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### CHAPTER 16 Low-Dose Cancer-Yields by the Cancer-Rate Ratio Method, for the A-Bomb Survivors and for a United States' Population

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This chapter is arranged in six parts:

1. Minimum Fatal Cancer-Yield for the A-Bomb Survivors, p.1
2. Lifetime Fatal Cancer-Yield for the A-Bomb Survivors, p.1
3. Lifetime Fatal Cancer-Yield for a USA Population, p.2
4. Comparison of Results, This Method versus the Cancer Difference Method, p.3
5. Merits and Pitfalls of the Methods, p.4
6. The Bottom Line from the Cancer-Rate Ratio Method, p.4
Then tables.
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1.   Minimum Fatal Cancer-Yield for the A-Bomb Survivors

The K-values provided by the A-Bomb Study represent the fractional increase in the spontaneous cancer death-rate per centi-sievert (or per rem) of whole-body internal organ-dose -- for a specific period of observation. Our "in-the-box" low-dose K-values come from observations in the 1950-1982 period. As usual, the Reference Group (1+2) is regarded as unexposed, and cancer death-rates are the cumulative rates among a set of initial persons.

To illustrate how the low-dose K-values in Table 15-L convert into Minimum Fatal Cancer-Yields, we can ask this question, which uses numbers from Table 11-E, Entries F72 and N72:

If 38 cancers occurred spontaneously in the time-period 1950-1982 among a set of 6,935 unexposed children at Hiroshima and Nagasaki, how many radiation-induced cancers must have occurred during the same period in a comparable group of 6,935 children exposed to 1 cSv of whole-body organ-dose? The low-dose K-value from Table 15-L enables us to calculate directly what that number of radiation-induce cancers must have been.

```         Persons        = 6935
Cancers        =   38
```
K-Value, T65DR Dosimetry = 0.04615

If 38 cancers occurred without radiation exposure, and if K is 0.04615 per centi-sievert (rem) of exposure, we multiply (38) by (0.04615) to ascertain the radiation-induced increment in cancers for 1950-1982 per centi-sievert. This yields 1.7537 cancers among 6,935 initial persons each exposed to one cSv (rem).

And 1.75 is the entry found in Table 16-B, Column G, for the youngest age-band of females. Table 16-A provides the customary details about Table 16-B (where space was insufficient).

Calculations comparable to the one just illustrated provide the additional entries in Column G, for the other 9 age-sex subsets. For the period 1950-1982, the sum from all ten subsets is 29.59 radiation-induced cancers per 66,028 initial persons each exposed to an average whole-body organ-dose of 1 cSv (rem). When this rate is converted (in the next row) to the equivalent rate per 10,000 persons, it becomes the Minimum Fatal Cancer-Yield, prior to the adjustment for under- ascertainment of cancer-deaths -- which is shown on the next row.

The final Minimum Fatal Cancer-Yield in the T65DR dosimetry, by the Cancer-Rate Ratio Method, is 5.51 "in-the-box." The corresponding value from a "constant-cohort, dual-dosimetry" analysis yields 5.17 in the current version of the DS86 dosimetry.

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2.   Lifetime Fatal Cancer-Yield for the A-Bomb Survivors

The Necessity of Making Assumptions :

Every estimate of a Lifetime Fatal Cancer-Yield incorporates assumptions, by one analyst or another (or by some committee), about what future follow-ups will show in the A-Bomb Study. Estimates which we make by the Cancer-Rate Ratio Method incorporate two assumptions.

Spontaneous Rate:   We are assuming that the lifetime follow-up will show a spontaneous cancer-rate in the Reference Group which is close to our estimate of 14.5 percent (from Table 28-D, entry G13).

Constant K-Values:   We are assuming that the low-dose K-values observed from the 1950-1982 evidence will persist at about their same magnitude in the additional observations beyond 1982. The best available evidence on duration would justify no other assumption at this time, in my opinion (Chapter 17). Indeed, RERF analysts seem to have reached the same conclusion, for they project their own current risk-coefficients into the remainder of the follow-up when they make their lifetime estimates (TR-9-87, p.34, and TR-5-88, p.50+53;   current risk-coefficients in the latter report explicitly exclude the 1950-1955 data, p.50).

In assuming constant K-values, all of us realize, of course, that the best available evidence is just the best available evidence in science, and that subsequent observations are "entitled" to change the story.

The Method for Obtaining Lifetime Fatal Cancer-Yields :

Table 16-A, Note 7 onward, explains the method step-by-step. We just apply the low-dose K-values, which are valid for 1950-1982, to the estimated number of spontaneous cancers expected to occur ultimately in each subset of the Reference Group, and then sum those contributions. The result is adjusted to the denominator of 10,000 persons, and then adjusted by the BEIR-RERF underascertainment factor, and "that is that."

The final best estimate is 31.65 in the T65DR dosimetry, and 30.43 in the current version of the DS86 dosimetry.

The Role of the Youngest Age-Band :

Inspection of Table 16-B, Columns G and J, shows what a trivial contribution is made by the youngest age-band to the minimum Fatal Cancer-Yield. In the T65DR dosimetry, for instance, the share is only (1.25 from the males + 1.75 from the females), or 3 out of the total of 29.59 (Column G). This low contribution, in spite of the higher K-values in this age-band, comes from the very low spontaneous rates in the youngest age-band during the 1950-1982 follow-up period, compared with every other age-band (Column D).

By contrast, inspection of Columns H and K shows what a very big contribution is made by the youngest age-band to the estimated lifetime Fatal Cancer-Yield. In the T65DR dosimetry, for instance, the share is (54.79 from the males + 39.21 from the females), or 94 out of the total of 169.91 (Column H). This result comes not from an extraordinarily high lifetime spontaneous rate (indeed, Column E shows a somewhat lower estimate for the ultimate lifetime spontaneous rate in this age-band). This shift from a trivial role to a dominant role comes from the combination of a spontaneous cancer "story" which has hardly even begun for this age-band during the 1950-1982 follow-up period, with the relatively high K-values for this same age-band.

Cancer-Yield as Percent Increase per Rad :

A Lifetime Fatal Cancer-Yield can be easily converted to "percent increase in the spontaneous cancer death-rate per cSv."

For instance, our estimates in Table 16-B are based on the estimate that 14.47 % of the LSS mixed-age population sample will die of spontaneous cancer (Table 29-D, entry G13). Out of each 10,000 initial persons, the estimated spontaneous cancer deaths will be 1,447. Table 16-B estimates that about 31 additional cases will occur per cSv of whole-body internal organ-dose, per 10,000 initial persons.

Thus, for this particular mixed-age group of persons, the percent increase in the lifetime spontaneous rate is (31 / 1,447) x (100), or 2.14 % per cSv.

In principle, the conversion is clearly easy. In reality, it is often hard to ascertain the post-irradiation lifetime spontaneous rate which was assumed in someone else's analysis. For some limited purposes, a "ball-park" spontaneous rate for a mixed-age population may suffice.

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3.   Lifetime Fatal Cancer-Yield for a USA Population

The Cancer-Rate Ratio Method makes it self-evident that the relative distribution of ages and sexes in an irradiated population will affect the population's Minimum and Lifetime Fatal Cancer-Yields. The minimum (or interim) values will come predominantly from the older and less sensitive age-bands, and increments to the minimum values will come predominantly from the younger and more sensitive age-bands.

There is no reason to assume that the age-sex distribution in the Reference Group of the A-Bomb Study is comparable to the age-sex distribution in the current United States population;   indeed, we know that the distributions differ. Therefore, we want to provide a Cancer-Yield which is appropriate for the United States.

We can provide a lifetime Fatal Cancer-Yield for the U.S. population if we make just one reasonable approximation. We will say that the fractional increase in the spontaneous cancer death-rate will be the same for humans here as for humans there, per centi-sievert of exposure.

Table 16-C provides both the input and output for the estimate.

The best lifetime estimate is 26.64 in the T65DR dosimetry, and 25.56 in the current version of the DS86 dosimetry. These lifetime estimates are somewhat lower for the U.S. population than the A-bomb survivors, even though we have estimated that the A-bomb survivors will have the lower ultimate spontaneous cancer-rate (see Note 3, Table 16-C).

The explanation is no mystery, however. Table 28-D, Column E, shows that in the normalized Reference Group, 24626.32 out of 66028.01 initial persons are in the two youngest and most radio-sensitive age-bands at the time of exposure. This share is 37.3 percent. By contrast, Table 16-C, Column C, shows a lower percentage in the United States' population:   3,169 out of 10,000 persons, or 31.7 percent. In addition, the USA population has a higher percentage of males than the normalized Reference Group -- 49 percent versus 42 percent -- and males have generally lower K-values than females (so far).

The estimates in Table 16-C are not new iterations, revisions, or replacements of my earlier estimate of 37.71. See Table 16-C, Note 7.

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4.   Comparison of Results, This Method vs. Cancer Difference Method

Minimum Fatal Cancer-Yields :

How do the Minimum Fatal Cancer-Yields derived by the Cancer-Rate Ratio Method compare with the values derived by the Cancer Difference Method with the best-fit curve? The values below come from Table 14-A, Row 2, and from Table 16-B:

T65DR:   Cancer Difference = 5.80 fatal cancers/cSv
T65DR:   Cancer-Rate Ratio = 5.51 fatal cancers/cSv

DS86:      Cancer Difference = 5.41 fatal cancers/cSv
DS86:      Cancer-Rate Ratio = 5.17 fatal cancers/ cSv

The two methods produce closely similar answers, although the methods appear to be quite different.

One method kept the observations combined for all ages and sexes, subtracted the best-fit cancer-rates at zero-dose from the best-fit cancer-rates at 5 cSv, and divided the answer by five.

The other method subdivided the same observations into ten age-sex subsets, and for each subset of observations, derived an equation of best fit, based on observations exclusively from that subset together with the common dose-exponent of 0.75. Then it used the equation to predict best-fit points at zero-dose and 5 cSv, used those two points to derive a low-dose K-value (fractional increase in the spontaneous cancer-rate per cSv), applied the K-value to the corresponding number of spontaneous cancers in the subdivided Reference Group to obtain the radiation-induced increment from a dose of one cSv, and obtained the Minimum Fatal Cancer-Yield by adding up the increments expected from each of the ten subsets.

In spite of the difference in method, if computational errors are absent, one should expect good agreement when two valid but different approaches are made to exactly the same set of observations. When the observations are "in-the-box," the residual uncertainty lies in sampling variation, which could work in either direction -- either to underestimate or to overestimate the true value.

How do the findings for lifetime Fatal Cancer-Yields compare in the two methods?

T65DR:   Cancer Difference = 12.90 fatal cancers/cSv
T65DR:   Cancer-Rate Ratio = 31.65 fatal cancers/cSv

DS86:      Cancer Difference = 12.03 fatal cancers/cSv
DS86:      Cancer-Rate Ratio = 30.43 fatal cancers/cSv

It was predictable that the Cancer Difference Method would give much lower values for the lifetime Cancer-Yields than does the Cancer-Rate Ratio Method. The reason is that every estimate of lifetime values necessarily uses assumptions and approximations to fill in for the missing observations, and the two methods use one crucially different approximation.

The Cancer Difference Method, with its conversion-factor of 2.223 from minimum to lifetime values, is using the approximation that the cancers which will occur beyond 1982 will be arising from a population with the same age-distribution and radiation-sensitivity as the population which produced the cancers observed between 1950-1982. This approximation is simply unrealistic, as already noted in Chapter 13.

For the 1950-82 period, the cancer deaths are coming predominantly from the older and less sensitive groups ATB, whereas in the post-1982 period, the cancer deaths will be coming predominantly from the younger and much more sensitive groups ATB. The Cancer-Rate Ratio Method takes this into account, whereas the Cancer Difference Method does not.

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5.   Merits and Pitfalls of the Methods

The comparisons in Part 4 above show that two methods, which produce nearly identical estimates for the Minimum "in-the-box" Fatal Cancer-Yields, produce lifetime estimates which differ by 2.5-fold. The factor of 2.5 is a measure of the potential error one would make by ignoring the fact that the residual population-sample beyond 1982 is not like the sample which generated the 1950-1982 observations. In other words, the Cancer-Rate Ratio Method is more realistic in its underlying assumptions about the lifetime risk than is the Cancer Difference Method. That is its great merit.

But this does not necessarily mean that the estimates of 30 or 32 fatal cancers per 10,000 persons per rem will match the ultimate estimate for low-dose exposure, when the full lifespan study is complete. We have made it clear how much depends on the future "behavior" of the youngest age-band, and also on the ultimate spontaneous cancer death-rate in the Reference Group. These unknowns are the biggest "pitfalls" in any such estimate.

o -- The true Lifetime Fatal Cancer-Yield for low-dose exposure could turn out considerably lower than 30 or 32 :

(A) If the ultimate spontaneous cancer death-rates in the Reference Group have been overestimated in our analysis;

(B) If the observed K-values in the youngest age-band "droop" or "melt down" during additional years of observation;   this could happen due to sampling variation in the presently sparse observations, or due to a true (biological) reduction of effect beyond 40 years post-irradiation, or due to a reduced degree of supra-linearity in all age-bands after additional observations, or due to a less supra-linear dose-response in children than in adults.

o -- The true Lifetime Fatal Cancer-Yield for low-dose exposure could turn out considerably higher than 30 or 32 :

(A) If the ultimate spontaneous cancer death-rates in the Reference Group have been underestimated in our analysis;

(B) If the observed K-values in the youngest age-band increase during additional years of observation;   this could happen due to sampling variation in the presently sparse observations, or due to an increased degree of supra-linearity in all age-bands after additional observations, or due to a greater supra-linear dose-response in children than adults. This would be very serious, since our estimate of 30-32 has ignored supra-linearity between 0 and 5 cSv, and has used the linear approximation in that dose-region.

Conclusion regarding Uncertainties :

These uncertainties are simply unavoidable. But they do not make it reasonable to accept the unrealistic premise of the Cancer Difference Method with respect to lifetime estimates -- namely, that the population which will generate the cancers beyond 1982 is like the population which generated the cancers between 1950-1982.

Moreover, since the uncertainties in the Cancer-Rate Ratio Method could readily operate toward underestimating the risk, which may turn out much higher than 30-32, it would be a sign of bias if I "preferred" using lifetime estimates which are 2.5-fold lower (from the Cancer Difference Method).

As a physician, I might add that information does not always need to be exact, in order to be extremely useful for human health.

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6.   The Bottom-Line from the Cancer-Rate Ratio Method

1.   The Cancer-Rate Ratio Method produces about the same minimum Fatal Cancer-Yields for low-dose exposure as the Cancer Difference Method, in both dosimetries (text, Part 4). With their close agreement, the two analyses are excellent confirmation of each other with respect to evidence "in-the-box." By both methods, the Minimum Fatal Cancer-Yield is about 5.5 fatal radiation-induced cancers among 10,000 persons per cSv (rem) of whole-body organ-dose.

2.   The Cancer-Rate Ratio Method produces estimates of lifetime Fatal Cancer-Yields for low-dose exposure which are predictably higher, and inherently more realistic, than the estimates produced -- for comparison -- by the Cancer Difference Method (text, Part 5). The Lifetime Fatal Cancer-Yields produced by the Cancer-Rate Ratio Method are 30-32 fatal radiation-induced cancers among 10,000 A-bomb survivors per cSv (rem) of whole-body organ-dose (Table 16-B). When the estimates are adjusted for a United States' population, they are 26-27 fatal radiation-induced cancers among 10,000 persons per cSv (rem) of whole-body organ-dose (Table 16-C). These values apply directly to low-dose exposure, acute or slow, between 0 and 5 cSv (rems).

3.   Lifetime values in the range of 26 (USA) to 30 (A-bomb survivors) are very much higher than the values of 1-2 which are routinely used by the radiation community. Nonetheless, values like 26-30 may underestimate the cancer-hazard from X-ray exposure by about two-fold (see Chapter 13, Part 4).

4.   Unlike some other analyses, our work does not throw away any of the evidence (follow-up years, or Dose-Groups) in the A-Bomb Study. It is based on the whole story, 1950-1982, and its legitimate prospective structure. We look forward to the time when the data become available to do a "constant-cohort, dual dosimetry" analysis with the additional observations through 1985.

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Table 16-A
Notes for Table 16-B, Cancer-Yields by the Cancer-Rate Ratio Method,
for the A-Bomb Survivors.

1. In Col.A, "H+N" abbreviates Hiroshima plus Nagasaki.
2. In Col.B, mean age ATB for RERF's five age-bands is calculated for the Reference Group from Master Table 26-A,B,C,D, in excellent agreement with Tables 11-C,E.
3. Col.C and Col.D entries are the age-sex normalized values from Tables 11-C and 11-E. These entries can also be found in Table 28-D, Columns E and H. Persons are those enrolled for the study in RERF Dose-Groups 1+2 (the Reference Class) in 1950. Spontaneous cancers are those cancer-deaths already observed (1950-1982) in this cohort.
4. Col.E entries for lifetime spontaneous cancers are from Table 28-D, Col.F. They are the estimated spontaneous cancer-deaths which will have accumulated among this cohort during the post-irradiation period, beginning in 1950 through the time when the last member of this cohort has died of one cause or another. These numbers may be underestimated (see Chapter 13, Part 6).
5. Col.F entries for low-dose K-values come from the body of Table 15-L, for the T65DR dosimetry. K is defined as the fractional increase in the spontaneous cancer death-rate per cSv of average whole-body organ-dose. Low-dose K-values apply to a total dose up to 5 cSv. Because the dose-response relationship is supra-linear (concave-downward), different dose-ranges have different K-values.
6. Col.G entries for radiation-induced cancer-deaths 1950-1982 per cSv are (Col.F x Col.D). Entries represent the number of radiation-induced cancers which would occur among an identical exposed group of comparable size during 1950-1982, per cSv of average whole-body organ-dose.
7. Col.H entries for lifetime radiation-induced cancer-deaths per cSv are (Col.F x Col.E). This step incorporates the approximation that the low-dose K-values observed during the first 32 years of follow-up will remain at about the same magnitude for the cohort's remaining lifespan. The evidence at hand justifies no other presumption at this time (Chapter 17).
8. Cols.I, J, and K represent the appropriate entries based on the current version of the DS86 dosimetry.
9. The row of sums apply to the 66,028 persons in the Reference Group, not to 10,000 persons. Therefore the values are reduced by the factor (10,000 / 66,028) in the next row.
10. The values must then be increased by the RERF-BEIR factor of 1.23 for underascertainment of cancer (see Chapter 11, page 5).
11. The box at the foot of Table 16-B presents the final MINIMUM FATAL CANCER-YIELD BY THE CANCER-RATE RATIO METHOD:
5.51     by T65DR, or 5.51 cancers x 10^-4 persons x rem^-1.
5.17     by DS86, or 5.17 cancers x 10^-4 persons x rem^-1.
12. The box presents the final estimated LIFETIME FATAL CANCER-YIELD BY THE CANCER-RATE RATIO METHOD:
31.65     by T65DR, or 31.65 cancers x 10^-4 persons x rem^-1.
30.43     by DS86, or 30.43 cancers x 10^-4 persons x rem^-1.
13. Cancer-hazard from X-rays may be underestimated by the A-Bomb Study (see Chapter 13, Part 4).

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Table 16-B
Estimation of Minimum and Lifetime Fatal Cancer-Yields
for Hiroshima + Nagasaki A-Bomb Survivors.

By the Cancer-Rate Ratio Method, for Low-Dose Whole-Body Exposure per cSv, up to 5 cSv. Leukemia Excluded.

```|==================================================================================================================|
| Initial persons and spontaneous cancer-deaths are from the Reference Group (Dose-Groups 1+2).                    |
|                                                                                                                  |
|       Col.A    Col.B   Col.C    Col.D     Col.E  ||   Col.F    Col.G     Col.H   ||    Col.I    Col.J     Col.K  |
|  Population    Mean           taneous   taneous  ||       K  Induced   Induced   ||        K  Induced   Induced  |
|      Sample    Age   Initial  Cancers   Cancers  ||     per  Cancers   Cancers   ||      per  Cancers   Cancers  |
|                                                  ||          per cSv   per cSv   ||           per cSv   per cSv  |
|================================================  ||  ==========================  ||  ==========================  |
|                                                  ||    T65DR   T65DR     T65DR   ||     DS86     DS86      DS86  |
|                                                  ||                              ||                              |
|  Males, H+N   4.16   4976.25    18.25  799.7347  ||  0.06851    1.25     54.79   ||  0.06617     1.21     52.92  |
|  Males, H+N  13.95   5312.07    94.11  920.2082  ||  0.01519    1.43     13.98   ||  0.01484     1.40     13.66  |
|  Males, H+N  28.04   6644.57   451.98  1124.797  ||  0.00343    1.55      3.85   ||  0.00334     1.51      3.76  |
|  Males. H+N  42.60   6341.76  1018.02  1125.653  ||  0.00494    5.02      5.56   ||  0.00463     4.72      5.22  |
|  Males, H+N  58.14   4310.36   631.71  637.6347  ||  0.00345    2.18      2.20   ||  0.00311     1.97      1.99  |
|Females. H+N   4.08      6935       38   849.648  ||  0.04615    1.75     39.21   ||  0.04388     1.67     37.28  |
|Females, H+N  14.90      7403      116  1064.396  ||  0.02457    2.85     26.15   ||  0.02470     2.87     26.29  |
|Females, H+N  26.69      9260      396  1234.162  ||  0.01073    4.25     13.24   ||  0.01000     3.96     12.34  |
|Females, H+N  41.71      8838      925  1169.435  ||  0.00615    5.69      7.19   ||  0.00557     5.15      6.51  |
|Females, H+N  59.05      6007      608   627.055  ||  0.00595    3.61      3.73   ||  0.00543     3.30      3.40  |
|                                                  ||                              ||                              |
| SUM OF ALL             66028  4297.07  9552.724  ||            29.59    169.91   ||             27.74    163.36  |
|                                                  ||                              ||                              |
| Cancers/10,000 persons         650.80            ||             4.48     25.73   ||              4.20     24.74  |
|                                                  ||                              ||                              |
| RERF-BEIR Correction Factor of 1.23 for          ||                              ||                              |
| Underascertainment of Cancer                     ||             5.51     31.65   ||              5.17     30.43  |
|                                                                                                                  |
| FATAL CANCER-YIELD =                                                                                             |
|                                                                                                                  |
| NUMBER OF FATAL RADIATION-INDUCED CANCERS AMONG 10,000 PERSONS PER cSv OF AVERAGE WHOLE-BODY ORGAN-DOSE.         |
|                                                                                                                  |
|        |------------------------------------------------------------------------------------------------|        |
|        |                 SUMMARY OF FATAL CANCER-YIELDS BY THE CANCER-RATE RATIO METHOD                 |        |
|        |                        After correction for underascertainment of cancer.                      |        |
|        |                                                                                                |        |
|        |                                               T65DR       |         DS86                       |        |
|        |                                           ------------    |    -------------                   |        |
|        |                   MINIMUM "IN-THE-BOX"         5.51       |         5.17                       |        |
|        |                                                           |                                    |        |
|        |                   LIFETIME                    31.65       |        30.43                       |        |
|        |                                                                                                |        |
|        |------------------------------------------------------------------------------------------------|        |
|                                                                                                                  |
|          Cancer-hazard from X-rays may be underestimated by the A-Bomb Study.  See Chapter 13, Part 4.           |
|                                                                                                                  |
| NOTES:  See Table 16-A.                                                                                          |
|__________________________________________________________________________________________________________________|
```

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```

Table 16-C
Estimation of Lifetime Fatal Cancer-Yield for the United States' Population.
By the Cancer-Rate Ratio Method, for Low-Dose Whole-Body Exposure per cSv, up to 5 cSv. Leukemia Excluded.
```|===========================================================================================================|
|                                                    ||     T65DR Dosimetry     ||     DS86 Dosimetry       |
|   Col.A    Col.B    Col.C      Col.D        Col.E  ||   Col.F          Col.G  ||   Col.H          Col.I   |
|                                                    ||                         ||                          |
|    Age-                     Fraction    Number of  ||       K  Rad'n-Induced  ||       K  Rad'n-Induced   |
|    Band                        Dying  Spontaneous  ||     per  Fatal Cancers  ||     per  Fatal Cancers   |
| (Years)      Sex  Persons  of Cancer    Ca-Deaths  ||     cSv        per cSv  ||     cSv        per cSv   |
|                                                    ||                         ||                          |
|     0-9    Males   721.95      0.185       133.56  || 0.06851           9.15  || 0.06617           8.84   |
|   10-19    Males   896.45      0.185       165.84  || 0.01519           2.52  || 0.01484           2.46   |
|   20-34    Males  1238.98      0.188       232.93  || 0.00343           0.80  || 0.00334           0.78   |
|   35-49    Males    814.4      0.190       154.74  || 0.00494           0.76  || 0.00463           0.72   |
|     50+    Males  1206.59      0.183       220.81  || 0.00345           0.76  || 0.00311           0.69   |
|     0-9  Females   687.71      0.160       110.03  || 0.04615           5.08  || 0.04388           4.83   |
|   10-19  Females   863.27      0.160       138.12  || 0.02457           3.39  || 0.02470           3.41   |
|   20-34  Females  1233.53      0.161       198.60  || 0.01073           2.13  || 0.01000           1.99   |
|   35-49  Females   841.38      0.159       133.78  || 0.00615           0.82  || 0.00557           0.74   |
|     50+  Females  1495.75      0.137       204.92  || 0.00594           1.22  || 0.00543           1.11   |
|                                                    ||                         ||                          |
|  Totals             10000                 1693.33  ||                  26.64  ||                  25.56   |
|                                                                                                           |
|  LIFETIME FATAL CANCER-YIELD =                                                                            |
|  NUMBER OF FATAL RADIATION-INDUCED CANCERS AMONG 10,000 PERSONS PER cSv OF AVERAGE WHOLE-BODY ORGAN-DOSE. |
|                                                                                                           |
|              -------------------------------------------------------------------------------              |
|              |                    U.S. POPULATION (1978 COMPOSITION):                      |              |
|              |         LIFETIME FATAL CANCER-YIELD BY THE CANCER-RATE RATIO METHOD         |              |
|              |                                                                             |              |
|              |               Based on T65DR        |         Based on DS86                 |              |
|              |                                     |                                       |              |
|              |                    26.64            |             25.56                     |              |
|              -------------------------------------------------------------------------------              |
|                                                                                                           |
=============================================================================================================
```

NOTES:

1. Col.A has grouped the U.S. population into the same age-bands used by RERF for the A-Bomb Study.
2. Col.C gives the age-sex distribution for 1978 in the U.S., for a sample of 10,000 persons calculated from data in Nrc85, p.I-78, Table A.6). When the distributions change in the future, so will the estimated Lifetime Fatal Cancer-Yield.
3. Col.D gives the estimated fraction of persons in Col.C who will die spontaneously -- without extra radiation-exposure -- over the entire remaining lifespan of the cohort (from Go81, Tables 31 and 32);   these fractions are higher than the fractions used for the A-bomb survivors (Table 28-D, Col.G).
4. Col.E = (Col.C x Col.D).
5. Col.F and Col.H are the low-dose K-values from Table 15-L for the two dosimetries.
6. By K's definition, lifetime radiation-induced fatal cancers per cSv = (K-value) x (Lifetime Spontaneous Cancers). Therefore, Col.G = (Col.F x Col.E). Likewise, Col.I = (Col.H x Col.E).
7. The estimate of 26-27 above is not an iteration or revision of my earlier estimate of 37.71 (Go81, p.314). The estimate above is a new entity. The 1981 estimate and this one come out of very different input in terms of approximations and data (for instance, the 1981 estimate used some 20 different studies, not just the A-Bomb Study).
8. Cancer-hazard from X-rays may be underestimated by the A-Bomb Study. See Chapter 13, Part 4.

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