Investigation on circular asymmetry of geographical distribution in cancer mortality of Hiroshima atomic bomb survivors based on risk maps: analysis of spatial survival data
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Abstract
While there is a considerable number of studies on the relationship between the risk of disease or death and direct exposure from the atomic bomb in Hiroshima, the risk for indirect exposure caused by residual radioactivity has not yet been fully evaluated. One of the reasons is that risk assessments have utilized estimated radiation doses, but that it is difficult to estimate indirect exposure. To evaluate risks for other causes, including indirect radiation exposure, as well as direct exposure, a statistical method is described here that evaluates risk with respect to individual location at the time of atomic bomb exposure instead of radiation dose. In addition, it is also considered to split the risks into separate risks due to direct exposure and other causes using radiation dose. The proposed method is applied to a cohort study of Hiroshima atomic bomb survivors. The resultant contour map suggests that the region west to the hypocenter has a higher risk compared to other areas. This in turn suggests that there exists an impact on risk that cannot be explained by direct exposure.
Keywords
Atomic bomb survivors Direct exposure Indirect exposure Spatial survival data Spatially varying coefficientIntroduction
The risk of disease or death caused by exposure to atomic bomb radiation has been evaluated using estimated radiation doses based on information concerning age, shielding conditions, and distance from the hypocenter under the assumption that the radiation dose decreases with increasing distance from the hypocenter (see, e.g., Preston et al. 2007; Matsuura et al. 1997). For details of the dosimetry system used, see for example the DS02 system (Cullings et al. 2006; Young and Kerr 2005). The corresponding risk analyses focused solely on the risk from direct exposure to the atomic bomb, while the risk from indirect exposure due to residual radioactivity has been not evaluated in previous analyses. This means that the geographical distribution of risk has been structurally restricted to concentric circles under the assumption that the influence of direct exposure essentially depends on the distance from the hypocenter. For example, Peterson et al. (1983) have fitted Cox’s proportional hazard models to cancer mortality rates, to investigate circular asymmetry around the hypocenter in Hiroshima and Nagasaki. Gilbert and Ohara (1984) have analyzed data on acute symptoms. They divided the survivors in the Life Span Study (LSS) cohort, registered at the Radiation Effect Research Foundation (RERF), into eight groups according to the survivors’ location at the time of atomic bomb exposure relative to the hypocenter and evaluated the relative risk of each octant compared with that for survivors in the octant of east–north-east direction. However, we consider their approach to be not enough to investigate circular asymmetry around the hypocenter, because they evaluated only relative risks for each octant with respect to the location at exposure relative to the hypocenter and did not consider heterogeneity of risk in each octant.
Recently, survivors suspected of having suffered from indirect exposure were reported by Kamada et al. (2006), Kamada and Kawakami (2008), and Tonda et al. (2008) through biological studies and statistical analyses of the incidence of leukemia among the survivors who entered Hiroshima City on August 6, 1945, after the explosion of the atomic bomb. Furthermore, several questionnaire surveys (Uda et al. 1953; Masuda 1989) showed that so-called Black Rain, which might have included radioactivity, fell around the western part of Hiroshima City and the northwest suburbs for several hours just after the explosion. Ohtaki (2011) demonstrated spatial-time distributions of Black Rain using a nonparametric smoothing method applied to data from a questionnaire survey conducted by Hiroshima City in 2008, of about 37,000 inhabitants of Hiroshima and its suburbs that might have experienced Black Rain.
In the present paper, a statistical method is applied to evaluate the risk with respect to individual location at exposure rather than dose and construct a “risk map,” that is, a map based on the risk evaluated by location, to visually grasp the geographical distribution of risk without structural restrictions. The risk map allows discussing possible effects of indirect exposure due to “Black Rain” and other radioactivity on risk of mortality.
Materials and methods
Data
The database of atomic bomb survivors (ABS), registered at the Research Institute for Radiation and Medicine (RIRBM) at Hiroshima University, was used in the present study. The ABS differs from the LSS of the RERF, because the ABS cohort includes examined survivors residing in Hiroshima Prefecture, and data on health status for survivors also have been cumulatively compiled in the database. The extent of overlap between survivors in the ABS and the LSS was examined by Hayakawa et al. (1994) and Hoshi et al. (1996). Hayakawa et al. (1994) showed that the dose estimates of the ABS were close to those of the LSS among the overlapped subjects. However, it has not been tested how they agree to DS02.
Statistical analyses
Data containing information on location are called “spatial data.” Several methods for analyzing spatial data have been proposed, depending on the type of outcome. Geographically weighted regression (GWR), proposed by Fotheringham et al. (2002), corresponds to multiple linear regression analysis of spatial data. GWR is essentially repeated local multiple linear regressions applied to data in the neighborhood of a given location. The GWR approach can be extended to logistic regression for spatial binary data and Poisson regression for spatial count data, but the methodology for spatial survival data, such as those in the study of atomic bomb survivors, still remains to be developed. Recently, Tonda and coworkers (Tonda et al. 2010) proposed a statistical method for spatial data by extending a method proposed for longitudinal data (Satoh and Yanagihara 2010; and Satoh et al. 2009). Their approach is applicable not only to spatial continuous and discrete data but also to spatial survival data. In the present paper, a method is developed for estimating the geographical distribution of mortality risk for atomic bomb exposure by extending Cox’s proportional hazards model for spatial survival data (Tonda et al. 2010); the resulting method is applied to a cohort study of Hiroshima atomic bomb survivors.
Hazard model with spatially varying coefficients
In addition, a circular surface basis is expressed by \( \user2{x}(u,v) = \left( {1,u^{2} + v^{2} } \right)^{\prime } . \) To obtain a smoother shape for the spatially varying coefficient, one can use, for example, a B-spline or a Gaussian basis. Details are given in Satoh et al. (2003), Ruppert et al. (2003), and Konishi and Kitagawa (2010).
Dose effect model
Equation (8) was used for modeling the relationship between the mortality risk and risk from direct exposure in previous studies [see, e.g., Pierce and Vaeth (2003)].
Results
The proposed method was applied to data from a cohort study of Hiroshima atomic bomb survivors. The method is easy to implement using statistical packages that execute Cox model, such as SAS, SPSS, and R. We used the “survival” package version 2.36-2 in R version 2.12.0 [R Development Core Team (2010)].
Comparison of goodness-of-fit among five models
Type of basis | Circular | Polynomial | |||
---|---|---|---|---|---|
q = 1 | q = 2 | q = 3 | q = 4 | ||
Number of parameters | 3 | 5 | 10 | 17 | 26 |
AIC | 38,009.9 | 38,039.7 | 38,004.7 | 38,010.0 | 38,016.1 |
Estimated coefficients for the quadratic polynomial model
Parameter | Estimate | se | z | p |
---|---|---|---|---|
β_{s} | 0.784 | 0.041 | 19.2 | <0.001 |
β_{a} | −0.087 | 0.003 | −30.4 | <0.001 |
Estimated coefficients for the dose effect model
Parameter | Estimate | se | z | p |
---|---|---|---|---|
β_{s} | 0.770 | 0.046 | 16.6 | <0.001 |
β_{a} | −0.087 | 0.003 | −27.0 | <0.001 |
λ_{d} | 79.946 | 25.727 | 3.1 | 0.002 |
λ_{a} | −1.662 | 1.008 | −1.6 | 0.099 |
Estimated coefficients for the ordinary Cox model
Parameter | Estimate | se | z | p |
---|---|---|---|---|
β_{s} | 0.742 | 0.046 | 16.1 | <0.001 |
β_{a} | −0.088 | 0.003 | −26.2 | <0.001 |
λ_{d} | 94.215 | 23.437 | 4.0 | <0.001 |
λ_{a} | −1.196 | 0.917 | −1.3 | 0.190 |
Discussion
Equation (7) is now derived by substituting Eq. 10 into Eq. 9. According to Fig. 6, the resultant risk map, excluding the risks for direct exposure, still has contours skewed toward the west direction. In addition, the test for the hypothesis on spatial homogeneity, formulated by Eq. 5, was rejected (p < 0.001). These results may provide further evidence of risks for causes other than direct exposure.
As was mentioned in the introduction, several questionnaire surveys showed that Black Rain, which might have included radioactivity, fell around the western part of Hiroshima city and north–west suburbs for several hours just after the explosion. According to the latest results on the geographical distribution of Black Rain (Ohtaki 2011) and Uda’s rainfall area described in Fig. 2, the area of rainfall appears roughly similar to the region of high risk in Fig. 2. This similarity suggests that Black Rain might be a possible risk factor accounting for the geographical distribution of cancer mortality in Fig. 2. It should be noted, however, that there might be other risk factors affecting mortality such as socioeconomic status, life style, and environmental factors that are probably unrelated to radiation exposure due to the atomic bomb. These factors might correlate through association with particular regions, but this will be difficult check.
Note that Peterson et al. (1983) have also studied the circular asymmetry around the hypocenter in Hiroshima and Nagasaki for the LSS cohort of RERF. They divided the survivors into eight groups by the octants according the survivors’ location at exposure and fitted a Cox’s proportional hazard model. According to their results, the survivors in the west–north–west octant had the highest risk and the relative risk of survivors in the west–north–west compared with those in the east–north–east was about 1.24. As was mentioned in the introduction, their approach suffered from a lack of continuity of risks within groups and between groups. Therefore, they could not grasp any regional spatial trend of risk within and between octants. On the other hand, our results for the ABS cohort of RIRBM can be used to understand the spatial trend visually. Our result in Fig. 3 is roughly consistent with the areas with higher risks in Peterson et al. (1983). In addition, Fig. 4 shows that the differences in the relative risk among angles of location at exposure become larger with increasing distance from the hypocenter, while Peterson et al. (1983) could only evaluate the relative risks by octants. In this sense, our results are somewhat more valuable than those of Peterson et al. (1983).
Conclusion
The risk map shown in the present work can be interpreted in terms of the radiation dose required to explain the fitted contours for the hazard ratio in Fig. 6. For this, we focused on the hazard ratios at the locations with 2-km distance from the hypocenter in Fig. 6. The relative risk between highest and lowest risk at such locations is about 1.6. This suggests an excess relative risk (ERR) of about 0.6 due to causes other than direct exposure. This value might correspond to quite a large dose (i.e., of more than a Gray) if most of this additional risk is caused by external exposure not yet included in the estimated direct doses, because the ERR per Gray for solid cancer among atomic bomb survivors is on the order of about 0.5 (see, e.g., National Research Council 2006). This is quite unlikely as direct radiation doses where verified experimentally for example by retrospective thermoluminescence measurements on environmental samples (see, e.g., Cullings et al. 2006; Young and Kerr 2005). However, it might be possible that additionally chronic continuous exposure and individual variability caused by internal exposure, that is not included in the current (direct) dose estimates for the atomic bomb survivors, had a large effect on cancer mortality risk among atomic bomb survivors. Unfortunately, data on incorporated radionuclides from fallout are limited, and the effect of any internal exposure requires further clarification. Therefore, the doses corresponding to the contours of risk shown in Fig. 6 also should be an issue in the future. As already mentioned, there might be additional risk factors affecting mortality such as socioeconomic status, life style, and environmental factors that could also explain part of the observed asymmetry, but these factors are difficult to investigate due to limited data available.
Notes
Acknowledgments
We wish to thank the referees for their comments, which led to many improvements in the paper. Part of this research was supported by the Ministry of Education, Culture, Sports, Science and Technology, Scientific Research (A) #21249041 (2009–2011), Grant-in-Aid for Young Scientists (B) #21700306 (2009–2010), # 23790694(2011–2013), #23700337(2011–2013), the Fujii Fund of Hiroshima University (2008–2009) and the ISM Cooperative Research Program (2011-ISM-CRP-4202).
Open Access
This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.
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