### Study population

The Life Span Study cohort, defined on the basis of the Japanese national census in 1950 and special surveys between 1950 and 1953, consists of 86 611 atomic bomb survivors with estimated radiation doses. It includes a large proportion of the survivors who were within 2.5 km of the hypocentres at the time of the bombings and still resided in Hiroshima or Nagasaki in 1950, plus a random age and sex matched sample of people 2.5 to 10 km from the hypocentre who sustained small to negligible radiation doses.20 This study population was of all ages and both sexes at the time of the bombings.

Individual doses have been carefully estimated using the recent improved DS02 dosimetry system, primarily on the basis of people’s location and shielding at the time of the atomic bomb.21 22 We estimated risks by using weighted colon doses in gray (Gy) for all analyses. We used weighted doses, the sum of the γ dose plus 10 times the smaller neutron dose, to allow for the greater biological effectiveness of neutrons.

The follow-up of vital status took place from 1 October 1950 to the end of 2003 and was based on the nationwide obligatory family registration system (koseki) that documents mortality and is virtually 100% complete. Causes of death came from the official vital statistics death schedules based on the death certificates. Underlying and contributing causes of death were classified according to the ICD-7 (international classification of diseases, 7th revision) (for deaths in 1950-68), ICD-8 (in 1969-78), ICD-9 (in 1979-97), and ICD-10 (in 1998-2003). However, for the purposes of these analyses we converted them to ICD-9 codes 390-459 for all circulatory disease, 430-438 for stroke, and 393-429 (excluding 401, 403, and 405) for heart disease. We used only underlying causes of death in the primary analyses but examined underlying plus contributing causes in a subsidiary analysis.

### Statistical analysis

We based the analyses on a detailed summary table of the number of deaths and person years stratified by dose, city, sex, and five year intervals of age at exposure, attained age, and follow-up period. We divided participants into categories according to the weighted colon dose (in Gy=γ dose plus 10 times neutron dose): 0-, 0.005-, 0.02-, 0.04-, 0.06-, 0.08-, 0.1-, 0.125-, 0.15-, 0.175-, 0.2-, 0.25-, 0.3-, 0.5-, 0.75-, 1-, 1.25-, 1.5-, 1.75-, 2-, 2.5-, and ≥3. As described elsewhere, we truncated the colon doses to correspond to the 4 Gy shielded kerma level,20 but this affected only 317 participants.

We used Poisson regression methods for grouped survival data to describe the dependence of risk on radiation dose and to evaluate the variation of the dose-response effects with respect to city, sex, age at exposure, time since exposure, and attained age,23 essentially identical to the methods used previously to examine mortality from cancer in this cohort.20 We used Epicure software for parameter estimation and tests,24 and we based significance tests and 95% confidence intervals on likelihood profiles.

The primary models used here are excess relative risk (ERR) models of the form λ_{0} (c,s,a,b) [1+ERR (d,e,s,a)], where λ_{0} (⋅) is the baseline, or background death rate (that is, the rate for people with zero dose), which depended on city (c), sex (s), attained age (a), and birth year (b). The function ERR (d,e,s,a) describes the relative change in rates associated with dose (d), allowing for the effects of sex, age at exposure (e), and attained age. We examined effect modifiers by using models corresponding to those in Preston et al.20 25 We examined both dose and dose squared terms to evaluate the degree of linearity or curvature in the dose-response forms. We also tested a linear threshold model. We used differences in maximum likelihood to compare nested models or the Akaike information criterion for non-nested models.26 We evaluated a linear threshold model repeatedly for a wide range of possible values of a threshold dose (d_{0}), modelling the risk function ERR on doses d as β(d−d_{0}) for d>d_{0} or d=0 for d≤d_{0}. We empirically determined the values yielding the maximum likelihood and 95% confidence bounds.

We examined the impact of the possible confounding factors of smoking (never, past, present <20/day, present ≥20/day), alcohol intake (regular, seldom/never), education (primary or less, secondary, college/university), occupation for household (professional/technical, clerical/sales, farmer/craftsman, transportation/service), obesity (body mass index <20, 20-24, ≥25), and diabetes (yes, no) on the estimates of radiation risk, including codes for missing information, for the Life Span Study participants included in the 1978 mail survey. We included Cox-type regression models fitted to the individual data, where radiation dose was modelled as a linear excess relative risk, and indicator variables for the potential confounders jointly in the models as conventional exponential relative risk terms by using the Peanuts program in Epicure.24

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