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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.

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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.

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```
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.

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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.

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```
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 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    0.83      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 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    0.65      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 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    0.63      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             |
|_________________________________________________________________________________________________________|
```

```
```

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             |
|_________________________________________________________________________________________________________|
```

```
```

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             |
|_________________________________________________________________________________________________________|
```

```
```

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             |
|_________________________________________________________________________________________________________|
```

```
```

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             |
|_________________________________________________________________________________________________________|
```

```
```

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             |
|_________________________________________________________________________________________________________|
```

```
```

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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