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.
What about Irradiation Which Occurred after 1959?
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.
Part 2. Description of Every Column, Followed by Numerical Entries
o - 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.
o - 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.
o - 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).
o - 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.
o - 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.
o - Column E, Acute Mastitis: X-ray breast-dose in therapy of acute mastitis (inflammation of the mammary gland). Chapter 13.
o - 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.
o - 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.
o - 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.
o - Column I, Mass Screening for Tuberculosis: X-ray breast-dose in mass screening-programs to detect tuberculosis (unlike Column G). Chapter 16.
o - Column J, Bronchial Asthma: X-ray breast-dose in the therapy of bronchial asthma (the Mayo Clinic experiences). Chapter 17.
o - 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.
o - 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.
o - 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.
o - Column N, Whooping Cough: X-ray breast-dose in the therapeutic management of pertussis (whooping cough). Chapter 19.
o - Column O, Fission-Product Fallout: Equivalent medical rads to breasts from radioactive fallout in the 1945-1960 period of weapons-testing. Chapter 25.
o - Column P, General Diagnostic X-ray Exams: X-ray breast-dose from general diagnostic exams, roentgenograms plus fluoroscopic examination. Chapter 23.
o - Column Q, Occupational Exposures: X-ray breast-dose, occupationally incurred. Chapter 24.
o - 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.
o - Column S, Pneumonia: X-ray breast-dose in the roentgen therapy of pneumococcal pneumonia. Chapter 18.
o - 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.
o - Column U, Person-Rads: The product of multiplying Column A (total persons irradiated) times Column T (the rads received by each, on the average). Persons x Rads = Person-Rads (Chapter 8, Part 2, Item 9). Of course, in this table, person-rads refers to female breast-rads, not whole-body rads.
o - 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.
o - 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%
No. of Med. Med. Med. Med. Med. Med. Med. Med. Med.
Age- Persons Rads Rads Rads Rads Rads Rads Rads Rads Rads
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
MASTER TABLE, Columns K through S
Med. Med. Med. Med. Med. Med. Med. Med. Med.
Age- Rads Rads Rads Rads Rads Rads Rads Rads Rads
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
Age- Rads Rads Person-Rads Cancers
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
Predicted Radiation-Induced Cancers--> 114336.4 114336.42
Observed Incidence 1993 --> 182000
"I use not only all the brains I have, but all I can borrow." o - T. Woodrow Wilson, 1856-1924,
28th President of the USA.