Decisive Epidemiological Evidence from Humans
This chapter is arranged in three parts:
The Nine Human Epidemiological Studies Used in Chapter 18, p.1 Inconclusive Evidence on a Threshold; Types and Supply, p.10 Decisive Evidence on a Threshold; Types and Supply, p.17
1. The Nine Human Epidemiological
Studies Used in Chapter 18
Our earlier presentation of the case against existence of any threshold, for induction of human cancer by ionizing radiation (Go86), included five studies of cancer-induction at very low doses or dose-rates. This expanded analysis considers a total of nine human epidemiological investigations, generally recognized to be well done and valid, which show radiation-induction of cancer at very low doses and dose-rates. Readers are acquainted only with the "bottom line" of these studies, from Chapter 18. Below, we describe the nature of each study.
It is the coupling of these critical studies at very low radiation doses and dose-rates, with the information from Chapter 20 concerning the frequency of radiation tracks in cell-nuclei, which makes it possible to refute speculation that there is a safe dose or dose-rate with respect to induction of human cancer. (See Chapter 18.)
-- Study 1,
Nova Scotia Fluoroscopy Study :
In the Nova Scotia Fluoroscopy Study, Myrden and Hiltz (My69) studied 243 women who (in the course of tuberculosis treatment) had chest fluoroscopies with the beam traveling from front to back. According to Boice et al, " . . . all the Nova Scotia women faced the X-ray tube during the fluoroscopy examination . . . " (Boice78, p.389).
The estimated absorbed breast-dose was 7.5 rads per fluoroscopy (Beir80, p.276). Time between fluoroscopies was days or weeks. The total breast-dose accumulated per woman was about 1,221 rads when the pneumothorax therapy was bilateral, and about 741 rads when it was unilateral. The average breast-dose in this series of women was about 850 rads (Go81, pp.242-243).
Breast-cancer was observed at more than six times the expected rate during a limited follow-up period (My69; Boice78, p.388, Table 11).
The Implication of Serial Doses :
Here at the outset, we will briefly review the explanation in Chapter 18 of why a study with such a high total dose is appropriately included in a series of low-dose, low-dose-rate epidemiological studies.
Whenever there is any dose at all, some cell-nuclei are being traversed by tracks.
Every track, acting alone, has a chance of inducing fully competent carcinogenic lesions.
It follows that there can never be any safe dose or dose-rate . . . unless every carcinogenic alteration is successfully and invariably "un-done" by repair processes, whenever exposures are sufficiently low and slow.
"Sufficiently low and slow" refers not to the total dose of radiation accumulated, but rather, to the dose per exposure and the time between exposures. If there were some low dose whose carcinogenic damage could always be flawlessly un-done within a certain time-interval, then people could receive such a dose once every interval, safely, because they would never have any cancer-risk left from the previous exposure when they received the subsequent exposure. If this were true, the total dose would not be of any importance, and people would be able to accumulate huge doses without any cancer-risk at all, if the huge doses were delivered by a series of small doses -- each of which were safe.
Although the Nova Scotia Fluoroscopy Study looks as if it were a high-dose study, it is able to reveal whether or not a low dose -- 7.5 rads -- is safe, when accompanied by ample time for repair to do everything of which repair is capable. In Chapter 18, it was shown that repair certainly has ample opportunity to do the best it can, in periods of well under 24 hours, likely under 12 hours. In the Nova Scotia Fluoroscopy Study, the radiation doses were far more widely separated, by periods of days or more. Hence, there can be no question that the repair-systems had every possible opportunity to perform flawless repair -- if that is indeed possible.
If carcinogenic injury was produced in the irradiated women at their first fluoroscopy exposure-session, but if repair-systems were able to perform flawless repair afterwards, then that particular exposure-session would have left no residual harm, in terms of any increased risk of future breast-cancer.
Similar carcinogenic injury inflicted at every subsequent fluoroscopy session would also have been without residual harm, if a flawless repair-system operated at a total dose per exposure-session of 7.5 rads. And thus, after accumulating 850 rads in this fashion, the irradiated women would have had no radiation-induced breast-cancer.
The Dose-Entry in Table 21-A :
The Nova Scotia Fluoroscopy Study by itself is an important test of whether or not it is reasonable even to consider flawless repair as a hypothesis. Readers are reminded that 7.5 rads from 30 KeV X-rays is a tissue-dose which corresponds with an average of only about 10 primary ionization tracks per nucleus (Table 21-A).
The Nova Scotia Study is certainly not a high-dose study; at every critical step along the way, it is a test of how perfectly the repair-system can un-do carcinogenic injury produced by 7.5 rads, or 10 nuclear tracks on the average -- a low dose and dose-rate.
The test supplies strong evidence that the flawless-repair hypothesis fails -- at least for single doses of 7.5 rads, or an average track-rate of only 10 tracks per nucleus. A greater than six-fold increase in the breast-cancer rate, among those women who were in the exposed group, is far from a small increase. It is large and definitive.
In this study, carcinogenic damage -- inflicted by the individual low-dose exposure-sessions -- accumulated in the women from each exposure, by unrepaired, unrepairable, or misrepaired injury. This is not the behavior of a flawless repair-system for low radiation doses.
-- Study 2,
Israeli Scalp-Irradiation Study
(Thyroid-Cancer Endpoint) :
In the Israeli Scalp-Irradiation Study, Modan and co-workers (Modan77) reported on the excess of thyroid-cancers observed among over 10,000 children in Israel who received X-irradiation for ringworm of the scalp. The estimated thyroid dose per child was 7.5 rads, total.
Thyroid-cancer was observed at five times the expected rate during a limited follow-up period.
In a later publication (Modan89), the dose was stated to have been 9 rads, rather than the 7.5 rads reported earlier. Also, the thyroid-cancer rate was given as four times that of the children who were not irradiated. Neither of the changes materially alters the study for our present considerations. The control group in this study appears to be carefully matched by age, sex, and demographics, and a second control group of unirradiated siblings is also part of the study (Un86, p.228, Para.388).
This is totally a low-dose study, since there was only a single exposure, from a dose of 7.5 or 9 rads to the thyroid gland.
This study by itself is another crucial test of the hypothesis that the repair system, given sufficient time to operate, will flawlessly un-do carcinogenic injury from low-dose radiation injury (in this case, a total dose of 7.5 to 9.0 rads). The hypothetical flawless repair-system failed the test, and a four-fold increase in the incidence of thyroid-cancer was the result -- surely the result of unrepaired, unrepairable, or misrepaired injury -- even at a dose-level corresponding with only 10 or 12 primary ionization tracks per nucleus, on the average (Table 21-A).
Modan on the Pituitary Dose :
In their most recent follow-up study (Modan89), Modan and co-workers mention that one might wish to consider the possibility that radiation delivered to the pituitary, in the course of scalp-irradiation, might have been an indirect basis for the development of thyroid-cancer, perhaps in addition to the direct effect of radiation on the thyroid. The authors stated that the dose to the pituitary was between 4.8 and 6.6 rads.
Modan's suggestion, if accepted, would not be helpful to a safe-dose proposition. The suggestion implies that a few primary ionization tracks per cell-nucleus in the pituitary gland may contribute to a multi-fold increase in cancer at sites affected by pituitary hormones (and such sites are numerous).
However, we wonder if Modan et al may have erroneously stated the pituitary dose in Modan89, because in UNSCEAR 1986 (p.228, para.391), the pituitary dose is referred to as perhaps of the order of 50 rads (not 5). Modan et al will surely address this question of which pituitary dose is correct.
UNSCEAR 1986, citing the work of Lee et al (Lee82) with rats, comments; "The role of pituitary irradiation in the induction of thyroid cancer was . . . explored by delivering doses of 4.1 Gy of x rays to the pituitary alone, or to the thyroid and the pituitary together: findings were negative in this respect" (Un86, p.208, para.253). Un86 is not commenting in para.253 specifically on the Modan Study.
-- Study 3,
Massachusetts Fluoroscopy Study :
In the Massachusetts Fluoroscopy Study, Boice and Monson (Boice77) also studied women who had received repeated chest fluoroscopy during tuberculosis treatment (see Study 1).
In the Massachusetts series, the beam was usually from back to front. Boice and co-workers make the approximation that in 75 % of the exams, patients had their backs to the X-ray tube, and in 25 % of exams, patients were facing the tube (Boice78, Table 10). Overall, the estimated average absorbed breast-dose per single exam was 1.5 rads (Boice77; Boice78, p.385).
The accumulated breast-dose was about 150 rems, total. Among the women whose average age was 20 years at the time of irradiation, breast-cancer was observed at more than twice the expected rate during a limited follow-up period. "For the exposed women, the onset of the period of risk for breast cancer development was assumed to be the date of the first fluoroscopic examination, and, for the non-irradiated controls, the date of admission to the sanitorium" (Un86, p.225, para.370).
What was stated above concerning Study 1, the Nova Scotia Fluoroscopy Study, applies here too. This is another study of repeated, or serial, low-dose exposures separated by sufficient time for repair to un-do whatever carcinogenic injuries it was ever capable of un-doing. The Massachusetts series is another test of the speculation that the repair-system may operate flawlessly for low-dose damage. And the study represents another failure for perfect repair.
The Dose-Entry in Table 21-A :
Just how low was the dose, in the terms which matter -- namely, average number of tracks per nucleus, per exam?
In this study, unlike the Nova Scotia Study, the answer is not self-evident. For diagnostic X-rays, tracks per nucleus at one rad are about 1.3378 (from Table 20-K), so tracks per nucleus from 1.5 rad would be 2.0067 tracks on the average. But (unlike Go86), we have decided that two tracks would not be the appropriate track-rate to use under the conditions described above.
In this chapter, we are investigating the hypothesis of perfect repair. We start with the premise that, for a given type of radiation, injury per cell-nucleus is proportional to the number of primary ionization tracks which traverse ("disturb") the nucleus. This premise is explained by the nature of the interaction of ionizing radiation with living tissue (Chapter 19). For a given type of radiation, the number of tracks is an index of the strain on the repair-system.
If we want a realistic measure of strain, we have to take account of the fact that there is a substantial difference in breast-dose caused by orientation with respect to the X-ray beam. For instance, in Go85 at p.404, we estimate that the absorbed breast dose is about 19 times higher when the woman is facing the beam than when she has her back to the beam. UNSCEAR 88, discussing the Canadian Fluoroscopy Study (Study 4 in this chapter), refers to a 20-fold difference too (Un88, p.456, para.367).
So, even though the average breast-dose per exam was only 1.5 rad, almost all of the rads received had to be rads which were received while the woman was facing the beam. Indeed, we will show below that 87 % of the rads were received while facing the beam.
The estimate of 1.5 rad per exam sets an upper-limit on the dose from exams done facing the beam. To simplify, we can imagine that in 3 out of 4 exams or 75 % of exams, when the women were told to face away from the beam, their breasts received no dose at all. We can imagine that in 1 out of 4 exams or 25 % of exams, when the women were told to face the beam, their breasts received 6 rads. Then the weighted average dose per exam would be (0.75 x 0 rads) + (0.25 x 6 rads) = 1.5 rad.
But the dose facing away from the beam was not zero rads, so we must calculate what it was. We will call the low dose (while facing away from the beam) "d". Then 20d = the higher dose (while facing the beam). The lower dose, d, was received during 75 % of the exams. The higher dose, 20d, was received during 25 % of the exams. Their weighted average = 1.5 rads. Thus:(0.75d) + (0.25 x 20d) = 1.5 (0.75d) + (5d) = 1.5 (5.75d) = 1.5 d = 0.261 20d = 5.22
For every four exams performed, 6 rads were received, since we are told that the average dose per exam was 1.5 rads. The six rads per four exams were delivered as follows; 3 exams (each 0.261 rad) contributed 0.783 rad, and 1 exam (delivering 5.22 rads) contributed 5.22 rads. And (5.22 rads / 6 rads) x (100) = 87 %. In other words, 87 % of the rads received in this study were received at a rate of 5.22 rads per delivery or exposure-session, not 1.5 rad per exposure.
Therefore, we think we are not entitled to regard this study as a test of the flawless-repair hypothesis at the average rate of two tracks per nucleus (from 1.5 rads). The weighted average rate of tracks will be higher. Some 87 % of tracks will arrive at the rate set by 5.22 rads per exam. This rate is (1.3378 tracks per nucleus at 1 rad) x (5.22 rads), or 6.9833 tracks per nucleus per exam. Some 13 % of tracks will arrive at the rate set by 0.261 rad per exam. This rate is (1.3378 tracks per nucleus at 1 rad) x (0.261 rad), or 0.3492 track per nucleus per exam. So the weighted average delivery-rate which we will use for this study is as follows:(0.87 x 6.9833 tracks) + (0.13 x 0.3492 track) = 6.1209 tracks per nucleus, on the average.
We will check this answer by obtaining the weighted average delivery-rate for rads, and then converting it to tracks per nucleus. Some 87 % of the rads are delivered at the rate of 5.22 rads per exam, and 13 % are delivered at the rate of 0.261 rad per exam. So the weighted average delivery rate is:(0.87 x 5.22) + (0.13 x 0.261) = 4.575 rads per delivery, or per exposure-session. (1.3378 tracks per nucleus at 1 rad) x (4.575 rads) = 6.1204 tracks per nucleus, on the average.
Before making an entry into Table 21-A, we will round the dose to 4.6 rads per exposure-session, and adjust the tracks to 6.1539 .
Readers who have followed this presentation will understand that we are not changing the facts as reported at all. The average dose per exam remains 1.5 rads. But for a test of the flawless-repair hypothesis, it is more appropriate to consider the average delivery-rate of the rads, and we have shown this to be 4.6 rads at one time.
-- Study 4,
Canadian Fluoroscopy Study :
This is a very large on-going study in Canada based upon patients with a history of hospitalization for pulmonary tuberculosis (Howe84; Mi89).
Originally, the plan was to incorporate the Nova Scotia fluoroscopy cases with the larger Canadian series. However, because the Nova Scotia patients were fluoroscoped with the beam entering the front of the body -- with consequently a much larger radiation dose to the breasts than was the case for all other parts of the Canadian study, where the fluoroscopy was conducted primarily with beam-entry from the back -- it was decided to keep the study in two separate parts. We have therefore considered the total Canadian experience as two separate large studies, one labeled Canadian Fluoroscopy Study, and the other labeled Nova Scotia Fluoroscopy Study (Study 1, above).
According to Miller and co-workers, who released another interim report on this study in November 1989, "The principal difference among sanatoriums was that in Nova Scotia the patients usually faced the x-ray source, whereas in other provinces they usually faced away from it" (Mi89, p.1286).
We cannot find any estimate of dose per exam in the Howe or Miller reports. However, since irradiation conditions in the Canadian Study were closest to those of the Massachusetts Fluoroscopy Study, and since the authors say that they used data from Boice78 to help themselves estimate dose per patient (Mi89, p.1286), we will use the approximation that the average absorbed dose in the Canadian Study was also 1.5 rads to the breast for each fluoroscopic examination. Thus, we will say that the weighted average rate at which these rads were delivered was 4.6 rads per exam, as we did in Study 3. This means, per exam, an average of only about 6 primary ionization tracks per nucleus.
Like the Nova Scotia and Massachusetts Studies, the Canadian Study must be regarded as a very low-dose study, since it involved single low-dose exposures, given serially and separated by ample time for the repair-system to operate flawlessly, if it can. The result was that the hypothesis of flawless repair failed, again. For instance, for breast tissue-doses in the range 200-499 rads, the breast-cancer mortality was 2.2 times that for the unexposed persons, in a limited follow-up (Howe84). The later paper (Mi89) does not give relative risk for the non-Nova-Scotia segment separately. (Additional discussion of this study will be found in Chapter 22.)
-- Study 5,
Stewart In-Utero Studies :
In the In-Utero Series, Stewart and co-workers compared the X-ray history (maternal) for children who died of cancer or leukemia, with the X-ray history for matched controls who had no malignant disease (Stew56; Stew58; Stew70). Stewart and co-workers demonstrated that diagnostic X-rays during pregnancy, irradiating the fetus-in-utero, provoked about a 50 % increase in the frequency of childhood cancer and leukemia. This study, widely known as the "Oxford Study," is the original work of this type on in-utero irradiation.
The results of this long-term study have recently been up-dated in three publications (Knea87 at p.215; Knox87; and Gilm88). Two features are to be noted. First, all three papers are in agreement that for obstetric radiography, which Gilman and co-workers take to be synonymous with third-trimester X-rays, the best estimate for mean dose to the fetus was 0.5 rad per obstetric examination. They suggest a best estimate per film to have been 0.3 rad. Second, the estimated relative risk of cancer associated with obstetric radiography is now estimated to be about 1.94, which is appreciably higher than the earlier estimates for the Oxford Studies. Knox (Knox87, p.11) explains this as follows:
"The radiation-RR [RR= relative risk] was larger than previously suspected. The confounding factors had masked rather than exaggerated its true extent. Over the whole period it was about 1.94, reducing from greater values in the earlier years to a lower value in the later years."
The Dose-Entry in Table 21-A :
On the basis of the papers cited above, we shall use the dose-estimate of 0.5 rads to the fetus for obstetric radiography in the Stewart In-Utero Studies.
This dose corresponds with an average rate of only 0.67 track per nucleus (Table 21-A). The Poisson equation shows that, when the average is 0.67, only 14.5 % of the cell-nuclei receive two or more tracks (Table 21-B). The overwhelming percentage of nuclei is either receiving the Least Possible Disturbance (a single primary ionization track per nucleus) or no disturbance at all.
The Stewart In-Utero Studies provide powerful additional evidence for failure of the hypothesis that, if dose were just sufficiently low and slow, then repair of carcinogenic injury would be flawless. If repair had been flawless, no radiation-induced malignancies would have occurred from the in-utero irradiation by only 0.5 rad.
The Causality Issue :
The number of persons who doubt the Stewart findings seems to decline steadily. The observations themselves are not questioned, but the causal nature of the relationship is sometimes challenged.
A few persons still suggest that some "third factor" leads some women to "need" to have obstetric radiography and the same "third factor" leads them to have children with cancer or leukemia, so that radiation is exonerated. No such third factor has ever been identified. One can say that, with all the evidence relating radiation to cancer and leukemia under all sorts of different circumstances, it is really a violation of the law of minimum hypotheses to invoke some "third factor" as the cause of the excess malignancies in this series.
Of course, confidence in the causal relationship, between in-utero irradiation and excess childhood malignancies, rises appropriately when the same result is found among a wholly different set of children in a wholly different set of circumstances by a wholly different set of investigators. The Stewart In-Utero Studies have been confirmed in this manner, and more than once (Studies 6 and 8, below).
Nonetheless, the 1988 UNSCEAR Committee (Un88, pp.427-429, para.157,162,163,169) -- challenges all these findings by pointing repeatedly to the failure to find a comparable result in the A-bomb in-utero series -- a series where the total expectation of childhood cancer was a maximum of only six cases (two cases were observed).
However, I have shown elsewhere (Go81, pp.753-756) that undue weight has been given to this "failure." Those who emphasize it are ignoring the presence of undeniable bias-problems in diagnosis during the early post-bombing period within the A-bomb in-utero series, and later, probable diagnostic error associated with an excess rate of severe mental retardation in this in-utero series. Such problems (shown in detail in Go81) can distort conclusions badly in the A-bomb in-utero series, where so very few cases of childhood cancer were expected at all.
UNSCEAR 1988 neither mentions these specific bias-problems nor rebuts their significance.
At the end of its discussion, however, UNSCEAR says that " . . . it would be prudent to assume that pre-natal irradiation does have an effect, especially with regard to leukaemogenesis" (Un88, p.429, para.170).
It might be noted that RERF is now beginning to report an excess of adult-type cancers occurring in the A-bomb in-utero series (Yoshi88). In this current phase of the follow-up, diagnostic bias is still a concern.
It has long been my opinion that the case in favor of causality in the Stewart In-Utero Studies is very strong indeed. I note that Dr. Robin H. Mole, a former member of the ICRP, has explicitly gone on record as follows (Mole88); "A clear statistical association between excess childhood cancer and prenatal abdominal radiography of the mother was established by Dr. Alice Stewart some time ago. The scientific issue was whether this meant causation. If so, the no-threshold hypothesis for cancer induction would be virtually unassailable, instead of being merely a prudent assumption by ICRP. Good scientific reasons exist (Mole74) for accepting that the small dose involved in the radiography did cause the cancer."
-- Study 6,
MacMahon In-Utero Study :
In a totally separate study of in-utero irradiation, MacMahon (Mac62) carried through a study of childhood mortality from neoplastic diseases (leukemia and other malignancies) in relation to diagnostic X-ray examinations during the relevant pregnancy. His population sample was a 1 % sample of 734,243 children born in and discharged alive from any of 37 large maternity hospitals in the Northeast United States in the years 1947-1954.
A highly significant increase in mortality from malignant disease was found in children whose mothers received diagnostic X-rays to the abdominal or pelvic region during the relevant pregnancy. The majority of the X-rays were performed in the third trimester. In this study, hospital records were examined to ascertain X-ray exposure, whereas the original Stewart Study was based on mothers stating whether or not they had had X-rays in the pregnancy. No study is perfect in this regard, since neither hospital records nor memories are flawless.
The careful study by MacMahon included correction for possible confounding variables, and concluded, in MacMahon's direct words, that:
"The higher frequency of prenatal X ray in the cancer cases than in the sample was statistically significant. After correction for birth order and other complicating variables, it was estimated that cancer mortality [including leukemia mortality] was about 40% higher in the X-rayed than in the unX-rayed members of the study population. This relationship held for each of the three major diagnostic categories -- leukemia, neoplasms of the central nervous system, and other neoplasms."
While no estimates of X-ray exposure-dose were made by MacMahon, he provided the following information which we will use to make a dose-estimate. The X-rayed cases were ranked into three categories in order of probable dose (adapted from MacMahon's Table 8):
Number of X-Ray Exposure : Exams ---------------- --------- Abdominal flat plate, often for diagnosis of twins; usually 1-film or 2-films per woman. 183 Pelvimetry; usually 3 films per woman. 520 Multiple procedures; these combinations included flat plates with pelvimetry; repeated pelvimetry; additional exams of kidneys, intestines, etc. 67 --------- Total Exams 770
With the overwhelming representation of pelvimetries, and with the greater frequency of "abdominal flat plate" than "multiple procedures," it is reasonable to assign an average of 3 films for the X-ray exposures experienced during these pregnancies. And since "repair time" was most uncommon between films, these exams were acute exposures.
The Dose-Entry for Table 21-A :
Since MacMahon did not provide an average dose per film, we shall use the central estimate of Knox and co-workers (Study 5), which is 0.3 rad per film. Using this estimate of dose per film, and the estimate above of three films per examination in the MacMahon series, we arrive at an average exposure of 0.9 rad to the fetus. This dose increased the rate of childhood cancer or leukemia among the exposed children to 1.4 times the rate observed for children who were not exposed during gestation.
The MacMahon study is still another instance in which the hypothesis of flawless repair of carcinogenic injury has failed, despite very low dose. In this case, flawless repair failed after a single exposure-session with a dose of 0.9 rad (0.9 cGy), which corresponds with an average number of tracks of only 1.2 per cell-nucleus (Table 21-A).
The question of causality between the X-ray exposure and the childhood malignancies has, of course, been raised for this study just as it was for the Stewart Study. My opinion is that the grounds for questioning causality in either study are very poor indeed. Study 8 (below) is another study, undertaken by Harvey and co-workers to address the speculation that some unidentified "third factor" could be causing occurrence of the X-rays as well as occurrence of the excess childhood malignancies.
-- Study 7,
British Luminizer Study :
Baverstock and co-workers studied the experience of British workers involved in the preparation of instrument-dials made luminous with radium (Bav81, Bav83). They reported highly significant proof of breast-cancer induction by gamma radiation in young female workers who applied the radium-226 to the instruments. These investigators were able to rule out internal radiation by alpha particles as the cause, and identified external gamma radiation as the source of the breast exposure. The total breast-dose accumulated by the young women was 40 rads (centi-grays).
The dose-rate of external gammas to the breasts was, by measurement, 0.5 rad (cGy) per week or less. For a 40-hour week, this represents a dose of 0.1 rad per 8 hours (per work-day). In Table 21-A, we treat each work-day as one exposure. Of course, the "repair time" available with each exposure-session was a minimum of 16 hours (between the end of one work-day and the beginning of the next). After we consider the Poisson distribution of tracks (below), we will see that the average repair-time was actually greater than 24 hours.
Among the women whose average age was 20 years at the time of first employment, breast-cancer was observed at twice the expected rate during a limited follow-up period. Follow-up will continue in this UK Radium Luminizer Survey, as noted in Chapter 18, Part 6.
Like the fluoroscopy studies cited above, the British Luminizer Study also converts an apparent "high-dose" study into what should appropriately be considered a low-dose radiation study. The true dose with which repair-systems had to cope in this study was 0.1 rad per exposure -- which corresponds with an average of approximately 0.2937 track per cell-nucleus (Table 21-A). This is certainly far down on the scale of low-doses.
And repair-time between exposures was ample. The time is affected by the Poisson distribution of tracks. The Poisson equation shows that, when the average is 0.2937 track per nucleus, about 75 % of the nuclei are receiving no primary ionization track at all (Table 21-C). Because the tracks received during one work-day cannot be targeted upon the 25 % of nuclei which were hit by tracks during the previous work-day, in reality, most nuclei had more than a work-day between any disturbance at all, in the British Luminizer Study.
It should be noted, from Table 21-C, that only 3.6 % of nuclei receive two or more tracks per exposure. About 96.4 % of cell-nuclei either experience the Least Possible Disturbance per exposure (a single primary ionization track, with ample time for repair to operate) or no disturbance at all per exposure.
The British Luminizer Study, with an exceedingly low dose and dose-rate per exposure-session, constitutes still another failure of the hypothesis that flawless repair of carcinogenic injury occurs at minimal doses and dose-rates.
British Luminizers -- An Up-Date :
After our initial use (Go86) of this study, Baverstock and Papworth issued an interim up-date report which brings ascertainment of deaths up to January 1986 (Bav87). There are now 243 total deaths from all causes, up from 89 in the initial report. About 80 % of the study population is still living.
Our use of this study is limited to the women who were younger than age 30 at the start of luminizing. Due to declining radio-sensitivity with advancing age, one does not expect to find a provable excess of breast-cancer in such a study among the luminizers who began their luminizing work beyond age 30 (total breast-cancer deaths equals 7). For the group under age 30 at first exposure, the up-dated report by Baverstock and Papworth provides the following data in their recent interim report:
------ Exposure Category -------- Breast Cancers <0.2 Gy =>0.2 Gy Total Group Observed 5 16 21 Expected 3.00 10.62 13.62 O / E 1.67 1.51 1.54 p-value (1-tailed) 0.18 0.074 0.04 Significance N.S. Suggestive Significant Mean Absorbed Dose (in rads) 8.5 51 40 ------------------------------------------------- Person-years 8,569 27,299 35,868 Persons at risk 255 678 933
When p-values are between 0.05 and 0.1, the significance is often called "Suggestive."
The O / E value (relative risk) of 1.54 for breast-cancer deaths is significantly elevated in the study population compared with expectation, which is based on the general population. This result is for a total mean absorbed dose of 40 breast-rads, accumulated gradually by the luminizer women.
For these women, the O / E value is reduced from about 2.0 in the early interim report (Bav81) to about 1.5 in the follow-up to January 1986. However, the precise value of O / E is of no concern for the purpose of assessing flawless repair of carcinogenic lesions. Any significant radiation-induced elevation of O / E above 1.0 means that repair is not operating flawlessly. Thus, the up-dated interim report alters nothing about our use of this study in analyzing the threshold issue.
In neither the initial report nor the recent up-date are the data strong enough to permit a meaningful test for internal dose-response relationship among the luminizer women. A positive dose-response trend (a rising relative risk with rising dose) would be a powerful indication of causality in this study between the irradiation and the excess mortality from breast cancer.
Meanwhile, the presumption is reasonable that radiation is indeed the cause of the observed excess. It would seem unreasonable to attribute the excess breast-cancer deaths to a more efficient ascertainment of total deaths or cancer deaths in the study population. All causes of death (omitting cancer) show an O / E value of 0.81, when all the luminizers are contrasted with the general population. And all cancer-deaths (breast-cancer excluded) show an O / E value of 1.02, so a more diligent search for cancer-deaths in particular does not seem like a reasonable suspicion. By contrast, the O / E for breast-cancer deaths is 1.37 when all the luminizers (regardless of age at exposure) are compared with the general population.
The nature of the radiation exposure makes it extremely reasonable to expect that the radiation dose to the breasts was higher than dose to other organs. And this is consistent with the observation that breast-cancer deaths are provably in excess whereas other cancers are not. Nonetheless, pending a positive dose-response it remains possible that some unidentified variable, other than radiation, accounts for the excess.
The British Luminizer Study once again illustrates the "small-numbers" problem which manifests itself most severely when a single type of cancer is under study in a population of limited size. Even in the A-Bomb Study, despite combining all cancer-sites and despite much higher cancer expectations than in the Baverstock study, considerable sampling variation occurred from one follow-up interval to the next, as plainly seen in Chapter 17, Table 17-B. In the British Luminizers, Baverstock and Papworth find a decline in relative risk from about 2.0 to about 1.5 from one follow-up to the next. Whether this decline is the result of sampling variation alone or is a meaningful time-trend cannot be ascertained within the data.
Like Baverstock and Papworth, we will be highly interested in whatever is shown by future follow-ups in the Luminizer Study.
-- Study 8,
Harvey In-Utero Twins Study :
Because of suggestions that some underlying medical status led women to being X-rayed during pregnancy and also led to giving birth to children likely to develop cancer or leukemia, Harvey and co-workers (Har85) elected to do a case-control study in twins. The reasoning was that the likelihood of medical selection bias would be reduced in the study of twins. Harvey and co-workers stated:
"Twins were exposed to prenatal x-rays more frequently than singletons to confirm their twin status or to determine the fetal position before birth and not necessarily because of any medical condition of the mother or child that could conceivably predispose to cancer. It is generally believed that the demonstration of excess childhood cancer in twins would be the best evidence that prenatal x-ray exposure is truly causal and not merely correlated indirectly with an increase in cancer frequency."
The records of over 32,000 twins born in Connecticut from 1930 to 1969 were used. These were linked to the Connecticut Tumor Registry with the result that 31 incident cases of cancer were identifed. These were each matched with four twin controls, according to sex, year of birth, and race. A twin was considered exposed if the mother had been exposed to X-rays in the abdominal region during the twin pregnancy -- e,g., pelvimetry or plain films of the abdomen.
Radiation dose to the fetus was estimated to have had an average value of 1.0 rad.
Analysis showed a significant excess of X-rays in the twins who developed childhood cancer, contrasted with the controls. The final estimated overall relative risk associated with prenatal X-ray exposure was 2.4, adjusted only for twin birth-weight.
The authors point out; "The observed 2.4-fold risk of childhood cancer associated with prenatal x-ray exposure in twins is consistent with the results of two major investigations from England and the northeastern United States [reference to Stew58 and Mac62] and with a reanalysis of the twin segment from the English series" [reference to Mole74].
While it would have been helpful if the entire series of cases in the Harvey Twins Study were larger, the 95 % confidence limits on the relative risk were 1.0 to 5.9. We consider that this study is a valid addition to the seven studies already considered here.
The Harvey Twin Study indicates that repair was not able to un-do all the carcinogenic injury from a single, acute dose of only 1.0 rad, which corresponds with a track-average of 1.3 per cell-nucleus.
-- Study 9, Breast-Cancer in
the Israeli Scalp-Irradiation Study
Very recently, Modan and co-workers (Modan89) have published an update of some aspects of the same scalp-irradiation study described as Study 2 above. In this update, the incidence of breast-cancer was examined for the 1982-1986 period, as part of an on-going evaluation of various cancers occurring in the children irradiated between 1949 and 1959 in the Israeli tinea capitis series.
Their finding is that the relative risk of breast-cancer in the period 1982-1986 is 2.11 for the irradiated female children contrasted with unirradiated controls. The 90 % confidence-limits are 1.05 and 4.24. Modan and co-workers point out that they used 90 % confidence-limits " . . . since we did not expect a protective anti-carcinogenic effect of radiation."
The radiation dose estimated for the breasts of the female children is given as 1.6 rads. The authors of the paper were themselves surprised by the magnitude of the effect for this dose-level. They explored possible underestimates of dose to the breast as a result of movement of some of the children during the scalp-irradiation, but did not reach any definitive conclusions on this point. Also they explored the possibility that the dose received by the pituitary might have indirectly been involved in producing the breast-cancer.
It is my opinion that retroactive re-evaluation of radiation dose, simply because findings surprise the investigator, leaves much to be desired and can lead to bias. The appropriate use of these data is to take the observations as they were made.
This study, taken at face value, would represent another failure of repair in un-doing carcinogenic injury, from a single acute dose of only 1.6 rads, which corresponds with an average of 2.1 tracks per cell-nucleus (Table 21-A). Even if one were to double the estimated radiation dose to the breast, this would still be a study with only 4.2 tracks per cell-nucleus, on the average.
Summary and a Key Question :
With respect to all nine studies described above, Table 21-A summarizes the crucial information which demonstrates failure of the hypothesis that very low-dose carcinogenic injury is flawlessly repaired. It should be noted that the same evidence is perfectly consistent with the hypothesis of an approximately constant fraction of unrepaired, unrepairable, and misrepaired damage throughout the dose-range, right down to the complete disappearance of dose.
Five of the nine epidemiological studies have their total doses evaluated in Table 21-A. Four studies in the table have dose-entries which are very low per exposure, even though many repetitions of the exposure finally added up to large doses. Large total doses may be required in order to detect an excess of a few types of cancer when a limited sample of adults is exposed and followed-up for a limited time-period, but this statement is certainly not a suggestion that large doses of radiation are required to cause any excess cancer. The two statements are very different, as every epidemiologist knows. With respect to the hypothesis that repair can flawlessly un-do all carcinogenic damage from tracks, provided dose is sufficiently low and slow, these four studies of successive small doses qualify as highly relevant evidence.
Readers may note that Arthur Upton, chairman of the BEIR-5 radiation committee, explicitly selects the fluoroscopy studies, the Baverstock Luminizer Study, the Modan tinea capitis study, and the in-utero studies, when he states; "Several lines of epidemiological evidence support the hypothesis that there may be no threshold in the dose-incidence relationship . . . " (Up87, p.300; full context provided in our Chapter 34).
Regrettably, Upton makes no attempt to analyse the extremely low rate of tracks per nucleus in these studies -- an analysis which is the crucial step in showing that the combined evidence amounts to proof that there is no threshold.
In Table 21-A, the doses per exposure range from 9 rads right down to 0.1 rad per exposure, and in five of the nine studies, the average number of tracks per nucleus was between 2.14 and 0.2937. Since the Least Possible Disturbance is one primary track per nucleus, plus time for repair to un-do it, these studies are most certainly studies of very low radiation doses and dose-rates.
In Chapter 18, we have asserted that -- by any reasonable standard -- repair's failure to prevent excess cancer in these studies is proof that there is no dose or dose-rate where repair is flawless with respect to carcinogenic injuries. And in the title of Chapter 21, we have referred to "decisive" epidemiological evidence on the threshold issue.
The question which many readers will have, of course, is; "Why should I believe the studies which do show excess cancer at such low doses and dose-rates, instead of the more numerous studies which fail to show any excess at such doses?" Part 2 will address that question.2. Inconclusive Evidence on a Threshold :
Types and Supply
An inconclusive study with respect to the threshold issue is, of course, any study which is incapable of helping to resolve it. Below, we will provide some examples of such studies from influential journals. A study whose results are consistent with opposites (safe dose, no safe dose) is obviously inconclusive with respect to the safe-dose issue.
The abstracts of many such studies feature the phrase "no significant risk was found." Unfortunately, even some people in medicine mistakenly interpret the phrase to mean, "If radiation were carcinogenic, an elevated cancer-risk should have been found," and so they mistakenly treat the study as evidence in favor of a safe dose. If they looked hard enough in such papers, however, they would usually find that the authors warned them somewhere, directly or indirectly, against this mistake. (We include one example, however, where the authors do otherwise.)
Here at the outset of this section, it should be stressed that observations, reported in studies which are inconclusive on the threshold issue, can be fully correct data which are valuable with respect to other issues. A classic example is the A-Bomb Study itself. Dose-Groups 1 and 2 are separated by a total dose less than 2 rems (Table 11-H) -- and even this small difference is not so certain (see Chapter 8, Part 4). A provable excess of cancer in Dose-Group 2 does not lie within expectation. Thus the A-Bomb Study cannot possibly address the threshold issue directly. Yet the A-Bomb Study is by far the most valuable study on many other issues -- issues which cannot be addressed by the nine studies of Table 21-A.
Although inconclusive studies are commonly treated as if they were evidence supporting a safe dose and dose-rate, they are not. Such "no-effect-found" studies are merely studies which are consistent with both the existence and non-existence of a threshold.
This is a very different status from a study where a cancer-effect from radiation clearly should have been found, but was not. By definition, such a study would not be consistent with the thesis of no safe dose or dose-rate.
It is still difficult, however, for analysts to know when radiogenic cancer should have been found in a particular study, or should not have been found. The radiogenic expectation depends critically on knowing in advance the magnitude of the radiation's carcinogenicity. It is self-evident that the accuracy of radiogenic risk-values for specific cancer-sites and for limited classes of cancer (e.g., "childhood cancers") is far lower than that for cancers overall. (See discussion in Chapter 22, Part 5.)
What threshold proponents need is a collection of mutually reinforcing human studies in which the magnitude of radiogenic risk is firm enough to say, with reasonable certainty, that an excess of cancer should have been found and was not found.
However, an accumulation of inappropriate evidence would be worse than worthless -- it would be a misleading distortion. When scientists speak of "the weight of the evidence" in any field, they mean the weight of appropriate evidence.
The human studies commonly cited as supporting a safe dose or dose-rate do not qualify as studies where an excess of cancer clearly should have been found, but was not found, as we will illustrate here in Part 2.
We are not suggesting that readers disbelieve the data reported in those studies, but we are emphatically pointing out that such data cannot be believed to represent evidence for a safe dose or dose-rate of ionizing radiation.
-- Occupational Exposure :
In 1985, in the British Medical Journal, Beral and co-workers reported on a follow-up of 39,546 atomic power workers in Britain (Ber85). Of these, 20,382 with a radiation record received a mean whole-body exposure of 3.24 cSv (rems), and 19,164 had no record of radiation exposure. The average follow-up time was 16 years for both groups of workers. (These data come from Table 1 and p.441 of Ber85.) We must comment here that 16 years is a rather short follow-up period.
Beral and co-workers clearly acknowledged that their study was inconclusive with respect to excess cancer when they said, in a later version (Ber87, p105); "The findings so far are consistent with there being no increased cancer risk at all, and at the same time, with a risk ten to fifteen times the ICRP figures."
A study which is compatible both with a safe dose, and with no safe dose, is simply incapable of helping to resolve the threshold issue. It would be a real mistake to regard it as relevant evidence.
In an additional report on the UK atomic workers, these investigators add a comment which is highly pertinent to our topic of inconclusive negative studies (Ins87, p.87); "In conclusion, the data presented here illustrate some of the problems encountered in relating the mortality of a workforce to different levels of occupational radiation exposure when the exposures themselves are low, cannot be measured accurately, and have been assessed in different ways over time."
Their statement needs recognition as an appropriate warning that there are some severe limits to what such studies can ever reveal. It is a warning against exaggerated expectations. My own analysis of radiation-induced cancer in the Hanford atomic workers also pointed up some difficulties and inherent limitations of such studies (Go79).
-- Medical Exposure :
The Linos Study :
In 1980, in the New England Journal Of Medicine, Linos and co-workers at the Mayo Clinic authored the report "Low Dose Radiation and Leukemia" (Lin80). They say at the beginning; "No statistically significant increase was found in the risk of developing leukemia after radiation doses of 0 to 300 rads (3 Gy) to the bone marrow when these amounts were administered in small doses over long periods of "time, as in routine medical care."
However, in the conclusion of the same paper they write; "Consequently, we maintain that low levels of exposure to medical radiation most probably did not increase the risk of leukemia in this community, but that if it did, the factor of increase is almost surely less than 2.0."
Linos and colleagues are saying, in short, that the size of their sample and their procedure were of such a design that, even if low-dose medical exposures were nearly doubling the leukemia-rate in a community, their study could have missed the effect. Thus the study is inherently inconclusive on the threshold issue because it is compatible with opposite conclusions (safe dose, no safe dose). Specifics of the paper are discussed in detail elsewhere (Go81, pp. 699-706; Go85, pp.290-291).
The Spengler Study :
Another typical example of an inconclusive negative study, with respect to medical irradiation, appeared in the journal Pediatrics in 1983. By Spengler and co-workers, the paper is "Cancer Mortality Following Cardiac Catheterization; A Preliminary Follow-Up Study of 4,891 Irradiated Children" (Spen83). Its abstract reports that "The preliminary findings did not demonstrate a significant leukemia risk arising from diagnostic catheterization."
Later, near the conclusion, the authors state; "In essence, the size of our cohort is not sufficient to detect accurately a low-dose radiation effect." That is true.
When we checked this out independently, by using our own risk estimates (Go85, p.291-296), we found that the expectation of leukemia without irradiation was 1.88 case, and the expectation with irradiation was 2.07 cases. The observation of leukemia in the irradiated group was 3.0 cases.
Even though the observation slightly exceeded expectations, the difference between 1.88 and 3.0 was not statistically significant under the circumstances. Therefore the Spengler study is a negative study -- "no-effect-found" -- or as its abstract announces, "The preliminary findings did not demonstrate a significant leukemia risk arising from diagnostic catheterization." And none should have been found, unless low-dose radiogenic risk is greater than our own estimates. In terms of the perfect-repair hypothesis, the Spengler Study is just inconclusive.
The Davis Study vs. the Hrubec Study :
In 1987, in the Journal Of The National Cancer Institute (USA), Davis, Boice, Kelsey, and Monson authored the report "Cancer Mortality after Multiple Fluoroscopic Examinations of the Chest" (Davis87). Their paper reports on a previously unstudied group of Massachusetts tuberculosis patients who experienced multiple chest fluoroscopies during pneumothorax therapy between 1930 and 1954.
This study has the potential, if extended, to study fractionated radiation doses for lung cancer and for breast cancer, but in its current state, it can only be regarded as an inconclusive study, compatible either with no safe dose or a safe dose.
We are not going to discuss the lung-cancer aspect of this study at all, due to severe confounding variables. For instance, the authors report only 1/3 of the cancer cases were verifiable, in part because some hospitals were no longer in existence, and records are gone. A real hazard exists for under-diagnosis of lung-cancer in patients with a history of tuberculosis of the lung. Additionally, the authors themselves report their study has a "large number of subjects with incomplete smoking data" and that "it is possible that greater consumption [of cigarettes] among unexposed relative to exposed may have masked any radiation effect for smoking-related cancer sites "(Davis87, p.651).
The results for breast cancer are quite inconclusive for several reasons. Davis et al state; "The SRR [standardized relative risk] for breast cancer mortality was 1.1 (95% C.I. = 0.6-2.1) when we compared the exposed to unexposed groups and controlled for time since exposure and age at exposure" (Davis87, p.649). In other words, the observed excess was not provably significant.
Defects of Davis study as of this time; (a) Only mortality cases are available -- 24 in all for exposed group (only 1/3 verifiable); (b) mortality studies are clearly inferior to incidence studies early in a follow-up (see discussion below) -- even for histologically-verified cases, and (c) average breast-dose is much lower in Davis study than in our Study 3 (this chapter).
We expect that the Davis study will be amplified, that incidence cases will be sought, and that some definitive conclusions will become possible following such additional follow-up research.
In great contrast, in 1989 Hrubec, Boice, Monson, and Rosenstein have reported an extended follow-up of this chapter's Study 3 (to 30.2 years); "Breast Cancer after Multiple Chest Fluoroscopies. Second Follow-Up of Masachusetts Women with Tuberculosis" (Hru89). The search for cases, by incidence and mortality is very much more exhaustive, both in exposed and unexposed women. By now, a total of 74 histologically-verified cases of breast cancer are available for analysis (56 among exposed, and 18 among unexposed, women).
The findings are that the relative risk of breast cancer induction from multiple fluoroscopic exams is even greater than observed in the earlier follow-up (our Study 3). The findings are statistically stronger than before. And over 97% of the individuals have been located, with 63% still living.
The Hrubec study not only confirms and strengthens the excess breast-cancer findings of Study 3, but it is also now showing that the dose-response is supra-linear (a significantly negative coefficient of the quadratic term in an L-Q analysis, p.232).
We are not at all critical of the Davis study. Both the Davis and the Hrubec studies emanate from the investigations of the Boice-Monson group. What is clear is that the Hrubec study is much further along than is the Davis study. Further the Hrubec study has a complement of younger women than does the Davis study, and it is clear that the radiation-sensitivity for breast-cancer is greater in the younger women.
Another point; In the earlier follow-up of the Hrubec cohort (our Study 3) -- in which all 56 cases were histologically confirmed -- those breast-cancers ascertained by incidence showed a strikingly higher association with radiation (Relative Risk) than did those ascertained from mortality, We have calculated the following for those earlier cases (data from Boice81):Mortality cases: Relative risk = (16/9.4) / (8/5.5) = 1.17. Incidence cases: Relative risk = (25/13.9) / (7/8.6) = 2.21.
The lesson is that in the early years of follow-up, the radiation-excess is not nearly so manifest in mortalities as in incidence for breast-cancer in exposed young women. Therefore, we should not be surprised that the Davis Study of mortalities only (and poorly verified at that) provides no conclusive results for breast-cancer.
In terms of the flawless repair hypothesis, the Davis Study is simply another inconclusive study, with confidence limits of 0.6 to 2.1 on the relative risk (Davis87, p.649). Thus it is consistent with both the existence and non-existence of a threshold.
Patients Receiving Diagnostic Radio-Iodine :
We have examined a number of studies in the medical literature which report finding no excess cancer in patients who received radio-iodine (Go81, pp.642-658). We have used our own risk-per-rad estimates to find out how many excess (radiation-induced) cancers should be expected in those negative studies. It turned out that the studies were so small and the follow-up periods were so short that the expectation was a very low fraction of one extra case per study -- a surely undetectable excess.
Instead of being studies where excess cancer should have been detected but was not, these studies turned out to be studies where excess cancer should not have been detected (unless the risk-per-rad were much higher than our own estimates). In other words, the results of the studies were bound to be negative before the studies were ever undertaken.
There is no limit to the number of such studies which can be performed. Even a huge collection of such studies would contribute no weight at all to the argument for a safe dose or dose-rate.
The Holm Study in Sweden :
In Chapter 22, Part 5, a Swedish study of over 35,000 patients who received radio-iodine (Holm88) is examined by us in detail. This study is commonly cited as a study (A) showing no excess thyroid-cancer from the radio-iodine, and (B) showing that slow dose-delivery is less carcinogenic in humans than acute delivery. In reality, this is a study in which a very large excess of thyroid-cancer occurred (relative risk of about 3.9), and from which no conclusions in any direction should be drawn -- for the many reasons shown in Chapter 22, Part 5.
-- Natural Background Radiation :
There have been many studies comparing cancer mortality in regions which have different background doses of natural radiation. We call such studies "Denver-Type" studies because so many Americans must have heard threshold advocates using the refrain, "If there is no safe dose of radiation, why isn't the cancer-rate higher in Denver (Colorado), since Denver has a higher natural background dose than most other places?"
This section will show why one cannot expect high background doses to correlate with high cancer mortality, and low background doses to correlate with low cancer mortality, with any regularity.
Rule 1 -- Signal-to-Noise Ratio :
To test whether or not a study is inherently capable of detecting a cancer-effect from a difference in background radiation, the first thing to check is whether other variables are important enough to confound the results, to conceal the radiation-effect which is supposedly tested.
The cardinal rule is that we should never look for a relatively small carcinogenic effect from low-dose radiation in the presence of massively larger variation in non-radiation effects. Land has appropriately described the essence of this type of problem as a low "signal-to-noise" ratio (Land88, p.269). In a related context, Upton has spoken of "trying to listen to one violin when the whole orchestra is playing. You can't hear it" (Up89, p.418). Failure to detect the signal and the violin does not mean that they are absent.
Non-radon background doses, which vary with altitude and other factors, are roughly in the "ballpark" of 100 millirads per year of whole-body dose, mostly low-LET. Elsewhere I have estimated that, for a U.S. population of mixed ages, one should expect about a l6 % increment in cancer mortality-rate from doubling such exposure (Go81, p.307, pp.566-567; also pp.232-233). The estimate used 1976 age-specific cancer mortality-rates, and would likely be only slightly different if it used the 1986 age-specific rates -- even though the fraction of all deaths which are cancer-deaths has risen, from about 17 % in 1976, to about 22 % in 1986 (Silver90, p.12).
In terms of the signal-to-noise problem, one can regard the estimated 16 % elevation in cancer mortality per additional 100 millirads as the signal. The question is; Should this signal be detectable, despite the noise of variations in cancer mortality which are unrelated to low-LET radiation? Later in this part, we will demonstrate that this signal is fully compatible with the observation of below-normal cancer mortality, normal cancer mortality, and above-normal cancer mortality.
Rule 2 -- Comparability of Populations :
Another cardinal rule, directly related to the first one, has been discussed already in connection with the A-Bomb Study; One should be very careful about drawing conclusions about radiation carcinogenesis from comparisons of cancer-rates in various groups, unless there is a good basis for confidence that the underlying non-radiation cancer-rates -- the so-called spontaneous rates -- are alike (Chapters 11 and 12). Unless groups are equivalent, or can be rendered equivalent, in all the important variables which determine the non-radiation-induced cancer-rate, such groups certainly cannot be used to study the effect of small radiation doses on cancer-rate. Moreover, until better ways develop to quantify radon exposure and its carcinogenicity, radon alone is sufficient to confound "Denver-Type" studies. In what follows, we used measured exposures from the literature, but we know that ostensibly equal doses may really be different. This would not alter the point.
Two "Denver-Type" Studies :
In 1976, Frigerio and co-workers compared the average natural background dose in all 50 states of the USA with the Vital Statistics on cancer death-rates per state (Frig76). One of their findings was that the cancer death-rate was lowest in the fourteen states with the highest natural background radiation. However, the fourteen states with the lowest natural background radiation did not have the highest cancer death-rate. The twenty-two states with the intermediate background doses had the highest cancer death-rate. In other words, the relationship was irregular (Go81, 567-70).
This should surprise no one. Data in their Figure 1 demonstrate that in 10 states where Frigerio and Stowe report the same average yearly background dose of 135 millirems / year, the annual cancer mortality ranged from 125 up to 170 per 100,000. Thus the highest cancer-rate is some 36 % higher than the lowest rate, without there being any difference at all in average background dose. This very large variation in the non-radiation cancer-rate is the "noise" in the signal-to-noise ratio. I concluded that such a study is inherently incapable of testing whether or not background doses affect cancer death-rates in the general population, in either direction. The BEIR-3 Committee also reached the same conclusion (Beir80, pp.469-471).
In 1981, in Health Physics, a similar study appeared by Hickey and co-workers (Hic81). The authors claim in their abstract (Hic81, p.625) that their work "suggests that models implying important long-term deleterious effects of low-levels of ionizing radiation on humans may be invalid," and they claim again in their conclusions (Hic81, p.635) that their negative bi-variate correlations -- the two variables being cancer-rate and background dose of radiation -- "are not compatible with models that assert that all levels of radiation, no matter how low, are damaging." We will demonstrate, in the section entitled "Demonstration," that such findings are fully compatible with there being no safe dose. But first, we have other observations to make.
The statistical work in the Hickey paper confirms what can be shown far more directly below; The background dose of radiation is a small signal, compared with the noise from other factors which cause variation in the cancer-rate. In the Hickey study, 43 metropolitan areas of the USA were included, of which ten are southern (lying below the latitude of 36 degrees) and ten are in the northeast. When Hickey's data are tabulated by regions, as they are below, we discover immediately that confounding variables are having the dominant impact on cancer-rates:South & All Areas except North- South Northeast East NATURAL BACKGROUND DOSE 85.10 87.17 87.29 (Millirems per year) ANNUAL CANCER DEATH-RATE 131.54 150.86 185.04 PER 100,000 (1961-1964)
What is obvious from the tabulation is that cancer death-rates vary enormously at the same average background dose -- the Frigerio "story" all over again. Cancer-rates for those years were 41 % higher in the ten northeastern areas than in the ten southern areas even though the background radiation exposures were almost identical.
The Frigerio and Hickey studies, and others like them, are not capable of addressing the threshold question because it is evident that something other than background exposure is causing big differences in cancer-mortality. When cancer-mortality varies by 36 % or 41 % at the same background dose, whatever the non-radiation causes of the variation may be, those non-radiation causes are clearly important enough to confound a much smaller radiation effect (see "Demonstration" section).
Comparison of "Denver-Type" Studies with the A-Bomb Study :
In the A-Bomb Study, after normalization for age and sex differences across the Dose-Groups, we were able to have confidence that all Dose-Groups shared a closely similar underlying rate of spontaneous cancer, unrelated to their exposures to bomb radiation. In Chapter 4, we mentioned the fact that one of the study's most important scientific virtues is the fact that it provides its own internal reference group.
In sharp contrast with the A-Bomb Study, the "Denver-Type" studies are looking for an effect of small differences in radiation dose upon groups of people, in different regions, who are not alike in variables other than radiation dose. Indeed, by comparing cancer-rates in groups in different regions who receive the same background doses, we ascertain that the underlying non-radiation-induced cancer-rates are far from uniform in all regions.
So the fatal flaw of the "Denver-Type" studies is that they lack any way to know or to achieve the crucial comparability of the non-radiation cancer-rates across dose-groups (the dose-groups being the populations in different regions with different background doses), and yet because of their very low signal-to-noise ratio, they need to be superior to other studies on matching those underlying rates.
A Demonstration with Realistic Numbers :
Notwithstanding the fallacy of addressing the threshold issue with "Denver-Type" studies, such studies are often mentioned as evidence in favor of a safe dose or dose-rate (for instance, see Webs87, p.425; Alex88b, p.592-593; Sag89, p.574).
Therefore, we think it is worthwhile to use some realistic numbers to demonstrate exactly how an elevated natural background dose -- actively inducing extra cancer in the population -- is fully compatible with observation of cancer-rates which are below expectation, normal, and above expectation.
First, we have already shown with Hickey's own data that great variation exists from one region to another in cancer mortality, with rates 41 % greater in one region than in another region, when the background radiation dose is the same.
Second, we need to remember that cancer mortality consists of two parts; Non-radiation-induced, and radiation-induced. As stated above, my estimate is that a yearly dose of 0.1 rad per year (100 millirads per year) is expected to increase cancer-mortality by approximately 16 % over the non-radiation rate.
Third, we can use the approximation that about 17 % of all deaths were cancer-deaths in the United States, when the Frigerio and Hickey studies were done.
We can let x = the non-radiation-induced part of the cancer death-rate, and we can let the average background dose be 0.1 rad per year.
Then, total cancer-rate = x + (0.16)(x) = 17 percent.
Or, we can say (1.16)(x) = 17 percent, and x = 14.7 percent.
But we showed above that some places have non-radiation cancer death-rates much above normal, and some have such rates well below normal -- all occurring at the same average natural dose of ionizing radiation. Let us consider three possible regions, where the non-radiation-induced cancer-rates are as follows, instead of the normal 14.7 % :Region Considered Non-Radiogenic Cancer-Rate A 11.7 % B 12.7 % C 16.7 %
Let us also suppose that measurements show background radiation to be twice the average of 0.1 rad per year, namely 0.2 rad per year, in all three regions. The numbers below demonstrate that under these circumstances, despite the doubled background dose -- alike in all three regions -- analysts will observe one cancer-rate below normal, one rate normal, and one rate above normal.
If the elevated natural background dose of 0.2 rad is actively inducing extra cancer in the population, with an increment of 16 % for each 0.1 rad, we would have the following radiation-induced cancer death-rates (0.32 times the non-radiation cancer-rate):Region Radiation-Induced Ca-Rate ( % ) Considered A 0.32 x 11.7 % = 3.74 % B 0.32 x 12.7 % = 4.06 % C 0.32 x 16.7 % = 5.34 %
And the observed cancer death-rates would be as follows:Region OBSERVED Ca-Rate ( % ) Considered (Spontaneous + Radiogenic) A 11.7 % + 3.74 % = 15.44 % B 12.7 % + 4.06 % = 16.76 % C 16.7 % + 5.34 % = 22.04 %
It is self-evident that Region A would have a cancer mortality rate below the normal 17 percent. Region B's rate would look normal. Region C's rate would be above normal. Using a risk-increment per 0.1 rad (100 millirads) which we think is realistic, we have just demonstrated (in Regions A and B) how carcinogenesis at very low doses is fully compatible with finding cancer-rates below normal, or not above normal, in "Denver-Type" studies. Such findings lie within expectations, in our scenario, because of differences in the underlying non-radiation-induced cancer-rates.
In our scenario, if people failed to consider the fact that non-radiation cancer-rates differ markedly from one region to another, and if they carelessly assumed that such rates were the same everywhere, then some of them might even "interpret" the observed cancer-rate in Region A as evidence that an extra dose of 100 millirads per year is "protective" against cancer if you live in Region A . . . although the same dose is "without any effect" in Region B . . . notwithstanding the observation that the same dose is "extremely carcinogenic" if you live in Region C.
This would be nonsense. No one would be entitled to draw any of those conclusions from such a study. The assumption, that the underlying non-radiation-induced cancer-rates are the same in all three regions, is unjustified. Yet no one would have a believable way of finding out the three non-radiation rates which were associated with each of the three observed rates. (We "know" the underlying non-radiation-induced cancer-rates in Regions A, B, and C only because we wrote the scenario.) Therefore, no one could evaluate the possible contribution from the radiation to the observed rates.
And that is the fatal flaw, in "Denver-Type" studies. Such studies are just inconclusive, and will remain so.
The Proper Exclusion of Inconclusive Studies :
Our Table 21-A included none of the "no-effect-found" studies described above. The purpose of Part 2 has been to show why they are properly excluded from any true effort to resolve the safe-dose issue.
We pointed out that studies which are consistent with both the existence and non-existence of a threshold are irrelevant. They cannot contribute to the weight of the evidence, in either direction.
For instance, in our medical examples above, when Spengler and co-workers said, "In essence, the size of our cohort is not sufficient to detect accurately a low-dose radiation effect," they were saying that absence of a provable excess of leukemia in their study was within expectations.
The absence of a radiation effect in that study presented no mystery, no puzzle, and no challenge to the thesis that there is no safe dose or dose-rate. The Spengler Study is just another inconclusive study which is unable to address the threshold issue at all.
"A Myth with Every Shot" :
There will never be any shortage of inconclusive "no-effect-found" studies about ionizing radiation which people can cite. In fact, such studies could be designed in an infinite number if the sponsorship were to be sufficiently generous. I am reminded of a classic statement on the subject by F.A. Harper (Harpe57, p.537), a genuine free-market economist and expositor of liberty and harmony:
"As to the number of forms myths can take, consider the possible answers to 2 plus 2. The only non-mythical answer is 4. But there are infinite mythical answers . . . So if [a person's] aim were perfect and he could shoot a myth with every shot, he could spend his entire lifetime shooting myths released by only one myth factory, without ever demolishing all this factory could produce."
There is no scientific obligation to shoot at myths, or to discuss the limits of every inconclusive study. In Chapter 22, Part 5, readers will see the length sometimes required to discuss just one inconclusive study (Holm88) with appropriate thoroughness.
The samples discussed above are sufficient to illustrate the characteristics of studies which are inconclusive with respect to the threshold issue, and to show why such studies are properly excluded from any genuine effort to settle the question of a safe dose or dose-rate.3. Decisive Evidence on a Threshold :
Types and Supply
"Proof" or "disproof" in the biomedical sciences is unlike possible proof and disproof in mathematics or logic, where some proofs may be claimed to be final. In the empirical sciences, proof is always a provisional matter, pending contrary evidence of an appropriate nature and amount.
We have repeatedly said in Chapter 18 that the evidence in Table 21-A amounts to disproof of any safe dose or dose-rate, by any reasonable standard. And if a series of decisive studies were to develop in which no excess cancer was observed, when it clearly should have been observed, we would certainly not reach the same conclusion as we do now. In other words, we are not trying to evade the meaning of such evidence, if it should develop. On the contrary. We would welcome it. We take no pleasure in reporting bad news for human health.
But when the news is bad -- and Table 21-A shows that it is -- then human health is far better protected by facing reality than by ignoring it.
Thus we are critical of the 1988 UNSCEAR Report for appearing to ignore the implications of the studies in Table 21-A with regard to the threshold issue. Although all the studies except one were available, UNSCEAR-88 offers no analysis of the rate of primary ionization tracks per nucleus associated with the doses in those studies. It offers no hint that the positive cancer-excesses in those studies occurred from approximately the lowest conceivable doses and dose-rates in the cell-nuclei. It offers no acknowledgment that these human studies can address the hypothesis of flawless repair and safe doses and dose-rates.
We wish that UNSCEAR-88 had addressed these matters, because current speculations about safe doses and dose-rates have profound implications for human health (Chapters 24 and 25).
The Decisive Nature of Table 21-A :
As we showed in Part 2 of this chapter, our Table 21-A properly excludes studies which are inconclusive. Studies which are consistent with both the existence and non-existence of a safe dose are irrelevant here.
By contrast, the nine studies which qualify for Table 21-A are highly relevant because they are not consistent with both positive and negative answers.
The results of these studies do not lie within threshold-expectations, because these are studies of human response to just about the Least Possible Disturbance from ionizing radiation. If a threshold is supposed to show up if the dose or dose-rate is just "low enough," how can one explain the observation that excess cancer is what shows up in nine separate human studies, even when the average dose-rate is only a few primary ionization tracks per cell-nucleus? The combined weight of these nine studies is consistent with only one answer; There is no flawless repair and no safe dose or dose-rate with respect to radiogenic cancer.
So the crucial distinction between decisive evidence and inconclusive evidence is this; Decisive studies are consistent with only one answer to a question, and inconclusive studies are consistent with both positive and negative answers.
Reliance on Human Epidemiology :
Our disproof of the existence of any safe dose or dose-rate, with respect to human cancer-induction, relies exclusively on human epidemiological evidence, with the exception of cell-studies which we used for establishing the capacity for, and speed of, repair of radiation-induced lesions in DNA and chromosomes.
Our reliance on human epidemiological evidence is not a casual choice. It is by definite preference.
Everyone recognizes that evidence from other species can mislead us about humans, and that the same potential irrelevance surrounds evidence from in-vitro cell-studies. This is no denigration of those studies. It is just an acknowledgment that observations of real, whole humans are the only credible reality-check on ideas about how human beings "should" respond to low doses and irreducible dose-rates of ionizing radiation. The reality-check tells us how humans actually do respond.
We readily acknowledge that single epidemiological studies can be flawed, just as laboratory experiments can be flawed, and mistaken conclusions can be drawn. For instance, an elevated cancer-rate can be falsely attributed to radiation, if the compared groups are not sufficiently comparable in their spontaneous cancer-rates (the "Denver-Type" fallacy). In other words, a proper worry in epidemiology is that causation will be falsely inferred if some confounding variables -- which really explain the observations -- were not identified. In addition, it is inevitable that in any large body of studies, some statistical "flukes" will occur -- studies in which a highly significant result is nonetheless false. But experimental studies, with irradiated cells and irradiated animals of other species, also suffer from occasional statistical "flukes," and they suffer enormously from confounding variables with respect to the response of real, whole humans.
Although we remain appropriately skeptical about single epidemiological studies, the nine epidemiological studies in Table 21-A reinforce and support each other, with features which make it reasonable to regard them as conclusive.
Basis for Confidence in the 9 Studies :
With respect to radiation as the cause of the excess cancer, readers will note that Table 21-A has five separate studies of excess breast-cancer in women. In addition to those five studies, excess breast-cancer is observed in the women of Hiroshima and Nagasaki, from their single acute exposure, in Swedish women irradiated for various benign breast lesions at the Radiumhemmet (Bara77) and in women irradiated for acute post-partum mastitis (Sho77; Sho86), both with some fractionation of dose, but not nearly so much fractionation as in the case of the fluoroscoped women. So, the epidemiologic studies available on radiation-induction of breast-cancer encompass virtually all the possible dose-rates and total doses. Moreover, the radiation sources include medical X-rays, A-bomb radiation, and gamma rays from radium-226 and daughters. In the aggregate, the case for causation is overwhelming.
In the studies -- singly -- of course there are bound to be some differences between the exposed and unexposed groups which will make the carcinogenic effect look bigger than it really is in some studies, and smaller than it really is in other studies. However, in studying the threshold issue, it is not necessary to know the exact magnitude of the effect. As long as the excess is real, the excess shows that repair-systems did not un-do all the carcinogenic damage flawlessly.
The breast-cancer studies are outstanding for their power. Four separate studies provide evidence of excess cancer after a large total dose was given in a series of very small doses, with the small doses well enough separated in time that any repair which could operate has had an abundant opportunity to operate. These circumstances provide the best feature of high-dose studies -- namely large, clear results in terms of excess breast-cancers -- while still having the necessary features of low-dose studies with respect to the repair (threshold) issue. Thus analysts are not confronted by the usual problem at low doses; Small numbers of radiation-induced cancers against a background of large numbers of spontaneous cancers -- the low signal-to-noise ratio.
With the recent addition of breast-cancer evidence from the Israeli Scalp-Irradiation Study -- evidence gained from a single low total dose -- we have broadened the range of coverage to include females in the 5-15 year age-group at the time of their irradiation.
Three of the nine studies in our disproof of any safe dose or dose-rate are studies of in-utero irradiation at exceedingly low total doses of radiation, with a large effect in terms of excess cancers produced. Having three studies which mutually reinforce each other strengthens confidence in the meaning of each, and disposes of "third factor" ideas beyond a reasonable doubt.
It is possible that an important feature of the in-utero studies is that -- because they deal with children -- the studies are spared from many of the confounding variables which characterize radiation-studies of older groups. The focus on childhood cancers and leukemias means that the chance for non-radiation sources of cancer-induction to muddy the studies is reduced, because the studies can already become definitive in a single decade between exposure and cancer occurrence. Moreover, the greater radiation-sensitivity of the young makes for a larger excess than would be the case for older groups. Both features would tend to promote a favorable signal-to-noise ratio.
Lastly, in the Israeli Study, we now have two separate types of cancer induced -- thyroid and breast -- in a single large group of individuals, so that consistency of results is available to be checked. At this time, the consistency appears quite reasonable. The subjects should certainly be available for further follow-up, and therefore, the results, however they turn out, should not lack for adequate numbers of cases.
It is the combination of all these features which gives us full confidence that these nine studies are not aberrant or misleading. By any reasonable standard of evidence, their meaning is solid with respect to the threshold issue.
Epidemiology plus Track-Evaluation :
In recent years, it has been fashionable to suggest that epidemiologic investigations cannot usefully address the low-dose radiation question (e.g., Beir80, pp.22-23). The epidemiologic studies described here make it apparent that this is incorrect.
The effective use of case-control investigations, as in the in-utero studies, indicates that it is possible to overcome the difficulty of low cancer-rates. And the technique of "converting" high-dose studies to low-dose studies, as in the four breast-cancer investigations, permits having the large yield of cancers from a high-dose study while still providing full opportunity for any low-dose repair-mechanisms to prove their existence.
When the effort is made to evaluate the doses in such studies, in terms of tracks-per-nucleus, then it becomes evident that studies whose doses are not "next-to-zero" are nonetheless studies of truly minimal doses and dose-rates.
We suspect that, in terms of low-dose radiation questions, there must exist further opportunities of great value in still uninvestigated epidemiologic settings.
The "Not Proved in Peoria" Response :
The real-world, epidemiological evidence against any safe dose or dose-rate, summarized in Table 21-A, includes adults, children, high-energy gamma rays, diagnostic X-rays, acute single doses, and slow (chronic) occupational delivery. The average number of tracks per nucleus from each exposure was only 10-12 in the two studies with the highest track-rate. In five of the nine studies, the average track-rate was only 0.2937 up to 2.140. The observation of radiation-induced cancer in these studies is not compatible with the hypothesis that repair-systems un-do all carcinogenic damage, provided that the dose is sufficiently low and slow.
In the face of the evidence from Chapters 18 through 21, we anticipate that threshold proponents may demand that disproof of a threshold be made separately for each of over 100 sub-sets of cancer. Such a demand would be equivalent to saying, "So you've proven that the law of gravity is correct in Dallas, Texas, and in eight additional cities, but we don't accept that it is correct for Peoria, Illinois, until you prove it in Peoria specifically."
This position, which can be called "Not Proved in Peoria" or just "Peoria!" for short, has been the response to unwelcome evidence on a related issue (see Chapter 22). Therefore we anticipate it on the threshold issue, too.
We regard "Peoria!" as a scientifically inappropriate position, for the reasons below.
Scientists never have comprehensive data. We always are extending observations from a limited set of data and applying them to more general situations -- and the presumption of applicability is the reasonable presumption, in the absence of contrary evidence or logic. Indeed, when analysts refuse to do this and when they prefer sheer speculation to reasonable presumption grounded in evidence, then it may be a sign that objectivity has yielded to some sort of bias.
The radiation-inducibility of human cancer is now proven for most of the major sites of cancer-mortality, and also for many of the minor sites (Go85, pp.18-19). UNSCEAR is acknowledging it too; "It now appears that most (indeed, probably all) organs are vulnerable to radiation-induced cancer, given the right conditions of exposure" (Un88, p.460, para.394).
Here, then, we have a wide variety of cell-types which all display the same response to ionizing radiation, namely an excess of cancer above its spontaneous frequency. So the evidence demonstrates that, regardless of cell-type, there is a unity in the way human cells respond to ionizing radiation.
If this response were the only evidence at hand, and if there were no evidence available on the threshold-issue, it would be hard to find any scientist predicting, "When we get the evidence about the threshold-issue, it will turn out that some cell-types have a threshold and others do not." On the contrary. In view of the identical response of all cell-types to the agent (ionization tracks), the presumption would necessarily favor the same behavior by all cell-types on the threshold-issue. Most scientists understand the law of minimum hypotheses.
Additional Bases for Generalizing :
Now evidence on the threshold-issue does exist, and where it exists (childhood cancers, breast-cancer, thyroid-cancer), it shows that the threshold is provably absent. It would not be scientifically reasonable to presume that some cell-types have a threshold, when the threshold is provably absent where evidence does exist. The scientifically reasonable presumption clearly is that a threshold is absent in other cell-types also.
This presumption is further strengthened by related evidence, such as the evidence for a linear or supra-linear dose-response not only for breast-cancer and thyroid-cancer, but for all types of cancer in the aggregate (see Chapter 14), by strong evidence linking cancer with aberrations in DNA and chromosomal material, and by the evidence on the nature of radiation's interaction with cells regardless of their particular type (Chapter 19).
We do not overlook the fact that five of the nine decisive studies, in the disproof of any safe dose or dose-rate, are of breast-cancer. This fact increases the strength of the finding, because the evidence is arising from one of the two most serious and prominent cancers in women. Breast-cancer accounts for about 20 % of all their cancer mortality in the United States. Under the circumstances, it would be unthinkable to regard the disproof as limited to some rare type of cancer. With respect to the no-threshold finding, it is fully reasonable to generalize from one of the most common cancer-sites to all cancer-sites.
=========================================================================== | Col.A Col.B | ( Col.A times Col.B )| | | | |Number Tracks- | | |Assigned Rads per- | Average Number of | |in the per Nucleus | Tracks-per-Nucleus | |Text Exposure at 1 Rad | from Each Exposure | | | | |=========================================================================| |1. Nova Scotia 7.5 1.3378 | 10.0335 10 | | Fluoroscopy | Rounded | |=========================================================================| |2. Israeli Scalp- 7.5 1.3378 | 10.0335 10 | | Irradiation | Rounded | | (Authors' revised est.) 9.0 1.3378 | 12.0402 12 | | | Rounded | |=========================================================================| |3. Massachusetts 4.6 1.3378 | 6.1539 6 | | Fluoroscopy | Rounded | |=========================================================================| |4. Canadian 4.6 1.3378 | 6.1539 6 | | Fluoroscopy | Rounded | | (Excludes Nova Scotia) | | |=========================================================================| |5. Stewart In-Utero 0.5 1.3378 | 0.6689 < One | | Series | | | | 51 % with | | | no track. | |=========================================================================| |6. MacMahon In-Utero 0.9 1.3378 | 1.2040 ~ One | | Series | | |=========================================================================| |7. British Luminizers 0.1 2.9370 | 0.2937 < One | | | | | | 75 % with | | | no track. | |=========================================================================| |8. Harvey Twins 1.0 1.3378 | 1.3378 ~ One | | In-Utero Series | | | | | |=========================================================================| |9. Israeli Breast-Cancer 1.6 1.3378 | 2.140 ~ 2 | | in Scalp-Irradiation Study | | ===========================================================================
For 30 KeV X-rays: The Stewart In-Utero Study
Mean number of TRACKS = 0.6689 TRACKS per cell-nucleus.
Question: How many nuclei will get 0,1,2,3,4,5,6,7,8 TRACKS?
0.512272 PROBABILITY OF EXACTLY ZERO TRACKS PER CELL-NUCLEUS
0.342659 PROBABILITY OF EXACTLY ONE TRACK PER CELL-NUCLEUS
0.114602 PROBABILITY OF EXACTLY TWO TRACKS PER CELL-NUCLEUS
0.025552 PROBABILITY OF EXACTLY THREE TRACKS PER CELL-NUCLEUS
0.004273 PROBABILITY OF EXACTLY FOUR TRACKS PER CELL-NUCLEUS
0.000572 PROBABILITY OF EXACTLY FIVE TRACKS PER CELL-NUCLEUS
0.000064 PROBABILITY OF EXACTLY SIX TRACKS PER CELL-NUCLEUS
0.000006 PROBABILITY OF EXACTLY SEVEN TRACKS PER CELL-NUCLEUS
0.0000005 PROBABILITY OF EXACTLY EIGHT TRACKS PER CELL-NUCLEUS
0.999999 SUM OF ALL THE ABOVE PROBABILITIES
0.855 or 85.5 percent of nuclei receive either the Least Possible Disturbance (a single track) or no track at all, per exposure.
For Radium-226 and daughters: The British Luminizer Series.
Mean number of TRACKS = 0.2937 TRACKS per cell-nucleus.
Question: How many nuclei will get 0,1,2,3,4,5 TRACKS?
0.745500 PROBABILITY OF EXACTLY ZERO TRACKS PER CELL-NUCLEUS
0.218953 PROBABILITY OF EXACTLY ONE TRACK PER CELL-NUCLEUS
0.032153 PROBABILITY OF EXACTLY TWO TRACKS PER CELL-NUCLEUS
0.003148 PROBABILITY OF EXACTLY THREE TRACKS PER CELL-NUCLEUS
0.000231 PROBABILITY OF EXACTLY FOUR TRACKS PER CELL-NUCLEUS
0.000013 PROBABILITY OF EXACTLY FIVE TRACKS PER CELL-NUCLEUS
0.999999 SUM OF ALL THE ABOVE PROBABILITIES
Since the probability of more than five events (tracks) is so low, it is reasonable to refer to two-to-five events as "two or more".
0.9644 or 96.4 percent of nuclei receive either the Least Possible Disturbance (a single track) or no track at all, per exposure.
Additional tables in Chapter 20
provide additional Poisson distributions.