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Abstract

For stochastic effects such as cancer, linear-quadratic models of dose are often used to extrapolate from the experience of the Japanese atomic bomb survivors to estimate risks from low doses and low dose rates. The low dose extrapolation factor (LDEF), which consists of the ratio of the low dose slope (as derived via fitting a linear-quadratic model) to the slope of the straight line fitted to a specific dose range, is used to derive the degree of overestimation (if LDEF > 1) or underestimation (if LDEF < 1) of low dose risk by linear extrapolation from effects at higher doses. Likewise, a dose rate extrapolation factor (DREF) can be defined, consisting of the ratio of the low dose slopes at high and low dose rates. This paper reviews a variety of human and animal data for cancer and non-cancer endpoints to assess evidence for curvature in the dose response (i.e. LDEF) and modifications of the dose response by dose rate (i.e. DREF). The JANUS mouse data imply that LDEF is approximately 0.2–0.8 and DREF is approximately 1.2–2.3 for many tumours following gamma exposure, with corresponding figures of approximately 0.1–0.9 and 0.0–0.2 following neutron exposure. This paper also cursorily reviews human data which allow direct estimates of low dose and low dose rate risk.

Keywords

Low dose extrapolation factor (LDEF)Dose rate extrapolation factor (DREF)Dose and dose rate reduction factor (DDREF)Cancer JANUS animal data

1. INTRODUCTION

At low and moderate doses, radiation risks are primarily stochastic effects, in particular somatic effects (cancer), rather than tissue reaction (formerly deterministic) effects which are characteristic of higher dose exposure (Committee to Assess Health Risks from Exposure to Low Levels of Ionizing Radiation, 2006; ICRP, 2007; UNSCEAR, 2008). In contrast to tissue reaction (formerly deterministic) effects, for stochastic effects, scientific committees generally assume that at sufficiently low doses, there is a positive linear component to the dose response, i.e. that there is no threshold (Committee to Assess Health Risks from Exposure to Low Levels of Ionizing Radiation, 2006; ICRP, 2007; UNSCEAR, 2008); this does not preclude there being higher order (e.g. quadratic) powers of dose in the dose response that may be of importance at higher doses. It is on this basis that linear-quadratic models of dose are often used to extrapolate from the experience of the Japanese atomic bomb survivors [typically exposed at a high dose rate to moderate doses (average of approximately 0.1 Gy)] to estimate risks from low doses and low dose rates (Committee to Assess Health Risks from Exposure to Low Levels of Ionizing Radiation, 2006; ICRP, 2007; UNSCEAR, 2008). The so-called ‘low dose extrapolation factor’ (LDEF) consists of the ratio of the low dose slope (as derived via fitting a linear-quadratic model) to the slope of the straight line fitted to a specific dose range. Estimates of LDEF have been made for cancer in the atomic bomb survivors Life Span Study (LSS) cohort data (Pierce and Vaeth, 1991; Little and Muirhead, 2000).

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 has led to the concept of a dose rate extrapolation factor (DREF), consisting of the ratio of the low dose slopes at high and low dose rates, and dose and dose rate reduction factor (DDREF), which measures the ratio of effect per unit dose at high dose and high dose rate to the effect per unit dose at low dose and low dose rate. As such, DDREF incorporates both the effect of dose–response curvature (e.g. via LDEF) and the effect of reduction in dose rate (e.g. via DREF). Recommended values of DDREF vary among scientific groups and have changed over time. Based on a combination of data from animal studies, evidence for curvilinearity in the data from the Japanese atomic bomb survivors LSS cohort, and other epidemiological studies, the International Commission on Radiological Protection (ICRP) recommended a value of DDREF of 2 for doses <200 mGy and dose rates <6 mGy h^–1 (ICRP, 2007). For high-linear energy transfer (LET) radiations, such as neutrons and alpha particles, no such reduction factor is indicated because the dose response for tumour induction and hereditary effects following exposure to these sorts of radiation is generally linear, with no variation in effect with dose fractionation (ICRP, 1991; UNSCEAR, 1993).

There are no single epidemiological studies that permit a direct internal comparison – to facilitate calculation of DDREF – between: (1) exposures that are high dose and high dose rate; and (2) exposures that are highly fractionated or protracted. A second-best alternative is to compare risk estimates from the available high dose and high dose rate studies with those from fractionated or protracted dose studies. This approach has been used in some recent meta-analyses of cancer risks in various groups of nuclear workers for comparison with the LSS data, and suggested that DDREF could be <1 (Jacob et al., 2009; Shore et al., 2017). However, such comparisons are fraught with difficulties as they are based on comparison of risks in different exposed populations (e.g. nuclear workers from generally western European and North American countries compared with the Japanese atomic bomb survivors).

The difficulty of using human data is such that reliance will continue to be placed on experimental animal data, where both dose and dose rate can be varied independently in a controlled way. Among the largest sets of animal data are the set of mice irradiated in the JANUS reactor at Argonne National Laboratory (Grahn et al., 1995; Northwestern University, 2016), and the various mouse datasets that comprise the European Radiobiological Archive (ERA) (Bundesamt für Strahlenschutz, 2016). Many studies have analysed the JANUS data, with earlier publications focusing on estimating relative biological effectiveness of various radiation qualities in relation to life shortening (Thomson et al., 1981a,b, 1983, 1985a,b; Thomson and Grahn, 1988; Carnes and Grahn, 1991), and the effects of mouse strain differences (Thomson et al., 1986). Some of these papers also examined the gamma and neutron dose response for various specific causes of death, mainly in relation to tumour or all-cause mortality (Thomson et al., 1985a,b, 1986; Thomson and Grahn, 1988; Carnes and Grahn, 1991; Grahn et al., 1992), and more recently in relation in cardiovascular disease mortality (Hoel and Carnes, 2017). Combining the JANUS and ERA data archives, Haley et al. (2015) recently estimated what they termed ‘DDREF_LSS’ (so-called because of its derivation from the Japanese atomic bomb survivor LSS data) modelling inverse mean lifespan, mostly using linear regression with a simple linear-quadratic model of dose recommended by the BEIR VII committee (Committee to Assess Health Risks from Exposure to Low Levels of Ionizing Radiation, 2006). Haley et al. (2015), in fitting to the JANUS and ERA data, found that this linear model did not fit the mouse lifespan data well. However, there are statistical problems with the linear model fitted by Haley et al. (2015), which does not have the correct (normal) error structure.

In the present paper, a somewhat more general model than the simple linear-quadratic model fitted by Haley et al. (2015) was applied to the JANUS mouse data. The model incorporates adjustment for the effects of dose and dose rate (in contrast to Haley et al. who adjusted simply for dose) for specific cancer and non-malignant endpoints, assessing these effects separately following both low-LET gamma radiation and high-LET neutron radiation. This work provides updated insight into the ongoing debate about DDREF. Full analysis of the JANUS mouse data has been published previously (Tran and Little, 2017). The aim of the present study is to add to the body of knowledge on the effects at low dose and dose protraction to inform estimates of LDEF and DREF, and, to some extent, DDREF needed for radiological protection. This paper also cursorily reviews human data that allow direct estimates of low dose and low dose rate risk.

2. METHODS

2.1. Mouse data

Murine experiments were conducted at the JANUS reactor in Argonne National Laboratory from 1970 to 1992 to study the effect of acute and protracted radiation dose from gamma rays and fission neutron whole-body exposure (Grahn et al., 1995; Northwestern University, 2016). Survival time and gross pathology were recorded at death. The JANUS data archive (Northwestern University, 2016) contains 50,110 mice from 13 experiments. For each experiment, mice were allocated to a control group and a radiation group. With the exception of one experiment performed on male Peromyscus leucopus (white-footed deer mouse), all experiments were performed on Mus musculus (a laboratory strain derived from the house mouse). After exclusion of mice that were not autopsied, discarded, improperly irradiated, removed to another experiment, or died before or during the first irradiation (n = 9011), and mice from a radioprotection experiment (n = 3685), mice from a controls-only experiment (n = 660) (which would yield no information on radiation effect), mice that had sex-specific tumours that were discrepant with the sex of the mouse (n = 17), and mice that had only non-lethal pathologies or non-identifiable pathologies (n = 19), 36,718 mice remained. Of these, 16,973 mice were irradiated with neutrons, 13,638 mice were irradiated with gamma rays, and 6107 mice were controls. Of the control mice, 5080 were common to both radiation types, 671 were controls in neutron experiments alone, and 356 were controls in gamma experiments alone.

In total, 727 mice had no identifiable pathology at death and 35,991 mice had a lethal pathology, classified by macropathology (Grahn et al., 1995). Grouped by radiation type, Table 1 shows the number of mice exhibiting each type of pathology. Each mouse had, at most, one lethal pathology, and approximately 72% (gamma: 13,429/18,658, neutron: 15,955/22,261) were neoplasms. The non-tumour pathologies were: pulmonary, renal, liver, cardiovascular, ovarian cyst, and other non-tumour diseases. Three additional endpoints were created for analysis: all tumour, all non-tumour, and any lethal pathology, which last consisted of animals with tumour, animals with specified non-tumour endpoints, and animals with cause of death undetermined. However, only a subset of these endpoints is given here; the complete set of results is given in the companion paper (Tran and Little, 2017).

Table 1.

Number of pathologies by radiation type, dose range, and lag period applied.

Pathology endpoint	No lag		Lag = 60 days
	Full dose range		Full dose range		Restricted dose range
	Gamma	Neutron	Gamma	Neutron	Gamma	Neutron
					(<5.0 Gy)	(<0.1 Gy)
All tumour	13,429	15,955	13,425	15,949	9865	7279
Lymphoreticular	6876	7365	6874	7362	4997	4000
Respiratory	3594	4238	3592	4236	2646	1721
Vascular	893	896	893	896	628	396
Kidney and urinary bladder	137	261	137	261	75	44
All non-tumour^*	3469	4139	3441	4136	2169	1536
Pulmonary^*	851	1185	850	1184	605	517
Renal^*	324	311	324	311	229	162
Cardiovascular^*	74	77	74	77	59	38
Other non-tumour diseases^*	2055	2319	2028	2317	1155	726

Non-tumour outcomes.

A period of 60 days was used to lag doses and entry dates for irradiated mice.

2.2. Statistics

If the expected number of excess cancers that results from a single acutely delivered dose D is $α_{1} D + α_{2} D^{2}$ , then if a total dose D is administered in k equal sized and temporally well-separated (e.g. by >1 day) fractions, the total number of excess cancers that would be expected is $k [α_{1} (D / k) + α_{2} (D / k)^{2}] = α_{1} D + α_{2} D^{2} / k$ (UNSCEAR, 1993; Dasu and Toma-Dasu, 2005; Committee to Assess Health Risks from Exposure to Low Levels of Ionizing Radiation, 2006). Inspired by this, the models considered for estimating the relative risk of an endpoint associated with cumulative lagged radiation dose $D (t - t_{lag})$ in stratum i at age t, dose rate DR, cumulative lagged numbers of dose fractions to date, $k (t - t_{lag})$ , experiment E, age at study entry e, and sex s, which are all special cases of the following Cox proportional hazard model (Cox, 1972) with fixed (rather than random) treatment effects, were:

\begin{matrix} λ (t, D (t - t_{lag}), DR, k (t - t_{lag}), s, e, E | (α_{i})) \\ = λ_{i} (t, s, E) exp [\begin{matrix} α_{1} D (t - t_{lag}) + α_{2} D (t - t_{lag})^{2} \\ + α_{3} D (t - t_{lag})^{2} / k (t - t_{lag}) \\ + α_{4} D (t - t_{lag}) 1_{DR < 5 mGy h^{- 1}} + α_{5} D (t - t_{lag})^{2} 1_{DR < 5 mGy h^{- 1}} \\ + α_{6} [e - e_{0}] + α_{7} D (t - t_{lag}) [e - e_{0}] \\ + α_{8} D (t - t_{lag}) 1_{s = male} \end{matrix}] \end{matrix}

(1) where

λ_{i} (t, s, E)

is the baseline hazard for stratum i, and e₀ is the mean age at study entry. The model is fitted using age, t, as timescale, stratifying on sex and experiment.

α_{1}

is the linear effect and

α_{2}

is the quadratic effect of time varying cumulative dose

D (t - t_{lag})

in Gy, and

α_{4}

and

α_{5}

are the modifications to the linear and quadratic terms of dose by low dose rate (relative to high dose rate), which are defined to be dose rates of <5 mGy h^–1 (Wakeford and Tawn, 2010). Although dose rate effects are only expected for low-LET gamma exposure (Wakeford and Tawn, 2010), a model with the same threshold level (5 mGy h^–1) was applied to experiments involving neutrons; unfortunately there is limited scope for reducing this threshold, as the lowest neutron dose rate is 0.9 mGy h^–1, and at this dose rate, there is only a single cumulative dose group, 0.0205 Gy. A number of submodels for Eq. (1) were considered, but this model fitted best in the sense of minimising the Akaike information criterion (Akaike, 1973, 1981), whether for gamma or neutron exposure, for five summary disease endpoints (Tran and Little, 2017).

From Eq. (1), DREF, the ratio of acute to chronic low dose rate slopes, is:

DREF = \frac{α_{1} + α_{7} [e - e_{0}] + α_{8} 1_{s = male}}{α_{1} + α_{4} + α_{7} [e - e_{0}] + α_{8} 1_{s = male}}

(2)

For females exposed at mean age at exposure e₀, this reduces to:

DREF = \frac{α_{1}}{α_{1} + α_{4}}

(3)

It should be noted that, occasionally, DREF < 0. In these cases, it is generally because $α_{1} > 0, α_{1} + α_{4} < 0$ , implying a conventional sparing effect of low dose rate exposure. To derive LDEF, the linear version of Eq. (1) is:

\begin{matrix} λ' (t, D (t - t_{lag}), DR, k (t - t_{lag}), s, e | (α_{i})) \\ = λ_{i}' (t, s) exp [\begin{matrix} α_{1}' D (t - t_{lag}) + α_{4}' D (t - t_{lag}) 1_{DR < 5 mGy h^{- 1}} \\ + α_{6}' [e - e_{0}] + α_{7}' D (t - t_{lag}) [e - e_{0}] \\ + α_{8}' D (t - t_{lag}) 1_{s = male} \end{matrix}] \end{matrix}

(4)

LDEF is then given by the ratio of the limiting slope of Eq. (4) to the limiting slope of Eq. (1), namely:

LDEF = \frac{α_{1}' + α_{4}' 1_{DR < 5 mGy h^{- 1}} + α_{7}' [e - e_{0}] + α_{8}' 1_{s = male}}{α_{1} + α_{4} 1_{DR < 5 mGy h^{- 1}} + α_{7} [e - e_{0}] + α_{8} 1_{s = male}}

(5)

Therefore, LDEF at high dose rate for females at the mean age at study entry e₀ is given by:

{LDEF}_{high} = \frac{α_{1}'}{α_{1}}

(6) while LDEF at low dose rate for females at the mean age at study entry e₀ is given by:

{LDEF}_{low} = \frac{α_{1}' + α_{4}'}{α_{1} + α_{4}}

(7)

An LDEF (DREF) of 1 implies that there is no reduction in risk at low dose (low dose rate) compared with high dose (high dose rate). Values less than 1 imply greater risk at low dose (low dose rate), and values greater than 1 imply a risk reduction from high dose (high dose rate) to low dose (low dose rate). To arrive at confidence intervals for LDEF and DREF, non-parametric bootstrap techniques (Efron, 1981), sampling from the dataset with replacement, were used to generate at least 200 samples of the same size as the original data set, and 95% confidence intervals (CI) were calculated from the 2.5% and 97.5% percentiles. Parameter estimation was performed in the R packages ‘survival’ (Therneau, 2016) and ‘boot’ (Ripley, 2016). All R code used is contained in the electronic supplementary material of the companion paper (Tran and Little, 2017).

A latent period of $t_{lat} = 60$ days was used to lag doses and entry ages of irradiated mice, based on a mean age at exit of 900 days, multiplied by the ratio of latent period/mean lifespan of 5/80 in humans, 5 years being the commonly assumed latent period for many solid cancers (Committee to Assess Health Risks from Exposure to Low Levels of Ionizing Radiation, 2006; UNSCEAR, 2008). Table 1 gives counts of each pathology following application of a 60-day lag. Forty-two mice in gamma experiments and 17 mice in neutron experiments were excluded as they died within the lag period.

The linear-quadratic or linear models that underlie LDEF and DREF implicitly assume that the dose–response curve is approximately linear at sufficiently low doses (Pierce and Vaeth, 1991; Little and Muirhead, 2000). To assess the sensitivity of model fits to this assumption, a restricted dose range <5.0 Gy for gamma radiation and <0.1 Gy for neutron radiation was considered. The higher limit for gamma radiation was chosen to yield sufficient data for analysis. Survival models, LDEF, and DREF were estimated to test the assumption of linearity and dose rate effect in these lower dose ranges.

3. RESULTS

3.1. Gamma

Table 2 indicates that LDEF_high was modestly but significantly >1 for lymphoreticular tumours (LDEF_high = 1.159, 95% CI 1.062–1.313) and for a number of non-malignant endpoints, specifically all non-tumour diseases (LDEF_high = 1.630, 95% CI 1.429–1.995), other non-tumour diseases (LDEF_high = 1.473, 95% CI 1.290–1.822), and non-malignant pulmonary disease (LDEF_high = 1.695, 95% CI 1.166–2.755) (Table 2). However, for a rather larger group of malignant endpoints, LDEF_high was significantly <1, particularly for tumours of the respiratory system (LDEF_high = 0.758, 95% CI 0.667–0.874), vasculature (LDEF_high = 0.701, 95% CI 0.574–0.854), and kidney/urinary bladder (LDEF_high = 0.638, 95% CI 0.450–0.864). For all malignant endpoints, except kidney/urinary bladder, LDEF_low was <1. For all non-malignant endpoints, LDEF_low was <1, and this was significant in most cases (Table 2). These results are generally similar in unlagged analyses (results not shown).

Table 2.

Low dose extrapolation factor (LDEF) and dose rate extrapolation factor (DREF) estimates and 95% confidence intervals (CI) calculated from at least 200 bootstrap samples by pathology and radiation type resulting from fitting Eq. (1).

	Gamma
Disease endpoint	LDEF_high (95% CI)	LDEF_low (95% CI)	DREF (95% CI)
All tumour	1.056 (0.992–1.139)	0.857 (0.648–1.239)	1.190 (0.861–1.723)
Lymphoreticular	1.159 (1.062–1.313)	0.906 (0.563–2.217)	1.371 (0.802–3.681)
Respiratory	0.758 (0.667–0.874)	0.982 (0.637–2.392)	1.403 (0.878–3.843)
Vascular	0.701 (0.574–0.854)	0.645 (0.339–1.487)	1.193 (0.675–3.129)
Kidney and urinary bladder	0.638 (0.450–0.864)	2.035 (−8.704–11.173)	2.336 (−10.778–13.506)
All non-tumour^*	1.630 (1.429–1.995)	0.601 (0.346–1.287)	0.608 (0.365–1.393)
Pulmonary^*	1.695 (1.166–2.755)	0.336 (0.154–0.600)	0.275 (0.119–0.769)
Renal^*	−3.503 (−28.172–32.319)	−0.472 (−1.667–0.863)	−0.205 (−1.207–0.555)
Cardiovascular^*	0.983 (−2.397–3.540)	0.021 (−0.756–0.735)	0.169 (−0.238–0.815)
Other non-tumour diseases^*	1.473 (1.290–1.822)	0.800 (0.426–2.362)	0.783 (0.399–2.809)
	Neutron
All tumour	0.490 (0.450–0.526)	0.073 (−0.166–0.304)	−0.182 (−0.695 to −0.105)
Lymphoreticular	0.571 (0.470–0.691)	0.148 (−0.890–0.971)	−0.133 (−0.843–1.363)
Respiratory	0.507 (0.439–0.584)	0.004 (−0.358–0.305)	−0.095 (−0.379 to −0.051)
Vascular	0.413 (0.305–0.544)	0.539 (−3.440–4.360)	−0.214 (−1.940–1.661)
Kidney and urinary bladder	0.351 (0.255–0.458)	−0.408 (−4.389–3.745)	−0.187 (−1.460–1.301)
All non-tumour^*	0.791 (0.660–0.942)	−0.090 (−2.361–3.458)	0.226 (−1.938–1.135)
Pulmonary^*	0.808 (0.618–1.120)	0.259 (−3.185–3.248)	0.207 (−1.044–1.368)
Renal^*	−0.072 (−1.663–0.251)	0.048 (−4.113–2.807)	0.084 (−0.383–0.248)
Cardiovascular^*	0.530 (0.183–1.138)	0.153 (−1.978–4.204)	−0.081 (−0.530–0.379)
Other non-tumour diseases^*	0.902 (0.737–1.124)	−0.492 (−4.240–3.415)	0.202 (−0.750–1.337)

Non-tumour outcomes.

A period of 60 days was used to lag doses and entry dates for irradiated mice. The full dose range was employed. LDEF_high and LDEF_low were calculated using Eqs (6) and (7), respectively, and DREF was calculated using Eq. (3).

In contrast, Table 2 shows that DREF > 1 for many tumour sites, with most central estimates in the range 1.2–2.3, although this was not conventionally statistically significant. For most non-malignant endpoints, DREF < 1, and for some sites, this departure from 1 was statistically significant, particularly pulmonary disease (DREF = 0.275, 95% CI 0.119–0.769), renal disease (DREF = −0.205, 95% CI −1.207–0.555), and cardiovascular disease (DREF = 0.169, 95% CI −0.238–0.815) (Table 2). These results are generally similar in unlagged analyses (results not shown).

Applying the dose restriction ≤5.0 Gy results in significant LDEF_high estimates that are <1 for vascular tumours (LDEF_high = 0.484, 95% CI 0.238–0.950) (Table 3). LDEF_low and DREF are significantly <1 for the non-malignant endpoints: all non-tumour disease (LDEF_low = 0.214, 95% CI −0.258–0.719; DREF = 0.120, 95% CI −0.122–0.758) and other non-tumour diseases (LDEF_low = 0.192, 95% CI −0.090–0.480; DREF = 0.112, 95% CI −0.034–0.552) (Table 3).

Table 3.

	Gamma
Disease endpoint	LDEF_high (95% CI)	LDEF_low (95% CI)	DREF (95% CI)
All tumour	0.904 (0.711–1.227)	0.684 (−3.913–4.825)	1.212 (−8.779–10.251)
Lymphoreticular	0.877 (0.579–1.702)	−0.009 (−4.089–3.667)	1.289 (−10.116–12.229)
Respiratory	0.890 (0.503–2.215)	−2.654 (−13.175–9.875)	−3.185 (−16.729–11.047)
Vascular	0.484 (0.238–0.950)	0.442 (0.041–2.311)	0.480 (0.048–2.517)
Kidney and urinary bladder	0.363 (−1.403–1.259)	0.041 (−1.855–1.382)	0.787 (−3.101–6.853)
All non-tumour^*	1.828 (−13.251–16.502)	0.214 (−0.258–0.719)	0.120 (−0.122–0.758)
Pulmonary^*	−3.953 (−15.660–14.172)	−0.424 (−4.084–5.019)	−0.249 (−2.677–2.792)
Renal^*	NA	NA	NA
Cardiovascular^*	NA	NA	NA
Other non-tumour diseases^*	1.315 (−5.365–8.379)	0.192 (−0.090–0.480)	0.112 (−0.034–0.552)
	Neutron
All tumour	4.885 (−17.722–14.875)	−0.478 (−7.148–6.988)	−0.114 (−4.118–5.372)
Lymphoreticular	0.479 (−5.66–3.373)	0.156 (−2.141–2.929)	0.384 (−4.762–6.350)
Respiratory	−1.229 (−16.357–12.210)	−1.569 (−11.440–17.089)	1.338 (−10.180–11.386)
Vascular	0.036 (−3.132–2.840)	−0.006 (−5.102–6.228)	3.573 (−14.741–14.901)
Kidney and urinary bladder	−0.229 (−5.044–4.906)	1.185 (−3.380–4.052)	1.738 (−7.413–9.827)
All non-tumour^*	0.853 (0.309–4.145)	0.586 (−5.630–4.019)	1.967 (−14.395–12.866)
Pulmonary^*	0.416 (−0.002–1.192)	0.521 (−3.303–4.227)	1.540 (−9.359–15.730)
Renal^*	16.829 (−4.494–8.130)	0.237 (−4.189–2.740)	0.009 (−3.980–3.525)
Cardiovascular^*	NA	NA	NA
Other non-tumour diseases^*	1.047 (−5.844–7.409)	0.449 (−3.955–4.224)	2.775 (−11.205–13.774)

NA, not available.

Non-tumour outcomes.

A neutron dose restriction ≤0.1 Gy and a gamma dose restriction ≤5.0 Gy were employed. A 60-day dose lag and period from entry to start of follow-up was used. LDEF_high and LDEF_low were calculated using Eqs (6) and (7), respectively, and DREF was calculated using Eq. (3).

3.2. Neutron

In contrast to gamma, Table 2 shows that LDEF_high is generally significantly <1 for most malignant endpoints, with central estimates of LDEF_high mostly in the range 0.1–0.5. For non-malignant endpoints, the central estimates of LDEF_high are also <1, although not always significantly, but the reduction below 1 is significant for all non-tumour disease (LDEF_high = 0.791, 95% CI 0.660–0.942) and renal disease (LDEF_high = −0.072, 95% CI −1.663–0.251). Table 2 shows that LDEF_low is generally <1 for all endpoints, even if this was not conventionally statistically significant; the reduction below 1 was significant for all tumours (LDEF_low = 0.073, 95% CI −0.166–0.304), lymphoreticular tumours (LDEF_low = 0.148, 95% CI −0.890–0.971), and respiratory tumours (LDEF_low = 0.004, 95% CI −0.358–0.305). These results are generally similar in unlagged analyses (results not shown).

Again in contrast to gamma, Table 2 demonstrates that DREF was generally in the range 0.0–0.2 for most malignant and non-malignant endpoints, and in many cases (all tumours, respiratory tumours, non-malignant renal disease, and cardiovascular disease), DREF was significantly <1. These results are generally similar in unlagged analyses (results not shown).

Applying the dose restriction ≤0.1 Gy results in many endpoints having LDEF_high and LDEF_low <1, although not significantly (Table 3). DREF varies across endpoints, with none achieving significant departure from 1.

4. DISCUSSION

This paper reports the re-analysis of a large series of gamma- and neutron-irradiated mice. The optimal model used a relative risk formulation with linear and quadratic terms in cumulative lagged dose, with adjustments to both linear and quadratic dose terms for low dose rate irradiation (<5 mGy h^–1) and with adjustments to the dose for age at exposure and sex. In general, after gamma radiation, the dose response for both malignant and non-malignant disease is mostly upward curving, with reduced risk per unit dose at low doses; there is reduced risk per unit dose at low dose rates (<5 mGy h^–1) for most malignant endpoints, and increased risk per unit dose at low dose rates for all non-malignant endpoints. After neutron exposure, the dose response is generally downward curving, with increased risk per unit dose at low doses for most malignant and non-malignant endpoints; for most malignant endpoints, there are non-significant indications of reduced risk per unit dose at low dose rate (<5 mGy h^–1), but for most non-malignant endpoints, there are non-significant indications of increased risk per unit dose at low dose rate. For some tumour sites, after gamma radiation, LDEF is slightly >1, but for most, LDEF was either indistinguishable from 1 or significantly <1. For example, for all tumours, LDEF_high is 1.056 (95% CI 0.992–1.039) and LDEF_low is 0.857 (95% CI 0.648–1.239) (Table 2); however, there is considerable spread about this (what might be considered central) estimate. For many tumour sites after gamma radiation, DREF > 1, with most central estimates in the range 1.2–2.3, but generally not significantly different from 1. So, for example, the all tumour DREF is 1.190 (95% CI 0.861–1.723) (Table 2); again, however, there is considerable spread about this (what might be considered central) estimate, and the upper 95% CI in particular for certain sites attain or exceed 10. For many non-tumour sites after gamma radiation, DREF < 1, with most central estimates in the range 0.2–0.8. For all tumour and non-tumour sites after neutron radiation, LDEF generally lies in the range 0.1–0.9, and is mostly significantly <1. After neutron exposure, DREF was quite often near 0 or negative for most malignant and non-malignant endpoints, and in many cases was significantly <1. A limitation of the data for the purposes of inference on DREF is the limited numbers of mice exposed at low dose rates; only 5% of the gamma-irradiated animals and only 9% of the neutron-irradiated mice were exposed at <5 mGy h^–1 (Tran and Little, 2017). This limits power to infer DREF, but should not bias inference on this measure. The limits of the low dose groups used (5 Gy for gamma rays and 0.1 Gy for neutrons) are arguably not very low, but as the companion paper makes clear, there is little information at lower doses (Tran and Little, 2017). As with the analysis of Haley et al. (2015) of this data, it is reasonably clear that the simple linear-quadratic model proposed by the BEIR VII committee (Committee to Assess Health Risks from Exposure to Low Levels of Ionizing Radiation, 2006) does not fit the JANUS gamma or neutron data at all well (Tran and Little, 2017).

Perhaps the most remarkable aspects of the present findings relate to the dose and dose rate effects of neutrons. It is generally thought that LDEF = DREF = 1 for neutrons and other high-LET radiation (e.g. alpha particles) because, in general, the dose response for tumour induction following exposure to these types of radiation is linear, with no variation in effect with dose rate (ICRP, 1991; UNSCEAR, 1993). The reason for this may be connected to the fact that, at the level of the cell nucleus, there is no such thing as a low dose rate; although only approximately 1.5% of cells have a neutron traversal of the cell nucleus following a tissue dose of 3 mGy (30 mSv), every cell nucleus that is traversed by a neutron receives a large dose of approximately 0.2 Gy (2 Sv) (Brackenbush and Braby, 1988). Therefore, the instantaneous dose rate at the level of the cell nucleus is unavoidably high (>5 mGy h^–1 (Wakeford and Tawn, 2010).

It could be argued that DDREF is an unnecessary concept, as there is accumulating direct evidence of risk at low dose rate and, to some extent, at low dose. Analysis of the INWORKS nuclear worker study, a pooled analysis of radiation workers in three countries, has demonstrated significant excess risks of leukaemia (Leuraud et al., 2015) and solid cancer mortality (Richardson et al., 2015), which are slightly higher than but compatible with those in comparable (age-at-exposure- and sex-matched) subsets of the LSS. Trends of solid cancer risks with dose were still significant, if only barely, if analysis was restricted to the 0–100-mGy dose range (Richardson et al., 2015). However, it would be premature to infer from these studies that DDREF is 1. In a parallel editorial, it is highlighted that when the effects of radiation energy and endpoint heterogeneity are taken into account, a DDREF of 2 is still consistent with this data (Little, 2015). 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 (Wakeford and Little, 2003), as summarised in Table 4. This data and results of other similar obstetric case–control studies remain 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 fetus in utero of the order of 10 mSv discernibly increase the risk of childhood cancer’ (Wakeford and Little, 2003). There is also evidence of significant excess risk (P = 0.01) of childhood leukaemia associated with natural background radiation exposure, at doses of the order of 10–20 mGy, in a large population-based case–control study in Great Britain (GB) (Kendall et al., 2013), and borderline levels of significance (P = 0.054) in a much smaller Swiss dataset (Spycher et al., 2015), although not in a small Finnish case–control study (Nikkila et al., 2016) nor in a large French case–control study (Demoury et al., 2017) (Table 5). The CIs on risk in the French study are surprisingly narrow (Table 5) given that this study is of much the same size with a similar dose distribution as the GB study. There are weak indications (P = 0.49) of excess risk of brain and central nervous system tumours in the GB study (Kendall et al., 2013), and a surprisingly large and highly significant excess (P = 0.008) in the much smaller Swiss cohort (Spycher et al., 2015) (Table 5). At slightly higher doses, increased risks of leukaemia and brain cancer have been observed in paediatrically exposed groups given multiple computerised tomography examinations, at doses of approximately 60 mGy to the respective tissues (red bone marrow, brain) (Pearce et al., 2012). The excess risks in all of these studies are consistent with those in the Japanese atomic bomb survivor data (Tables 4 and 5).

Table 4.

Excess relative risk (ERR) coefficients for childhood cancer following radiation exposure in utero (Wakeford and Little, 2003).

Study	Endpoint	Reference	ERR coefficient (95% confidence interval), Gy^–1
Oxford Survey of Childhood Cancers (case–control study)	All cancers^*	Bithell and Stiller, 1988	28.8 (17.1–43.6)
		Mole, 1990	38 (7–79)
		Bithell, 1993	51 (28–76)
Japanese atomic bomb survivors (cohort study)	All cancers	Wakeford and Little, 2003	7 (−3–45)^†,^‡
			11 (−1–44)^‡^,§
		Delongchamp et al., 1997 ^¶	23 (2–88)^†,^^
	Leukaemia	Wakeford and Little, 2003	<0 (<0–50)^†,‡,§
	Solid tumours	Wakeford and Little, 2003	20 (−3–110)^†,^‡
			22 (0–78)^‡^,§

ERR coefficients for leukaemia and solid tumours are taken to be the same as that for all cancers (see Wakeford and Little, 2003).

†

Mortality data.

^‡Based on extended birth cohort.

Incidence data.

Obtained from follow-up commencing 1 October 1950.

90% confidence interval.

Table 5.

Excess relative risks (ERR) in the UK-NCI computed tomography study (Pearce et al., 2012), Japanese atomic bomb survivor Life Span Study (LSS) (Preston et al., 2007; Hsu et al., 2013), and various background radiation studies (Kendall et al., 2013; Spycher et al., 2015; Nikkila et al., 2016; Demoury et al., 2017).

Dataset	Leukaemia ERR Gy^–1 (95% CI)	Brain/central nervous system ERR Gy^–1 (95% CI)
UK-NCI computed tomography cohort (Pearce et al., 2012)	36 (5–120)	23 (10–49)
LSS age at exposure <20 years, follow-up <20 years after exposure (Preston et al., 2007; Hsu et al., 2013)	37.08 (14.22–172.2)	6.14 (0.12–63.93)
Natural background radiation studies
Great Britain (Kendall et al., 2013)	90 (20–170)	20 (−40–90)
Switzerland (Spycher et al., 2015)	46 (−1–96)	60 (15–106)
Finland (Nikkila et al., 2016)	−30 (−110–60)	NA
France (Demoury et al., 2017)	0 (−10–10)	NA

CI, confidence interval; NA, not available.

Nevertheless, the human data are uninformative regarding the effects of dose rate (i.e. DREF), as there is no single population exposed to the effects of both high and low dose rate radiation. As such, animal data, such as the data used here, represent the best source of information available at present on dose rate effects. However, there is human information on the effects of extrapolation of dose (i.e. LDEF). In the LSS, there is emerging mortality and incidence data suggesting that there is modest upward curvature in the solid cancer dose response (Ozasa et al., 2012; Grant et al., 2017); as such, the ratio of quadratic/linear coefficients $α_{2} / α_{1} \approx 0.2 {Gy}^{- 1}$ (Grant et al., 2017) is somewhat higher than but, given the statistical uncertainties, very likely consistent with that derived here and in the companion paper for all tumours after gamma exposure ( $α_{2} / α_{1} \approx 0.09 {Gy}^{- 1}$ ) (Tran and Little, 2017).

Footnotes

5. Acknowledgements

The author is grateful for the detailed and helpful comments of the two referees. This work was supported by the Intramural Research Program of the National Institutes of Health, National Cancer Institute, Division of Cancer Epidemiology and Genetics, and by ICRP Committee 1 Task Group 91.

References

Akaike, H., 1973. Information theory and an extension of the maximum likelihood principle. In: Petrov, B.N., Czáki, F. (Eds.), 2nd International Symposium on Information Theory. Akadémiai Kiadó, Budapest, pp. 267–281.

Akaike

, 1981. Likelihood of a model and information criteria. J Econometrics 16: 3–14.

Bithell, J.F., 1993. Statistical issues in assessing the evidence associating obstetric irradiation and childhood malignancy. In: Lengfelder, E., Wendhausen, H. (Eds.), Neue Bewertung des Strahlenrisikos. Niedrigdosis-Strahlung und Gesundheit. MMV Medizin Verlag, Munich, pp. 53–60.

Bithell

J.F.

Stiller

C.A.

, 1988. A new calculation of the carcinogenic risk of obstetric X-raying. Stat. Med. 7: 857–864.

Brackenbush

L.W.

Braby

L.A.

, 1988. Microdosimetric basis for exposure limits. Health Phys. 55: 251–255.

Bundesamt für Strahlenschutz, 2016. European Radiobiology Archive (ERA). Bundesamt für Strahlenschutz, Salzgitter.

Carnes

B.A.

Grahn

, 1991. Issues about neutron effects: the JANUS program. Radiat. Res. 128(Suppl.), S141–S146.

Committee to Assess Health Risks from Exposure to Low Levels of Ionizing Radiation, 2006. Health Risks from Exposure to Low Levels of Ionizing Radiation: BEIR VII – Phase 2. National Academy Press, Washington, DC.

Cox

D.R.

, 1972. Regression models and life-tables. J. R. Stat. Soc. Ser. B 34: 187–220.

10.

Dasu

Toma-Dasu

, 2005. Dose-effect models for risk-relationship to cell survival parameters. Acta Oncol. 44: 829–835.

11.

Delongchamp

R.R.

Mabuchi

Yoshimoto

Preston

D.L.

, 1997. Cancer mortality among atomic bomb survivors exposed in utero or as young children, October 1950–May 1992. Radiat. Res. 147: 385–395.

12.

Demoury

Marquant

Ielsch

et al. , 2017. Residential exposure to natural background radiation and risk of childhood acute leukemia in France, 1990–2009. Environ. Health Perspect. 125: 714–720.

13.

Efron

, 1981. Censored data and the bootstrap. J. Am. Statist. Assoc. 76: 312–319.

14.

Grahn

Lombard

L.S.

Carnes

B.A.

, 1992. The comparative tumorigenic effects of fission neutrons and cobalt-60 γ rays in the B6CF₁ mouse. Radiat. Res. 129: 19–36.

15.

Grahn, D., Wright, B.J., Carnes, B.A., Williamson, F.A., Fox, C., 1995. Studies of Acute and Chronic Radiation Injury at the Biological and Medical Research Division, Argonne National Laboratory, 1970–1992: the JANUS Program Survival and Pathology Data. Argonne National Laboratory, Argonne, IL.

16.

Grant

E.J.

Brenner

Sugiyama

et al. , 2017. Solid cancer incidence among the Life Span Study of atomic bomb survivors: 1958–2009. Radiat. Res. 187: 513–537.

17.

Haley

B.M.

Paunesku

Grdina

D.J.

Woloschak

G.E.

, 2015. The increase in animal mortality risk following exposure to sparsely ionizing radiation is not linear quadratic with dose. PLoS One 10: e0140989.

18.

Hoel

D.G.

Carnes

B.A.

, 2017. Cardiovascular effects of fission neutron or ⁶⁰Co γ exposure in the B6CF₁ mouse. Int. J. Radiat. Biol. 93: 563–568.

19.

Hsu

W-L.

Preston

D.L.

Soda

et al. , 2013. The incidence of leukemia, lymphoma and multiple myeloma among atomic bomb survivors: 1950–2001. Radiat. Res. 179: 361–382.

20.

ICRP, 1991. 1990 Recommendations of the International Commission on Radiological Protection. Ann. ICRP 21(1–3).

21.

ICRP, 2007. The 2007 Recommendations of the International Commission on Radiological Protection. ICRP Publication 103. Ann. ICRP 37(2–4).

22.

Jacob

Rühm

Walsh

Blettner

Hammer

Zeeb

, 2009. Is cancer risk of radiation workers larger than expected? Occup. Environ. Med. 66: 789–796.

23.

Kendall

G.M.

Little

M.P.

Wakeford

et al. , 2013. A record-based case–control study of natural background radiation and the incidence of childhood leukaemia and other cancers in Great Britain during 1980–2006. Leukemia 27: 3–9.

24.

Leuraud

Richardson

D.B.

Cardis

et al. , 2015. Ionising radiation and risk of death from leukaemia and lymphoma in radiation-monitored workers (INWORKS): an international cohort study. Lancet Haematol. 2: e276–e281.

25.

Little

M.P.

, 2015. Ionising radiation in the workplace. BMJ 351: h5405.

26.

Little

M.P.

Muirhead

C.R.

, 2000. Derivation of low-dose extrapolation factors from analysis of curvature in the cancer incidence dose response in Japanese atomic bomb survivors. Int. J. Radiat. Biol. 76: 939–953.

27.

Mole

R.H.

, 1990. Childhood cancer after prenatal exposure to diagnostic X-ray examinations in Britain. Br. J. Cancer 62: 152–168.

28.

Nikkila

Erme

Arvela

et al. , 2016. Background radiation and childhood leukemia: a nationwide register-based case–control study. Int. J. Cancer 139: 1975–1982.

29.

Northwestern University, 2016. Janus Tissue Archive. Northwestern University, Evanston, IL. Available at: http://janus.northwestern.edu/janus2/index.php (last accessed 24 January 2018).

30.

Ozasa

Shimizu

Suyama

et al. , 2012. Studies of the mortality of atomic bomb survivors. Report 14, 1950–2003: an overview of cancer and noncancer diseases. Radiat. Res. 177: 229–243.

31.

Pearce

M.S.

Salotti

J.A.

Little

M.P.

et al. , 2012. Radiation exposure from CT scans in childhood and subsequent risk of leukaemia and brain tumours: a retrospective cohort study. Lancet 380: 499–505.

32.

Pierce

D.A.

Vaeth

, 1991. The shape of the cancer mortality dose–response curve for the A-bomb survivors. Radiat. Res. 126: 36–42.

33.

Preston

D.L.

Ron

Tokuoka

et al. , 2007. Solid cancer incidence in atomic bomb survivors: 1958–1998. Radiat. Res. 168: 1–64.

34.

Richardson

D.B.

Cardis

Daniels

R.D.

et al. , 2015. Risk of cancer from occupational exposure to ionising radiation: retrospective cohort study of workers in France, the United Kingdom, and the United States (INWORKS). BMJ 351: h5359.

35.

Ripley, B., 2016. R Package ‘Boot': Version 1.3–18. Comprehensive R Archive Network (CRAN).

36.

Shore

Walsh

Azizova

Rühm

, 2017. Risk of solid cancer in low dose-rate radiation epidemiological studies and the dose-rate effectiveness factor. Int. J. Radiat. Biol. 93: 1064–1078.

37.

Spycher

B.D.

Lupatsch

J.E.

Zwahlen

et al. , Swiss Pediatric Oncology Group, Swiss National Cohort Study Group, 2015. Background ionizing radiation and the risk of childhood cancer: a census-based nationwide cohort study. Environ. Health Perspect. 123: 622–628.

38.

Therneau, T.M., 2016. R Package ‘Survival': Version 2.39–5. Comprehensive R Archive Network (CRAN).

39.

Thomson

J.F.

Williamson

F.S.

Grahn

Ainsworth

E.J.

, 1981a. Life shortening in mice exposed to fission neutrons and γ rays I. Single and short-term fractionated exposures. Radiat. Res. 86: 559–572.

40.

Thomson

J.F.

Williamson

F.S.

Grahn

Ainsworth

E.J.

, 1981b. Life shortening in mice exposed to fission neutrons and γ rays II. Duration-of-life and long-term fractionated exposures. Radiat. Res. 86: 573–579.

41.

Thomson

J.F.

Williamson

F.S.

Grahn

, 1983. Life shortening in mice exposed to fission neutrons and γ rays. III. Neutron exposures of 5 and 10 rad. Radiat. Res. 93: 205–209.

42.

Thomson

J.F.

Williamson

F.S.

Grahn

, 1985a. Life shortening in mice exposed to fission neutrons and γ rays. IV. Further studies with fractionated neutron exposures. Radiat. Res. 103: 77–88.

43.

Thomson

J.F.

Williamson

F.S.

Grahn

, 1985b. Life shortening in mice exposed to fission neutrons and γ rays. V. Further studies with single low doses. Radiat. Res. 104: 420–428.

44.

Thomson

J.F.

Williamson

F.S.

Grahn

, 1986. Life shortening in mice exposed to fission neutrons and γ rays. VI. Studies with the white-footed mouse, Peromyscus leucopus. Radiat. Res. 108: 176–188.

45.

Thomson

J.F.

Grahn

, 1988. Life shortening in mice exposed to fission neutrons and γ rays. VII. Effects of 60 once-weekly exposures. Radiat. Res. 115: 347–360.

46.

Tran

Little

M.P.

, 2017. Dose and dose rate extrapolation factors for malignant and non-malignant health endpoints after exposure to gamma and neutron radiation. Radiat. Environ. Biophys. 56: 299–328.

47.

UNSCEAR, 1993. Sources and Effects of Ionizing Radiation. United Nations Scientific Committee on the Effects of Atomic Radiation 1993 Report to the General Assembly, with Scientific Annexes Vol. E.94.IX.2. United Nations, New York, pp. 1–922.

48.

UNSCEAR, 2008. United Nations Scientific Committee on the Effects of Atomic Radiation 2006 Report. Annex A. Epidemiological Studies of Radiation and Cancer. United Nations, New York, pp. 13–322.

49.

Wakeford

Little

M.P.

, 2003. Risk coefficients for childhood cancer after intrauterine irradiation: a review. Int. J. Radiat. Biol. 79: 293–309.

50.

Wakeford

Tawn

E.J.

, 2010. The meaning of low dose and low dose-rate. J. Radiol. Prot. 30: 1–3.

Evidence for dose and dose rate effects in human and animal radiation studies

Abstract

Keywords

1. INTRODUCTION

2. METHODS

2.1. Mouse data

2.2. Statistics

3. RESULTS

3.1. Gamma

3.2. Neutron

4. DISCUSSION

Footnotes

5. Acknowledgements

References