Low-Dose Cancer-Yields by the Cancer-Rate Ratio Method,
for the A-Bomb Survivors and for a United States' Population
This chapter is arranged in six parts:
Minimum Fatal Cancer-Yield for the A-Bomb Survivors, p.1 Lifetime Fatal Cancer-Yield for the A-Bomb Survivors, p.1 Lifetime Fatal Cancer-Yield for a USA Population, p.2 Comparison of Results, This Method versus the Cancer Difference Method, p.3 Merits and Pitfalls of the Methods, p.4 The Bottom Line from the Cancer-Rate Ratio Method, p.4
Then tables.
1. Minimum Fatal Cancer-Yield for the A-Bomb Survivors
The K-values provided by the A-Bomb Study represent the fractional increase in the spontaneous cancer death-rate per centi-sievert (or per rem) of whole-body internal organ-dose -- for a specific period of observation. Our "in-the-box" low-dose K-values come from observations in the 1950-1982 period. As usual, the Reference Group (1+2) is regarded as unexposed, and cancer death-rates are the cumulative rates among a set of initial persons.
To illustrate how the low-dose K-values in Table 15-L convert into Minimum Fatal Cancer-Yields, we can ask this question, which uses numbers from Table 11-E, Entries F72 and N72:
If 38 cancers occurred spontaneously in the time-period 1950-1982 among a set of 6,935 unexposed children at Hiroshima and Nagasaki, how many radiation-induced cancers must have occurred during the same period in a comparable group of 6,935 children exposed to 1 cSv of whole-body organ-dose? The low-dose K-value from Table 15-L enables us to calculate directly what that number of radiation-induce cancers must have been.
Persons = 6935 Cancers = 38K-Value, T65DR Dosimetry = 0.04615If 38 cancers occurred without radiation exposure, and if K is 0.04615 per centi-sievert (rem) of exposure, we multiply (38) by (0.04615) to ascertain the radiation-induced increment in cancers for 1950-1982 per centi-sievert. This yields 1.7537 cancers among 6,935 initial persons each exposed to one cSv (rem).
And 1.75 is the entry found in Table 16-B, Column G, for the youngest age-band of females. Table 16-A provides the customary details about Table 16-B (where space was insufficient).
Calculations comparable to the one just illustrated provide the additional entries in Column G, for the other 9 age-sex subsets. For the period 1950-1982, the sum from all ten subsets is 29.59 radiation-induced cancers per 66,028 initial persons each exposed to an average whole-body organ-dose of 1 cSv (rem). When this rate is converted (in the next row) to the equivalent rate per 10,000 persons, it becomes the Minimum Fatal Cancer-Yield, prior to the adjustment for under- ascertainment of cancer-deaths -- which is shown on the next row.
The final Minimum Fatal Cancer-Yield in the T65DR dosimetry, by the Cancer-Rate Ratio Method, is 5.51 "in-the-box." The corresponding value from a "constant-cohort, dual-dosimetry" analysis yields 5.17 in the current version of the DS86 dosimetry.
2. Lifetime Fatal Cancer-Yield for the A-Bomb Survivors
The Necessity of Making Assumptions :
Every estimate of a Lifetime Fatal Cancer-Yield incorporates assumptions, by one analyst or another (or by some committee), about what future follow-ups will show in the A-Bomb Study. Estimates which we make by the Cancer-Rate Ratio Method incorporate two assumptions.
Spontaneous Rate: We are assuming that the lifetime follow-up will show a spontaneous cancer-rate in the Reference Group which is close to our estimate of 14.5 percent (from Table 28-D, entry G13).
Constant K-Values: We are assuming that the low-dose K-values observed from the 1950-1982 evidence will persist at about their same magnitude in the additional observations beyond 1982. The best available evidence on duration would justify no other assumption at this time, in my opinion (Chapter 17). Indeed, RERF analysts seem to have reached the same conclusion, for they project their own current risk-coefficients into the remainder of the follow-up when they make their lifetime estimates (TR-9-87, p.34, and TR-5-88, p.50+53; current risk-coefficients in the latter report explicitly exclude the 1950-1955 data, p.50).
In assuming constant K-values, all of us realize, of course, that the best available evidence is just the best available evidence in science, and that subsequent observations are "entitled" to change the story.
The Method for Obtaining Lifetime Fatal Cancer-Yields :
Table 16-A, Note 7 onward, explains the method step-by-step. We just apply the low-dose K-values, which are valid for 1950-1982, to the estimated number of spontaneous cancers expected to occur ultimately in each subset of the Reference Group, and then sum those contributions. The result is adjusted to the denominator of 10,000 persons, and then adjusted by the BEIR-RERF underascertainment factor, and "that is that."
The final best estimate is 31.65 in the T65DR dosimetry, and 30.43 in the current version of the DS86 dosimetry.
The Role of the Youngest Age-Band :
Inspection of Table 16-B, Columns G and J, shows what a trivial contribution is made by the youngest age-band to the minimum Fatal Cancer-Yield. In the T65DR dosimetry, for instance, the share is only (1.25 from the males + 1.75 from the females), or 3 out of the total of 29.59 (Column G). This low contribution, in spite of the higher K-values in this age-band, comes from the very low spontaneous rates in the youngest age-band during the 1950-1982 follow-up period, compared with every other age-band (Column D).
By contrast, inspection of Columns H and K shows what a very big contribution is made by the youngest age-band to the estimated lifetime Fatal Cancer-Yield. In the T65DR dosimetry, for instance, the share is (54.79 from the males + 39.21 from the females), or 94 out of the total of 169.91 (Column H). This result comes not from an extraordinarily high lifetime spontaneous rate (indeed, Column E shows a somewhat lower estimate for the ultimate lifetime spontaneous rate in this age-band). This shift from a trivial role to a dominant role comes from the combination of a spontaneous cancer "story" which has hardly even begun for this age-band during the 1950-1982 follow-up period, with the relatively high K-values for this same age-band.
Cancer-Yield as Percent Increase per Rad :
A Lifetime Fatal Cancer-Yield can be easily converted to "percent increase in the spontaneous cancer death-rate per cSv."
For instance, our estimates in Table 16-B are based on the estimate that 14.47 % of the LSS mixed-age population sample will die of spontaneous cancer (Table 29-D, entry G13). Out of each 10,000 initial persons, the estimated spontaneous cancer deaths will be 1,447. Table 16-B estimates that about 31 additional cases will occur per cSv of whole-body internal organ-dose, per 10,000 initial persons.
Thus, for this particular mixed-age group of persons, the percent increase in the lifetime spontaneous rate is (31 / 1,447) x (100), or 2.14 % per cSv.
In principle, the conversion is clearly easy. In reality, it is often hard to ascertain the post-irradiation lifetime spontaneous rate which was assumed in someone else's analysis. For some limited purposes, a "ball-park" spontaneous rate for a mixed-age population may suffice.
3. Lifetime Fatal Cancer-Yield for a USA Population
The Cancer-Rate Ratio Method makes it self-evident that the relative distribution of ages and sexes in an irradiated population will affect the population's Minimum and Lifetime Fatal Cancer-Yields. The minimum (or interim) values will come predominantly from the older and less sensitive age-bands, and increments to the minimum values will come predominantly from the younger and more sensitive age-bands.
There is no reason to assume that the age-sex distribution in the Reference Group of the A-Bomb Study is comparable to the age-sex distribution in the current United States population; indeed, we know that the distributions differ. Therefore, we want to provide a Cancer-Yield which is appropriate for the United States.
We can provide a lifetime Fatal Cancer-Yield for the U.S. population if we make just one reasonable approximation. We will say that the fractional increase in the spontaneous cancer death-rate will be the same for humans here as for humans there, per centi-sievert of exposure.
Table 16-C provides both the input and output for the estimate.
The best lifetime estimate is 26.64 in the T65DR dosimetry, and 25.56 in the current version of the DS86 dosimetry. These lifetime estimates are somewhat lower for the U.S. population than the A-bomb survivors, even though we have estimated that the A-bomb survivors will have the lower ultimate spontaneous cancer-rate (see Note 3, Table 16-C).
The explanation is no mystery, however. Table 28-D, Column E, shows that in the normalized Reference Group, 24626.32 out of 66028.01 initial persons are in the two youngest and most radio-sensitive age-bands at the time of exposure. This share is 37.3 percent. By contrast, Table 16-C, Column C, shows a lower percentage in the United States' population: 3,169 out of 10,000 persons, or 31.7 percent. In addition, the USA population has a higher percentage of males than the normalized Reference Group -- 49 percent versus 42 percent -- and males have generally lower K-values than females (so far).
The estimates in Table 16-C are not new iterations, revisions, or replacements of my earlier estimate of 37.71. See Table 16-C, Note 7.
4. Comparison of Results, This Method vs. Cancer Difference Method
Minimum Fatal Cancer-Yields :
How do the Minimum Fatal Cancer-Yields derived by the Cancer-Rate Ratio Method compare with the values derived by the Cancer Difference Method with the best-fit curve? The values below come from Table 14-A, Row 2, and from Table 16-B:
T65DR: Cancer Difference = 5.80 fatal cancers/cSv
T65DR: Cancer-Rate Ratio = 5.51 fatal cancers/cSvDS86: Cancer Difference = 5.41 fatal cancers/cSv
DS86: Cancer-Rate Ratio = 5.17 fatal cancers/ cSvThe two methods produce closely similar answers, although the methods appear to be quite different.
One method kept the observations combined for all ages and sexes, subtracted the best-fit cancer-rates at zero-dose from the best-fit cancer-rates at 5 cSv, and divided the answer by five.
The other method subdivided the same observations into ten age-sex subsets, and for each subset of observations, derived an equation of best fit, based on observations exclusively from that subset together with the common dose-exponent of 0.75. Then it used the equation to predict best-fit points at zero-dose and 5 cSv, used those two points to derive a low-dose K-value (fractional increase in the spontaneous cancer-rate per cSv), applied the K-value to the corresponding number of spontaneous cancers in the subdivided Reference Group to obtain the radiation-induced increment from a dose of one cSv, and obtained the Minimum Fatal Cancer-Yield by adding up the increments expected from each of the ten subsets.
In spite of the difference in method, if computational errors are absent, one should expect good agreement when two valid but different approaches are made to exactly the same set of observations. When the observations are "in-the-box," the residual uncertainty lies in sampling variation, which could work in either direction -- either to underestimate or to overestimate the true value.
Lifetime Fatal Cancer-Yields :
How do the findings for lifetime Fatal Cancer-Yields compare in the two methods?
T65DR: Cancer Difference = 12.90 fatal cancers/cSv
T65DR: Cancer-Rate Ratio = 31.65 fatal cancers/cSvDS86: Cancer Difference = 12.03 fatal cancers/cSv
DS86: Cancer-Rate Ratio = 30.43 fatal cancers/cSvIt was predictable that the Cancer Difference Method would give much lower values for the lifetime Cancer-Yields than does the Cancer-Rate Ratio Method. The reason is that every estimate of lifetime values necessarily uses assumptions and approximations to fill in for the missing observations, and the two methods use one crucially different approximation.
The Cancer Difference Method, with its conversion-factor of 2.223 from minimum to lifetime values, is using the approximation that the cancers which will occur beyond 1982 will be arising from a population with the same age-distribution and radiation-sensitivity as the population which produced the cancers observed between 1950-1982. This approximation is simply unrealistic, as already noted in Chapter 13.
For the 1950-82 period, the cancer deaths are coming predominantly from the older and less sensitive groups ATB, whereas in the post-1982 period, the cancer deaths will be coming predominantly from the younger and much more sensitive groups ATB. The Cancer-Rate Ratio Method takes this into account, whereas the Cancer Difference Method does not.
5. Merits and Pitfalls of the Methods
The comparisons in Part 4 above show that two methods, which produce nearly identical estimates for the Minimum "in-the-box" Fatal Cancer-Yields, produce lifetime estimates which differ by 2.5-fold. The factor of 2.5 is a measure of the potential error one would make by ignoring the fact that the residual population-sample beyond 1982 is not like the sample which generated the 1950-1982 observations. In other words, the Cancer-Rate Ratio Method is more realistic in its underlying assumptions about the lifetime risk than is the Cancer Difference Method. That is its great merit.
But this does not necessarily mean that the estimates of 30 or 32 fatal cancers per 10,000 persons per rem will match the ultimate estimate for low-dose exposure, when the full lifespan study is complete. We have made it clear how much depends on the future "behavior" of the youngest age-band, and also on the ultimate spontaneous cancer death-rate in the Reference Group. These unknowns are the biggest "pitfalls" in any such estimate.
o -- The true Lifetime Fatal Cancer-Yield for low-dose exposure could turn out considerably lower than 30 or 32 :
(A) If the ultimate spontaneous cancer death-rates in the Reference Group have been overestimated in our analysis;
(B) If the observed K-values in the youngest age-band "droop" or "melt down" during additional years of observation; this could happen due to sampling variation in the presently sparse observations, or due to a true (biological) reduction of effect beyond 40 years post-irradiation, or due to a reduced degree of supra-linearity in all age-bands after additional observations, or due to a less supra-linear dose-response in children than in adults.
o -- The true Lifetime Fatal Cancer-Yield for low-dose exposure could turn out considerably higher than 30 or 32 :
(A) If the ultimate spontaneous cancer death-rates in the Reference Group have been underestimated in our analysis;
(B) If the observed K-values in the youngest age-band increase during additional years of observation; this could happen due to sampling variation in the presently sparse observations, or due to an increased degree of supra-linearity in all age-bands after additional observations, or due to a greater supra-linear dose-response in children than adults. This would be very serious, since our estimate of 30-32 has ignored supra-linearity between 0 and 5 cSv, and has used the linear approximation in that dose-region.
Conclusion regarding Uncertainties :
These uncertainties are simply unavoidable. But they do not make it reasonable to accept the unrealistic premise of the Cancer Difference Method with respect to lifetime estimates -- namely, that the population which will generate the cancers beyond 1982 is like the population which generated the cancers between 1950-1982.
Moreover, since the uncertainties in the Cancer-Rate Ratio Method could readily operate toward underestimating the risk, which may turn out much higher than 30-32, it would be a sign of bias if I "preferred" using lifetime estimates which are 2.5-fold lower (from the Cancer Difference Method).
As a physician, I might add that information does not always need to be exact, in order to be extremely useful for human health.
6. The Bottom-Line from the Cancer-Rate Ratio Method
1. The Cancer-Rate Ratio Method produces about the same minimum Fatal Cancer-Yields for low-dose exposure as the Cancer Difference Method, in both dosimetries (text, Part 4). With their close agreement, the two analyses are excellent confirmation of each other with respect to evidence "in-the-box." By both methods, the Minimum Fatal Cancer-Yield is about 5.5 fatal radiation-induced cancers among 10,000 persons per cSv (rem) of whole-body organ-dose.
2. The Cancer-Rate Ratio Method produces estimates of lifetime Fatal Cancer-Yields for low-dose exposure which are predictably higher, and inherently more realistic, than the estimates produced -- for comparison -- by the Cancer Difference Method (text, Part 5). The Lifetime Fatal Cancer-Yields produced by the Cancer-Rate Ratio Method are 30-32 fatal radiation-induced cancers among 10,000 A-bomb survivors per cSv (rem) of whole-body organ-dose (Table 16-B). When the estimates are adjusted for a United States' population, they are 26-27 fatal radiation-induced cancers among 10,000 persons per cSv (rem) of whole-body organ-dose (Table 16-C). These values apply directly to low-dose exposure, acute or slow, between 0 and 5 cSv (rems).
3. Lifetime values in the range of 26 (USA) to 30 (A-bomb survivors) are very much higher than the values of 1-2 which are routinely used by the radiation community. Nonetheless, values like 26-30 may underestimate the cancer-hazard from X-ray exposure by about two-fold (see Chapter 13, Part 4).
4. Unlike some other analyses, our work does not throw away any of the evidence (follow-up years, or Dose-Groups) in the A-Bomb Study. It is based on the whole story, 1950-1982, and its legitimate prospective structure. We look forward to the time when the data become available to do a "constant-cohort, dual dosimetry" analysis with the additional observations through 1985.
By the Cancer-Rate Ratio Method, for Low-Dose Whole-Body Exposure per cSv, up to 5 cSv. Leukemia Excluded.
|==================================================================================================================| | Initial persons and spontaneous cancer-deaths are from the Reference Group (Dose-Groups 1+2). | | | | Col.A Col.B Col.C Col.D Col.E || Col.F Col.G Col.H || Col.I Col.J Col.K | | Spon- Spon- || Rad'n- Rad'n || Rad'n- Rad'n | | Population Mean taneous taneous || K Induced Induced || K Induced Induced | | Sample Age Initial Cancers Cancers || per Cancers Cancers || per Cancers Cancers | | (Ref Grp) ATB Persons 1950-82 LIFETIME || cSv 1950-82 LIFETIME || cSv 1950-82 LIFETIME | | || per cSv per cSv || per cSv per cSv | |================================================ || ========================== || ========================== | | || T65DR T65DR T65DR || DS86 DS86 DS86 | | || || | | Males, H+N 4.16 4976.25 18.25 799.7347 || 0.06851 1.25 54.79 || 0.06617 1.21 52.92 | | Males, H+N 13.95 5312.07 94.11 920.2082 || 0.01519 1.43 13.98 || 0.01484 1.40 13.66 | | Males, H+N 28.04 6644.57 451.98 1124.797 || 0.00343 1.55 3.85 || 0.00334 1.51 3.76 | | Males. H+N 42.60 6341.76 1018.02 1125.653 || 0.00494 5.02 5.56 || 0.00463 4.72 5.22 | | Males, H+N 58.14 4310.36 631.71 637.6347 || 0.00345 2.18 2.20 || 0.00311 1.97 1.99 | |Females. H+N 4.08 6935 38 849.648 || 0.04615 1.75 39.21 || 0.04388 1.67 37.28 | |Females, H+N 14.90 7403 116 1064.396 || 0.02457 2.85 26.15 || 0.02470 2.87 26.29 | |Females, H+N 26.69 9260 396 1234.162 || 0.01073 4.25 13.24 || 0.01000 3.96 12.34 | |Females, H+N 41.71 8838 925 1169.435 || 0.00615 5.69 7.19 || 0.00557 5.15 6.51 | |Females, H+N 59.05 6007 608 627.055 || 0.00595 3.61 3.73 || 0.00543 3.30 3.40 | | || || | | SUM OF ALL 66028 4297.07 9552.724 || 29.59 169.91 || 27.74 163.36 | | || || | | Cancers/10,000 persons 650.80 || 4.48 25.73 || 4.20 24.74 | | || || | | RERF-BEIR Correction Factor of 1.23 for || || | | Underascertainment of Cancer || 5.51 31.65 || 5.17 30.43 | | | | FATAL CANCER-YIELD = | | | | NUMBER OF FATAL RADIATION-INDUCED CANCERS AMONG 10,000 PERSONS PER cSv OF AVERAGE WHOLE-BODY ORGAN-DOSE. | | | | |------------------------------------------------------------------------------------------------| | | | SUMMARY OF FATAL CANCER-YIELDS BY THE CANCER-RATE RATIO METHOD | | | | After correction for underascertainment of cancer. | | | | | | | | T65DR | DS86 | | | | ------------ | ------------- | | | | MINIMUM "IN-THE-BOX" 5.51 | 5.17 | | | | | | | | | LIFETIME 31.65 | 30.43 | | | | | | | |------------------------------------------------------------------------------------------------| | | | | Cancer-hazard from X-rays may be underestimated by the A-Bomb Study. See Chapter 13, Part 4. | | | | NOTES: See Table 16-A. | |__________________________________________________________________________________________________________________|
|===========================================================================================================| | || T65DR Dosimetry || DS86 Dosimetry | | Col.A Col.B Col.C Col.D Col.E || Col.F Col.G || Col.H Col.I | | || || | | Lifetime Lifetime || Lifetime || Lifetime | | Age- Fraction Number of || K Rad'n-Induced || K Rad'n-Induced | | Band Dying Spontaneous || per Fatal Cancers || per Fatal Cancers | | (Years) Sex Persons of Cancer Ca-Deaths || cSv per cSv || cSv per cSv | | || || | | 0-9 Males 721.95 0.185 133.56 || 0.06851 9.15 || 0.06617 8.84 | | 10-19 Males 896.45 0.185 165.84 || 0.01519 2.52 || 0.01484 2.46 | | 20-34 Males 1238.98 0.188 232.93 || 0.00343 0.80 || 0.00334 0.78 | | 35-49 Males 814.4 0.190 154.74 || 0.00494 0.76 || 0.00463 0.72 | | 50+ Males 1206.59 0.183 220.81 || 0.00345 0.76 || 0.00311 0.69 | | 0-9 Females 687.71 0.160 110.03 || 0.04615 5.08 || 0.04388 4.83 | | 10-19 Females 863.27 0.160 138.12 || 0.02457 3.39 || 0.02470 3.41 | | 20-34 Females 1233.53 0.161 198.60 || 0.01073 2.13 || 0.01000 1.99 | | 35-49 Females 841.38 0.159 133.78 || 0.00615 0.82 || 0.00557 0.74 | | 50+ Females 1495.75 0.137 204.92 || 0.00594 1.22 || 0.00543 1.11 | | || || | | Totals 10000 1693.33 || 26.64 || 25.56 | | | | LIFETIME FATAL CANCER-YIELD = | | NUMBER OF FATAL RADIATION-INDUCED CANCERS AMONG 10,000 PERSONS PER cSv OF AVERAGE WHOLE-BODY ORGAN-DOSE. | | | | ------------------------------------------------------------------------------- | | | U.S. POPULATION (1978 COMPOSITION): | | | | LIFETIME FATAL CANCER-YIELD BY THE CANCER-RATE RATIO METHOD | | | | | | | | Based on T65DR | Based on DS86 | | | | | | | | | 26.64 | 25.56 | | | ------------------------------------------------------------------------------- | | | =============================================================================================================
NOTES: