Low-Dose Extrapolation Factors Implied by Mortality and Incidence Data from the Japanese Atomic Bomb Survivor Life Span Study Data

Abstract

Assessment of the effect of low dose and low-dose-rate exposure depends critically on extrapolation from groups exposed at high dose and high-dose rates such as the Japanese atomic bomb survivor data, and has often been achieved via application of a dose and dose-rate effectiveness factor (DDREF). An important component of DDREF is the factor determining the effect of extrapolation of dose, the so-called low-dose extrapolation factor (LDEF). To assess LDEF models linear (or linear quadratic) in dose are often fitted. In this report LDEF is assessed via fitting relative rate models that are linear or linear quadratic in dose to the latest Japanese atomic bomb survivor data on solid cancer, leukemia and circulatory disease mortality (followed from 1950 through 2003) and to data on solid cancer, lung cancer and urinary tract cancer incidence. The uncertainties in LDEF are assessed using parametric bootstrap techniques. Analysis is restricted to survivors with <3 Gy dose. There is modest evidence for upward curvature in dose response in the mortality data. For leukemia and for all solid cancer excluding lung, stomach and breast cancer there is significant curvature (P < 0.05). There is no evidence of curvature for circulatory disease (P > 0.5). The estimate of LDEF for all solid cancer mortality is 1.273 [95% confidence intervals (CI) 0.913, 2.182], for all solid cancer mortality excluding lung cancer, stomach cancer and breast cancer is 2.183 (95% CI 1.090, >100) and for leukemia mortality is 11.447 (95% CI 2.390, >100). For stomach cancer mortality LDEF is modestly raised, 1.077 (95% CI 0.526, >100), while for lung cancer, female breast cancer and circulatory disease mortality the LDEF does not much exceed 1. LDEF for solid cancer incidence is 1.186 (95% CI 0.942, 1.626) and for urinary tract cancer is 1.298 (95% CI <0, 7.723), although for lung cancer LDEF is not elevated, 0.842 (95% CI 0.344, >100).

INTRODUCTION

It has long been assumed that radiation-induced cancer rates (per unit dose) at low doses or low-dose rates are lower than those at higher doses and dose rates (1, 2). Based on a mixture of experimental and epidemiologic evidence the International Commission on Radiological Protection (ICRP) recommended the use of a dose and dose-rate effectiveness factor (DDREF) of 2 to reduce solid cancer rates obtained from moderate-to-high acute dose studies (e.g., those derived from the Japanese atomic bomb survivors) when applied to low dose or low-dose-rate exposures (1).

Determining the effect of curvature in the dose response and its impact on low-dose effects is separate from the effect that may be produced by amelioration of dose rate. This suggests that DDREF can be decomposed into two components, specifically a factor determining the effect of extrapolation of dose, the so-called low-dose extrapolation factor (LDEF), as well as the effect of reduction from high dose rate to low dose rate, via the dose rate extrapolation factor (DREF) (3). To assess LDEF models linear (or linear quadratic) in dose are often fitted. LDEF can then be defined as the ratio of the slope of the straight line fitted to a specific dose range to the low-dose slope (as derived via fitting a linear-quadratic model). In particular this has been done for cancer in the atomic bomb survivor Life Span Study (LSS) cohort data (4, 5).

Recently the ICRP Task Group 91 (TG 91) has reexamined the evidence for such ameliorating effects of lower dose or lower dose-rate exposures. An important reanalysis of the recently released Japanese atomic bomb survivor LSS mortality data suggested that risks (per unit dose) at low dose for a number of cancer mortality endpoints were less than those at high dose, suggesting that LDEF was greater than 1, although LDEF was not formally evaluated in the way outlined above (6).

Here we more formally evaluate evidence for LDEF in the LSS mortality data previously analyzed by Ozasa et al. (7), and in incidence data previously analyzed by Grant et al. (8), Cahoon et al. (9) and Grant et al. (10). We shall compare our assessments of LDEF with those derived from a recent analysis of the LSS cancer mortality and incidence data by Brenner et al. (11). This work was undertaken as part of work done for ICRP TG 91 by the first author.

METHODS

Poisson disease models were used for all fitting to the LSS mortality and incidence data, following closely the structure of the existing publicly available datasets of Ozasa et al. (7), Grant et al. (8), Cahoon et al. (9) and Grant et al. (10). The models that were used in this paper are functions of the mean organ/tissue dose, D_id, averaged over the survivors in stratum i and dose group d. Stratified relative rate models were used for all malignant and circulatory disease endpoints, where the expected number of cancer or circulatory disease deaths, or cancer cases in the stratum i [for the mortality data defined by city, sex, attained age, age at exposure, calendar period of follow-up, Adult Health Study (AHS) status, and for the incidence data defined by city, sex, attained age, age at exposure, calendar period of follow-up, and smoking status] with mean age at exposure e, mean attained age a and dose group d with average organ/tissue dose, D_id is:

$$P{Y}_{id}{h}_i\left[1+\left(\alpha D_{id}+\beta D_{id}^2\right)\exp \left({\text{γ}}_1{1}_{sex1=f}+{\text{γ}}_2\left[e_{id}-e_{av}\right]+{\text{γ}}_3\text{In}\left[a_{id}/a_{av}\right]\right)\right]$$ (1)

Where PY_id is the number of person-years of follow-up in the stratum, and h_i is the baseline cancer (or circulatory disease) mortality/incidence rate. In the full mortality dataset of Ozasa et al. (7) the centering values of e_av = 22.41 y and a_av = 50.49 y are used, the mean person-year weighted values of age at exposure and attained age in the full dataset, respectively, while in the incidence datasets of Grant et al. (8), Cahoon et al. (9) and Grant et al. (10) the values of e_av = 21.99 y and a_av = 55.52 y are employed. The dose D_id is measured in Gy, weighted by a neutron relative biological effectiveness (RBE) value of 10 (1), as employed in most previous LSS analyses (12–14). The appropriate RBE-weighted organ/tissue dose was used for the relevant analyses of each cancer site (lung, stomach, breast, red bone marrow); for all solid cancers combined, colon dose was used, and for circulatory disease lung dose was employed. For urinary tract cancer incidence urinary bladder dose was employed. The adjustments for sex, age at exposure and attained age given in Eq. (1) are exactly those used by Ozasa et al. (7). For female breast cancer the adjustment for sex was irrelevant (so setting γ₁ = 0), and for stomach cancer the given model exhibited convergence problems with certain bootstrap samples, and so a simpler model having adjustment to the excess relative rate (ERR) only for attained age was employed (setting γ₁ = γ₂ = 0). Unadjusted ERR models were also fitted (setting the adjustment factors γ₁ = γ₂ = γ₃ = 0). The Dosimetry System 2002 (DS02) organ doses are those employed by Ozasa et al. (7), and incorporate the customary Radiation Effects Research Foundation (RERF) determined adjustments for dose errors, using standard regression calibration techniques (15). For the three cancer incidence datasets (8–10) a slightly revised dosimetry, DS02R1 is used. For the urinary tract cancer incidence data convergence was much slower, and so we used only 399 bootstrap samples, rather than the 999 used for all other endpoints.

Models were fitted by Poisson maximum likelihood (16). To get periods of follow-up more comparable with that for the LSS incidence data, we also fitted models to the mortality data with follow-up starting in 1961 (through 2003), as well as for the full follow-up (1950–2003). (1/1/1961 is the beginning of the first follow-up group in the publicly released version of the mortality data which entirely post-dates the start of incidence follow-up in 1/1/1958.) We fitted a linear model (estimating α_L with β_L = 0) and a linear quadratic model (estimating α_LQ and β_LQ), and estimated LDEF via LDER = α_L/α_LQ. To estimate uncertainties on the LDEF parametric bootstrap simulation was employed, with numbers of deaths or cases in each cell of the person year table simulated from Poisson random variables with mean given by the mean number of deaths or cases predicted for that cell by the linear-quadratic model as given by Eq. (1). The bootstrap simulations were used to assess the variance and covariance in the linear coefficients for the linear and linear-quadratic models, and Fieller’s theorem (17, 18) was then employed to assess the confidence interval (CI) in the ratio of these linear coefficients. In a few cases the estimates provided by Fieller’s theorem were non-informative (because the CI were complex) and in these cases the bootstrap sample was used directly to estimate the CI.

RESULTS

Table 1 illustrates the modest evidence for upward curvature in dose response in the mortality data. In general, only for leukemia and solid cancer excluding lung, stomach and breast cancer is this significant (P < 0.05), although the curvature is not significant for the latter endpoint over the restricted period of follow-up (1961–2003). Of the solid cancer mortality sites given in the publicly released data cancers of the colon and kidney are the only endpoints with significant (upward) curvature (P < 0.05). There is no evidence of curvature for circulatory disease (P > 0.5).

TABLE 1.

Maximum Likelihood Fits of Stratified Linear and Linear-Quadratic Excess Relative Rate (ERR) Models in Dose to LSS Mortality Data of Ozasa et al. (7), Restricted to Unadjusted Weighted Colon Dose <3 Gy, with Full Follow-up (from 1950–2003) or with Partial Follow-up (1961–2003), and Estimated LDEF

	Linear model	Linear-quadratic model
Endpoint	ERR/Gy (+95% CI)	ERR/Gy (+95% CI)	ERR/Gy2 (+ 95% CI)	P valuea	LDEF (+95% CI)
Under 3 Gy colon dose, all years of follow-up (1950–2003), unadjusted
All solid cancerb	0.516 (0.416, 0.622)	0.428 (0.237, 0.627)	0.061 (−0.055, 0.179)	0.307	1.204 (0.880, 1.939)
Lungc	0.693 (0.438, 0.998)	0.893 (0.400, 1.441)	−0.121 (−0.367, 0.142)	0.357	0.777 (0.507, 1.484)
Stomachd	0.291 (0.143, 0.463)	0.218 (−0.076, 0.536)	0.044 (−0.113, 0.212)	0.586	1.335 (0.572, >100)
Female breaste	2.098 (1.239, 3.273)	2.189 (0.924, 3.783)	−0.060 (−0.631, 0.684)	0.855	0.959 (0.614, 2.142)
All solid excluding lung, stomach, breastb	0.474 (0.345, 0.616)	0.264 (0.011, 0.530)	0.145 (−0.012, 0.309)	0.071	1.799 (0.983, 31.677)
Leukemiaf	5.282 (3.679, 7.432)	1.169 (−0.772, 3.518)	3.795 (1.880, 6.315)	<0.001	4.519 (1.754, >100)
All circulatory diseasec	0.155 (0.097, 0.217)	0.149 (0.033, 0.269)	0.004 (−0.054, 0.062)	0.905	1.041 (0.603, 3.572)
Under 3 Gy colon dose, all years of follow-up (1950–2003), adjusted for sex, age at exposure, attained ageg
All solid cancerb	0.608 (0.395, 0.864)	0.477 (0.247, 0.792)	0.084 (−0.042, 0.224)	0.186	1.273 (0.913, 2.182)
Lungc	0.614 (0.158, 1.507)	0.761 (0.180, 2.006)	−0.084 (−0.433, 0.172)	0.459	0.806 (0.313, 1.760)h
Stomachd	0.536 (0.280, 0.856)	0.497 (0.019, 1.047)	0.024 (−0.236, 0.309)	0.859	1.077 (0.526, >100)
Female breaste	2.818 (1.382, 4.843)	2.964 (1.142, 5.553)	−0.096 (−0.889, 0.930)	0.826	0.951 (0.578, 2.369)
All solid excluding lung, stomach, breastb	0.790 (0.459, 1.214)	0.362 (−0.024, 0.882)	0.282 (0.031, 0.613)	0.027	2.183 (1.090, >100)
Leukemiaf	4.655 (2.596, 7.895)	0.407 (−0.635, 2.352)	3.430 (1.708, 6.339)	<0.001	11.447 (2.390, >100)
All circulatory diseasec	0.150 (0.049, 0.293)	0.148 (0.038, 0.343)	0.002 (−0.059, 0.061)	0.953	1.019 (<0, 2.316)h
Under 3 Gy colon dose, later follow-up (1961–2003), unadjusted
All solid cancerb	0.537 (0.430, 0.652)	0.459 (0.254, 0.673)	0.054 (−0.069, 0.180)	0.394	1.170 (0.835, 1.966)
Lungc	0.694 (0.436, 1.004)	0.853 (0.354, 1.409)	−0.097 (−0.348, 0.173)	0.471	0.814 (0.525, 1.593)
Stomachd	0.308 (0.144, 0.501)	0.206 (−0.118, 0.558)	0.062 (−0.111, 0.249)	0.490	1.500 (0.550, >100)
Female breaste	2.154 (1.250, 3.416)	2.121 (0.780, 3.829)	0.022 (−0.604, 0.842)	0.950	1.016 (0.635, 2.576)
All solid excluding lung, stomach, breastb	0.482 (0.345, 0.634)	0.319 (0.050, 0.604)	0.112 (−0.053, 0.282)	0.186	1.512 (0.846, 9.799)
Leukemiaf	3.507 (2.173, 5.398)	0.475 (−1.260, 2.674)	2.543 (0.976, 4.658)	<0.001	7.385 (1.546, >100)
All circulatory diseasec	0.159 (0.096, 0.226)	0.175 (0.050, 0.305)	−0.009 (−0.071, 0.054)	0.774	0.908 (0.526, 2.921)
Under 3 Gy colon dose, later follow-up (1961–2003), adjusted for sex, age at exposure, attained ageg
All solid cancerb	0.764 (0.488, 1.106)	0.642 (0.335, 1.067)	0.078 (−0.084, 0.253)	0.333	1.191 (0.850, 1.991)
Lungc	0.706 (0.185, 1.726)	0.840 (0.199, 2.226)	−0.078 (−0.461, 0.224)	0.549	0.841 (0.330, 1.840)h
Stomachd	0.646 (0.312, 1.080)	0.602 (0.017, 1.317)	0.027 (−0.297, 0.374)	0.870	1.073 (0.504, >100)
Female breaste	2.944 (1.325, 5.451)	2.998 (1.054, 6.060)	−0.036 (−0.915, 1.118)	0.938	0.982 (0.554, 4.164)
All solid excluding lung, stomach, breastb	0.994 (0.550, 1.589)	0.601 (0.103, 1.349)	0.245 (−0.072, 0.632)	0.126	1.654 (0.947, 10.731)
Leukemiaf	3.762 (1.762, 7.190)	0.353 (−1.246, 2.848)	2.957 (1.106, 6.415)	<0.001	10.671 (1.229, >100)
All circulatory diseasec	0.225 (0.079, 0.439)	0.254 (0.081, 0.542)	−0.019 (−0.109, 0.069)	0.615	0.886 (0.320, >100)

Notes. Profile likelihood confidence intervals (CI) are given for the linear and quadratic coefficients, and bootstrap CI for the LDEF are based on n = 999 samples. Strata defined by city, sex, ground distance category, attained age category, age at exposure category, calendar period, AHS group. Unless otherwise indicated all CI for LDEF use the composite method, via Fieller’s theorem.

^aP value of improvement in fit of linear-quadratic model vs. linear model.

^bUsing colon dose.

^cUsing lung dose.

^dUsing stomach dose.

^eUsing breast dose.

^fUsing red bone marrow dose.

^gERR models for female breast cancer are adjusted for age at exposure and attained age, for stomach cancer adjusted for attained age, and for all other endpoints adjusted for sex, age at exposure and attained age.

^hCI based on Fieller’s theorem was not feasible (imaginary roots of defining equation), so that CI are based on centiles of bootstrap sample.

Nevertheless, the LDEF for some sites was above 1, in particular for all solid cancer (LDEF = 1.273, 95% CI 0.913, 2.182), for stomach cancer (LDEF = 1.077, 95% CI 0.526, >100), all solid cancer excluding lung, stomach and breast cancer (LDEF = 2.183, 95% CI 1.090, >100), and leukemia (LDEF = 11.447, 95% CI 2.390, >100) (Table 1). The LDEF did not generally much exceed 1 for lung cancer, female breast cancer and circulatory disease. Analysis in which adjustment was made for sex, age at exposure, attained age yielded estimates of LDEF mostly close to those of the unadjusted analysis (Table 1). However, for stomach cancer the central estimate of LDEF in the unadjusted analysis was markedly higher (LDEF = 1.335, 95% CI 0.572, >100) than that for the adjusted analysis (LDEF = 1.077, 95% CI 0.526, >100). On the other hand, for leukemia the central estimate of LDEF in the unadjusted analysis was markedly lower (LDEF = 4.519, 95% CI 1.754, >100) than that for the adjusted analysis (LDEF = 1.447, 95% CI 2.390, >100) (Table 1). It should be noted that the uncertainties in each case are considerable.

Analyses of cancer incidence reported in Table 2 suggest generally modest curvature, so that for no endpoint did this approach statistical significance (P > 0.1). Nevertheless, as with the mortality analysis the LDEF for some endpoints were above 1, in particular for all solid cancer (LDEF = 1.186, 95% CI 0.942, 1.626) and for urinary tract cancer (LDEF = 1.298, 95% CI <0, 7.723) (Table 2). Very minor difference was made by the exclusion of autopsy only cases from all solid cancer (Table 2).

TABLE 2.

Maximum Likelihood Fits of Stratified Linear and Linear-Quadratic Excess Relative Rate (ERR) Models in Dose to LSS Solid Cancer Incidence Data of Grant et al. (8), Lung Cancer Incidence Data of Cahoon et al. (9) and Urinary Tract Incidence Data of Grant et al. (10) Restricted to Unadjusted Weighted Dose < 3 Gy, and Estimated LDEF

	Linear model	Linear-quadratic model
Endpoint	ERR/Gy (+95% CI)	ERR/Gy (+ 95% CI)	ERR/Gy2 (+95% CI)	P valuea	LDEF (+95% CI)
Under 3 Gy dose, unadjusted
All solid cancerb	0.658 (0.578, 0.741)	0.557 (0.392, 0.724)	0.086 (−0.037, 0.213)	0.173	1.182 (0.936, 1.617)
All solid cancer, excluding autopsy only casesb	0.684 (0.602, 0.769)	0.608 (0.441, 0.778)	0.064 (−0.060, 0.192)	0.316	1.124 (0.903, 1.496)
Lung cancerc	0.559 (0.358, 0.785)	0.649 (0.201, 1.122)	−0.066 (−0.350, 0.240)	0.666	0.862 (0.526, 2.162)
Urinary tract cancerd	0.798 (0.431, 1.235)	0.655 (−0.126, 1.524)	0.121 (−0.481, 0.767)	0.701	1.218 (0.543, >100)
Under 3 Gy dose, adjusted for sex, age at exposure, attained age
All solid cancerb	0.553 (0.421, 0.698)	0.466 (0.313, 0.652)	0.069 (−0.026, 0.169)	0.155	1.186 (0.942, 1.626)
All solid cancer, excluding autopsy only casesb	0.585 (0.449, 0.734)	0.509 (0.346, 0.704)	0.060 (−0.040, 0.163)	0.237	1.150 (0.920, 1.554)
Lung cancerc	0.429 (0.109, 0.867)	0.510 (0.122, 1.165)	−0.063 (−0.335, 0.177)	0.558	0.842 (0.344, >100)
Urinary tract cancerd	0.618 (0.080, 1.444)	0.476 (0.003, 1.545)	0.114 (−0.364, 0.703)	0.570	1.298 (<0, 7.723)e

Notes. Profile likelihood confidence intervals (CI) are given for the linear and quadratic coefficients, and bootstrap CI for the LDEF are based on n = 999 samples (n = 399 samples for urinary tract cancer). Strata defined by city, sex, attained age category, age at exposure category, calendar period, smoking group. Unless otherwise indicated all CI for LDEF use the composite method, via Fieller’s theorem.

^aP value of improvement in fit of linear-quadratic model vs linear model.

^bUsing colon dose.

^cUsing lung dose.

^dUsing urinary bladder dose.

^eCI based on Fieller’s theorem was not feasible (imaginary roots of defining equation), so that CI are based on centiles of bootstrap sample.

Analysis for mortality in which each gender was analyzed separately (Table 3) suggested that there was borderline significant upward curvature for male stomach cancer (P = 0.095), although not for female stomach cancer (P = 0.500). For all solid cancer excluding lung, stomach and breast cancer there was significant upward curvature for females (P = 0.042) but not for males (P = 0.300). Analysis in which follow-up was restricted to 1961 onwards in general yielded similar results, although the statistical evidence of curvature for both stomach cancer and all solid cancer excluding lung, stomach and breast cancer was no longer even borderline.

TABLE 3.

Maximum Likelihood Fits of Stratified Linear and Linear-Quadratic Excess Relative Rate (ERR) Models in Dose to LSS Mortality Data of Ozasa et al. (7) for Males and Females Separately, Restricted to Unadjusted Weighted Colon Dose <3 Gy, with Full Follow-up (from 1950–2003) or with Partial Follow-up (1961–2003)^a

		Linear model	Linear-quadratic model
Endpoint	Sex	ERR/Gy (+95% CI)	ERR/Gy (+95% CI)	ERR/Gy2 (+95% CI)	P valueb
Under 3 Gy colon dose, all years of follow-up (1950–2003), adjusted for age at exposure and attained age
All solid cancerc	Males	0.687 (0.434, 0.997)	0.557 (0.049, 1.093)	0.088 (−0.193, 0.422)	0.554
	Females	1.313 (0.996, 1.678)	1.046 (0.556, 1.595)	0.208 (−0.111, 0.555)	0.205
Lungd	Males	1.452 (0.451, 3.330)	1.917 (0.253, 4.787)	−0.291 (−1.281, 0.783)	0.499
	Females	1.022 (0.256, 2.581)	1.159 (0.250, 3.156)	−0.092 (−0.679, 0.461)	0.670
Stomache	Males	0.241 (0.004, 0.625)	−0.125 (−0.469, 0.490)	0.118 (0.003, 0.422)	0.095
	Females	0.993 (0.509, 1.621)	0.765 (0.038, 1.698)	0.150 (−0.291, 0.632)	0.500
All solid excluding lung, stomach, breastc	Males	0.816 (0.443, 1.305)	0.508 (−0.188, 1.273)	0.216 (−0.184, 0.740)	0.300
	Females	1.015 (0.625, 1.463)	0.389 (−0.254, 1.119)	0.468 (0.016, 0.986)	0.042
Leukemiaf	Males	4.758 (2.461, 8.312)	0.394 (−1.263, 3.495)	3.704 (1.430, 7.166)	<0.001
	Females	5.134 (2.713, 8.971)	−0.002 (−1.490, 2.659)	4.280 (2.018, 7.797)	<0.001
All circulatory diseased	Males	0.163 (0.043, 0.324)	0.093 (−0.185, 0.358)	0.039 (−0.070, 0.197)	0.479
	Females	0.273 (0.090, 0.502)	0.312 (0.067, 0.680)	−0.020 (−0.159, 0.095)	0.729
Under 3 Gy colon dose, later years of follow-up (1961–2003), adjusted for age at exposure and attained age
All solid cancerc	Males	0.883 (0.550, 1.307)	0.809 (0.197, 1.499)	0.052 (−0.295, 0.464)	0.777
	Females	1.508 (1.090, 2.001)	1.254 (0.663, 1.952)	0.196 (−0.180, 0.607)	0.310
Lungd	Males	1.397 (0.401, 3.323)	1.693 (−0.027, 4.567)	−0.184 (−1.176, 0.997)	0.676
	Females	1.225 (0.275, 3.297)	1.399 (0.269, 4.061)	−0.110 (−0.870, 0.567)	0.672
Stomache	Males	0.312 (0.000, 0.819)	−0.092 (−0.498, 0.765)	0.076 (0.000, 0.462)	0.138
	Females	1.132 (0.520, 1.971)	0.871 (−0.041, 2.096)	0.171 (−0.396, 0.792)	0.544
All solid excluding lung, stomach, breastc	Males	1.047 (0.543, 1.741)	0.827 (−0.047, 1.894)	0.150 (−0.366, 0.804)	0.569
	Females	1.171 (0.618, 1.825)	0.611 (−0.114, 1.564)	0.399 (−0.114, 0.997)	0.127
Leukemiaf	Males	3.410 (0.523, 7.020)	0.474 (−1.408, 4.325)	2.506 (0.168, 6.210)	0.034
	Females	5.414 (2.459, 11.144)	−0.495 (−2.849, 3.067)	4.933 (1.946, 10.146)	<0.001
All circulatory diseased	Males	0.264 (0.076, 0.517)	0.209 (−0.151, 0.588)	0.035 (−0.118, 0.259)	0.662
	Females	0.310 (0.081, 0.626)	0.401 (0.100, 0.874)	−0.059 (−0.227, 0.083)	0.377

Notes. Profile likelihood confidence intervals (CI) are given for the linear and quadratic coefficients. Models adjusted for age at exposure and attained age^a. Strata defined by city, sex, ground distance category, attained age category, age at exposure category, calendar period, AHS group (and summed/averaged over ground distance).

^aERR models for stomach cancer adjusted for attained age, and for all other endpoints adjusted for age at exposure and attained age.

^bP value of improvement in fit of linear-quadratic model vs linear model.

^cUsing colon dose.

^dUsing lung dose.

^eUsing stomach dose.

^fUsing red bone marrow dose.

DISCUSSION

In this paper a class of linear-quadratic ERR models was fitted to the most current LSS mortality data, as recently used by Ozasa et al. (7), and to the latest solid cancer incidence data, as recently used by Grant et al. (8), Cahoon et al. (9) and Grant et al. (10). We find some evidence of upward curvature for leukemia and solid cancer mortality excluding lung, stomach and breast cancer, but much weaker evidence of curvature in the solid cancer incidence data. These generally reinforce the findings of previous analysis of Little et al. (6). However, Little et al. (6) observed stronger indications of upward curvature for all solid cancers overall, although this was mostly driven by the remainder category of all solid cancers excluding lung, stomach and breast cancer, as we also document (Tables 1 and 3). Nevertheless, for all solid cancer excluding lung, stomach and breast cancer and for leukemia the LDEF generally exceeds 1.5. For stomach cancer the LDEF is somewhat lower, in the range 1.1–1.5, and for female breast cancer, lung cancer and circulatory disease the LDEF is about 1 or sometimes a little less (Table 1).

There has been considerable interest engendered by a recent analysis of the LSS incidence data, which showed evidence of upward curvature for solid cancer among males but not females (8). However, a recent reanalysis of the LSS solid cancer incidence and mortality data by Brenner et al. (11) using a common period of follow-up (1958–2009) demonstrated a borderline significant (P = 0.062) upward curvature in male mortality, as well as the significant curvature for females (P = 0.010). We reproduce this data in Table 4, and as indicated there the derived LDEFs are generally above 1, and for the mortality data and male incidence data above 2, irrespective of whether the full dose range (0–4 Gy) or the restricted dose range (0–2 Gy) are employed; however, for the female incidence data the LDEF is lower, in the range 1.1–1.4. It is perhaps noteworthy that the estimates of LDEF are somewhat higher when the lower dose range (0–2 Gy) is used, both for incidence and mortality. This is consistent with what was observed by Little et al. (6), and probably reflects a turnover in the dose response above 3 Gy. It was for this reason that Little et al. (6) decided for most analyses to use 0–3 Gy data, as here. The curvature that can be seen in the higher dose groups may reflect dose errors, which could be more substantial in these groups of survivors (6, 19). It may also reflect the effect of selection, since these higher doses are close to the human mean lethal dose (LD₅₀) for acute gamma radiation doses, thought to be 3–5 Gy for healthy adults (20). Interestingly, a previous analysis of older versions of the LSS incidence data also found evidence of upward curvature, which was more pronounced at low doses (<2 Gy), with LDEF for certain solid cancer and leukemia endpoints markedly above 2, although as here with little evidence of such curvature for female breast cancer or lung cancer (4).

TABLE 4.

Linear Coefficients from Fits to All Solid Cancer Mortality and Incidence Data (1958–2009) in Paper of Brenner et al. (11), and Derived Estimates of Low-Dose Extrapolation Factor (LDEF)

Sex	Linear model ERR/Gy	Linear-quadratic model linear ERR/Gy	LDEF
Mortality data
Full (0–4 Gy) dose range
Males	0.28	0.10	2.80
Females	0.60	0.28	2.14
Dose range 0–2 Gy
Males	0.27	0.05	5.40
Females	0.57	0.17	3.35
Incidence data
Full (0–4 Gy) dose range
Males	0.28	0.08	3.50
Females	0.64	0.56	1.14
Dose range 0–2 Gy
Males	0.26	0.02	13.00
Females	0.65	0.48	1.35

The low dose cancer mortality risks that we observe, as given by the linear coefficient, α_LQ, from the fitted linear-quadratic model may be directly compared with those that have been derived in groups exposed at low-dose rate. For example, the adjusted all solid cancer ERR/Gy of 0.608 (95% CI 0.395, 0.864) (Table 1) is comparable with that derived from the International Nuclear Workers Study (INWORKS), which yielded an ERR/Gy of 0.47 (90% CI 0.18, 0.79) (21). Likewise, the adjusted lung cancer ERR/Gy of 0.614 (95% CI 0.158, 1.507) (Table 1) is similar to the ERR/Gy that can be derived from the INWORKS study, namely 0.51 (90% CI 0.00, 1.09) (22), although the adjusted stomach cancer risk, 0.536 (95% CI 0.280, 0.856) (Table 1) is appreciably lower than, although statistically compatible with, the ERR/Gy given by the INWORKS study of 1.31 (90% CI −0.07, 3.16) (22).

In comparing the sex-specific ERR/Gy given in table 3 of Ozasa et al. (7) with those in Table 3 of the present paper note should be made of the quite different models used. City, age at the time of the bombings and attained age were employed in the background model used by Ozasa et al. (7), and there was no adjustment to the radiation effect for these or anything else; however, separate models were fitted to males and females so that the baseline was thereby adjusted for that also. The model employed here (as described in the Methods) has semi-parametric adjustment (via stratification) for city, sex, attained age, age at exposure, calendar period of follow-up, AHS status, and with adjustment to the ERR/Gy for ln[attained age], age at exposure and sex. Conceivably the differences between our results and those of Ozasa et al. (7) may reflect their simpler baseline model or the lack of adjustment to the ERR for age at exposure or attained in the previous analysis.

Likewise, there are certain differences from the models here and those fitted by Brenner et al. (11). Brenner et al. (11) fitted models with baseline cancer risk given by parametric functions of sex, age, year of birth, ground distance from hypocenter, and various smoking related terms (e.g., packyears). There were multiplicative radiation and smoking modifications of the baseline risk, with ERR/Gy modified by attained age × sex, age at exposure and a separate adjustment for >4 Gy shielded kerma survivors. In the present paper, for the mortality data we employed semi-parametric adjustment (via stratification) for city, sex, attained age, age at exposure, calendar period of follow-up, and AHS status. For the incidence data the baseline models used semi-parametric adjustment for city, sex, attained age, age at exposure, calendar period of follow-up, and smoking status. (Smoking information is only available in the publicly released versions of the three incidence datasets used here.) For both incidence and mortality data adjustments to the ERR/Gy were for ln[attained age], age at exposure and sex, and all analyses were restricted to <3 Gy, in relation to various organ dose metrics, and in all cases survivors with >4 Gy shielded kerma were excluded. These models are in some ways simpler than those employed by Brenner et al. (11), in particular in relation to the smoking adjustments, although the baseline adjustment for city, sex, age, age at exposure and time allow for much richer interactions between these variables than those of Brenner et al. (11). The paper of Brenner et al. (11) employed the latest DS02R1 dosimetry throughout, whereas the analysis employed here used DS02 for the analysis of the mortality data, reflecting that of Ozasa et al. (7) but used DS02R1 for the three incidence datasets (8–10).

There are additional uncertainties in the atomic-bomb survivor doses used here, not reflected in what we present. It is likely that the RBE for cancer of the neutron component of dose will slightly decrease with increasing distance from the hypocenters in Hiroshima and Nagasaki, because of the hardening of the free-in-air neutron energy spectrum with increasing distance in both cities (23, 24), although this may be slightly modified by transport through housing, structures and other bodies. However, even when neutron absorbed doses are weighted by the RBE of 10 used here, they comprise only about 9% and 3% of the total weighted absorbed dose in Hiroshima and Nagasaki about 1,000 m from the respective hypocenters, a fraction that decreases with increasing distance from the hypocenters (14). Possibly of greater significance is the hardening of the gamma energy spectrum with distance from the two hypocenters (25), which is likely to induce some decrease in the biological effectiveness of the photon component of dose (26).

In general, the suggestions of modest dose-response curvature for certain malignant endpoints, both for our own analysis (Table 1) as well as those of Brenner et al. (11) (Table 3) suggest that there is a moderate ameliorating effect of low-dose exposure compared with high-dose exposure for these endpoints, consistent with LDEF being greater than 1. There is much (quite old) experimental data yielding information on LDEF, and the somewhat related idea of DREF) accounting for the ameliorating effect of low dose rate (3). Our findings are consistent with this older body of data (3), also consistent with results of a recent reanalysis of the JANUS experimental animal data, which suggested modest LDEF, of about 1.2 for all solid tumors and generally no more than 2 (27). The LDEF we find for most malignant endpoints is less than the DDREF of 2 adopted by ICRP (1). The ICRP DDREF (1) also incorporates adjustment for DREF, for which the calculations in this paper provide no information. The JANUS reanalysis suggests a DREF, independent of LDEF, in the range 1.2–2.3 (27). Set against that, recent analyses of nuclear workers exposed at predominantly low dose rate do not suggest radiation risks markedly different from those in comparable (age/sex matched) subsets of the LSS (21, 28). While this may suggest a DREF (and indeed DDREF) of close to 1, this inference may be faulty. The radiation received by nuclear workers is mostly in the 0.1–3 MeV range, although with most radiation in the range 0.3–3 MeV (29, 30). It is therefore possible that radiation in the INWORKS study could be more effective (per unit dose) by up to approximately a factor of 2 than the radiation received by the atomic bomb survivors, with energy predominantly in the 2–5 MeV range (31–33), so that the risks in the nuclear workers and the LSS are still consistent with a DDREF of 2 (34). Further, account should be taken of uncertainties in occupational doses and their effect on the dose response (35). Errors are likely to be a mixture of Berkson and classical form. The classical component of error will tend to bias the dose response downwards, although the Berkson error component will not, the effect being mainly to increase the width of the trend CI (15).

There have been a number of recent attempts at assessing the effect of extrapolation of DREF via direct comparison of risks in low-dose rate occupational studies and appropriately age/sex adjusted analyses of the Japanese atomic bomb survivors. In particular this method has been employed in the studies of Jacob et al. (36), who derived a DREF of 1.21, Shore et al. (37), who derived solid cancer DREFs in the range 0.89-3.03 depending on data used, Hoel (38), who derived a solid cancer DREF of 2.63, and Kocher et al. (39) who calculated a solid cancer DREF of 1.3. Although a DREF was not explicitly computed, a DREF can be derived from Leuraud et al. (40) of 0.97 for solid cancer and 0.87 for leukemia. As discussed by Little et al. (41) there are certain statistical issues that require attention in the ratio of ERR estimates that is employed in the studies of Jacob et al. (36), Shore et al. (37), Hoel (38) and Kocher et al. (39). As shown by Little et al. (41) dealing with these issues results in central estimates of DREF and associated CI that are somewhat different than those given in these studies, with CI in particular tending to be wider.

The findings of the present paper have some bearing on the existence or otherwise of a threshold in dose. There is evidence of excess risk of most types of cancer associated with radiation exposures of the order of 10–20 mGy from diagnostic X-ray exposure in the Oxford Survey of Childhood Cancers and in various other groups exposed in utero (42). This data remains somewhat controversial, but as Wakeford and Little note “the consistency of the childhood cancer risk coefficients derived from the Oxford Survey and from the Japanese cohort irradiated in utero supports a causal explanation of the association between childhood cancer and an antenatal X-ray examination found in case-control studies. This implies that doses to the foetus in utero of the order of 10 mSv discernibly increase the risk of childhood cancer” (42). The data on radiation exposure at moderate and low doses in childhood has been recently reviewed (43, 44). These data suggest excess risk of cancer and benign neoplasms at doses of the order of 20 mGy. The excess risks in all of these studies are consistent with those in the Japanese atomic bomb survivor data (43, 44). A review of the totality of radiobiological data suggested that “there remains good justification for the use of a nonthreshold model for risk inference” for radiation protection purposes (45).