Part 1. Patients Often in the Dark about Their Doses
One item has been missing for a long time in the use of medical x-rays: The ability of a patient to find out (a) whether a particular facility knows what it is doing, and (b) what dose of radiation the patient is getting from any particular procedure. Later (Chapter 42), we will discuss whose responsibility it is to obtain such information for patients, for this is not a problem only of the past.
Talking to the general public in Science Digest, two radiation physicists described the situation rather memorably in 1984.
One of them was Dr. Joel Gray (of the Mayo Clinic), whose admirable work on reducing radiation dose for scoliosis patients was already described in Chapter 21. In the 1984 interview, he commented about offices which do not tell patients the estimated dose of radiation which they will receive (Gray 1984, p.96):
"My feeling is that if they won't tell you, they don't know, and if they don't know, they could be among the facilities delivering a hundred times the necessary dose."
The other physicist commented specifically on mammography. Dr. Edward Webster, of the Massachusetts General Hospital, said (Webster 1984, p.96):
"When a woman arrives at a doctor's office for a mammogram, she has no way of knowing whether she's getting three hundred or three thousand millirads."
A Lesson from Recent History: The 1960s and 1970s
If we go back to the 1960s and 1970s, the reality of mammographic doses was startling --- for breast-doses were very high compared with the current levels. Of course, we have no entry at all for mammography in our Master Table, because the table considers only common procedures of the 1920-1960 period.
We will explore, later in the chapter, what it would have meant for women if mammography had become common when the doses were so much higher than today. It did not become common, thanks to some people with a willingness to say "No!" to various pressures to make it common. The history of mammography provides women with a reason to think very seriously about the need for eternal vigilance --- and for "watchdogging" of some technology buffs who are inclined to claim that their pet technology is "safe," without any evidence for such claims.Part 2. Breast-Doses from Mammography in the 1960s and 1970s
Periodic reports on various aspects of ionizing radiation are issued by UNSCEAR, which is the United Nations Scientific Committee on the Effects of Atomic Radiation. The committee consists of members of the radiation community in interested nations. About mammography, the UNSCEAR 1977 report stated (p.318, para.70):
"Direct radiography of the female breast, i.e., mammography, is of particular interest because the technique is also being used in health investigations. The organization of a number of large population mass-screening surveys caused concern when high-dose techniques were in use and when regular re-examinations were carried out on young women. The justification for such examinations was questioned because of the increase in breast-cancer that might be induced by radiation [references cited]." And:
"In the 1972 report [UNSCEAR 1972] the radiation dose to the breast per mammography examination was reported to be in the range of 10-35 rad. However, since then considerable progress has occurred in techniques for reduction of radiation dose ..." And: with "... the two-film techniques being accepted for screening examinations, surveys can be undertaken with a breast dose of less than 200-300 mrad ..."
So UNSCEAR 1972 reported 10 to 35 rads as the mammographic dose in the 1960s. To make the coming comparison, we will say 20 rads. And UNSCEAR 1977 reported that it was technically possible to reduce doses to 0.2 rads (200 milli-rads) or less by 1977. That is a reduction of 100-fold. But as we shall see (Part 5), a large screening project had been undertaken in 1972 with 10-fold higher doses --- about 2 rads per exam.Part 3. Breast-Doses from Mammography in Current Times
Improvements continue, and it appears that mammography will finally have sufficient surveillance to insure that low doses become commonplace. The Food and Drug Administration was asked by Congress to set comprehensive standards for the nation's 11,000 mammography clinics, and to issue certification when such standards are met. The FDA requirements, as described in late 1994, include the following:
o - Workers who perform mammography and physicians who interpret the images must be properly trained and experienced. For physicians, that includes interpreting at least 40 mammograms per month. Each clinic must track its accuracy and insure that women with suspicious results are promptly called for follow-ups. FDA-trained inspectors will inspect each clinic annually.
o - Only up-to-date mammography machines are allowed. They must be monitored closely to insure that the images remain clear and that the radiation dose does not exceed 0.3 rad (300 milli-rads, or 0.3 centi-gray) mean glandular dose per view. The standard exam has 2 views per breast (top to bottom, and side to side). So, on the average, internal cells of each breast may receive up to 0.6 rad of absorbed dose per exam --- but actual doses today per exam are often as low as 0.2 rad for each breast.Part 4. The Estimated Price in Breast-Cancers
from Full Implementation of Mammography
Although I consider myself an enthusiast for technological progress, I recognize that the history of applied technology has often been "act now, think later." Part 5 will describe an example. So it would be worthwhile to ask what the price in extra breast-cancer could be from various programs of mammography, if fully implemented in the United States at a current dose of about 0.2 rads per exam. Mammography, of course, has nothing to do with prevention of breast-cancer. It has to do with detection of a problem not prevented.
Because there is no safe dose (risk-free dose) of ionizing radiation, we can be certain at the outset that mammographic programs will cause some number of radiation-induced breast-cancers. The question is: How many?
No one should equate the desire to have a "ballpark" answer, with a desire to obstruct. A desire not to estimate the consequences would be peculiar, in our opinion.
So we have prepared an "If-Then" table from which we obtain some estimates (Table 28-A, on the next page). Table 28-A provides estimates from annual mammography at every age-year, starting with age-30 and ending with age-64. We are well aware that no one today is proposing annual mammograms starting at age-30. We stress that Table 28-A is an "If-Then" table. Its purpose is to enable readers to ask "What if?" about a variety of possible programs with differing frequencies of mammography for different age-groups.
Later, in Part 8, we will also show how to estimate an individual's personal risk from mammography today.Part 5. Why Worry about "Only" 2 Extra Rads to the Breasts per Year?
In 1972, the "Breast Cancer Detection and Demonstration Project" (BCDDP) was launched in the United States. It included mammography for the participants. A detailed description of the project was given by Herbert Seidman and colleagues (Seidman 1987). We quote from the "Materials" section of that article (p.266):
"The BCDDP was established in 1972 when the American Cancer Society funded 12 centers to do annual physical examinations and mammography on 5,000 women in each center. The program was later expanded when the NCI [National Cancer Institute] funded additional centers and the number of women increased to 10,000 per center. Screening began early in 1973; by 1975 there were 29 centers in 27 locations that had enrolled more than 280,000 women ages 35 to 74." And:
"Almost all of the centers recruited about 10,000 women each over a two-year period to be screened for breast cancer free of charge at an initial screening and four subsequent annual screenings. Those who joined were screened with a combination of medical history, physical examination, mammography, and thermography."
We doubt that the program could have recruited persons if there were any suggestion made that breast-cancer could be a result for some segment of the women enrolled. Seidman and colleagues reported (at page 266) that about 51 percent of the women who joined the project completed all five screenings.
The Average Breast-Dose Which Was Received in the BCDDP
In 1976, John C. Bailar III reviewed the dosimetry for the mammographic studies in the BCDDP. He reported as follows (Bailar 1976, p.80):
"A very recent survey of the demonstration clinics supported jointly by the National Cancer Institute and the American Cancer Society has shown average doses of about 1 to 5 rads with the use of radiation detectors thought to be significantly more accurate than those used in the studies cited above. A current average depth dose to breast tissue of 2 rads per film set seems a reasonable and conservative estimate after allowance for the use of xeromammography and other low-dose methods."
Table 28-AAssumes all women (age-30 and up) in the United States received 0.2 rad in Annual Mammographies.
An "If-Then" Table For Mammography.
Col. A Col. B Col. C Col. D Col. E Col. F Breast- Dose Cancers Annual Age Number of Medical Person- per 10,000 Breast- Year Women* Rads Rads Person-Rads** Cancers 30 1,670,816 0.2 334,163 44.95 1,502 31 1,669,424 0.2 333,885 44.95 1,501 32 1,667,946 0.2 333,589 44.95 1,499 33 1,666,364 0.2 333,273 44.95 1,498 34 1,664,697 0.2 332,939 44.95 1,497 35 1,662,910 0.2 332,582 26.38 877 36 1,660,984 0.2 332,197 26.38 876 37 1,658,904 0.2 331,781 26.38 875 38 1,656,652 0.2 331,330 26.38 874 39 1,654,176 0.2 330,835 26.38 873 Annual Mammogram-Induced Breast Cancers (30-39 year-olds). Sum = 11,873 40 1,651,443 0.2 330,289 26.38 871 41 1,648,418 0.2 329,684 26.38 870 42 1,645,083 0.2 329,017 26.38 868 43 1,641,422 0.2 328,284 26.38 866 44 1,637,399 0.2 327,480 26.38 864 45 1,632,982 0.2 326,596 26.38 862 46 1,628,151 0.2 325,630 26.38 859 47 1,622,856 0.2 324,571 26.38 856 48 1,617,098 0.2 323,420 26.38 853 49 1,610,858 0.2 322,172 26.38 850 Annual Mammogram-Inducod Breast Cancers (40-49 year-olds). Sum = 8,619 50 1,604,120 0.2 320,824 24.56 788 51 1,596,848 0.2 319,370 24.56 784 52 1,588,992 0.2 317,798 24.56 781 53 1,580,517 0.2 316,103 24.56 776 54 1,571,372 0.2 314,274 24.56 772 55 1,561,522 0.2 312,304 24.56 767 56 1,550,950 0.2 310,190 24.56 762 57 1,539,588 0.2 307,918 24.56 756 58 1,527,332 0.2 305,466 24.56 750 59 1,514,026 0.2 302,805 24.56 744 60 1,501,100 0.2 300,220 24.56 737 61 1,483,790 0.2 296,758 24.56 729 62 1,466,720 0.2 293,344 24.56 720 63 1,448,518 0.2 289,704 24.56 712 64 1,429,452 0.2 285,890 24.56 702 Annual Mammogram-Induced Breast Cancers (50-64 year-olds). Sum = 11,280
Notes: Col.D = Col.B x Col.C
Col.F = (Col.D / 10,000) x Col.E
* Column B entries are for the number of women present at each age for an equilibrium population of 250,000,000 total persons. Taken from Table 24 of Gofman 1981.
** Conversion factors taken from Chapter 39, Master Table, Column V.
The Status of Knowledge at the Time of the BCDDP Initiation
When the Project was initiated in 1972, was there any reason to worry that two extra rads of breast-irradiation every year might cause some breast-cancers?
Seven years earlier, in 1965, MacKenzie had published his findings on radiation-induced breast-cancer (discussed in Chapter 1). In 1968, Wanebo had published his findings concerning breast-cancer in A-bomb survivors. In 1970, Tamplin and Gofman had published estimates, based upon MacKenzie and Wanebo and a relative risk analysis, of a doubling dose for breast-cancer of about 20 to 50 rads. In 1972, the Committee on the Biological Effects of Ionizing Radiations (the BEIR Committee of the National Academy of Sciences, USA) had estimated a doubling dose for radiation-induced breast-cancer of 28 to 120 rads (BEIR 1972, p.141).
Despite all this, a project was launched to give women an extra 10 rads to their breasts (2 extra rads per year for 5 years). It would seem that someone must have had misgivings about initiation of this project, in light of the information on radiation-induced breast-cancer already published and available to the ACS and NCI.
The Breast Cancer Detection and Demonstration Project (BCDDP) was an illustration of the "technological imperative" at work, coupled with all the political propaganda in those years about the "war on cancer."
Mammogram-Induced Breast-Cancers: An "If-Then" Table Based on BCDDP
We will set up another "If-Then Table" to explore the consequences if this program had "carried the day" and had expanded indefinitely, with all U.S. women enrolled at age-35 to receive an annual mammogram thereafter at 2 breast-rads per exam. This is Table 28-B. Since it uses the same population-size as Table 28-A, with a dose ten-fold higher, it shows estimates which are ten-fold higher for the mammogram-induced breast-cancers.
Because of the variable latency period (Chapter 2), the mammogram-induced breast-cancers would not have shown up all at once. Table 28-B estimates the number which would have been put "on the shelf" each year, for delivery later. After a few decades of this program, at two rads per examination, the annual production of mammogram-induced breast-cancers and the annual "delivery" (incidence) of mammogram-induced breast-cancers would have become about equal in number (Chapter 4). And what would the equilibrium number have been?Ages at Mammogram-Induced Breast-Cancers: Production Annual "Delivery" at Equilibrium (Chapter 4) 35-39 43,757 40-49 86,187 50-64 112,803 Total 35-64 242,747
Table 28-BAssumes all U.S. women (age-35 and up) received 2 rads per year in a universal, continuous "Breast Cancer Detection and Demonstration Project."
An "If-Then" Table For Mammography.
Col. A Col. B Col. C Col. D Col. E Col. F Breast- Dose Cancers Annual Age Number of Medical Person- per 10,000 Breast - Year Women* Rads Rads Person-Rads** Cancers 35 1,662,910 2 3,325,820 26.38 8,774 36 1,660,984 2 3,321,968 26.38 8,763 37 1,658,904 2 3,317,808 26.38 8,752 38 1,656,652 2 3,313,304 26.38 8,740 39 1,654,176 2 3,308,352 26.38 8,727 Annual Mammogram Induced Breast Cancers (35-39 year-olds). Sum = 43,757 40 1,651,443 2 3,302,886 26.38 8,713 41 1,648,418 2 3,296,836 26.38 8,697 42 1,645,083 2 3,290,166 26.38 8,679 43 1,641,422 2 3,282,844 26.38 8,660 44 1,637,399 2 3,274,798 26.38 8,639 45 1,632,982 2 3,265,964 26.38 8,616 46 1,628,151 2 3,256,302 26.38 8,590 47 1,622,856 2 3,245,712 26.38 8,562 48 1,617,098 2 3,234,196 26.38 8,532 49 1,610,858 2 3,221,716 26.38 8,499 Annual Mammogram Induced Breast Cancers (40-49 year-olds). Sum = 86,187 50 1,604,120 2 3,208,240 24.56 7,879 51 1,596,848 2 3,193,696 24.56 7,844 52 1,588,992 2 3,177,984 24.56 7,805 53 1,580,517 2 3,161,034 24.56 7,763 54 1,571,372 2 3,142,744 24.56 7,719 55 1,561,522 2 3,123,044 24.56 7,670 56 1,550,950 2 3,101,900 24.56 7,618 57 1,539,588 2 3,079,176 24.56 7,562 58 1,527,332 2 3,054,664 24.56 7,502 59 1,514,026 2 3,028,052 24.56 7,437 60 1,501,100 2 3,002,200 24.56 7,373 61 1,483,790 2 2,967,580 24.56 7,288 62 1,466,720 2 2,933,440 24.56 7,205 63 1,448,518 2 2,897,036 24.56 7,115 64 1,429,452 2 2,858,904 24.56 7,021 Annual Mammogram-Induced Breast Cancers (50-64 year-olds). Sum = 112,803
Notes: Col.D = Col.B x Col.C
Col.F = (Col.D / 10,000) x Col.E
* Column B entries are for the number of women present at each age for an equilibrium population of 250,000,000 total persons. Taken from Table 24 of Gofman 1981.
** Conversion factors taken from from Chapter 39, Master Table, Column V.
The BCDDP program was intended to help women. But if it had been expanded and continued, it had the potential to have produced mammogram-induced breast-cancer at the rate of about 243,000 cases every year --- a number to be compared with the 182,000 breast-cancers in 1994 from all causes combined.
Of course, there will be readers who believe our estimate above should not be 243,000 cases per year --- but "only" 50,000 or 100,000 or 150,000 or 200,000. This is not the chapter where we show the basis of the "conversion-factors" in the table's Column E (see Chapter 40). But those who believe that the potential number of mammogram-induced breast-cancers would have been "only" 50,000 cases every year, can surely join in some gratitude to the people who prevented the BCDDP project from expanding and continuing at "only" 2 rads per mammographic exam.Part 6. The Gradual Development of Mammography: 1913-1964
In a very interesting summary article published in 1964, entitled "Mammography of Cancer," Dr. J. Gershon-Cohen and his colleague, Myron Forman, described the early origins of the mammography technology. Dr. Gershon-Cohen is one of the real pioneers of clinical mammography. We quote from it briefly (1964, p.674):
"Mammography is not new. Fifty years ago, when the science of radiology was still in its 'teens, Salomon in Germany produced credible mammograms of excised breasts (1913). His observations of some 3,000 mastectomy specimens correlated the roentgen findings with the gross and microscopic anatomy of tumors. His descriptions and roentgenograms contain a wealth of interesting information. The differences in the roentgen appearances of the most common forms of mammary cancer were recognized with amazing accuracy and he could differentiate scirrhous and infiltrating types of malignancy from the circumscribed or the nodular forms. He even described the punctate calcifications seen in many cancers, especially of the duct variety. Finally Salomon is to be credited with the first roentgenographic detection of an occult cancer found in a breast which was removed because of the presence of a large cyst."
Nonetheless, Dr. Gershon-Cohen related that it was only in the later 1920s and early 1930s that references began to appear concerning mammography. Despite excellent work being reported from several clinics in the United States and abroad, he stated that interest in the subject was simply not sustained.
In 1938, Gershon-Cohen and Strickler published a paper on the roentgen examination of the normal breast which emphasized that knowledge of the normal breast at all ages and stages of activity was a prerequisite for recognizing pathologic conditions.
"The Rising Sweep of Interest" in the 1950s and 1960s
Raul Leborgne's work in 1951 was cited by Gershon-Cohen (1964) for bringing to the attention of roentgenologists the importance of punctate calcifications as a pathognomonic [uniquely predictive] sign of malignant processes. Then Gershon-Cohen named a host of workers who stood out prominently with "the rising sweep of interest in this subject during the 1950s" --- all of whom shared in developing techniques and diagnostic criteria.
Speaking of his own institution, Gershon-Cohen cited the collaboration of the pathologist, Dr. Helen Ingleby, as the key event which led to a sustained interest in the subject of mammography. About Dr. Ingleby, Gershon-Cohen stated: "She made notable progress in bringing order out of the chaotic pathologic nomenclature so that the roentgenologist could reconcile his findings with pathologic conceptions."
Dr. Robert L. Egan was cited by Gershon-Cohen (1964, p.679) as another important pioneer in this field:
"More recently, Egan's efforts [1962, 1963] to improve technology and his report of excellent results generated intense interest in the subject. The impact of his work seems to have centered on his preoccupation with technique. It goes without saying that without optimum technique, no substantial reliability can be placed on any roentgenographic procedure. Good contrast and the best possible detail are essential if maximum information is to be obtained from the x-ray film ..."
Efforts to Prove the Value of Mammography
The work described above led to many investigations and consultations between the surgeons and the roentgenologists, to ascertain if mammography could improve the outlook in the breast-cancer problem. At a time when little progress was apparent in therapy, the hope was widespread that perhaps earlier diagnosis of breast-cancer might make treatments more successful.
Radiologists such as Dr. Robert Egan realized that, in order for mammography to be accepted as a valuable technique, capable of providing information over and above techniques already being applied, the radiologists had to prove several things, among which were:
(a) Ability to provide their diagnosis without any knowledge of the clinical findings. They were very wise in setting up this hurdle for themselves, for otherwise it could be stated that they made their analysis of the mammogram after knowing what the clinical picture was.
(b) Ability to diagnose cases by mammogram which could not be diagnosed by the clinicians either by history or physical examination or both. This was a major key, for the clinicians were always very worried about their own "false negatives" --- failures to recognize a case as being a cancer when it truly was a cancer.
(c) A low rate of "false positives" from mammography. The more often a mammogram caused a biopsy to be taken, with the finding of a negative result with respect to malignancy, the less useful would the mammogram be.
Gershon-Cohen appreciated the need to have true screening tests of mammography, where no clinical symptoms or signs caused the women to come in for mammography. That is not easy to accomplish. But he and his colleagues tried, in January 1956, to set up such a program in the Radiology Department of Albert Einstein Medical Center. All x-ray examinations in the survey were provided free to the volunteers --- with a single condition: Every candidate wishing to participate in the program must be free of breast symptoms. However, one can be at the mercy of the candidates, with respect to their truthfulness about absence of symptoms.
With All This Activity: Why No Entry in Our Master Table?
With only minor exceptions, we found that the studies done before 1960 were not suitable for inclusion in our Master Table. Most of the work involved women who were really under suspicion for possible breast-cancer and were having a mammogram as part of their work-up. As we have said before, we want not to count breast-doses administered to women who were already at the stage of clinical breast-cancer. We do not want to consider them as candidates for radiation-induced breast-cancer. We are trying to evaluate what breast-dose of radiation was being accumulated in the population not under study for possible breast-cancer. This, in essence, is why several major studies in the late 1950s were not appropriate for our purposes.Part 7. Early 1960s: "No Concern about Excessive Radiation Is Entertained"
In 1961, Gershon-Cohen and colleagues made a report on their screening program, mentioned in Part 6. It was entitled "Detection of Breast Cancers by Periodic X-Ray Examinations: A Five-Year Survey." In it, they reported:
"At present 1,055 women still remain in the program [out of 1,312 enlisted in the program]; 257 dropped out after one or more examinations. Each volunteer is examined every six months." What about the dose to the breasts in these repeated mammographic examinations? Gershon-Cohen and associates did indeed consider the safety of their program. They stated:
"Since we find nonscreen films satisfactory for our purposes and since each exposure entails less than 1.5 rad to the breast alone, no concern about excessive radiation is entertained."
It was not even "entertained" in 1961.
By contrast, we have illustrated in Table 28-B that people had better be very concerned about doses of 1.5 rads to the breasts twice a year, in any program which enlists large numbers of women. In Table 28-B, the dismal entries in Column F would be 50 % higher from an annual dose of three rads rather than two.
Annual Breast-Doses Well above 10 Rads: Called "Safe"
In 1964, Dr. Robert Egan --- whose work we also admire --- was apparently making the same mistaken assumption about safety as Dr. Gershon-Cohen. Dr. Egan described his evaluation of 1,217 consecutive mammograms on patients who came to biopsy. He used three views, rather than two. And he assumed the total dose was "safe." He stated (p.125):
"Mammography is a highly accurate, reproducible, safe, simple, and non-traumatic roentgenographic technique that provides a new objective approach to the diagnosis of breast diseases. It is the only means by which cancer of the intact breast can be demonstrated before signs and symptoms are present. In a series of 1,217 consecutive mammograms on patients who came to biopsy, 85 clinically unsuspected carcinomas were detected. The mammograms were interpreted without knowledge of clinical findings." And:
" ... From all three views, the central point of the average breast receives a total of 3.3 rads. Radiation to the eyes and gonads is negligible. Since only a small volume of tissue, which can be considered an appendage, is in a low-energy x-ray beam, this dose is quite acceptable for use in frequent re-examinations." How frequent? In a 1963 paper, Dr. Egan indicated that this dose would safely allow repeating the examination several times during each quarter year. So he was talking about annual breast-doses well above 10 rads per woman.
Such advice from a pioneer expert in mammography is just the opposite of what might have set the entire mammography effort on a good track, in our opinion. Three rads, in frequent re-examinations, widely practiced, would not be acceptable at all to that small-volume "appendage," the breasts. Such a regime, if applied to all women in the United States, would have breast-cancer consequences more than five times the magnitude estimated in Table 28-B.
The Only Target of Our Criticism
We most certainly do not fault Dr. Gershon-Cohen and Dr. Egan for not knowing in 1961 and 1964 what no one knew. Dr. MacKenzie's ground-breaking paper (see Chapter 1) did not even appear until 1965. And we certainly recognize an individual woman's right to accept voluntary medical risks of unknown sizes for herself.
What we fault is something quite different. We fault the policy of making sweeping assertions about safety --- instead of warning everyone about the actual state of ignorance at any given time.Part 8. How to Estimate a Personal Radiation Risk from Mammography
Women who want a "ballpark" estimate of their personal radiation risk, per mammographic exam, can easily obtain it by borrowing from Table 28-A, Column E. By answering some questions, we will illustrate how to do it.
o - Question One. I am age 33. What would be my risk from having a baseline exam at this age?
The lifetime rate at age 33 is 44.95 radiation-induced breast-cancers per 10,000 women who each receive 1 rad (Table 28-A, Column E). But the dose per exam is 0.2 rads, not a whole rad, so the rate will be lower. It will be (44.95 cases x 0.2) per 10,000 women = 8.99 radiation-induced cases / 10,000 women.
To make this fraction easier to grasp, just divide both the top and the bottom of the fraction by 8.99. The result is: 1 radiation-induced breast-cancer per 1,112 women --- or a lifetime individual risk of 1 chance in 1,112. Your chance of not developing a radiation-induced breast-cancer from the one exam is 1,111 chances out of 1,112.
o - Question Two. How does my radiation risk accumulate from a series of several mammographic exams?
If you have 15 exams, you add up the risks from each one. Suppose you have 15 mammograms beginning at age 50. The lifetime rate is 24.56 radiation-induced breast-cancers per 10,000 women who each receive 1 rad (Table 28-A, Column E). But the dose per exam is only 0.2 rad, not a whole rad, so the rate will be lower. On the other hand, we need to consider 15 exams. Multiplying by 15 is equivalent to adding the rate 15 times, of course. So the rate would be:
(24.56 radiation-induced cases x 0.2 x 15) per 10,000 women = 73.68 radiation-induced cases / 10,000 women. Then divide both the top and the bottom of the fraction by 73.68. The result is 1 radiation-induced breast-cancer per 136 women, or a lifetime individual risk of 1 chance in 136. Your chance of not developing a radiation-induced breast-cancer from the series of 15 exams is 135 chances out of 136.
o - Question Three. How do I combine my risk from the baseline exam with the risk from the later exams?
Using the illustrations above, we just do the addition while both fractions still have a denominator of 10,000 women. So: (8.99 cases / 10,000 women) + (73.68 cases / 10,000 women) = 82.67 cases / 10,000 women. Then we can divide both the top and the bottom of the fraction by 82.67. The result is 1 radiation-induced breast-cancer per 121 women, or a lifetime individual risk of 1 chance in 121. Your chance of not developing a radiation-induced breast-cancer from all 16 exams combined is 120 chances out of 121.
Variable Doses, and Variable Risks
The illustrations above use the approximation that "one size fits all." Throughout this book, we are dealing with average doses and average risks. In reality, there is variation around the average values. Neither the dose nor the risk is uniform. For example, dose has to vary with breast-thickness. And even at exactly the same dose, two women of the same age do not necessarily have the same risk of radiation-induced breast-cancer. One reason: Each woman has a unique genetic heritage.
There is debate over whether women born with one faulty copy of the gene for ataxia telangiectasia (the AT gene) have a truly elevated risk of breast-cancer and whether they are especially vulnerable to radiation-induced breast-cancer (Swift 1991; Boice 1992; Easton 1994). Resolution will require additional evidence. And the AT gene is just one of many genes which --- if faulty at conception --- might predispose their carriers to breast-cancer. For example, let us consider people who inherit genes which mean an elevated rate of non-repair or misrepair of new genetic injuries, including new injuries induced by ionizing radiation. It is probable (but not proven) that such people have a higher rate of radiation-induced cancer, per rad of radiation exposure, than people who inherit a better repair-system.
# # # # #
"From error to error, one discovers the entire truth."
o - Sigmund Freud, 1856-1939,
founder of psychoanalysis.