Radiation Risk by Age and Sex, from the Cancer-Rate Ratio Method

This chapter is arranged in eight parts:

- Overview and Definitions, p.1
- Origin of the Key Equation, p.2
- Obtaining Raw K-Values for Each Age and Sex, p.2
- Discussion of the Raw K-Values, p.3
- Obtaining K-Values for Low-Dose Exposure, p.4
- Discussion of Low-Dose K-Values, p.6
- Some Ties between K-Values, Supra-Linearity, Duration, p.7
- Bottom Line on Radiation Risk by Age and Sex, p.9

Then tables.

1. Overview and Definitions

Unlike the Cancer Difference Method, the Cancer-Rate Ratio Method will obtain Minimum and Lifetime Fatal Cancer-Yields, for a population of mixed ages, by summing the

separatecontributions made by distinct age-sex subsets of the population.This chapter evaluates the risk of radiation-induced cancer observed so far in each of the five age-bands of the A-bomb survivors, males and females separately. The risks are expressed in terms of ten different "K-values" (defined below). The next chapter will use the K-values from this chapter to obtain the Minimum and Lifetime Fatal Cancer-Yields.

The Definition of K-Value :

K is defined here as the fractional increase in the spontaneous cancer death-rate per centi-sievert of whole-body internal organ-dose. (Multiplied by 100, K would be the

percentincrease in the spontaneous cancer death-rate per cSv.) The definition of K needs comparison with the definition of Fatal Cancer-Yield.Fatal Cancer-Yield is defined as the number of radiation-induced fatal cancers among 10,000 initial persons per cSv average whole-body internal organ-dose.

Therefore, if the observed K-values are applied to the spontaneous cancer-deaths observed so far in the Reference Group per 10,000 initial persons, the result is the

minimumFatal Cancer-Yield. If these observed K-values are applied to the estimatedultimatespontaneous cancer-deaths per 10,000 initial persons in the Reference Group, the result is thelifetimeFatal Cancer-Yield. Readers who look ahead to Tables 16-A and 16-B, in the next chapter, can see immediately how K-values and spontaneous cancer-rates are used to estimate Cancer-Yields (the "per 10,000" step occurs at the end).That is the easy part. The work comes beforehand, in obtaining the proper K-values to use in the range of common low-dose exposures, up to 5 cSv.

Raw versus Low-Dose K-Values :

The evidence in Chapters 14 and 29 shows that the dose-response relationship is presently concave-downward (supra-linear), and that the dose-exponent which produces the best-fit is Dose^0.75. Therefore it would be inexcusable -- indeed, a sign of bias -- if we ignored this information in deriving the best estimates we can of K-values.

Our method for taking supra-linearity into account, however, uses a series of linear equations. The analysis begins in Part 2 by developing the simple linear equations which yield Equation (7), which is the key one.

We shall use Equation (7) first to obtain a set of "raw K-values" which do

nottake supra-linearity into account, and then a set of "low-dose K-values" whichdotake supra-linearity into account. It is not necessary to obtain the raw K-values in order to obtain the low-dose K-values, but we do it so that everyone (ourselves included) can know how raw and low-dose K-values compare in magnitude.The input data which are assembled and consolidated in Tables 15-B through 15-K are needed equally for obtaining raw and low-dose K-values.

2. Origin of the Key Equation

We will use the following symbols; when a digit follows a letter, the digit is serving as a subscript.

D2= some dose of ionizing radiation greater than zero-dose.

R2= cancer death-rate (1950-1982) atD2, per 10,000 exposed persons.

D1= some dose less thanD2.

R1= cancer death-rate (1950-1982) atD1, per 10,000 exposed persons.

Ro= spontaneous cancer death-rate (1950-1982) when dose is zero.

K= fractional increase inRoper cSv of dose.When the dose-response relationship in a set of observations is linear, then the fractional increase in the spontaneous cancer death-rate per cSv of dose is the the same everywhere in the dose-range, high-dose and low-dose alike. Of course, this is definitely not true when dose-response is either concave-downward or concave-upward. But in a linear dose-response, K is a constant.

Equations (1) and (4) below are nothing other than the equation for a straight line, where

Rois the intercept on the y-axis, where the quantity (KRo) is the slope of the straight line, and where the intercept and points (D2,R2) and (D1,R1) all lie along thesamestraight line. Since Equation (7) below is derived from Equations(1)and(4), Equation(7)produces K-values which are valid if the dose-response relationship islinear.Factoring-outo -- Equation (1) :R2 = Ro + (K)(Ro)(D2)Ro, and then re-arranging, we haveAnd also for the lower dose,o -- Equation (2) :R2 = Ro (1 + KD2) , then R2/Ro = 1 + KD2 , theno -- Equation (3) :(R2/Ro) - 1 K = --------------- D2D1, we can writeo -- Equation (4) :R1 = Ro + (K)(Ro)(D1)o -- Then Equation (5) :R1 = Ro (1 + KD1)If we need to solve for

Kwithout usingRoat all, it can be done without using Equation(3), if we simply divide Equation(2)by Equation(5)-- which causesRoto cancel out in Equation(6).And, as we begin to isolate K, we have:o -- Equation (6) :(1 + KD2) (R2/R1) = ----------- (1 + KD1)(R2/R1)(1 + KD1) = (1 + KD2) , then (R2/R1) + (R2/R1)(KD1) = 1 + KD2Transposing terms and factoring-outK, we have:(KD2) - (R2/R1)(KD1) = (R2/R1) - 1 , then K [ D2 - (R2/R1)(D1) ] = (R2/R1) - 1 , theno -- Equation (7) :(R2/R1) - 1 K = ------------------ (D2) - (R2/R1)(D1)So

Kcan be evaluated with Equation(7)fromanytwo observations, sinceR2,D2,R1, andD1are all known from two observations. Equation(7)is the one which we will use repeatedly in this chapter. Indeed, its term (R2/R1) is the basis for calling this the Cancer-Rate Ratio Method.3. Obtaining Raw K-Values for Each Age and Sex

In Part 1 of this chapter, we drew a distinction between two sets of K-values: "Low-dose K-values" which take account of supra-linearity, and "raw K-values" which do

nottake account of supra-linearity. Before this new use of the word "raw" causes any confusion, we must point out thatboththe low-dose and the raw K-values are derived from the raw (pre-normalized) A-bomb data.The work in this chapter uses only the raw data. It is completely unnecessary to use age-normalized data when we are keeping each age-band separate, and completely unnecessary to use sex-normalized data when we are keeping males and females separate. Therefore, we are using the raw data from Tables 11-B (males) and 11-D (females). In addition, we use Master Tables 26-A,B,C,D in order to show the data for Dose-Groups 6, 7, and 8 separately.

Elsewhere, we established that

withina single age-band, the slight age-differences ATB across Dose-Groups are appropriately disregarded (see Chapter 11).

Dose-Increment for Small Body-Size :

As indicated by Table 4-B, the average age of the 0-9 year-olds ATB was only 4.1 years. The organ-doses in Master Tables 26-A,B,C,D, and in Tables 11-B and 11-D, do not include any correction for the small body-size of this age-band. Chapter 31 presents the method used for making the adjustment, and the findings are presented in Table 15-A.

In the Cancer-Rate Ratio Method, which examines each age-band separately, the 4-year-olds ATB take on importance in the estimates of

lifetimeFatal Cancer-Yield for a population of mixed-ages. Therefore, the work in Chapter 31 is worthwhile, in order to avoid preventable error.The effect of the adjustment is to increase dose by about 13-20 percent for this age-band, without changing the cancer-observations of course. The result is to

reducethe K-values for the very young children ATB, and thus toreducethe Lifetime Fatal Cancer-Yield for the overall population, compared with estimates calculated without this dose-adjustment, in the Cancer-Rate Ratio Method.

All analysts who begin to subdivide the Dose-Groups of the A-Bomb Study are immediately confronted with the small-numbers problem, especially for RERF's two age-bands who were youngest ATB (0-9 years and 10-19 years).

For example, inspection of Tables 11-B and 11-D, Column N, shows that it would be scientifically meaningless, at this stage of the follow-up, to base K-values on comparing observations in Dose-Group 3 with the Reference Group (1+2)

afterthe database has been subdivided into ten age-sex groups. After subdivision, analysts are confronted in Dose-Group 3 with statistically unstable numbers of cancer-deaths like 1 cancer for males 0-9 years ATB, 19 cancers for males 10-19 years ATB, 9 cancers for females 0-9 years ATB, and 23 cancers for females 10-19 years ATB.Therefore the comparison of Dose-Group 3 with the Reference Group, which was statistically strong in the Cancer Difference Method when observations were not subdivided, is ruled out by the small-numbers problem after subdivision. To reduce the instability of small numbers, all good analysts must decide on some combination of age-bands, sexes, or dose-groups (see for instance RERF TR-9-87, Table 7, p.21; and TR-5-88, Table 2-4, p.64).

The Consolidation of Dose-Groups :

This chapter lessens the small-numbers problem by consolidating the observations within each age-sex group into two classes: Low-dose and high-dose. The low-dose class is composed of RERF Dose-Groups 1 + 2 + 3, and represents an average organ-dose in the neighborhood of 3 cSv (specifics are in Tables 15-B through 15-K). The high-dose class is composed of Dose-Groups 4 + 5 + 6 + 7 + 8, and represents an average organ-dose in the neighborhood of 70-100 cSv (specifics are in Tables 15-B through 15-K).

This consolidation provides real-world observations to use for D2, R2, D1, and R1 in Equation (7), and provides them for each of the ten age-sex groups separately.

Calculation of Raw K-Values :

Tables 15-B through 15-K show the derivation of twenty raw K-values (ten in each dosimetry), step-by- step, from the input data to the result. Each calculation amounts to having a two-point dose-response at about 3 cSv and at about 85 cSv. One can imagine a straight line connecting these two points. By using Equation (7), the K-value which applies to this straight line is determined.

4. Discussion of the Raw K-Values

The raw K-values derived in Tables 15-B through 15-K are assembled for convenience at the bottom of Table 15-L (Note 2).

Higher Hazard for Those Who Are Young at Exposure :

The raw K-values reflect a greater sensitivity to radiation carcinogenesis in those who are young at exposure (the two youngest age-bands ATB) than in those who are older. This is seen in both sexes independently. It is even seen for each sex in the age-band 0-9 years ATB, in spite of the severe small-numbers problem in those groups.

In the females, sensitivity falls with advancing age in a remarkably regular way. In the males, there is an irregularity in the age-band 20-34 years ATB. We regard this as more likely to be an artifact from sampling than to be biologically meaningful, but only time will tell with certainty. Meanwhile, we shall not use any smoothing operation for either the raw K-values or (later) the low-dose K-values.

Male versus Female K-Values :

When we compare K-values for males and females, we find that the males seem generally less radio-sensitive than the females. In the one age-band (50+) where these are the final results -- because almost everyone has died -- this is what we see. On the other hand, the age-band 35-49 years ATB is the age-band which accounts for the most cancer-deaths in the study by far (Table 4-B), which makes it the most reliable to date. In this age-band, radio-sensitivity is about the

samein males and females.

Independence from Hypotheses and Models :

It is self-evident that there necessarily exists some ratio between two cancer-rates (R2 and R1) observed at two different doses (D2 and D1). The ratio may be greater than 1.0, equal to 1.0, or less than 1.0, but whatever its value, it exists. Equation (7) simply uses the observed ratio and the doses to calculate the value of K: The fractional increase in the spontaneous cancer-rate per cSv of dose.

Thus the raw K-values in Table 15-L are independent from any forward projection, hypothesis, or model of radiation carcinogenesis. They are "in-the-box" observations with respect to the follow-up through 1982. Whether or not they will keep the same value during the remaining follow-up periods is a separate question, which no one can answer with certainty, of course.

Raw K-Values Not Applicable for Low-Doses :

Because dose-response is concave-downward instead of linear, and because raw K-values are derived from a D2 in the range of 70-100 cSv of average organ-dose, the raw K-values would (if used) necessarily underestimate the Cancer-Yield -- the radiation hazard -- from low-dose exposure. In Part 6, we will determine the size of the underestimate.

5. Obtaining K-Values for Low-Dose Exposure

The Key Assumption, and Overview of the Method :

In Chapters 14 and 29, it was demonstrated that

(A)the dose-response relationship in the A-Bomb Study -- for both cities, both sexes, and all five age-bands combined -- is concave-downward in shape (supra-linear), and(B)the best fit to the data is obtained by using Dose^0.75 in the equation of cancer death-rate versus dose. Indeed, the fit is excellent, with R-Squared values of 0.9831 for the T65DR dosimetry (Table 29-B) and 0.9825 for the DS86 dosimetry (Table 29-C).Since the ten age-sex subsets examined here, by the Cancer-Rate Ratio Method, represent the entire substrate which generated that dose-exponent, it is a reasonable expectation that approximately the same dose-exponent characterizes the ten age-sex groups individually.

Because of the small-numbers problem, this expectation cannot yet be tested; another decade or more of follow-up will perhaps produce adequate numbers to do curvilinear regression analysis for the ten groups separately. Meanwhile, the assumption that they

doshare a similar dose-response curve seems far more reasonable than a speculative claim that they donot. Therefore, we will make the approximation that the dose-exponent of 0.75, which characterizes dose-response for the overall population, also applies individually to each of the population's ten subsets.With this single assumption, we can write individual equations of best fit for each subset, based on the real-world observations belonging to that particular age-sex group (from Tables 15-B through 15-K), and then we can use the equations to determine the corresponding

low-doseK-values for each age-sex group.Before demonstrating the two-step procedure, first we will show the origin of the additional equations to be used. In the end, we also use Equation (7) again.

Equations (8) Through (12) :

With our combined dose-groups, we can refer to two categories:

The "L" Group is the Lower Group

(Dose-Groups 1 + 2 + 3).

The "H" Group is the Higher Group

(Dose-Groups 4 + 5 + 6 + 7 + 8).

In Group L, we have a dose, D1, where the

observed cancer-rate is R1.

In Group H, we have a dose, D2, where the

observed cancer-rate is R2.Equation

(8)below states the general dose-response relationship which, as noted in Chapter 29, is an equation which produces a straight line if dose is plotted in units of cSv^0.75 instead of cSv:Readers will recognize that the format of Equationo -- Equation (8) :Cancer-Rate = (Coefficient)(Dose^0.75) + (Constant)(8)is the analytic expression of a straight line: y = mx + b. Since b is the line's y-intercept, the Constant in Equation(8)is the cancer-rate when dose is zero (the spontaneous cancer-rate).We can write Equation

(9)for Group L, and Equation(10)for Group H.o -- Equation (9) :R1 = (Coefficient)(D1^0.75) + (Constant)o -- Equation (10) :R2 = (Coefficient)(D2^0.75) + (Constant)Since these linear equations necessarily share the same Coefficient and Constant, and since Tables 15-B through 15-K provide the values of R1, R2, D1, and D2, we will be able to solve these two equations for both the Coefficient and the Constant. Solving for the Coefficient first, we subtract Equation

(9)from Equation(10), to obtain:R2-R1 = (Coefficient)(D2^0.75 - D1^0.75) , and theno -- Equation (11) :(Coefficient) = (R2-R1) / (D2^0.75 - D1^0.75) For the Constant, we re-arrange Equation (9).o -- Equation (12) :Constant = (R1) - (Coefficient)(D1^0.75)Since we evaluated the Coefficient in Equation

(11), and since R1 and D1^0.75 are knowns, we now have the value of the Constant -- or would, if we had been using actual observations. In Step 1 below, we shall apply these equations to some real numbers from the tables.

Step 1 --o

Obtaining the Equation of Best Fit

The procedure to be demonstrated is general, and has been applied to all ten age-sex groups under study here. It will be illustrated below by using the input from Table 15-B for the males age 0-9 years ATB, in the T65DR dosimetry. Any other set of data (Tables 15-C through 15-K) would serve just as well. The results become entries in Table 15-L.

D1 = 2.90 cSv D2 = 96.64 cSv R1 = 31.08 cancers per 10,000 persons, 1950-82 R2 = 105.26 cancers per 10,000 persons, 1950-82 D1^0.75 = (2.9)^0.75 = 2.2222 D2^0.75 = (96.64)^0.75 = 30.822Applying Equation(11), we solve for Coefficient:Coefficient = (R2-R1) / (D2^0.75 - D1^0.75) Coefficient = (105.26-31.08) / (30.82248-2.222278) Coefficient = 2.593687Applying Equation(12), we solve for Constant:Constant = R1 - (Coefficient)(D1^0.75) Constant = 31.08 - (2.593687)(2.222278) Constant = 25.31610And now, with Equation

(8)as the model, we can write the entire Equation of Best Fit for this particular age- and sex-group:Cancer-Rate = (2.5937)(Dose^0.75) + (25.3161)Precisely this entry is to be found in Table 15-L for the Equation of Best Fit for males, 0-9 years of age ATB, in the T65DR dosimetry.

Step 2 --o

Obtaining (R2/R1) & Solving for Low-Dose K :

In order to calculate the appropriate K-value for a total dose up to 5 cSv, we now need to use this Equation of Best Fit to obtain the predicted cancer-rates at zero-dose and at 5 cSv.

For 5 cSv : Cancer-rate = (2.5937)(5^0.75) + (25.3161) Since 5^0.75 = 3.343701 Cancer-rate = (2.5937)(3.343701) + (25.3161) = 33.98865 For Zero cSv : Cancer-rate = (2.5937)(0^0.75) + (25.3161) Since 0^0.75 = 0, Cancer-rate = 25.3161 Thus, for these two doses and cancer-rates : D1 = 0 cSv D2 = 5 cSv R1 = 25.3161 R2 = 33.98865 R2/R1 = 33.98865 / 25.3161 = 1.3425Now, going back to Equation

(7)and making the approximation that dose-response is linear between 0 and 5 cSv, we can calculate the K-value which is appropriate for low-dose exposure:o -- Equation (7) :(R2/R1) - 1 K = ------------------ (D2) - (R2/R1)(D1)Substituting our values, we have for the average K-value up to 5 cSv of total dose:

1.34257 - 1 K = -------------------- 5 - (1.34257)(0) K = 0.34257 / 5 = 0.06851In Table 15-L of low-dose K-values, exactly this K-value of 0.06851 is entered for males 0-9 years of age ATB, in the T65DR dosimetry. All twenty low-dose K-values in Table 15-L are derived in the same way.

6. Discussion of Low-Dose K-Values

There are two checks which confirm that the method is correct for obtaining low-dose K-values from the evidence at hand.

Checking the Constants :

First, since the constants in the Equations of Best Fit in Table 15-L are the predicted spontaneous cancer-rates when the dose is zero, those constants should be consistent with the rates observed in the Reference Group, whose exposure was not far above zero. Since Tables 15-B through 15-K include the cancer-rate per 10,000 initial persons in the Reference Group, such comparisons are easily made with the constants in Table 15-L. The correspondence between predicted and observed rates is very good, especially for the older age-bands where the number of cancer-cases is statistically the most stable.

Checking the Ratio (Low-Dose K / Raw K) :

Second, the ratio between the low-dose K-values and the raw K-values for each of the ten subsets should be about the same magnitude as it would be, if the comparable ratio were determined for the

combinationof all age-bands and both sexes. We made this check by using Equation (7) with appropriate entries from Tables 14-A and 14-B.Because raw K-values for the subsets were calculated with D2 equal to about 85 cSv, and D1 equal to about 3 cSv, in making a calculation of the corresponding K-value with all ages and both sexes combined, we chose the closest values available in Tables 14-A and 14-B. We used D2 = 80 cSv and D1 = 2 cSv. For the low-dose K-value, of course we used D2 = 5 cSv and D1 = 0 cSv. The resulting ratios are below:

T65DR without age-sex subdivision: RATIO, LOW-DOSE K TO RAW K = 2.104 . DS86 without age-sex subdivision: RATIO, LOW-DOSE K TO RAW K = 2.103 .This assures us that the overall ratio is, indeed, about the same magnitude as the individual ratios shown in the tabulations which follow. Moreover, everything here is consistent with the ratios of low-dose and higher-dose Minimum Fatal Cancer-Yields in Table 13-B, Row 1.

-------------------- T65DR ---------------------- | Sex & Raw Low-Dose Ratio, Low-Dose K | | Age ATB K-Value K-Value over Raw K | | (Years) | | M 0-9 0.02749 0.068510 2.49 | | M 10-19 0.00677 0.015190 2.24 | | M 20-34 0.00157 0.003426 2.18 | | M 35-49 0.00228 0.004936 2.16 | | M 50+ 0.00162 0.003454 2.13 | | | | F 0-9 0.01922 0.046150 2.40 | | F 10-19 0.01097 0.024570 2.24 | | F 20-34 0.00492 0.010730 2.18 | | F 35-49 0.00289 0.006152 2.13 | | F 50+ 0.00288 0.005945 2.06 | --------------------------------------------------- -------------------- DS86 ---------------------- | Sex & Raw Low-Dose Ratio, Low-Dose K | | Age ATB K-Value K-Value over Raw K | | (Years) | | M 0-9 0.02565 0.066170 2.58 | | M 10-19 0.00647 0.014840 2.29 | | M 20-34 0.00150 0.003344 2.23 | | M 35-49 0.00207 0.004634 2.24 | | M 50+ 0.00140 0.003114 2.22 | | | | F 0-9 0.01771 0.043880 2.48 | | F 10-19 0.01081 0.024700 2.28 | | F 20-34 0.00442 0.010000 2.26 | | F 35-49 0.00250 0.005565 2.23 | | F 50+ 0.00252 0.005425 2.15 | --------------------------------------------------

It deserves emphasis, however, that correctness of method and computation can never overcome inherent sampling variation and the small-numbers problem in a set of observations. It is self-evident from the raw data in Tables 15-B through 15-K that every analyst who subdivides A-bomb data is dealing with some small and unstable numbers. Even if K-values are biologically constant for the lifespan which follows irradiation, future follow-ups may cause a K-value to rise or fall due to the random variation of sampling. (However, the values for the oldest age-band ATB are as stable as they will ever become, since almost all of this age-band had died before the end of the 1950-1982 follow-up.)

Effect of Extrapolation from High Doses :

The ratios between low-dose K-values, and their corresponding raw K-values, range from 2.1 to 2.5. Like Tables 13-B, 14-A, and 14-B, this indicates that failure to appreciate the supra-linearity of the dose-response relationship accounts for more than a 2-fold underestimate of fatal cancer-risk when high doses and the linear dose-response are used to evaluate the hazard from low-dose exposure.

This finding is in great contrast to the "old refrain" that extrapolation from high doses would exaggerate the cancer-risk at low doses from ionizing radiation. However, we repeat that it is not necessary for anyone to extrapolate at all. One should use the findings which are based

directlyupon human exposure in the low dose-range.

Free from Speculation :

Low-dose K-values, like the raw K-values, are "in-the-box." Readers have seen for themselves that low-dose K-values are derived from the actual observations (1950-1982) of D1, R1, D2, R2, in Tables 15-B through 15-K, without any reliance on speculation, hypotheses, or models of radiation carcinogenesis. As shown in Chapter 14, the dose-exponent of 0.75 (used in Steps 1 and 2)

alsocomes from the evidence itself, not from speculation, hypothesis, or pre-judgment.Low-dose K-values vary with age ATB, as do the raw K-values. Comments in Part 4 of this chapter regarding age and sex apply equally to raw and low-dose K-values.

7. Some Ties between K-Values, Supra-Linearity, Duration

K-Values and Supra-Linearity :

For the sake of exploration, we are going to use the

rawK-values at the bottom of Table 15-L, to predict the consequences of radiation exposure, regardless of dose-level.Let us say that the raw K-values at the bottom of Table 15-L, for the children who were age 0-9 years old ATB, are "good" -- by which we mean, if there were a billion such children in the study instead of 18402 children, we would still observe a raw K-value of about 0.02, or 2 % per rem, from the 1950-1982 follow-up. In other words, suppose there is no basis for thinking 0.02 is spuriously high or low, due to sampling variation.

If we use the approximation for this exploration that, in populations with a long lifespan, some 20 % of people die from

spontaneouscancer, and if we make the presumption that the magnitude of the raw K-value neither rises nor falls with further follow-up, then what would we expect for children irradiated between 0-9 years of age?

SCENARIO 1 :Among every 10,000 children who receive one rem (cSv) of whole-body internal organ-dose, we would expect that 2,000 would die eventually from spontaneous cancer, and from the definition of K -- which is the fractional increase in the spontaneous rate per rem -- we would also expect (2000 spontaneous cancers x 0.02 per rem x 1 rem), or 40 radiation-induced cancers. Combined lifelong cancer-deaths expected for this group = 2,040 per 10,000 initial persons.

SCENARIO 2 :Among every 10,000 children who receive 25 rems (cSv) of whole-body internal organ-dose, we would expect that 2,000 would die eventually from spontaneous cancer, and from using the raw K-value of 0.02, we would also expect (2000 spontaneous cancers x 0.02 per rem x 25 rems), or 1,000 radiation-induced cancers. Combined lifelong cancer-deaths expected for this group = 3,000 per 10,000 initial persons.

SCENARIO 3 :Among every 10,000 children who receive 200 rems of whole-body internal organ-dose, we would expect that 2,000 would die eventually from spontaneous cancer, and still using the raw K-value of 0.02, we would also expect (2000 spontaneous cancers x 0.02 per rem x 200 rems), or 8,000 radiation-induced cancers. Combined lifelong cancer-deaths expected for this group = 10,000 per 10,000 initial persons.Thus, use of the same K-value at high doses and low doses would, in certain circumstances, lead to absurd predictions at

highdoses.In the A-Bomb Study, there are about 200 children who survived the acute effects of 200 rems or more of whole-body internal organ-dose (see Dose-Groups 7 and 8, in Tables 15-B and 15-G). If a single raw K-value were applicable at every dose-level and if it persisted lifelong, then all of these 200 persons would be expected to die of cancer. (The expectation would be 40 spontaneous fatal cancers, plus 160 radiation-induced cases.)

But in reality, it would

nothappen that way, because non-cancer causes of death would "compete" with cancer in this group. As a result, the ultimate observation would be fewer than 200 cancers per 200 initial persons. Therefore, under these circumstances, the single raw K-value of 0.02 couldnotcharacterize all dose-levels. The K-value at 200 rems would have to belowerthan 0.02 -- and that would be consistent withsupra-linearity of dose-response.A recurrent finding in this field is that K-values are high for children. Unless dose-response is supra-linear (meaning lower K-values at high doses than at low doses), predictions based on high doses and on high, lifelong K-values will "require" lifetime cancer death-rates which exceed 100 percent. In contrast to such an absurdity, high and lifelong K-values at

lowdoses are consistent with predictions which are credible.

K-Values and Duration of Magnitude :

Absurd predictions for high-dose consequences, illustrated in Scenario 3 above, could be avoided by acceptance of different K-values for different dose-levels (in accordance with the current evidence from the A-bomb survivors), but there is also another route to credible high-dose estimates. One could speculate that K-values, though truly observed and reported for a given follow-up period, will not remain constant for the full remainder of a lifespan follow-up.

For instance, if one observed a very high K-value like 0.5 per rem (not 0.05 or 0.005 per rem) in some sample of irradiated children during an incomplete lifespan follow-up, then K = 0.5 per rem would mean that a dose of only 8 rems would cause everyone in that sample to die from cancer, if the K-value remained at the

samemagnitude of 0.5 for the remaining lifespan:(2,000 spontaneous cancers per 10,000 initial persons) x (0.5 per rem) x (8 rems) = 8,000 radiation-induced cancers. When the expected 2,000 spontaneous cancer-deaths are added, cancer would claim 10,000 out of every 10,000 initial persons in such a sample.

Nonetheless, the observation of K = 0.5 may be exactly right for the time-period which has passed. One cannot presently rule out the possibility that K-values vary with time -- as well as with dose-level. On the other hand, one cannot rule out predictions which come fairly close to 100 % cancer-mortality either. For instance, among persons with chronic hepatitis-B infection, the lifetime incidence of a

single typeof cancer alone (hepatocellular carcinoma) has been reported as high as 50 % (Ober89).

Supra-Linearity in the Absence of High K-Values :

Table 4-B is a reminder that the supra-linearity presently observed in the A-bomb survivors is overwhelmingly generated by the cancer-response of those who were already adults at the time of bombing, because fully 92.7 percent of all the cancers observed during the 1950-1982 follow-up have come from the three oldest age-bands ATB. Yet these three oldest age-bands are the

leastsensitive to radiation carcinogenesis. If we do an exploration with their highest raw K-value, which is near 0.005, we do not "run out of people" for the expected cancers, even at a very high dose:Among every 10,000 adults who receive 200 rems of whole-body internal organ-dose, we would expect that 2,000 would die eventually from spontaneous cancer, and under the specified K-value, we would also expect (2000 spontaneous cancers x 0.005 per rem x 200 rems), or 2,000 radiation-induced cancers. Combined lifelong cancers expected for this group would be 4,000 per 10,000 initial persons.

Therefore we can rule out pressure from competing causes of death as the main

causeof the supra-linearity observed in the 1950-1982 dose-response of the adult A-bomb survivors.8. The Bottom Line on Radiation Risk, by Age and Sex

1.K is defined as the fractional increase in the spontaneous cancer death-rate per centi-sievert of whole-body internal organ-dose. A K-value measures the size of an observed cancer-response, and is independent from any particular hypotheses and models of radiation carcinogenesis itself.

2.The main part of Table 15-L presents the low-dose K-values for each of RERF's five age-bands and both sexes. Separate sets of K-values have been calculated for the T65DR dosimetry and the current version of the DS86 dosimetry. These K-values come from observation of the A-bomb survivors from 1950-1982. No follow-up years -- and no Dose-Groups -- have been thrown out of our analysis (see Chapter 14, Part 2). All the available observations were included in finding the equation of best fit, for each of the ten groups.

3.The low-dose K-values from Table 15-L will be used in the next chapter to estimate the Minimum and Lifetime Fatal Cancer-Yields from low-dose exposure, not only for the A-bomb survivors, but also for a population with an age-sex distribution like the one of the United States.

Correction of Dose-Data for Small Body-Size: Ages 0-9 at Time of Bombing.

|========================================================================================================| |MALES AGE 0-9 ATB: T65DR Dosimetry, Neutron RBE = 2.0||MALES: DS86 Dosimetry, Neutron RBE = 20.| | || | | Col. A Col. B Col. C Col. D || Col. E Col. F Col. G Col. H | | Dose- Uncorrected Correction Corrected || Dose- Uncorrected Correction Corrected | | Group Dose Factor Dose Persons || Group Dose Factor Dose | | MALES in cSv MALES in cSv MALES || MALES in cSv MALES in cSv | |====================================================== || ============================================ | | Group 1 0 1.000 0.000 3787 || Group 1 0.08194 1.074 0.088 | | Group 2 1.450 1.171 1.698 3031 || Group 2 1.593 1.128 1.797 | | Group 3 10.49 1.179 12.368 1547 || Group 3 13.32 1.138 15.158 | | Group 4 34.78 1.175 40.867 359 || Group 4 39.79 1.162 46.236 | | Group 5 71.64 1.173 84.034 189 || Group 5 72.79 1.169 85.092 | | Group 6 120.19 1.172 140.863 105 || Group 6 116.90 1.179 137.825 | | Group 7 170.63 1.186 202.367 43 || Group 7 175.39 1.192 209.065 | | Group 8 256.45 1.182 303.124 64 || Group 8 305.99 1.203 368.106 | | SUM 9125 | |====================================================================================================== | | | |FEMALES AGE 0-9 ATB: T65DR Dosimetry, Neutron RBE = 2.0||FEMALES: DS86 Dosimetry, Neutron RBE = 20.| | || | | Col. A Col. B Col. C Col. D || Col. E Col. F Col. G Col. H | | Dose- Uncorrected Correction Corrected || Dose- Uncorrected Correction Corrected | | Group Dose Factor Dose Persons || Group Dose Factor Dose | | FEMALES in cSv FEMALES in cSv FEMALES || FEMALES in cSv FEMALES in cSv | |====================================================== || ============================================ | | Group 1 0 1.000 0.000 3842 || Group 1 0.08186 1.074 0.088 | | Group 2 1.429 1.173 1.676 3093 || Group 2 1.581 1.128 1.783 | | Group 3 10.700 1.178 12.605 1547 || Group 3 13.55 1.138 15.420 | | Group 4 34.65 1.173 40.644 372 || Group 4 39.23 1.161 45.546 | | Group 5 70.31 1.181 83.036 213 || Group 5 74.07 1.173 86.884 | | Group 6 122.17 1.177 143.794 99 || Group 6 122.06 1.183 144.397 | | Group 7 175.91 1.189 209.157 41 || Group 7 182.27 1.194 217.630 | | Group 8 267.01 1.176 314.004 70 || Group 8 313.59 1.199 375.994 | | SUM 9277 | |========================================================================================================|

Average age of the 0-9 year-old children ATB was 4.1 years (Table 26-E).

Entries in Col.B and Col.F are calculated from Master File 26 A,B,C,D.

Entries in Col.C and Col.G come from Tables 31-A and 31-B.

Entries in Col.D = (Col.B) x (Col.C).

Entries in Col.H = (Col.F) x (Col.G).

Cols. D and H provide the organ-doses for
Tables 15-B and 15-G.

Calculation of Raw K-Values for Males 0-9 Years of Age ATB.

|=========================================================================================================| |T65DR DOSIMETRY, NEUTRON RBE = 2.0||DS86 DOSIMETRY, NEUTRON RBE = 20| | || | | The Basic Data for 0-9 year-old Males ATB || The Basic Data for 0-9 year-old Males ATB | | (Hiroshima plus Nagasaki combined) || (Hiroshima plus Nagasaki combined) | | from Tables 15-A, 11-B, and 26-A,B. || from Tables 15-A,11-B, and 26-A,B. | |================================================= || ================================================ | | Dose- Organ- Total MALES Cancers || Dose- Organ Total MALES Cancers | | Group Dose Cancers Entered per || Group Dose Cancers Entered per | | in for into Initial || in for into Initial | | cSv 1950-82 Study 10,000 || cSv 1950-82 Study 10,000 | | || | | Group 1+2 0.75 25 6818 36.67 || Group 1+2 0.85 25 6818 36.67 | | Group 3 12.37 1 1547 6.46 || Group 3 15.16 1 1547 6.46 | | Group 4 40.87 0 359 0.00 || Group 4 46.24 0 359 0.00 | | Group 5 84.03 2 189 105.82 || Group 5 85.09 2 189 105.82 | | Group 6 140.86 5 105 476.19 || Group 6 137.83 5 105 476.19 | | Group 7 202.37 0 43 0.00 || Group 7 209.07 0 43 0.00 | | Group 8 303.12 1 64 156.25 || Group 8 368.11 1 64 156.25 | |================================================= || ================================================ | | Combining the dose-classes, we have || Combining the dose-classes we have, | | || | | Dose- Organ- Total Persons Cancers || Dose- Organ Total Persons Cancers | | Groups Dose Cancers Entered 10,000 || Groups Dose Cancers Entered 10,000 | | Com- in for into persons || Com- in for into persons | | bined cSv 1950-82 Study (R value) || bined cSv 1950-82 Study (R value) | | || | | 1+2+3 2.90 26 8365 31.08 || 1+2+3 3.49 26 8365 31.08 | | 4+5+6+7+8 96.64 8 760 105.26 || 4+5+6+7+8 104.87 8 760 105.26 | | || | |================================================= || ================================================ | | For application of Equation (7) to these data, || For application of Equation (7) to these data, | | || | | D1 = 2.90 centi-Sieverts ( rems ) || D1 = 3.49 centi-Sieverts ( rems ) | | D2 = 96.64 centi-Sieverts ( rems ) || D2 = 104.87 centi-Sieverts ( rems ) | | R1 = 31.08 cancers per 10,000 persons, 1950-82 || R1 = 31.08 cancers per 10,000 persons, 1950-82 | | R2 = 105.26 cancers per 10,000 persons, 1950-82 || R2 = 105.26 cancers per 10,000 persons, 1950-82 | | R2/R1 = 3.39 || R2/R1 = 3.39 | | || | | The numerator for Equation (7) is : || The numerator for Equation (7) is: | | (R2/R1) - 1 = 2.39 || (R2/R1) - 1 = 2.39 | | || | | The denominator for Equation (7) is : || The denominator for Equation (7) is : | | (D2) - (R2/R1)(D1) = (96.64) - (3.39)(2.90) || (D2) - (R2/R1)(D1) = (104.87) - (3.39)(3.49) | | = 86.81 || = 93.04 | | || | |The quotient, the K value = 0.02749||The quotient, the K value = 0.02565| |_________________________________________________________________________________________________________|

Calculation of Raw K-Values for Males 10-19 Years of Age ATB.

|=========================================================================================================| |T65DR DOSIMETRY, NEUTRON RBE = 2.0||DS86 DOSIMETRY, NEUTRON RBE = 20| | || | | The Basic Data for 10-19 year-old Males ATB || The Basic Data for 10-19 year-old Males ATB | | (Hiroshima plus Nagasaki combined) || (Hiroshima plus Nagasaki combined) | | from Tables 11-B and 26-A,B. || from Tables 11-B and 26-A,B. | |================================================= || ================================================ | | Dose- Organ- Total MALES Cancers || Dose- Organ Total MALES Cancers | | Group Dose Cancers Entered per || Group Dose Cancers Entered per | | in for into Initial || in for into Initial | | cSv 1950-82 Study 10,000 || cSv 1950-82 Study 10,000 | | || | | Group 1+2 0.83 113 6378 177.17 || Group 1+2 1.11 113 6378 177.17 | | Group 3 11.11 19 1112 170.86 || Group 3 13.92 19 1112 170.86 | | Group 4 35.24 9 342 263.16 || Group 4 36.53 9 342 263.16 | | Group 5 71.79 5 371 134.77 || Group 5 67.75 5 371 134.77 | | Group 6 124.73 7 167 419.16 || Group 6 117.37 7 167 419.16 | | Group 7 172.18 4 70 571.43 || Group 7 180.64 4 70 571.43 | | Group 8 265.93 6 126 476.19 || Group 8 325.58 6 126 476.19 | |================================================= || ================================================ | | Combining the dose-classes, we have || Combining the dose-classes we have, | | || | | Dose- Organ- Total Persons Cancers || Dose- Organ Total Persons Cancers | | Groups Dose Cancers Entered 10,000 || Groups Dose Cancers Entered 10,000 | | Com- in for into persons || Com- in for into persons | | bined cSv 1950-82 Study (R value) || bined cSv 1950-82 Study (R value) | | || | | 1+2+3 2.36 132 7490 176.23 || 1+2+3 3.01 132 7490 176.23 | | 4+5+6+7+8 97.65 31 1076 288.10 || 4+5+6+7+8 103.06 31 1076 288.10 | | || | |================================================= || ================================================ | | For application of Equation (7) to these data, || For application of Equation (7) to these data, | | || | | D1 = 2.36 centi-Sieverts ( rems ) || D1 = 3.01 centi-Sieverts ( rems ) | | D2 = 97.65 centi-Sieverts ( rems ) || D2 = 103.06 centi-Sieverts ( rems ) | | R1 = 176.23 cancers per 10,000 persons, 1950-82 || R1 = 176.23 cancers per 10,000 persons, 1950-82 | | R2 = 288.10 cancers per 10,000 persons, 1950-82 || R2 = 288.10 cancers per 10,000 persons, 1950-82 | | R2/R1 = 1.63 || R2/R1 = 1.63 | | || | | The numerator for Equation (7) is : || The numerator for Equation (7) is: | | (R2/R1) - 1 = 0.63 || (R2/R1) - 1 = 0.63 | | || | | The denominator for Equation (7) is : || The denominator for Equation (7) is : | | (D2) - (R2/R1)(D1) = (97.65) - (1.63)(2.36) || (D2) - (R2/R1)(D1) = (103.06) - (1.63)(3.01) | | = 93.80 || = 98.14 | | || | |The quotient, the K value = 0.00677||The quotient, the K value = 0.00647| |_________________________________________________________________________________________________________|

Calculation of Raw K-Values for Males 20-34 Years of age ATB.

|=========================================================================================================| |T65DR DOSIMETRY, NEUTRON RBE = 2.0||DS86 DOSIMETRY, NEUTRON RBE = 20| | || | | The Basic Data for 20-34 year-old Males ATB || The Basic Data for 20-34 year-old Males ATB | | (Hiroshima plus Nagasaki combined) || (Hiroshima plus Nagasaki combined) | | from Tables 11-B and 26-A,B. || from Tables 11-B and 26-A,B. | |================================================= || ================================================ | | Dose- Organ- Total MALES Cancers || Dose- Organ Total MALES Cancers | | Group Dose Cancers Entered per || Group Dose Cancers Entered per | | in for into Initial || in for into Initial | | cSv 1950-82 Study 10,000 || cSv 1950-82 Study 10,000 | | || | | Group 1+2 0.67 224 3293 680.23 || Group 1+2 0.99 224 3293 680.23 | | Group 3 11.57 54 703 768.14 || Group 3 15.34 54 703 768.14 | | Group 4 35.54 11 237 464.14 || Group 4 38.01 11 237 464.14 | | Group 5 71.15 22 224 982.14 || Group 5 70.73 22 224 982.14 | | Group 6 123.33 17 122 1393.44 || Group 6 116.33 17 122 1393.44 | | Group 7 171.24 2 53 377.36 || Group 7 174.19 2 53 377.36 | | Group 8 273.22 3 57 526.32 || Group 8 340.73 3 57 526.32 | |================================================= || ================================================ | | Combining the dose-classes, we have || Combining the dose-classes we have, | | || | | Dose- Organ- Total Persons Cancers || Dose- Organ Total Persons Cancers | | Groups Dose Cancers Entered 10,000 || Groups Dose Cancers Entered 10,000 | | Com- in for into persons || Com- in for into persons | | bined cSv 1950-82 Study (R value) || bined cSv 1950-82 Study (R value) | | || | | 1+2+3 2.59 278 3996 695.70 || 1+2+3 3.51 278 3996 695.70 | | 4+5+6+7+8 92.43 55 693 793.65 || 4+5+6+7+8 97.69 55 693 793.65 | | || | |================================================= || ================================================ | | For application of Equation (7) to these data, || For application of Equation (7) to these data, | | || | | D1 = 2.59 centi-Sieverts ( rems ) || D1 = 3.51 centi-Sieverts ( rems ) | | D2 = 92.43 centi-Sieverts ( rems ) || D2 = 97.69 centi-Sieverts ( rems ) | | R1 = 695.70 cancers per 10,000 persons, 1950-82 || R1 = 695.70 cancers per 10,000 persons, 1950-82 | | R2 = 793.65 cancers per 10,000 persons, 1950-82 || R2 = 793.65 cancers per 10,000 persons, 1950-82 | | R2/R1 = 1.14 || R2/R1 = 1.14 | | || | | The numerator for Equation (7) is : || The numerator for Equation (7) is: | | (R2/R1) - 1 = 0.14 || (R2/R1) - 1 = 0.14 | | || | | The denominator for Equation (7) is : || The denominator for Equation (7) is : | | (D2) - (R2/R1)(D1) = (92.43) - (1.14)(2.59) || (D2) - (R2/R1)(D1) = (97.69) - (1.14)(3.51) | | = 89.48 || = 93.68 | | || | |The quotient, the K value = 0.00157||The quotient, the K value = 0.00150| |_________________________________________________________________________________________________________|

Calculation of Raw K-Values for Males 35-49 Years of Age ATB.

|=========================================================================================================| |T65DR DOSIMETRY, NEUTRON RBE = 2.0||DS86 DOSIMETRY, NEUTRON RBE = 20| | || | | The Basic Data for 35-49 year-old Males ATB || The Basic Data for 35-49 year-old Males ATB | | (Hiroshima plus Nagasaki combined) || (Hiroshima plus Nagasaki combined) | | from Tables 11-B and 26-A,B. || from Tables 11-B and 26-A,B. | |================================================= || ================================================ | | Dose- Organ- Total MALES Cancers || Dose- Organ Total MALES Cancers | | Group Dose Cancers Entered per || Group Dose Cancers Entered per | | in for into Initial || in for into Initial | | cSv 1950-82 Study 10,000 || cSv 1950-82 Study 10,000 | | || | | Group 1+2 0.65 963 5999 1605.27 || Group 1+2 0.95 963 5999 1605.27 | | Group 3 11.47 240 1381 1737.87 || Group 3 15.47 240 1381 1737.87 | | Group 4 35.66 82 438 1872.15 || Group 4 40.56 82 438 1872.15 | | Group 5 69.45 72 368 1956.52 || Group 5 74.85 72 368 1956.52 | | Group 6 120.43 24 133 1804.51 || Group 6 121.05 24 133 1804.51 | | Group 7 171.23 12 70 1714.29 || Group 7 175.05 12 70 1714.29 | | Group 8 266.80 28 111 2522.52 || Group 8 326.23 28 111 2522.52 | |================================================= || ================================================ | | Combining the dose-classes, we have || Combining the dose-classes we have, | | || | | Dose- Organ- Total Persons Cancers || Dose- Organ Total Persons Cancers | | Groups Dose Cancers Entered 10,000 || Groups Dose Cancers Entered 10,000 | | Com- in for into persons || Com- in for into persons | | bined cSv 1950-82 Study (R value) || bined cSv 1950-82 Study (R value) | | || | | 1+2+3 2.67 1203 7380 1630.08 || 1+2+3 3.67 1203 7380 1630.08 | | 4+5+6+7+8 88.21 218 1120 1946.43 || 4+5+6+7+8 98.10 218 1120 1946.43 | | || | |================================================= || ================================================ | | For application of Equation (7) to these data, || For application of Equation (7) to these data, | | || | | D1 = 2.67 centi-Sieverts ( rems ) || D1 = 3.67 centi-Sieverts ( rems ) | | D2 = 88.21 centi-Sieverts ( rems ) || D2 = 98.10 centi-Sieverts ( rems ) | | R1 = 1630.08 cancers per 10,000 persons, 1950-82 || R1 = 1630.08 cancers per 10,000 persons, 1950-82 | | R2 = 1946.43 cancers per 10,000 persons, 1950-82 || R2 = 1946.43 cancers per 10,000 persons, 1950-82 | | R2/R1 = 1.19 || R2/R1 = 1.19 | | || | | The numerator for Equation (7) is : || The numerator for Equation (7) is: | | (R2/R1) - 1 = 0.19 || (R2/R1) - 1 = 0.19 | | || | | The denominator for Equation (7) is : || The denominator for Equation (7) is : | | (D2) - (R2/R1)(D1) = (88.21)-(1.19)(2.67) || (D2) - (R2/R1)(D1) = (98.10)-(1.19)(3.67) | | = 85.02 || = 93.72 | | || | |The quotient, the K value = 0.00228||The quotient, the K value = 0.00207| |_________________________________________________________________________________________________________|

Calculation of Raw K-Values for Males 50+ Years of Age ATB.

|=========================================================================================================| |T65DR DOSIMETRY, NEUTRON RBE = 2.0||DS86 DOSIMETRY, NEUTRON RBE = 20| | || | | The Basic Data for 50+ year-old Males ATB || The Basic Data for 50+ year-old Males ATB | | (Hiroshima plus Nagasaki combined) || (Hiroshima plus Nagasaki combined) | | from Tables 11-B and 26-A,B. || from Tables 11-B and 26-A,B. | |================================================= || ================================================ | | Dose- Organ- Total MALES Cancers || Dose- Organ Total MALES Cancers | | Group Dose Cancers Entered per || Group Dose Cancers Entered per | | in for into Initial || in for into Initial | | cSv 1950-82 Study 10,000 || cSv 1950-82 Study 10,000 | | || | | Group 1+2 0.63 747 5097 1465.57 || Group 1+2 0.90 747 5097 1465.57 | | Group 3 11.05 155 1145 1353.71 || Group 3 14.81 155 1145 1353.71 | | Group 4 35.67 51 308 1655.84 || Group 4 42.64 51 308 1655.84 | | Group 5 72.24 40 234 1709.40 || Group 5 81.51 40 234 1709.40 | | Group 6 122.73 15 74 2027.03 || Group 6 129.76 15 74 2027.03 | | Group 7 177.14 3 34 882.35 || Group 7 195.16 3 34 882.35 | | Group 8 269.80 8 65 1230.77 || Group 8 339.69 8 65 1230.77 | |================================================= || ================================================ | | Combining the dose-classes, we have || Combining the dose-classes we have, | | || | | Dose- Organ- Total Persons Cancers || Dose- Organ Total Persons Cancers | | Groups Dose Cancers Entered 10,000 || Groups Dose Cancers Entered 10,000 | | Com- in for into persons || Com- in for into persons | | bined cSv 1950-82 Study (R value) || bined cSv 1950-82 Study (R value) | | || | | 1+2+3 2.54 902 6242 1445.05 || 1+2+3 3.45 902 6242 1445.05 | | 4+5+6+7+8 84.66 117 715 1636.36 || 4+5+6+7+8 98.63 117 715 1636.36 | | || | |================================================= || ================================================ | | For application of Equation (7) to these data, || For application of Equation (7) to these data, | | || | | D1 = 2.54 centi-Sieverts ( rems ) || D1 = 3.45 centi-Sieverts ( rems ) | | D2 = 84.66 centi-Sieverts ( rems ) || D2 = 98.63 centi-Sieverts ( rems ) | | R1 = 1445.05 cancers per 10,000 persons, 1950-82 || R1 = 1445.05 cancers per 10,000 persons, 1950-82 | | R2 = 1636.36 cancers per 10,000 persons, 1950-82 || R2 = 1636.36 cancers per 10,000 persons, 1950-82 | | R2/R1 = 1.13 || R2/R1 = 1.13 | | || | | The numerator for Equation (7) is : || The numerator for Equation (7) is: | | (R2/R1) - 1 = 0.13 || (R2/R1) - 1 = 0.13 | | || | | The denominator for Equation (7) is : || The denominator for Equation (7) is : | | (D2) - (R2/R1)(D1) = (84.66)-(1.13)(2.54) || (D2) - (R2/R1)(D1) = (98.63)-(1.13)(3.45) | | = 81.78 || = 94.73 | | || | |The quotient, the K value = 0.00162||The quotient, the K value = 0.00140| |_________________________________________________________________________________________________________|

Calculation of Raw K-Values for Females 0-9 Years of Age ATB.

|=========================================================================================================| |T65DR DOSIMETRY, NEUTRON RBE = 2.0||DS86 DOSIMETRY, NEUTRON RBE = 20| | || | | The Basic Data for 0-9 year-old Females ATB || The Basic Data for 0-9 year-old Females ATB | | (Hiroshima plus Nagasaki combined) || (Hiroshima plus Nagasaki combined) | | from Tables 15-A, 11-D, and 26-C,D). || from Tables 15-A, 11-D, and 26-C,D). | |================================================= || ================================================ | | Dose- Organ- Total FEMALES Cancers || Dose- Organ Total FEMALES Cancers | | Group Dose Cancers Entered per || Group Dose Cancers Entered per | | in for into Initial || in for into Initial | | cSv 1950-82 Study 10,000 || cSv 1950-82 Study 10,000 | | || | | Group 1+2 0.75 38 6935 54.79 || Group 1+2 0.84 38 6935 54.79 | | Group 3 12.61 9 1547 58.18 || Group 3 15.42 9 1547 58.18 | | Group 4 40.64 3 372 80.65 || Group 4 45.55 3 372 80.65 | | Group 5 83.04 3 213 140.85 || Group 5 86.88 3 213 140.85 | | Group 6 143.79 4 99 404.04 || Group 6 144.40 4 99 404.04 | | Group 7 209.16 1 41 243.90 || Group 7 217.63 1 41 243.90 | | Group 8 314.00 1 70 142.86 || Group 8 375.99 1 70 142.86 | |================================================= || ================================================ | | Combining the dose-classes, we have || Combining the dose-classes we have, | | || | | Dose- Organ- Total Persons Cancers || Dose- Organ Total Persons Cancers | | Groups Dose Cancers Entered 10,000 || Groups Dose Cancers Entered 10,000 | | Com- in for into persons || Com- in for into persons | | bined cSv 1950-82 Study (R value) || bined cSv 1950-82 Study (R value) | | || | | 1+2+3 2.91 47 8482 55.41 || 1+2+3 3.50 47 8482 55.41 | | 4+5+6+7+8 97.61 12 795 150.94 || 4+5+6+7+8 106.90 12 795 150.94 | | || | |================================================= || ================================================ | | For application of Equation (7) to these data, || For application of Equation (7) to these data, | | || | | D1 = 2.91 centi-Sieverts ( rems ) || D1 = 3.50 centi-Sieverts ( rems ) | | D2 = 97.61 centi-Sieverts ( rems ) || D2 = 106.90 centi-Sieverts ( rems ) | | R1 = 55.41 cancers per 10,000 persons, 1950-82 || R1 = 55.41 cancers per 10,000 persons, 1950-82 | | R2 = 150.94 cancers per 10,000 persons, 1950-82 || R2 = 150.94 cancers per 10,000 persons, 1950-82 | | R2/R1 = 2.72 || R2/R1 = 2.72 | | || | | The numerator for Equation (7) is : || The numerator for Equation (7) is: | | (R2/R1) - 1 = 1.72 || (R2/R1) - 1 = 1.72 | | || | | The denominator for Equation (7) is : || The denominator for Equation (7) is : | | (D2) - (R2/R1)(D1) = (97.61)-(2.72)(2.91) || (D2) - (R2/R1)(D1) = (106.90)-(2.72)(3.50) | | = 89.68 || = 97.36 | | || | |The quotient, the K value = 0.01922||The quotient, the K value = 0.01771| |_________________________________________________________________________________________________________|

Calculation of Raw K-Values for Females 10-19 Years of Age ATB.

|=========================================================================================================| |T65DR DOSIMETRY, NEUTRON RBE = 2.0||DS86 DOSIMETRY, NEUTRON RBE = 20| | || | | The Basic Data for 10-19 year-old Females ATB || The Basic Data for 10-19 year-old Females ATB | | (Hiroshima plus Nagasaki combined) || (Hiroshima plus Nagasaki combined) | | from Tables 11-D and 26-C,D). || from Tables 11-D and 26-C,D). | |================================================= || ================================================ | | Dose- Organ- Total FEMALES Cancers || Dose- Organ Total FEMALES Cancers | | Group Dose Cancers Entered per || Group Dose Cancers Entered per | | in for into Initial || in for into Initial | | cSv 1950-82 Study 10,000 || cSv 1950-82 Study 10,000 | | || | | Group 1+2 0.65 116 7403 156.69 || Group 1+2 0.80 116 7403 156.69 | | Group 3 10.71 23 1663 138.30 || Group 3 13.79 23 1663 138.30 | | Group 4 36.46 7 543 128.91 || Group 4 39.15 7 543 128.91 | | Group 5 72.44 18 556 323.74 || Group 5 68.10 18 556 323.74 | | Group 6 122.62 8 264 303.03 || Group 6 110.72 8 264 303.03 | | Group 7 172.26 8 118 677.97 || Group 7 183.68 8 118 677.97 | | Group 8 263.31 6 111 540.54 || Group 8 324.60 6 111 540.54 | |================================================= || ================================================ | | Combining the dose-classes, we have || Combining the dose-classes we have, | | || | | Dose- Organ- Total Persons Cancers || Dose- Organ Total Persons Cancers | | Groups Dose Cancers Entered 10,000 || Groups Dose Cancers Entered 10,000 | | Com- in for into persons || Com- in for into persons | | bined cSv 1950-82 Study (R value) || bined cSv 1950-82 Study (R value) | | || | | 1+2+3 2.50 139 9066 153.32 || 1+2+3 3.18 139 9066 153.32 | | 4+5+6+7+8 89.20 47 1592 295.23 || 4+5+6+7+8 91.74 47 1592 295.23 | | || | |================================================= || ================================================ | | For application of Equation (7) to these data, || For application of Equation (7) to these data, | | || | | D1 = 2.50 centi-Sieverts (rems) || D1 = 3.18 centi-Sieverts (rems) | | D2 = 89.20 centi-Sieverts (rems) || D2 = 91.74 centi-Sieverts (rems) | | R1 = 153.32 cancers per 10,000 persons, 1950-82 || R1 = 153.32 cancers per 10,000 persons, 1950-82 | | R2 = 295.23 cancers per 10,000 persons, 1950-82 || R2 = 295.23 cancers per 10,000 persons, 1950-82 | | R2/R1 = 1.93 || R2/R1 = 1.93 | | || | | The numerator for Equation (7) is : || The numerator for Equation (7) is: | | (R2/R1) - 1 = 0.93 || (R2/R1) - 1 = 0.93 | | || | | The denominator for Equation (7) is : || The denominator for Equation (7) is : | | (D2) - (R2/R1)(D1) = (89.20)-(1.93)(2.50) || (D2) - (R2/R1)(D1) = (91.74)-(1.93)(3.18) | | = 84.39 || = 85.62 | | || | |The quotient, the K value = 0.01097||The quotient, the K value = 0.01081| |_________________________________________________________________________________________________________|

Calculation of Raw K-Values for Females 20-34 Years of Age ATB.

|=========================================================================================================| |T65DR DOSIMETRY, NEUTRON RBE = 2.0||DS86 DOSIMETRY, NEUTRON RBE = 20| | || | | The Basic Data for 20-34 year-old Females ATB || The Basic Data for 20-34 year-old Females ATB | | (Hiroshima plus Nagasaki combined) || (Hiroshima plus Nagasaki combined) | | from Tables 15-A, 11-D, and 26-C,D). || from Tables 15-A, 11-D, and 26-C,D). | |================================================= || ================================================ | | Dose- Organ- Total FEMALES Cancers || Dose- Organ Total FEMALES Cancers | | Group Dose Cancers Entered per || Group Dose Cancers Entered per | | in for into Initial || in for into Initial | | cSv 1950-82 Study 10,000 || cSv 1950-82 Study 10,000 | | || | | Group 1+2 0.66 396 9260 427.65 || Group 1+2 0.89 396 9260 427.65 | | Group 3 10.98 121 2189 552.76 || Group 3 14.85 121 2189 552.76 | | Group 4 35.61 36 670 537.31 || Group 4 42.38 36 670 537.31 | | Group 5 72.59 22 436 504.59 || Group 5 75.91 22 436 504.59 | | Group 6 122.38 22 192 1145.83 || Group 6 121.79 22 192 1145.83 | | Group 7 172.35 6 103 582.52 || Group 7 182.47 6 103 582.52 | | Group 8 256.22 13 152 855.26 || Group 8 320.87 13 152 855.26 | |================================================= || ================================================ | | Combining the dose-classes, we have || Combining the dose-classes we have, | | || | | Dose- Organ- Total Persons Cancers || Dose- Organ Total Persons Cancers | | Groups Dose Cancers Entered 10,000 || Groups Dose Cancers Entered 10,000 | | Com- in for into persons || Com- in for into persons | | bined cSv 1950-82 Study (R value) || bined cSv 1950-82 Study (R value) | | || | | 1+2+3 2.63 517 11449 451.57 || 1+2+3 3.56 517 11449 451.57 | | 4+5+6+7+8 87.38 99 1553 637.48 || 4+5+6+7+8 98.16 99 1553 637.48 | | || | |================================================= || ================================================ | | For application of Equation (7) to these data, || For application of Equation (7) to these data, | | || | | D1 = 2.63 centi-Sieverts (rems) || D1 = 3.56 centi-Sieverts ( rems ) | | D2 = 87.38 centi-Sieverts (rems) || D2 = 98.16 centi-Sieverts ( rems ) | | R1 = 451.57 cancers per 10,000 persons, 1950-82 || R1 = 451.57 cancers per 10,000 persons, 1950-82 | | R2 = 637.48 cancers per 10,000 persons, 1950-82 || R2 = 637.48 cancers per 10,000 persons, 1950-82 | | R2/R1 = 1.41 || R2/R1 = 1.41 | | || | | The numerator for Equation (7) is : || The numerator for Equation (7) is: | | (R2/R1) - 1 = 0.41 || (R2/R1) - 1 = 0.41 | | || | | The denominator for Equation (7) is : || The denominator for Equation (7) is : | | (D2) - (R2/R1)(D1) = (87.38)-(1.41)(2.63) || (D2) - (R2/R1)(D1) = (98.16)-(1.41)(3.56) | | = 83.66 || = 93.14 | | || | |The quotient, the K value = 0.00492||The quotient, the K value = 0.00442| |_________________________________________________________________________________________________________|

Calculation of Raw K-Values for Females 35-49 Years oF Age ATB.

|=========================================================================================================| |T65DR DOSIMETRY, NEUTRON RBE = 2.0||DS86 DOSIMETRY, NEUTRON RBE = 20| | || | | The Basic Data for 35-49 year-old Females ATB || The Basic Data for 35-49 year-old Females ATB | | (Hiroshima plus Nagasaki combined) || (Hiroshima plus Nagasaki combined) | | from Tables 15-A, 11-D, and 26-C,D). || from Tables 15-A, 11-D, and 26-C,D). | |================================================= || ================================================ | | Dose- Organ- Total FEMALES Cancers || Dose- Organ Total FEMALES Cancers | | Group Dose Cancers Entered per || Group Dose Cancers Entered per | | in for into Initial || in for into Initial | | cSv 1950-82 Study 10,000 || cSv 1950-82 Study 10,000 | | || | | Group 1+2 0.63 925 8838 1046.62 || Group 1+2 0.84 925 8838 1046.62 | | Group 3 10.99 274 2291 1195.98 || Group 3 15.22 274 2291 1195.98 | | Group 4 34.65 76 582 1305.84 || Group 4 43.00 76 582 1305.84 | | Group 5 70.01 42 366 1147.54 || Group 5 78.94 42 366 1147.54 | | Group 6 120.80 20 155 1290.32 || Group 6 127.99 20 155 1290.32 | | Group 7 176.89 12 74 1621.62 || Group 7 195.39 12 74 1621.62 | | Group 8 262.14 18 97 1855.67 || Group 8 328.33 18 97 1855.67 | |================================================= || ================================================ | | Combining the dose-classes, we have || Combining the dose-classes we have, | | || | | Dose- Organ- Total Persons Cancers || Dose- Organ Total Persons Cancers | | Groups Dose Cancers Entered 10,000 || Groups Dose Cancers Entered 10,000 | | Com- in for into persons || Com- in for into persons | | bined cSv 1950-82 Study (R value) || bined cSv 1950-82 Study (R value) | | || | | 1+2+3 2.76 1199 11129 1077.37 || 1+2+3 3.80 1199 11129 1077.37 | | 4+5+6+7+8 80.87 168 1274 1318.68 || 4+5+6+7+8 94.24 168 1274 1318.68 | | || | |================================================= || ================================================ | | For application of Equation (7) to these data, || For application of Equation (7) to these data, | | || | | D1 = 2.76 centi-Sieverts (rems) || D1 = 3.80 centi-Sieverts (rems) | | D2 = 80.87 centi-Sieverts (rems) || D2 = 94.24 centi-Sieverts (rems) | | R1 = 1077.37 cancers per 10,000 persons, 1950-82 || R1 = 1077.37 cancers per 10,000 persons, 1950-82 | | R2 = 1318.68 cancers per 10,000 persons, 1950-82 || R2 = 1318.68 cancers per 10,000 persons, 1950-82 | | R2/R1 = 1.22 || R2/R1 = 1.22 | | || | | The numerator for Equation (7) is : || The numerator for Equation (7) is: | | (R2/R1) - 1 = 0.22 || (R2/R1) - 1 = 0.22 | | || | | The denominator for Equation (7) is : || The denominator for Equation (7) is : | | (D2) - (R2/R1)(D1) = (80.87)-(1.22)(2.76) || (D2) - (R2/R1)(D1) = (94.24)-(1.22)(3.80) | | = 77.49 || = 89.59 | | || | |The quotient, the K value = 0.00289||The quotient, the K value = 0.00250| |_________________________________________________________________________________________________________|

Calculation of Raw K-Values for Females 50+ Years of Age ATB.

|=========================================================================================================| |T65DR DOSIMETRY, NEUTRON RBE = 2.0||DS86 DOSIMETRY, NEUTRON RBE = 20| | || | | The Basic Data for 50+ year-old Females ATB || The Basic Data for 50+ year-old Females ATB | | (Hiroshima plus Nagasaki combined) || (Hiroshima plus Nagasaki combined) | | from Tables 11-D and 26-C,D). || from Tables 11-D and 26-C,D). | |================================================= || ================================================ | | Dose- Organ- Total FEMALES Cancers || Dose- Organ Total FEMALES Cancers | | Group Dose Cancers Entered per || Group Dose Cancers Entered per | | in for into Initial || in for into Initial | | cSv 1950-82 Study 10,000 || cSv 1950-82 Study 10,000 | | || | | Group 1+2 0.62 608 6007 1012.15 || Group 1+2 0.82 608 6007 1012.15 | | Group 3 10.82 159 1365 1164.84 || Group 3 14.90 159 1365 1164.84 | | Group 4 35.35 39 374 1042.78 || Group 4 43.68 39 374 1042.78 | | Group 5 71.74 27 171 1578.95 || Group 5 77.44 27 171 1578.95 | | Group 6 119.04 9 70 1285.71 || Group 6 125.23 9 70 1285.71 | | Group 7 175.10 3 33 909.09 || Group 7 192.27 3 33 909.09 | | Group 8 274.06 7 34 2058.82 || Group 8 343.56 7 34 2058.82 | |================================================= || ================================================ | | Combining the dose-classes, we have || Combining the dose-classes we have, | | || | | Dose- Organ- Total Persons Cancers || Dose- Organ Total Persons Cancers | | Groups Dose Cancers Entered 10,000 || Groups Dose Cancers Entered 10,000 | | Com- in for into persons || Com- in for into persons | | bined cSv 1950-82 Study (R value) || bined cSv 1950-82 Study (R value) | | || | | 1+2+3 2.51 767 7372 1040.42 || 1+2+3 3.43 767 7372 1040.42 | | 4+5+6+7+8 71.73 85 682 1246.33 || 4+5+6+7+8 82.65 85 682 1246.33 | | || | |================================================= || ================================================ | | For application of Equation (7) to these data, || For application of Equation (7) to these data, | | || | | D1 = 2.51 centi-Sieverts (rems) || D1 = 3.43 centi-Sieverts (rems) | | D2 = 71.73 centi-Sieverts (rems) || D2 = 82.65 centi-Sieverts (rems) | | R1 = 1040.42 cancers per 10,000 persons, 1950-82 || R1 = 1040.42 cancers per 10,000 persons, 1950-82 | | R2 = 1246.33 cancers per 10,000 persons, 1950-82 || R2 = 1246.33 cancers per 10,000 persons, 1950-82 | | R2/R1 = 1.20 || R2/R1 = 1.20 | | || | | The numerator for Equation (7) is : || The numerator for Equation (7) is: | | (R2/R1) - 1 = 0.20 || (R2/R1) - 1 = 0.20 | | || | | The denominator for Equation (7) is : || The denominator for Equation (7) is : | | (D2) - (R2/R1)(D1) = (71.73)-(1.20)(2.51) || (D2) - (R2/R1)(D1) = (82.65)-(1.20)(3.43) | | = 68.72 || = 78.55 | | || | |The quotient, the K value = 0.00288||The quotient, the K value = 0.00252| |_________________________________________________________________________________________________________|

T65DR And DS86

K-Values for Low-Dose Exposure, up to 5

K is the fractional increase in the spontaneous cancer death-rate

per cSv of whole-body organ-dose.

|========================================================================================================================| | || | |T65DR DOSIMETRY, NEUTRON RBE = 2.0||DS86 DOSIMETRY, NEUTRON RBE = 20| | || | |============================================================= || =====================================================| | Low-Dose || Low-Dose | | AGE | MALES K || MALES K | | ATB | EQUATION OF BEST FIT Per cSv || EQUATION OF BEST FIT Per cSv | | | || | | 0-9 | Ca-Rate = (2.5937)(Dose^0.75)+(25.3161) 0.06851 || Ca-rate = (2.4549)(Dose^0.75)+(24.8117) 0.06617 | | | || | | 10-19 | Ca-Rate = (3.8365)(Dose^0.75)+(168.925) 0.01519 || Ca-Rate = (3.7215)(Dose^0.75)+(167.7256) 0.01484 | | | || | | 20-34 | Ca-Rate = (3.5274)(Dose^0.75)+(688.498) 0.003426 || Ca-Rate = (3.4358)(Dose^0.75)+(686.8894) 0.003344 | | | || | | 35-49 | Ca-Rate = (11.8508)(Dose^0.75)+(1605.326) 0.004936 || Ca-Rate = (11.0924)(Dose^0.75)+(1600.667) 0.004634 | | | || | | 50+ | Ca-Rate = (7.3871)(Dose^0.75)+(1430.187) 0.003454 || Ca-Rate = (6.6506)(Dose^0.75)+(1428.214) 0.003114 | |============================================================= || =====================================================| | | Low-Dose || Low-Dose | | AGE | FEMALES K || FEMALES K | | ATB | EQUATION OF BEST FIT Per cSv || EQUATION OF BEST FIT Per cSv | | | || | | 0-9 | Ca-Rate = (3.3140)(Dose^0.75)+(48.0263) 0.04615 || Ca-Rate = (3.1131)(Dose^0.75)+(47.4440) 0.04388 | | | || | | 10-19 | Ca-Rate = (5.2487)(Dose^0.75)+(142.885) 0.02457 || Ca-Rate = (5.2055)(Dose^0.75)+(140.9239) 0.02470 | | | || | | 20-34 | Ca-Rate = (7.0116)(Dose^0.75)+(437.0894) 0.01073 || Ca-Rate = (6.5018)(Dose^0.75)+(434.7191) 0.01000 | | | || | | 35-49 | Ca-Rate = (9.7200)(Dose^0.75)+(1056.556) 0.006152 || Ca-Rate = (8.7670)(Dose^0.75)+(1053.509) 0.005565 | | | || | | 50+ | Ca-Rate = (9.0896)(Dose^0.75)+(1022.294) 0.005945 || Ca Rate = (8.2725)(Dose^0.75)+(1019.570) 0.005425 | |========================================================================================================================|

- The two-step method for obtaining the Equation of Best Fit and
the low-dose K-value for each age-sex group is explained by the
text in detail.

- The raw K-values (assembled below from Tables 15-B through 15-K) were calculated for the purpose of comparison with the low-dose K-values above. The low-dose K-values are larger -- due to the supra-linearity of dose-response -- by a factor of about 2.3 (details in text). Therefore the raw K-values will underestimate cancer-risk from low-dose exposure by more than 2-fold, and should not be used for such exposures.

___________________________________________________________________________________ | | |T65DR Age-Band Males Females DS86 Age-Band Males Females| |ATB Raw K Raw K ATB Raw K Raw K| |0-9 0.02749 0.01922 0-9 0.02565 0.01771| |10-19 0.00677 0.01097 10-19 0.00647 0.01081| |20-34 0.00157 0.00492 20-34 0.00150 0.00442| |35-49 0.00228 0.00289 35-49 0.00207 0.00250| |50+ 0.00162 0.00288 50+ 0.00140 0.00252| |_________________________________________________________________________________|

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