow-up have come from the three oldest
age-bands ATB. Yet these three oldest age-bands are the LEAST
sensitive to radiation carcinogenesis. If we do an exploration
with their highest raw K-value, which is near 0.005, we do not
"run out of people" for the expected cancers, even at a very high
dose:
Among every 10,000 adults who receive 200 rems of whole-body
internal organ-dose, we would expect that 2,000 would die
eventually from spontaneous cancer, and under the specified
K-value, we would also expect (2000 spontaneous cancers x 0.005
per rem x 200 rems), or 2,000 radiation-induced cancers. Combined
lifelong cancers expected for this group would be 4,000 per 10,000
initial persons.
Therefore we can rule out pressure from competing causes of
death as the main CAUSE of the supra-linearity observed in the
1950-1982 dose-response of the adult A-bomb survivors.
8. The Bottom Line on Radiation Risk, by Age and Sex
=====================================================
1. K is defined as the fractional increase in the
spontaneous cancer death-rate per centi-sievert of whole-body
internal organ-dose. A K-value measures the size of an observed
cancer-response, and is independent from any particular hypotheses
and models of radiation carcinogenesis itself.
2. The main part of Table 15-L presents the low-dose
K-values for each of RERF's five age-bands and both sexes.
Separate sets of K-values have been calculated for the T65DR
dosimetry and the current version of the DS86 dosimetry. These
K-values come from observation of the A-bomb survivors from
1950-1982. No follow-up years -- and no Dose-Groups -- have been
thrown out of our analysis (see Chapter 14, Part 2). All the
available observations were included in finding the equation of
best fit, for each of the ten groups.
3. The low-dose K-values from Table 15-L will be used in the
next chapter to estimate the Minimum and Lifetime Fatal
Cancer-Yields from low-dose exposure, not only for the A-bomb
survivors, but also for a population with an age-sex distribution
like the one of the United States.
------------------------------------------------------------------
----------------------------------------------------------------------------
----------------------------------------------------------------------------
Table 15-A
Correction of Dose-Data for Small Body-Size: Ages 0-9 at Time of Bombing.
|========================================================================================================|
| MALES AGE 0-9 ATB: T65DR Dosimetry, Neutron RBE = 2.0 || MALES: DS86 Dosimetry, Neutron RBE = 20. |
| || |
| Col. A Col. B Col. C Col. D || Col. E Col. F Col. G Col. H |
| Dose- Uncorrected Correction Corrected || Dose- Uncorrected Correction Corrected |
| Group Dose Factor Dose Persons || Group Dose Factor Dose |
| MALES in cSv MALES in cSv MALES || MALES in cSv MALES in cSv |
|====================================================== || ============================================ |
| Group 1 0 1.000 0.000 3787 || Group 1 0.08194 1.074 0.088 |
| Group 2 1.450 1.171 1.698 3031 || Group 2 1.593 1.128 1.797 |
| Group 3 10.49 1.179 12.368 1547 || Group 3 13.32 1.138 15.158 |
| Group 4 34.78 1.175 40.867 359 || Group 4 39.79 1.162 46.236 |
| Group 5 71.64 1.173 84.034 189 || Group 5 72.79 1.169 85.092 |
| Group 6 120.19 1.172 140.863 105 || Group 6 116.90 1.179 137.825 |
| Group 7 170.63 1.186 202.367 43 || Group 7 175.39 1.192 209.065 |
| Group 8 256.45 1.182 303.124 64 || Group 8 305.99 1.203 368.106 |
| SUM 9125 |
|====================================================================================================== |
| |
|FEMALES AGE 0-9 ATB: T65DR Dosimetry, Neutron RBE = 2.0|| FEMALES: DS86 Dosimetry, Neutron RBE = 20. |
| || |
| Col. A Col. B Col. C Col. D || Col. E Col. F Col. G Col. H |
| Dose- Uncorrected Correction Corrected || Dose- Uncorrected Correction Corrected |
| Group Dose Factor Dose Persons || Group Dose Factor Dose |
| FEMALES in cSv FEMALES in cSv FEMALES || FEMALES in cSv FEMALES in cSv |
|====================================================== || ============================================ |
| Group 1 0 1.000 0.000 3842 || Group 1 0.08186 1.074 0.088 |
| Group 2 1.429 1.173 1.676 3093 || Group 2 1.581 1.128 1.783 |
| Group 3 10.700 1.178 12.605 1547 || Group 3 13.55 1.138 15.420 |
| Group 4 34.65 1.173 40.644 372 || Group 4 39.23 1.161 45.546 |
| Group 5 70.31 1.181 83.036 213 || Group 5 74.07 1.173 86.884 |
| Group 6 122.17 1.177 143.794 99 || Group 6 122.06 1.183 144.397 |
| Group 7 175.91 1.189 209.157 41 || Group 7 182.27 1.194 217.630 |
| Group 8 267.01 1.176 314.004 70 || Group 8 313.59 1.199 375.994 |
| SUM 9277 |
|========================================================================================================|
NOTES: -----
Average age of the 0-9 year-old children ATB was 4.1 years (Table 26-E).
Entries in Col.B and Col.F are calculated from Master File 26 A,B,C,D.
Entries in Col.C and Col.G come from Tables 31-A and 31-B.
Entries in Col.D = (Col.B) x (Col.C).
Entries in Col.H = (Col.F) x (Col.G).
Cols. D and H provide the organ-doses for Tables 15-B and 15-G.
----------------------------------------------------------------------------
----------------------------------------------------------------------------
----------------------------------------------------------------------------
----------------------------------------------------------------------------
Table 15-B
Calculation of Raw K-Values for Males 0-9 Years of Age ATB.
|=========================================================================================================|
| T65DR DOSIMETRY, NEUTRON RBE = 2.0 || DS86 DOSIMETRY, NEUTRON RBE = 20 |
| || |
| The Basic Data for 0-9 year-old Males ATB || The Basic Data for 0-9 year-old Males ATB |
| (Hiroshima plus Nagasaki combined) || (Hiroshima plus Nagasaki combined) |
| from Tables 15-A, 11-B, and 26-A,B. || from Tables 15-A,11-B, and 26-A,B. |
|================================================= || ================================================ |
| Dose- Organ- Total MALES Cancers || Dose- Organ Total MALES Cancers |
| Group Dose Cancers Entered per || Group Dose Cancers Entered per |
| in for into Initial || in for into Initial |
| cSv 1950-82 Study 10,000 || cSv 1950-82 Study 10,000 |
| || |
| Group 1+2 0.75 25 6818 36.67 || Group 1+2 0.85 25 6818 36.67 |
| Group 3 12.37 1 1547 6.46 || Group 3 15.16 1 1547 6.46 |
| Group 4 40.87 0 359 0.00 || Group 4 46.24 0 359 0.00 |
| Group 5 84.03 2 189 105.82 || Group 5 85.09 2 189 105.82 |
| Group 6 140.86 5 105 476.19 || Group 6 137.83 5 105 476.19 |
| Group 7 202.37 0 43 0.00 || Group 7 209.07 0 43 0.00 |
| Group 8 303.12 1 64 156.25 || Group 8 368.11 1 64 156.25 |
|================================================= || ================================================ |
| Combining the dose-classes, we have || Combining the dose-classes we have, |
| || |
| Dose- Organ- Total Persons Cancers || Dose- Organ Total Persons Cancers |
| Groups Dose Cancers Entered 10,000 || Groups Dose Cancers Entered 10,000 |
| Com- in for into persons || Com- in for into persons |
| bined cSv 1950-82 Study (R value) || bined cSv 1950-82 Study (R value) |
| || |
| 1+2+3 2.90 26 8365 31.08 || 1+2+3 3.49 26 8365 31.08 |
| 4+5+6+7+8 96.64 8 760 105.26 || 4+5+6+7+8 104.87 8 760 105.26 |
| || |
|================================================= || ================================================ |
| For application of Equation (7) to these data, || For application of Equation (7) to these data, |
| || |
| D1 = 2.90 centi-Sieverts ( rems ) || D1 = 3.49 centi-Sieverts ( rems ) |
| D2 = 96.64 centi-Sieverts ( rems ) || D2 = 104.87 centi-Sieverts ( rems ) |
| R1 = 31.08 cancers per 10,000 persons, 1950-82 || R1 = 31.08 cancers per 10,000 persons, 1950-82 |
| R2 = 105.26 cancers per 10,000 persons, 1950-82 || R2 = 105.26 cancers per 10,000 persons, 1950-82 |
| R2/R1 = 3.39 || R2/R1 = 3.39 |
| || |
| The numerator for Equation (7) is : || The numerator for Equation (7) is: |
| (R2/R1) - 1 = 2.39 || (R2/R1) - 1 = 2.39 |
| || |
| The denominator for Equation (7) is : || The denominator for Equation (7) is : |
| (D2) - (R2/R1)(D1) = (96.64) - (3.39)(2.90) || (D2) - (R2/R1)(D1) = (104.87) - (3.39)(3.49) |
| = 86.81 || = 93.04 |
| || |
| The quotient, the K value = 0.02749 || The quotient, the K value = 0.02565 |
|_________________________________________________________________________________________________________|
----------------------------------------------------------------------------
----------------------------------------------------------------------------
----------------------------------------------------------------------------
----------------------------------------------------------------------------
Table 15-C
Calculation of Raw K-Values for Males 10-19 Years of Age ATB.
|=========================================================================================================|
| T65DR DOSIMETRY, NEUTRON RBE = 2.0 || DS86 DOSIMETRY, NEUTRON RBE = 20 |
| || |
| The Basic Data for 10-19 year-old Males ATB || The Basic Data for 10-19 year-old Males ATB |
| (Hiroshima plus Nagasaki combined) || (Hiroshima plus Nagasaki combined) |
| from Tables 11-B and 26A,B. || from Tables 11-B and 26A,B. |
|================================================= || ================================================ |
| Dose- Organ- Total MALES Cancers || Dose- Organ Total MALES Cancers |
| Group Dose Cancers Entered per || Group Dose Cancers Entered per |
| in for into Initial || in for into Initial |
| cSv 1950-82 Study 10,000 || cSv 1950-82 Study 10,000 |
| || |
| Group 1+2 0.83 113 6378 177.17 || Group 1+2 1.11 113 6378 177.17 |
| Group 3 11.11 19 1112 170.86 || Group 3 13.92 19 1112 170.86 |
| Group 4 35.24 9 342 263.16 || Group 4 36.53 9 342 263.16 |
| Group 5 71.79 5 371 134.77 || Group 5 67.75 5 371 134.77 |
| Group 6 124.73 7 167 419.16 || Group 6 117.37 7 167 419.16 |
| Group 7 172.18 4 70 571.43 || Group 7 180.64 4 70 571.43 |
| Group 8 265.93 6 126 476.19 || Group 8 325.58 6 126 476.19 |
|================================================= || ================================================ |
| Combining the dose-classes, we have || Combining the dose-classes we have, |
| || |
| Dose- Organ- Total Persons Cancers || Dose- Organ Total Persons Cancers |
| Groups Dose Cancers Entered 10,000 || Groups Dose Cancers Entered 10,000 |
| Com- in for into persons || Com- in for into persons |
| bined cSv 1950-82 Study (R value) || bined cSv 1950-82 Study (R value) |
| || |
| 1+2+3 2.36 132 7490 176.23 || 1+2+3 3.01 132 7490 176.23 |
| 4+5+6+7+8 97.65 31 1076 288.10 || 4+5+6+7+8 103.06 31 1076 288.10 |
| || |
|================================================= || ================================================ |
| For application of Equation (7) to these data, || For application of Equation (7) to these data, |
| || |
| D1 = 2.36 centi-Sieverts ( rems ) || D1 = 3.01 centi-Sieverts ( rems ) |
| D2 = 97.65 centi-Sieverts ( rems ) || D2 = 103.06 centi-Sieverts ( rems ) |
| R1 = 176.23 cancers per 10,000 persons, 1950-82 || R1 = 176.23 cancers per 10,000 persons, 1950-82 |
| R2 = 288.10 cancers per 10,000 persons, 1950-82 || R2 = 288.10 cancers per 10,000 persons, 1950-82 |
| R2/R1 = 1.63 || R2/R1 = 1.63 |
| || |
| The numerator for Equation (7) is : || The numerator for Equation (7) is: |
| (R2/R1) - 1 = 0.63 || (R2/R1) - 1 = 0.63 |
| || |
| The denominator for Equation (7) is : || The denominator for Equation (7) is : |
| (D2) - (R2/R1)(D1) = (97.65) - (1.63)(2.36) || (D2) - (R2/R1)(D1) = (103.06) - (1.63)(3.01) |
| = 93.80 || = 98.14 |
| || |
| The quotient, the K value = 0.00677 || The quotient, the K value = 0.00647 |
|_________________________________________________________________________________________________________|
----------------------------------------------------------------------------
----------------------------------------------------------------------------
----------------------------------------------------------------------------
----------------------------------------------------------------------------
Table 15-D
Calculation of Raw K-Values for Males 20-34 Years of age ATB.
|=========================================================================================================|
| T65DR DOSIMETRY, NEUTRON RBE = 2.0 || DS86 DOSIMETRY, NEUTRON RBE = 20 |
| || |
| The Basic Data for 20-34 year-old Males ATB || The Basic Data for 20-34 year-old Males ATB |
| (Hiroshima plus Nagasaki combined) || (Hiroshima plus Nagasaki combined) |
| from Tables 11-B and 26-A,B. || from Tables 11-B and 26-A,B. |
|================================================= || ================================================ |
| Dose- Organ- Total MALES Cancers || Dose- Organ Total MALES Cancers |
| Group Dose Cancers Entered per || Group Dose Cancers Entered per |
| in for into Initial || in for into Initial |
| cSv 1950-82 Study 10,000 || cSv 1950-82 Study 10,000 |
| || |
| Group 1+2 0.67 224 3293 680.23 || Group 1+2 0.99 224 3293 680.23 |
| Group 3 11.57 54 703 768.14 || Group 3 15.34 54 703 768.14 |
| Group 4 35.54 11 237 464.14 || Group 4 38.01 11 237 464.14 |
| Group 5 71.15 22 224 982.14 || Group 5 70.73 22 224 982.14 |
| Group 6 123.33 17 122 1393.44 || Group 6 116.33 17 122 1393.44 |
| Group 7 171.24 2 53 377.36 || Group 7 174.19 2 53 377.36 |
| Group 8 273.22 3 57 526.32 || Group 8 340.73 3 57 526.32 |
|================================================= || ================================================ |
| Combining the dose-classes, we have || Combining the dose-classes we have, |
| || |
| Dose- Organ- Total Persons Cancers || Dose- Organ Total Persons Cancers |
| Groups Dose Cancers Entered 10,000 || Groups Dose Cancers Entered 10,000 |
| Com- in for into persons || Com- in for into persons |
| bined cSv 1950-82 Study (R value) || bined cSv 1950-82 Study (R value) |
| || |
| 1+2+3 2.59 278 3996 695.70 || 1+2+3 3.51 278 3996 695.70 |
| 4+5+6+7+8 92.43 55 693 793.65 || 4+5+6+7+8 97.69 55 693 793.65 |
| || |
|================================================= || ================================================ |
| For application of Equation (7) to these data, || For application of Equation (7) to these data, |
| || |
| D1 = 2.59 centi-Sieverts ( rems ) || D1 = 3.51 centi-Sieverts ( rems ) |
| D2 = 92.43 centi-Sieverts ( rems ) || D2 = 97.69 centi-Sieverts ( rems ) |
| R1 = 695.70 cancers per 10,000 persons, 1950-82 || R1 = 695.70 cancers per 10,000 persons, 1950-82 |
| R2 = 793.65 cancers per 10,000 persons, 1950-82 || R2 = 793.65 cancers per 10,000 persons, 1950-82 |
| R2/R1 = 1.14 || R2/R1 = 1.14 |
| || |
| The numerator for Equation (7) is : || The numerator for Equation (7) is: |
| (R2/R1) - 1 = 0.14 || (R2/R1) - 1 = 0.14 |
| || |
| The denominator for Equation (7) is : || The denominator for Equation (7) is : |
| (D2) - (R2/R1)(D1) = (92.43) - (1.14)(2.59) || (D2) - (R2/R1)(D1) = (97.69) - (1.14)(3.51) |
| = 89.48 || = 93.68 |
| || |
| The quotient, the K value = 0.00157 || The quotient, the K value = 0.00150 |
|_________________________________________________________________________________________________________|
----------------------------------------------------------------------------
----------------------------------------------------------------------------
----------------------------------------------------------------------------
----------------------------------------------------------------------------
Table 15-E
Calculation of Raw K-Values for Males 35-49 Years of Age ATB.
|=========================================================================================================|
| T65DR DOSIMETRY, NEUTRON RBE = 2.0 || DS86 DOSIMETRY, NEUTRON RBE = 20 |
| || |
| The Basic Data for 35-49 year-old Males ATB || The Basic Data for 35-49 year-old Males ATB |
| (Hiroshima plus Nagasaki combined) || (Hiroshima plus Nagasaki combined) |
| from Tables 11-B and 26A,B. || from Tables 11-B and 26A,B. |
|================================================= || ================================================ |
| Dose- Organ- Total MALES Cancers || Dose- Organ Total MALES Cancers |
| Group Dose Cancers Entered per || Group Dose Cancers Entered per |
| in for into Initial || in for into Initial |
| cSv 1950-82 Study 10,000 || cSv 1950-82 Study 10,000 |
| || |
| Group 1+2 0.65 963 5999 1605.27 || Group 1+2 0.95 963 5999 1605.27 |
| Group 3 11.47 240 1381 1737.87 || Group 3 15.47 240 1381 1737.87 |
| Group 4 35.66 82 438 1872.15 || Group 4 40.56 82 438 1872.15 |
| Group 5 69.45 72 368 1956.52 || Group 5 74.85 72 368 1956.52 |
| Group 6 120.43 24 133 1804.51 || Group 6 121.05 24 133 1804.51 |
| Group 7 171.23 12 70 1714.29 || Group 7 175.05 12 70 1714.29 |
| Group 8 266.80 28 111 2522.52 || Group 8 326.23 28 111 2522.52 |
|================================================= || ================================================ |
| Combining the dose-classes, we have || Combining the dose-classes we have, |
| || |
| Dose- Organ- Total Persons Cancers || Dose- Organ Total Persons Cancers |
| Groups Dose Cancers Entered 10,000 || Groups Dose Cancers Entered 10,000 |
| Com- in for into persons || Com- in for into persons |
| bined cSv 1950-82 Study (R value) || bined cSv 1950-82 Study (R value) |
| || |
| 1+2+3 2.67 1203 7380 1630.08 || 1+2+3 3.67 1203 7380 1630.08 |
| 4+5+6+7+8 88.21 218 1120 1946.43 || 4+5+6+7+8 98.10 218 1120 1946.43 |
| || |
|================================================= || ================================================ |
| For application of Equation (7) to these data, || For application of Equation (7) to these data, |
| || |
| D1 = 2.67 centi-Sieverts ( rems ) || D1 = 3.67 centi-Sieverts ( rems ) |
| D2 = 88.21 centi-Sieverts ( rems ) || D2 = 98.10 centi-Sieverts ( rems ) |
| R1 = 1630.08 cancers per 10,000 persons, 1950-82 || R1 = 1630.08 cancers per 10,000 persons, 1950-82 |
| R2 = 1946.43 cancers per 10,000 persons, 1950-82 || R2 = 1946.43 cancers per 10,000 persons, 1950-82 |
| R2/R1 = 1.19 || R2/R1 = 1.19 |
| || |
| The numerator for Equation (7) is : || The numerator for Equation (7) is: |
| (R2/R1) - 1 = 0.19 || (R2/R1) - 1 = 0.19 |
| || |
| The denominator for Equation (7) is : || The denominator for Equation (7) is : |
| (D2) - (R2/R1)(D1) = (88.21)-(1.19)(2.67) || (D2) - (R2/R1)(D1) = (98.10)-(1.19)(3.67) |
| = 85.02 || = 93.72 |
| || |
| The quotient, the K value = 0.00228 || The quotient, the K value = 0.00207 |
|_________________________________________________________________________________________________________|
----------------------------------------------------------------------------
----------------------------------------------------------------------------
----------------------------------------------------------------------------
----------------------------------------------------------------------------
Table 15-F
Calculation of Raw K-Values for Males 50+ Years of Age ATB.
|=========================================================================================================|
| T65DR DOSIMETRY, NEUTRON RBE = 2.0 || DS86 DOSIMETRY, NEUTRON RBE = 20 |
| || |
| The Basic Data for 50+ year-old Males ATB || The Basic Data for 50+ year-old Males ATB |
| (Hiroshima plus Nagasaki combined) || (Hiroshima plus Nagasaki combined) |
| from Tables 11-B and 26A,B. || from Tables 11-B and 26A,B. |
|================================================= || ================================================ |
| Dose- Organ- Total MALES Cancers || Dose- Organ Total MALES Cancers |
| Group Dose Cancers Entered per || Group Dose Cancers Entered per |
| in for into Initial || in for into Initial |
| cSv 1950-82 Study 10,000 || cSv 1950-82 Study 10,000 |
| || |
| Group 1+2 0.63 747 5097 1465.57 || Group 1+2 0.90 747 5097 1465.57 |
| Group 3 11.05 155 1145 1353.71 || Group 3 14.81 155 1145 1353.71 |
| Group 4 35.67 51 308 1655.84 || Group 4 42.64 51 308 1655.84 |
| Group 5 72.24 40 234 1709.40 || Group 5 81.51 40 234 1709.40 |
| Group 6 122.73 15 74 2027.03 || Group 6 129.76 15 74 2027.03 |
| Group 7 177.14 3 34 882.35 || Group 7 195.16 3 34 882.35 |
| Group 8 269.80 8 65 1230.77 || Group 8 339.69 8 65 1230.77 |
|================================================= || ================================================ |
| Combining the dose-classes, we have || Combining the dose-classes we have, |
| || |
| Dose- Organ- Total Persons Cancers || Dose- Organ Total Persons Cancers |
| Groups Dose Cancers Entered 10,000 || Groups Dose Cancers Entered 10,000 |
| Com- in for into persons || Com- in for into persons |
| bined cSv 1950-82 Study (R value) || bined cSv 1950-82 Study (R value) |
| || |
| 1+2+3 2.54 902 6242 1445.05 || 1+2+3 3.45 902 6242 1445.05 |
| 4+5+6+7+8 84.66 117 715 1636.36 || 4+5+6+7+8 98.63 117 715 1636.36 |
| || |
|================================================= || ================================================ |
| For application of Equation (7) to these data, || For application of Equation (7) to these data, |
| || |
| D1 = 2.54 centi-Sieverts ( rems ) || D1 = 3.45 centi-Sieverts ( rems ) |
| D2 = 84.66 centi-Sieverts ( rems ) || D2 = 98.63 centi-Sieverts ( rems ) |
| R1 = 1445.05 cancers per 10,000 persons, 1950-82 || R1 = 1445.05 cancers per 10,000 persons, 1950-82 |
| R2 = 1636.36 cancers per 10,000 persons, 1950-82 || R2 = 1636.36 cancers per 10,000 persons, 1950-82 |
| R2/R1 = 1.13 || R2/R1 = 1.13 |
| || |
| The numerator for Equation (7) is : || The numerator for Equation (7) is: |
| (R2/R1) - 1 = 0.13 || (R2/R1) - 1 = 0.13 |
| || |
| The denominator for Equation (7) is : || The denominator for Equation (7) is : |
| (D2) - (R2/R1)(D1) = (84.66)-(1.13)(2.54) || (D2) - (R2/R1)(D1) = (98.63)-(1.13)(3.45) |
| = 81.78 || = 94.73 |
| || |
| The quotient, the K value = 0.00162 || The quotient, the K value = 0.00140 |
|_________________________________________________________________________________________________________|
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Table 15-G
Calculation of Raw K-Values for Females 0-9 Years of Age ATB.
|=========================================================================================================|
| T65DR DOSIMETRY, NEUTRON RBE = 2.0 || DS86 DOSIMETRY, NEUTRON RBE = 20 |
| || |
| The Basic Data for 0-9 year-old Females ATB || The Basic Data for 0-9 year-old Females ATB |
| (Hiroshima plus Nagasaki combined) || (Hiroshima plus Nagasaki combined) |
| from Tables 15-A, 11-D, and 26-C,D. || from Tables 15-A, 11-D, and 26-C,D. |
|================================================= || ================================================ |
| Dose- Organ- Total FEMALES Cancers || Dose- Organ Total FEMALES Cancers |
| Group Dose Cancers Entered per || Group Dose Cancers Entered per |
| in for into Initial || in for into Initial |
| cSv 1950-82 Study 10,000 || cSv 1950-82 Study 10,000 |
| || |
| Group 1+2 0.75 38 6935 54.79 || Group 1+2 0.84 38 6935 54.79 |
| Group 3 12.61 9 1547 58.18 || Group 3 15.42 9 1547 58.18 |
| Group 4 40.64 3 372 80.65 || Group 4 45.55 3 372 80.65 |
| Group 5 83.04 3 213 140.85 || Group 5 86.88 3 213 140.85 |
| Group 6 143.79 4 99 404.04 || Group 6 144.40 4 99 404.04 |
| Group 7 209.16 1 41 243.90 || Group 7 217.63 1 41 243.90 |
| Group 8 314.00 1 70 142.86 || Group 8 375.99 1 70 142.86 |
|================================================= || ================================================ |
| Combining the dose-classes, we have || Combining the dose-classes we have, |
| || |
| Dose- Organ- Total Persons Cancers || Dose- Organ Total Persons Cancers |
| Groups Dose Cancers Entered 10,000 || Groups Dose Cancers Entered 10,000 |
| Com- in for into persons || Com- in for into persons |
| bined cSv 1950-82 Study (R value) || bined cSv 1950-82 Study (R value) |
| || |
| 1+2+3 2.91 47 8482 55.41 || 1+2+3 3.50 47 8482 55.41 |
| 4+5+6+7+8 97.61 12 795 150.94 || 4+5+6+7+8 106.90 12 795 150.94 |
| || |
|================================================= || ================================================ |
| For application of Equation (7) to these data, || For application of Equation (7) to these data, |
| || |
| D1 = 2.91 centi-Sieverts ( rems ) || D1 = 3.50 centi-Sieverts ( rems ) |
| D2 = 97.61 centi-Sieverts ( rems ) || D2 = 106.90 centi-Sieverts ( rems ) |
| R1 = 55.41 cancers per 10,000 persons, 1950-82 || R1 = 55.41 cancers per 10,000 persons, 1950-82 |
| R2 = 150.94 cancers per 10,000 persons, 1950-82 || R2 = 150.94 cancers per 10,000 persons, 1950-82 |
| R2/R1 = 2.72 || R2/R1 = 2.72 |
| || |
| The numerator for Equation (7) is : || The numerator for Equation (7) is: |
| (R2/R1) - 1 = 1.72 || (R2/R1) - 1 = 1.72 |
| || |
| The denominator for Equation (7) is : || The denominator for Equation (7) is : |
| (D2) - (R2/R1)(D1) = (97.61)-(2.72)(2.91) || (D2) - (R2/R1)(D1) = (106.90)-(2.72)(3.50) |
| = 89.68 || = 97.36 |
| || |
| The quotient, the K value = 0.01922 || The quotient, the K value = 0.01771 |
|_________________________________________________________________________________________________________|
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Table 15-H
Calculation of Raw K-Values for Females 10-19 Years of Age ATB.
|=========================================================================================================|
| T65DR DOSIMETRY, NEUTRON RBE = 2.0 || DS86 DOSIMETRY, NEUTRON RBE = 20 |
| || |
| The Basic Data for 10-19 year-old Females ATB || The Basic Data for 10-19 year-old Females ATB |
| (Hiroshima plus Nagasaki combined) || (Hiroshima plus Nagasaki combined) |
| from Tables 11-D and 26-C,D. || from Tables 11-D and 26-C,D. |
|================================================= || ================================================ |
| Dose- Organ- Total FEMALES Cancers || Dose- Organ Total FEMALES Cancers |
| Group Dose Cancers Entered per || Group Dose Cancers Entered per |
| in for into Initial || in for into Initial |
| cSv 1950-82 Study 10,000 || cSv 1950-82 Study 10,000 |
| || |
| Group 1+2 0.65 116 7403 156.69 || Group 1+2 0.80 116 7403 156.69 |
| Group 3 10.71 23 1663 138.30 || Group 3 13.79 23 1663 138.30 |
| Group 4 36.46 7 543 128.91 || Group 4 39.15 7 543 128.91 |
| Group 5 72.44 18 556 323.74 || Group 5 68.10 18 556 323.74 |
| Group 6 122.62 8 264 303.03 || Group 6 110.72 8 264 303.03 |
| Group 7 172.26 8 118 677.97 || Group 7 183.68 8 118 677.97 |
| Group 8 263.31 6 111 540.54 || Group 8 324.60 6 111 540.54 |
|================================================= || ================================================ |
| Combining the dose-classes, we have || Combining the dose-classes we have, |
| || |
| Dose- Organ- Total Persons Cancers || Dose- Organ Total Persons Cancers |
| Groups Dose Cancers Entered 10,000 || Groups Dose Cancers Entered 10,000 |
| Com- in for into persons || Com- in for into persons |
| bined cSv 1950-82 Study (R value) || bined cSv 1950-82 Study (R value) |
| || |
| 1+2+3 2.50 139 9066 153.32 || 1+2+3 3.18 139 9066 153.32 |
| 4+5+6+7+8 89.20 47 1592 295.23 || 4+5+6+7+8 91.74 47 1592 295.23 |
| || |
|================================================= || ================================================ |
| For application of Equation (7) to these data, || For application of Equation (7) to these data, |
| || |
| D1 = 2.50 centi-Sieverts (rems) || D1 = 3.18 centi-Sieverts (rems) |
| D2 = 89.20 centi-Sieverts (rems) || D2 = 91.74 centi-Sieverts (rems) |
| R1 = 153.32 cancers per 10,000 persons, 1950-82 || R1 = 153.32 cancers per 10,000 persons, 1950-82 |
| R2 = 295.23 cancers per 10,000 persons, 1950-82 || R2 = 295.23 cancers per 10,000 persons, 1950-82 |
| R2/R1 = 1.93 || R2/R1 = 1.93 |
| || |
| The numerator for Equation (7) is : || The numerator for Equation (7) is: |
| (R2/R1) - 1 = 0.93 || (R2/R1) - 1 = 0.93 |
| || |
| The denominator for Equation (7) is : || The denominator for Equation (7) is : |
| (D2) - (R2/R1)(D1) = (89.20)-(1.93)(2.50) || (D2) - (R2/R1)(D1) = (91.74)-(1.93)(3.18) |
| = 84.39 || = 85.62 |
| || |
| The quotient, the K value = 0.01097 || The quotient, the K value = 0.01081 |
|_________________________________________________________________________________________________________|
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----------------------------------------------------------------------------
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Table 15-(Eye)
Calculation of Raw K-Values for Females 20-34 Years of Age ATB.
|=========================================================================================================|
| T65DR DOSIMETRY, NEUTRON RBE = 2.0 || DS86 DOSIMETRY, NEUTRON RBE = 20 |
| || |
| The Basic Data for 20-34 year-old Females ATB || The Basic Data for 20-34 year-old Females ATB |
| (Hiroshima plus Nagasaki combined) || (Hiroshima plus Nagasaki combined) |
| from Tables 15-A, 11-D, and 26-C,D. || from Tables 15-A, 11-D, and 26-C,D. |
|================================================= || ================================================ |
| Dose- Organ- Total FEMALES Cancers || Dose- Organ Total FEMALES Cancers |
| Group Dose Cancers Entered per || Group Dose Cancers Entered per |
| in for into Initial || in for into Initial |
| cSv 1950-82 Study 10,000 || cSv 1950-82 Study 10,000 |
| || |
| Group 1+2 0.66 396 9260 427.65 || Group 1+2 0.89 396 9260 427.65 |
| Group 3 10.98 121 2189 552.76 || Group 3 14.85 121 2189 552.76 |
| Group 4 35.61 36 670 537.31 || Group 4 42.38 36 670 537.31 |
| Group 5 72.59 22 436 504.59 || Group 5 75.91 22 436 504.59 |
| Group 6 122.38 22 192 1145.83 || Group 6 121.79 22 192 1145.83 |
| Group 7 172.35 6 103 582.52 || Group 7 182.47 6 103 582.52 |
| Group 8 256.22 13 152 855.26 || Group 8 320.87 13 152 855.26 |
|================================================= || ================================================ |
| Combining the dose-classes, we have || Combining the dose-classes we have, |
| || |
| Dose- Organ- Total Persons Cancers || Dose- Organ Total Persons Cancers |
| Groups Dose Cancers Entered 10,000 || Groups Dose Cancers Entered 10,000 |
| Com- in for into persons || Com- in for into persons |
| bined cSv 1950-82 Study (R value) || bined cSv 1950-82 Study (R value) |
| || |
| 1+2+3 2.63 517 11449 451.57 || 1+2+3 3.56 517 11449 451.57 |
| 4+5+6+7+8 87.38 99 1553 637.48 || 4+5+6+7+8 98.16 99 1553 637.48 |
| || |
|================================================= || ================================================ |
| For application of Equation (7) to these data, || For application of Equation (7) to these data, |
| || |
| D1 = 2.63 centi-Sieverts (rems) || D1 = 3.56 centi-Sieverts ( rems ) |
| D2 = 87.38 centi-Sieverts (rems) || D2 = 98.16 centi-Sieverts ( rems ) |
| R1 = 451.57 cancers per 10,000 persons, 1950-82 || R1 = 451.57 cancers per 10,000 persons, 1950-82 |
| R2 = 637.48 cancers per 10,000 persons, 1950-82 || R2 = 637.48 cancers per 10,000 persons, 1950-82 |
| R2/R1 = 1.41 || R2/R1 = 1.41 |
| || |
| The numerator for Equation (7) is : || The numerator for Equation (7) is: |
| (R2/R1) - 1 = 0.41 || (R2/R1) - 1 = 0.41 |
| || |
| The denominator for Equation (7) is : || The denominator for Equation (7) is : |
| (D2) - (R2/R1)(D1) = (87.38)-(1.41)(2.63) || (D2) - (R2/R1)(D1) = (98.16)-(1.41)(3.56) |
| = 83.66 || = 93.14 |
| || |
| The quotient, the K value = 0.00492 || The quotient, the K value = 0.00442 |
|_________________________________________________________________________________________________________|
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----------------------------------------------------------------------------
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Table 15-J
Calculation of Raw K-Values for Females 35-49 Years oF Age ATB.
|=========================================================================================================|
| T65DR DOSIMETRY, NEUTRON RBE = 2.0 || DS86 DOSIMETRY, NEUTRON RBE = 20 |
| || |
| The Basic Data for 35-49 year-old Females ATB || The Basic Data for 35-49 year-old Females ATB |
| (Hiroshima plus Nagasaki combined) || (Hiroshima plus Nagasaki combined) |
| from Tables 15-A, 11-D, and 26-C,D. || from Tables 15-A, 11-D, and 26-C,D. |
|================================================= || ================================================ |
| Dose- Organ- Total FEMALES Cancers || Dose- Organ Total FEMALES Cancers |
| Group Dose Cancers Entered per || Group Dose Cancers Entered per |
| in for into Initial || in for into Initial |
| cSv 1950-82 Study 10,000 || cSv 1950-82 Study 10,000 |
| || |
| Group 1+2 0.63 925 8838 1046.62 || Group 1+2 0.84 925 8838 1046.62 |
| Group 3 10.99 274 2291 1195.98 || Group 3 15.22 274 2291 1195.98 |
| Group 4 34.65 76 582 1305.84 || Group 4 43.00 76 582 1305.84 |
| Group 5 70.01 42 366 1147.54 || Group 5 78.94 42 366 1147.54 |
| Group 6 120.80 20 155 1290.32 || Group 6 127.99 20 155 1290.32 |
| Group 7 176.89 12 74 1621.62 || Group 7 195.39 12 74 1621.62 |
| Group 8 262.14 18 97 1855.67 || Group 8 328.33 18 97 1855.67 |
|================================================= || ================================================ |
| Combining the dose-classes, we have || Combining the dose-classes we have, |
| || |
| Dose- Organ- Total Persons Cancers || Dose- Organ Total Persons Cancers |
| Groups Dose Cancers Entered 10,000 || Groups Dose Cancers Entered 10,000 |
| Com- in for into persons || Com- in for into persons |
| bined cSv 1950-82 Study (R value) || bined cSv 1950-82 Study (R value) |
| || |
| 1+2+3 2.76 1199 11129 1077.37 || 1+2+3 3.80 1199 11129 1077.37 |
| 4+5+6+7+8 80.87 168 1274 1318.68 || 4+5+6+7+8 94.24 168 1274 1318.68 |
| || |
|================================================= || ================================================ |
| For application of Equation (7) to these data, || For application of Equation (7) to these data, |
| || |
| D1 = 2.76 centi-Sieverts (rems) || D1 = 3.80 centi-Sieverts (rems) |
| D2 = 80.87 centi-Sieverts (rems) || D2 = 94.24 centi-Sieverts (rems) |
| R1 = 1077.37 cancers per 10,000 persons, 1950-82 || R1 = 1077.37 cancers per 10,000 persons, 1950-82 |
| R2 = 1318.68 cancers per 10,000 persons, 1950-82 || R2 = 1318.68 cancers per 10,000 persons, 1950-82 |
| R2/R1 = 1.22 || R2/R1 = 1.22 |
| || |
| The numerator for Equation (7) is : || The numerator for Equation (7) is: |
| (R2/R1) - 1 = 0.22 || (R2/R1) - 1 = 0.22 |
| || |
| The denominator for Equation (7) is : || The denominator for Equation (7) is : |
| (D2) - (R2/R1)(D1) = (80.87)-(1.22)(2.76) || (D2) - (R2/R1)(D1) = (94.24)-(1.22)(3.80) |
| = 77.49 || = 89.59 |
| || |
| The quotient, the K value = 0.00289 || The quotient, the K value = 0.00250 |
|_________________________________________________________________________________________________________|
----------------------------------------------------------------------------
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Table 15-K
Calculation of Raw K-Values for Females 50+ Years of Age ATB.
|=========================================================================================================|
| T65DR DOSIMETRY, NEUTRON RBE = 2.0 || DS86 DOSIMETRY, NEUTRON RBE = 20 |
| || |
| The Basic Data for 50+ year-old Females ATB || The Basic Data for 50+ year-old Females ATB |
| (Hiroshima plus Nagasaki combined) || (Hiroshima plus Nagasaki combined) |
| from Tables 11-D and 26-C,D. || from Tables 11-D and 26-C,D. |
|================================================= || ================================================ |
| Dose- Organ- Total FEMALES Cancers || Dose- Organ Total FEMALES Cancers |
| Group Dose Cancers Entered per || Group Dose Cancers Entered per |
| in for into Initial || in for into Initial |
| cSv 1950-82 Study 10,000 || cSv 1950-82 Study 10,000 |
| || |
| Group 1+2 0.62 608 6007 1012.15 || Group 1+2 0.82 608 6007 1012.15 |
| Group 3 10.82 159 1365 1164.84 || Group 3 14.90 159 1365 1164.84 |
| Group 4 35.35 39 374 1042.78 || Group 4 43.68 39 374 1042.78 |
| Group 5 71.74 27 171 1578.95 || Group 5 77.44 27 171 1578.95 |
| Group 6 119.04 9 70 1285.71 || Group 6 125.23 9 70 1285.71 |
| Group 7 175.10 3 33 909.09 || Group 7 192.27 3 33 909.09 |
| Group 8 274.06 7 34 2058.82 || Group 8 343.56 7 34 2058.82 |
|================================================= || ================================================ |
| Combining the dose-classes, we have || Combining the dose-classes we have, |
| || |
| Dose- Organ- Total Persons Cancers || Dose- Organ Total Persons Cancers |
| Groups Dose Cancers Entered 10,000 || Groups Dose Cancers Entered 10,000 |
| Com- in for into persons || Com- in for into persons |
| bined cSv 1950-82 Study (R value) || bined cSv 1950-82 Study (R value) |
| || |
| 1+2+3 2.51 767 7372 1040.42 || 1+2+3 3.43 767 7372 1040.42 |
| 4+5+6+7+8 71.73 85 682 1246.33 || 4+5+6+7+8 82.65 85 682 1246.33 |
| || |
|================================================= || ================================================ |
| For application of Equation (7) to these data, || For application of Equation (7) to these data, |
| || |
| D1 = 2.51 centi-Sieverts (rems) || D1 = 3.43 centi-Sieverts (rems) |
| D2 = 71.73 centi-Sieverts (rems) || D2 = 82.65 centi-Sieverts (rems) |
| R1 = 1040.42 cancers per 10,000 persons, 1950-82 || R1 = 1040.42 cancers per 10,000 persons, 1950-82 |
| R2 = 1246.33 cancers per 10,000 persons, 1950-82 || R2 = 1246.33 cancers per 10,000 persons, 1950-82 |
| R2/R1 = 1.20 || R2/R1 = 1.20 |
| || |
| The numerator for Equation (7) is : || The numerator for Equation (7) is: |
| (R2/R1) - 1 = 0.20 || (R2/R1) - 1 = 0.20 |
| || |
| The denominator for Equation (7) is : || The denominator for Equation (7) is : |
| (D2) - (R2/R1)(D1) = (71.73)-(1.20)(2.51) || (D2) - (R2/R1)(D1) = (82.65)-(1.20)(3.43) |
| = 68.72 || = 78.55 |
| || |
| The quotient, the K value = 0.00288 || The quotient, the K value = 0.00252 |
|_________________________________________________________________________________________________________|
----------------------------------------------------------------------------
----------------------------------------------------------------------------
----------------------------------------------------------------------------
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Table 15-L
T65DR And DS86
K-Values for Low-Dose Exposure, up to 5 CENTI-SIEVERTS.
K is the fractional increase in the spontaneous cancer death-rate
per cSv of whole-body organ-dose.
|========================================================================================================================|
| || |
| T65DR DOSIMETRY, NEUTRON RBE = 2.0 || DS86 DOSIMETRY, NEUTRON RBE = 20 |
| || |
|============================================================= || =====================================================|
| Low-Dose || Low-Dose |
| AGE | MALES K || MALES K |
| ATB | EQUATION OF BEST FIT Per cSv || EQUATION OF BEST FIT Per cSv |
| | || |
| 0-9 | Ca-Rate = (2.5937)(Dose^0.75)+(25.3161) 0.06851 || Ca-rate = (2.4549)(Dose^0.75)+(24.8117) 0.06617 |
| | || |
| 10-19 | Ca-Rate = (3.8365)(Dose^0.75)+(168.925) 0.01519 || Ca-Rate = (3.7215)(Dose^0.75)+(167.7256) 0.01484 |
| | || |
| 20-34 | Ca-Rate = (3.5274)(Dose^0.75)+(688.498) 0.003426 || Ca-Rate = (3.4358)(Dose^0.75)+(686.8894) 0.003344 |
| | || |
| 35-49 | Ca-Rate = (11.8508)(Dose^0.75)+(1605.326) 0.004936 || Ca-Rate = (11.0924)(Dose^0.75)+(1600.667) 0.004634 |
| | || |
| 50+ | Ca-Rate = (7.3871)(Dose^0.75)+(1430.187) 0.003454 || Ca-Rate = (6.6506)(Dose^0.75)+(1428.214) 0.003114 |
|============================================================= || =====================================================|
| | Low-Dose || Low-Dose |
| AGE | FEMALES K || FEMALES K |
| ATB | EQUATION OF BEST FIT Per cSv || EQUATION OF BEST FIT Per cSv |
| | || |
| 0-9 | Ca-Rate = (3.3140)(Dose^0.75)+(48.0263) 0.04615 || Ca-Rate = (3.1131)(Dose^0.75)+(47.4440) 0.04388 |
| | || |
| 10-19 | Ca-Rate = (5.2487)(Dose^0.75)+(142.885) 0.02457 || Ca-Rate = (5.2055)(Dose^0.75)+(140.9239) 0.02470 |
| | || |
| 20-34 | Ca-Rate = (7.0116)(Dose^0.75)+(437.0894) 0.01073 || Ca-Rate = (6.5018)(Dose^0.75)+(434.7191) 0.01000 |
| | || |
| 35-49 | Ca-Rate = (9.7200)(Dose^0.75)+(1056.556) 0.006152 || Ca-Rate = (8.7670)(Dose^0.75)+(1053.509) 0.005565 |
| | || |
| 50+ | Ca-Rate = (9.0896)(Dose^0.75)+(1022.294) 0.005945 || Ca Rate = (8.2725)(Dose^0.75)+(1019.570) 0.005425 |
|========================================================================================================================|
1. The two-step method for obtaining the Equation of Best Fit and the
low-dose K-value for each age-sex group is explained by the text in
detail.
-----------------------------------------------------------------------
2. The raw K-values (assembled below from Tables 15-B through 15-K) were
calculated for the purpose of comparison with the low-dose K-values
above. The low-dose K-values are larger -- due to the supra-linearity
of dose-response -- by a factor of about 2.3 (details in text).
Therefore the raw K-values will underestimate cancer-risk from low-dose
exposure by more than 2-fold, and should not be used for such
exposures.
___________________________________________________________________________________
| |
| T65DR Age-Band Males Females DS86 Age-Band Males Females |
| ATB Raw K Raw K ATB Raw K Raw K |
| 0-9 0.02749 0.01922 0-9 0.02565 0.01771 |
| 10-19 0.00677 0.01097 10-19 0.00647 0.01081 |
| 20-34 0.00157 0.00492 20-34 0.00150 0.00442 |
| 35-49 0.00228 0.00289 35-49 0.00207 0.00250 |
| 50+ 0.00162 0.00288 50+ 0.00140 0.00252 |
|_________________________________________________________________________________|
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