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### CHAPTER 39 Bottom Line:   The Master Table

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Part 1.   A Few Reminders about the Master Table

The description for each alphabetical column of the Master Table is provided in Part 2 of this chapter, and the three pages of numerical entries follow."

The rows of the Master Table represent 65 age-years, for breast-irradiation during" a single typical calendar-year of the 1920-1960 period. 65 ages, one year. Dose-estimates are provided in "medical rads," a term explained in Chapter 3, Part 1. The numerical entries for estimated breast-doses are added sideways by age-year, to obtain their sum for a typical calendar-year in Column T.

Readers who were born after 1959 may be the first to wonder:   Does the Master Table, based on a 1920-1960 study-period, apply to annual production of breast-cancer cases now? Yes, to a good "first approximation," as we noted in Chapter 5. This is discussed further in Part 2, in the section describing Column W.

Why Are the Doses in Column T So Low?

Why are the doses in Column T so low, despite some of the very high doses described in the text? One reason:   Not all of the female population received the various exposures (natural background radiation excepted). To obtain the average annual breast-dose applicable to the whole female population, we made downward adjustments to the breast-doses actually received by those who were irradiated (Chapter 5, Part 2). This was first demonstrated in Chapter 8, Part 2, Item 9. Another reason:   We adjusted the actual breast-doses downward, as appropriate, so that our low-dose conversion-factors would not overestimate the consequences from higher doses (Chapter 5, Part 5). This was first demonstrated in Chapter 8, Part 2, Item 8.

The Relationship of Annual Production and Annual Incidence

The dose-estimates in Column T allow us (and others) to estimate the annual production of radiation-induced breast-cancers from a single year of irradiation. The delivery of the single year's production happens gradually over many decades, due to variable latency periods (Chapter 2). If a female population of constant size receives a constant level of breast-irradiation year after year, finally the annual delivery rate of radiation-induced breast-cancer equals the annual production-rate (Chapter 4). As we said at the end of Chapter 4:

If we can figure out the annual production-rate for a specific period of exposure, then we already know the annual incidence-rate which will occur decades later related to that exposure --- and thus we can compare that to the total incidence and learn what fraction of the existing breast-cancer problem was caused by that ionizing radiation.

The sum of entries in Column W is a remarkable number, to be discussed in subsequent chapters.

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Part 2.   Description of Every Column, Followed by Numerical Entries

- Age-Years:   This column refers to age when irradiation occurs, not to age when cancer may occur. Age 0 means irradiation between birth and the first birthday.

- Column A, No. of Persons:   The number of female persons alive in each age-year, for an average calendar-year of the 1920-1960 study-period. The origin of these entries is shown in Chapter 8, Part 2, Item 6. By using the average population-size for the period 1920-1960, we can keep the population at a constant size --- which is a requirement for the "Law of Equality" (Chapter 4).

The sequence of the next columns, through S, is arbitrary.

- Column B, Irradiation from Natural Sources:   Typical whole-body annual dose (exclusive of radon and its daughters), adjusted to less energetic medical rads (Chapter 3, Part 1;   and Chapter 8, near the end).

- Column C, Enlarged Thymus Gland:   X-ray breast-dose, during first year of life (usually during first few months), in diagnosis and therapy of "enlarged thymus" and "status lymphaticus." Chapter 8.

- Column D, Enlarged Thymus Gland:   X-ray breast-dose, mainly during age-years 2 through 15, in screening and therapy for "enlarged thymus," prior to tonsillectomy, adenoidectomy, and other childhood surgeries. Chapter 10.

- Column E, Acute Mastitis:   X-ray breast-dose in therapy of acute mastitis (inflammation of the mammary gland). Chapter 13.

- Column F, Chronic Mastitis:   X-ray breast-dose in therapy of chronic mastitis, a disorder which has many names (including fibroadenosis, chronic cystic mastitis, benign fibroadenoma, or adenofibrosis), and is characterized by lumpy, tender breasts. Chapter 14.

- Column G, Management of Tuberculosis:   X-ray breast-dose in the fluoroscopic monitoring of artificial pneumothorax therapy, for patients having tuberculosis (the Detroit experience). Chapter 15.

- Column H, Management of Adolescent Scoliosis:   X-ray breast-dose from spinal x-rays in the monitoring of adolescent scoliosis (curvature of the spine). Chapter 21.

- Column I, Mass Screening for Tuberculosis:   X-ray breast-dose in mass screening-programs to detect tuberculosis (unlike Column G). Chapter 16.

- Column J, Bronchial Asthma:   X-ray breast-dose in the therapy of bronchial asthma (the Mayo Clinic experiences). Chapter 17.

- Column K, Pre-Birth Breast-Irradiation:   X-ray breast-dose to the fetus as a result of the mother's pelvic and abdominal x-ray examination while pregnant. Chapter 12. Due to a shortage of vertical space, we use the top row (age-0) for this entry rather than adding a "prenatal" row.

- Column L, Hyper-Thyroidism:   X-ray and gamma-ray (from radium and iodine-131) breast-dose in the radiation therapy of exophthalmic thyroid disease (hyper-thyroidism). Chapter 20.

- Column M, Enlarged Thymus Gland:   X-ray breast-dose, mainly during" age-years 1 through 9, in prophylactic therapy of "enlarged thymus" (the experience of the Massachusetts Eye and Ear Infirmary). Chapter 9.

- Column N, Whooping Cough:   X-ray breast-dose in the therapeutic management of pertussis (whooping cough). Chapter 19.

- Column O, Fission-Product Fallout:   Equivalent medical rads to breasts from radioactive fallout in the 1945-1960 period of weapons-testing. Chapter 25.

- Column P, General Diagnostic X-ray Exams:   X-ray breast-dose from general diagnostic exams, roentgenograms plus fluoroscopic examination. Chapter 23.

- Column Q, Occupational Exposures:   X-ray breast-dose, occupationally incurred. Chapter 24.

- Column R, Chiropractic Exams:   X-ray breast-dose in chiropractic applications, largely from full-spine x-rays used in diagnosis and follow-up. Chapter 22.

- Column S, Pneumonia:   X-ray breast-dose in the roentgen therapy of pneumococcal pneumonia. Chapter 18.

- Column T, Sum of Annual Breast-Doses:   The horizontal sums of the entries in Columns B through S. For each age-year, the dose represents the average breast-dose for every female in the age-group in an average year for the period 1920-1960. Moreover, each dose represents an average annual dose for persons of each age which recurs at the same level year after year, for the "new" people moving through that age-year. This constant level of exposure meets the requirement of the "Law of Equality" (Chapter 4). If the average annual doses were unchanged for a sixty-five year period, the average female breast-dose accumulated between birth and age 65 would be the sum of the dose-estimates in Column T:   27.88 medical rads.

- Column V, Cancers per 10,000 Person-Rads:   The conversion-factors which convert annual dose (in breast-rads) into annual breast-cancer production. There are five different conversion-factors in Column V --- for five different groups of ages at the time of irradiation. The number of breast-cancers produced per 10,000 person-rads declines as age at irradiation increases. This reflects the observation that the young are more vulnerable to induction of cancer by radiation. Chapter 40 explains the origin of these conversion-factors.

- Column W, Radiation-Induced Breast-Cancers:   For each row, the entry is the product of (Person-Rads, from Column U) times (Breast-Cancers per 10,000 Person-Rads, from Column V). Each entry represents the production from a single year's exposure.

Delivery of the breast-cancers from a single year's exposure occurs gradually, during the subsequent lifespan of the women in each age-group. After decades of such exposures occurring each year, the delivery of radiation-induced breast-cancer each year is equal to the production of radiation-induced cases per year (Chapter 4).

It is our thesis that the sum of the entries in Column W approximates both the past production of cases per year and the current delivery of new cases per year.

How Column W Applies to Breast-Cancer Production 1960-1995

In Part 1, we said that the Master Table extends to years beyond the 1920-1960 study-period, as a "first approximation." Suppose we assume that the average per-person annual dose-level to female breasts after 1960 fell appreciably below the average level of 1920-1960 (Column T). Even if it did, we have to recognize the large and undeniable increase in the average population of women (Column A) who are receiving the average annual per-person dose.

The entries in Column A of the Master Table are based on a female population of 69 million, for all ages combined (Chapter 8, Part 2, Item 6). By contrast, if we consider the midpoint of the 1960-1995 period as 1977, the female population was about 112 million (estimated from Table 2, located after the final chapter). And by 1993, the female population of the United States was about 132 million, for all ages combined.

An increase in the irradiated population (Column A), and a decrease in average dose received by each (Column T), tend to balance each other out in terms of person-rads (in Column U), since Column U = Column A times Column T.

Person-rads convert to radiation-induced cancers by applying conversion-factors (Column V) which are assumed to be independent of time. If they are independent, then as long as the value for person-rads maintains an approximately steady level beyond 1960, the annual production-rate of radiation-induced breast-cancer (Column W) will also maintain a steady level. At this time, it seems reasonable to think that the value for person-rads in Column U, and for radiation-induced cancers in Column W, are acceptable "first approximations" of the values for 1960-1995 too.

The Numerical Entries of the Master Table

The next three pages provide the numerical entries of the Master Table. The retention of many digits does not indicate that they are "significant figures" in the formal sense. We avoid "rounding off" merely to facilitate the tracing of computations.

The "bottom line" is the sum of Column-W entries:   An annual incidence-rate of radiation-induced breast-cancer equal to an unrounded value of 114,336 new cases per year in the USA --- prior to any upward adjustment for the many doses not yet evaluated (Chapter 38).

The five numbers to the right of Column W (which is shaded [in the book version--those numbers are shown in bold here in the web version -ratitor]) show how many of the total radiation-induced breast-cancers arise from the following ages (ages at the time of irradiation):

Age-years     0-9:   Cases = 34,857;   percent of 114,336 = 30.5%
Age-years 10-19:   Cases = 24,935;   percent of 114,336 = 21.8%
Age-years 20-34:   Cases = 26,185;   percent of 114,336 = 22.9%
Age-years 35-49:   Cases = 15,458;   percent of 114,336 = 13.5%
Age-years 50-64:   Cases = 13,265;   percent of 114,336 = 11.6%

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MASTER TABLE, Columns A through J
```        No. of    Med.    Med.    Med.    Med.    Med.    Med.    Med.    Med.   Med.
Years   Col. A  Col. B  Col. C  Col. D  Col. E  Col. F  Col. G  Col. H  Col. I  Col.J
0     905213    0.05   0.633                                          0.0021
1     892820    0.05                                                  0.0021
2     892097    0.05          0.1577                                  0.0021
3     891518    0.05          0.1577                                  0.0021
4     891047    0.05          0.1579                                  0.0021
5     890657    0.05          0.1579                                  0.0021
6     890332    0.05          0.1579                                  0.0021
7     890051    0.05          0.1580                                  0.0021
8     889806    0.05          0.1581                                  0.0021
9     889589    0.05          0.1581                          0.0112  0.0021
10    889390    0.05          0.1581                  0.0604  0.0112  0.0021
11    889209    0.05          0.1581                  0.0604  0.0112  0.0021
12    889028    0.05          0.1582                  0.0604  0.0112  0.0021
13    888829    0.05          0.1582                  0.0604  0.0112  0.0021
14    888585    0.05          0.1583  0.0045          0.0604  0.0112  0.0021
15    888277    0.05          0.1583  0.0045          0.0604  0.0112  0.0021
16    887906    0.05                  0.0045          0.0604          0.0021
17    887462    0.05                  0.0045          0.0604          0.0021
18    886973    0.05                  0.0045          0.0604          0.0021
19    886149    0.05                  0.0045          0.0604          0.0021
20    885914    0.05                  0.0368  0.0013  0.0604          0.0021
21    885371    0.05                  0.0368  0.0013  0.0604          0.0021
22    884810    0.05                  0.0368  0.0013  0.0604          0.0021
23    884231    0.05                  0.0368  0.0013  0.0604          0.0021
24    883642    0.05                  0.0368  0.0013  0.0604          0.0021
25    883045    0.05                  0.0533  0.0013  0.0604          0.0021
26    882438    0.05                  0.0533  0.0013  0.0604          0.0021
27    881823    0.05                  0.0533  0.0013  0.0604          0.0021
28    881189    0.05                  0.0533  0.0013  0.0604          0.0021
29    880528    0.05                  0.0533  0.0013  0.0604          0.0021
30    879840    0.05                  0.0274  0.0013  0.0604          0.0021  0.00190
31    879107    0.05                  0.0274  0.0013  0.0604          0.0021  0.00190
32    878329    0.05                  0.0274  0.0013  0.0604          0.0021  0.00190
33    877496    0.05                  0.0274  0.0013  0.0604          0.0021  0.00190
34    876618    0.05                  0.0274  0.0013  0.06C4          0.0021  0.00190
35    875677    0.05                  0.0110  0.0013  0.0604          0.0021  0.00190
36    874662    0.05                  0.0110  0.0013  0.0604          0.0021  0.00190
37    873567    0.05                  0.0110  0.0013  0.0604          0.0021  0.00190
38    872381    0.05                  0.0110  0.0013  0.0604          0.0021  0.00190
39    871077    0.05                  0.0110  0.0013  0.0604          0.0021  0.00190
40    869638    0.05                  0.0028  0.0013  0.0604          0.0021  0.00190
41    868045    0.05                  0.0028  0.0013  0.0604          0.0021  0.00190
42    866289    0.05                  0.0028  0.0013  0.0604          0.0021  0.00190
43    864361    0.05                  0.0028  0.0013  0.0604          0.0021  0.00190
44    862243    0.05                  0.0028  0.0013  0.0604          0.0021  0.00190
45    859917    0.05                          0.0013  0.0604          0.0021  0.00190
46    857373    0.05                          0.0013  0.0604          0.0021  0.00190
47    854585    0.05                          0.0013  0.0604          0.0021  0.00190
48    851552    0.05                          0.0013  0.0604          0.0021  0.00190
49    848266    0.05                          0.0013  0.0604          0.0021  0.00190
50    844718    0.05                          0.0013  0.0604          0.0021  0.00190
51    840889    0.05                          0.0013  0.0604          0.0021  0.00190
52    836752    0.05                          0.0013  0.0604          0.0021  0.00190
53    832289    0.05                          0.0013  0.0604          0.0021  0.00190
54    827473    0.05                          0.0013  0.0604          0.0021  0.00190
55    822286    0.05                                  0.0604          0.0021
56    816719    0.05                                  0.0604          0.0021
57    810736    0.05                                  0.0604          0.0021
58    804282    0.05                                  0.0604          0.0021
59    797275    0.05                                  0.0604          0.0021
60    790469    0.05                                  0.0604          0.0021
61    781353    0.05                                  0.0604          0.0021
62    772364    0.05                                  0.0604          0.0021
63    762779    0.05                                  0.0604          0.0021
64    752739    0.05                                  0.0604          0.0021
```
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```
MASTER TABLE, Columns K through S
```        Med.    Med.     Med.    Med.      Med.    Med.     Med.    Med.    Med.
Years  Col.K  Col. L   Col. M  Col. N    Col. O  Col. P   Col. Q  Col. R  Col. S
0     0.16                    0.154   0.00029   0.055
1                    0.0184   0.134   0.00029   0.055
2                    0.0184   0.145   0.00029   0.055
3                    0.0184   0.100   0.00029   0.055
4                    0.0184   0.115   0.00029   0.055
5                    0.0184   0.108   0.00029   0.055
6                    0.0184   0.077   0.00029   0.055
7                    0.0184   0.039   0.00029   0.055
8                    0.0184   0.017   0.00029   0.055
9                    0.0184   0.006   0.00029   0.055
10                            0.006   0.00029   0.055
11                            0.006   0.00029   0.055
12                            0.006   0.00029   0.055
13                            0.004   0.00029   0.055
14                            0.004   0.00029   0.055
15                            0.004   0.00029   0.145           0.0720  0.0216
16                            0.004   0.00029   0.145           0.0720  0.0216
17                            0.004   0.00029   0.145           0.0720  0.0216
18                            0.004   0.00029   0.145           0.0721  0.0216
19                            0.004   0.00029   0.145           0.0721  0.0216
20          0.00131           0.004   0.00029   0.145  0.00797  0.0721  0.0216
21          0.00131                   0.00029   0.145  0.00797  0.0722  0.0217
22          0.00131                   0.00029   0.145  0.00798  0.0722  0.0217
23          0.00131                   0.00029   0.145  0.00798  0.0723  0.0217
24          0.00131                   0.00029   0.145  0.00799  0.0723  0.0217
25          0.00131                   0.00029   0.194  0.00799  0.0724  0.0217
26          0.00131                   0.00029   0.194  0.00800  0.0724  0.0217
27          0.00131                   0.00029   0.194  0.00800  0.0725  0.0217
28          0.00131                   0.00029   0.194  0.00801  0.0725  0.0218
29          0.00131                   0.00029   0.194  0.00802  0.0726  0.0218
30          0.00094                   0.00029   0.194  0.00802  0.0726  0.0218
31          0.00094                   0.00029   0.194  0.00803  0.0727  0.0218
32          0.00094                   0.00029   0.194  0.00804  0.0728  0.0218
33          0.00094                   0.00029   0.194  0.00804  0.0728  0.0218
34          0.00094                   0.00029   0.194  0.00805  0.0729  0.0219
35          0.00094                   0.00029   0.225  0.00806  0.0730  0.0219
36          0.00094                   0.00029   0.225  0.00807  0.0731  0.0219
37          0.00094                   0.00029   0.225  0.00808  0.0732  0.0219
38          0.00094                   0.00029   0.225  0.00809  0.0733  0.0220
39          0.00094                   0.00029   0.225  0.00810  0.0734  0.0220
40          0.00094                   0.00029   0.225  0.00812  0.0735  0.0220
41          0.00094                   0.00029   0.225  0.00813  0.0736  0.0221
42          0.00094                   0.00029   0.225  0.00815  0.0738  0.0221
43          0.00094                   0.00029   0.225  0.00817  0.0739  0 0222
44          0.00094                   0.00029   0.225  0.00819  0.0741  0.0222
45          0.00094                   0.00029   0.250           0.0743  0.0223
46          0.00094                   0.00029   0.250           0.0745
47          0.00094                   0.00029   0.250           0.0748
48          0.00094                   0.00029   0.250           0.0751
49          0.00094                   0.00029   0.250           0.0753
50          0.00094                   0.00029   0.250           0.0757
51          0.00094                   0.00029   0.250           0.0760
52          0.00094                   0.00029   0.250           0.0764
53          0.00094                   0.00029   0.250           0.0768
54          0.00094                   0.00029   0.250           0.0772
55          0.00094                   0.00029   0.255           0.0777
56          0.00094                   0.00029   0.255           0.0783
57          0.00094                   0.00029   0.255           0.0788
58          0.00094                   0.00029   0.255           0.0795
59          0.00094                   0.00029   0.255           0.0802
60                                    0.00029   0.255           0.0809
61                                    0.00029   0.255           0.0818
62                                    0.00029   0.255           0.0827
63                                    0.00029   0.255           0.0838
64                                    0.00029   0.255           0.0849
```
```
```
MASTER TABLE, Columns T through W
```           Sum,                  Cancers    Radiation-
Medical     Person-    per 10000       Induced
Years    Col. T      Col. U       Col. V        Col. W
0       1.054      954448        92.74        8851.5
1       0.260      231901        92.74        2150.7
2       0.428      382210        92.74        3544.6
3       0.383      341844        92.74        3170.3
4       0.399      355252        92.74        3294.6
5       0.392      348861        92.74        3235.3
6       0.361      321134        92.74        2978.2
7       0.323      287300        92.74        2664.4
8       0.301      267734        92.74        2483.0
9       0.301      267846        92.74        2484.0  34856.6  Age-years 0-9
10      0.343      305141        76.13        2323.0
11      0.343      305079        76.13        2322.6
12      0.343      305106        76.13        2322.8
13      0.341      303260        76.13        2308.7
14      0.346      307264        76.13        2339.2
15      0.529      470185        76.13        3579.5
16      0.360      319523        76.13        2432.5
17      0.360      319405        76.13        2431.6
18      0.360      319275        76.13        2430.6
19      0.360      319135        76.13        2429.6  24920.2  Age-years 10-19
20      0.403      356978        44.95        1604.6
21      0.399      353273        44.95        1588.0
22      0.399      353106        44.95        1587.2
23      0.399      352934        44.95        1586.4
24      Q.399      352759        44.95        1585.7
25      0.465      410421        44.95        1844.8
26      0.465      410201        44.95        1843.9
27      0.465      409978        44.95        1842.9
28      0.465      409748        44.95        1841.8
29      0.465      409508        44.95        1840.7
30      0.441      387817        44.95        1743.2
31      0.441      387569        44.95        1742.1
32      0.441      387306        44.95        1740.9
33      0.441      387024        44.95        1739.7
34      0.441      386727        44.95        1738.3  25870.3  Age-years 20-34
35      0.456      399194        26.38        1053.1
36      0.456      398835        26.38        1052.1
37      0.456      398449        26.38        1051.1
38      0.456      398030        26.38        1050.0
39      0.456      397570        26.38        1048.8
40      0.448      389931        26.38        1028.6
41      0.449      389382        26.38        1027.2
42      0.449      388777        26.38        1025.6
43      0.449      388112        26.38        1023.8
44      0.449      387382        26.38        1021.9
45      0.464      398612        26.38        1051.5
46      0.441      378508        26.38         998.5
47      0.442      377485        26.38         995.8
48      0.442      376372        26.38         992.9
49      0.442      375166        26.38         989.7  15410.7  Age-years 35-49
50      0.443      373864        24.56         918.2
51      0.443      372459        24.56         914.8
52      0.443      370941        24.56         911.0
53      0.444      369304        24.56         907.0
54      0.444      367537        24.56         902.7
55      0.446      367114        24.56         901.6
56      0.447      365061        24.56         896.6
57      0.448      362855        24.56         891.2
58      0.448      360475        24.56         885.3
59      0.449      357891        24.56         879.0
60      0.449      354639        24.56         871.0
61      0.450      351286        24.56         862.8
62      0.451      347980        24.56         854.6
63      0.452      344454        24.56         846.0
64      0.453      340762        24.56         836.9  13278.7  Age-years 50-64

Observed Incidence 1993 -->                   182000
```

 "I use not only all the brains I have, but all I can borrow." - T. Woodrow Wilson, 1856-1924,             28th President of the USA.

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