### Introduction

^{th}Report of the Life Span Study (LSS-14) of Hiroshima and Nagasaki [7]. Mean years of life lost after exposure at ages of 10, 30, and 50 years to 1 Gy were indicated for males and females [5]. Cologne and Preston [8] also calculated the radiation risk using the LSS data and estimated the loss of life expectancy to be 2.6 years per Gy. For early-onset estimation, Sakata et al. [9] showed the cumulative incidence of menopause considering the age of menarche, as well as the survival probabilities from age 35 years for Japanese men and women born between 1920 and 1945 who were never smokers or who had smoked continuously since before the age of 20 [10].

### Materials and Methods

### 1. Epidemiological Data

### 2. Calculation of the IED

*y*is the cumulative mortality rate of all causes of death,

*x*is the variable of the attained-age category, and

*a*,

*b*, and

*c*are fitting parameters. Firstly, regression was conducted for dose category No. 1 (0–0.005 Gy group) as the reference case. Then, regression was performed for the other dose categories while fixing

*a*and

*c*, which were obtained from the reference case (

*a*=

*a*

_{ref},

*c*=

*c*

_{ref}). The difference in

*x*between the reference case and the interest dose category, i.e.,

*x*–

*x*

_{ref}, can be obtained using Equation (2), which can be regarded as the IED after multiplying by five to account for the width of the attained-age category.

### 3. Different Endpoints and Additional Detailed Analysis

### Results and Discussion

### 1. Cumulative Death Rate and Fitting for Reference Case and Other Dose Categories

*a*

_{ref}=0.625,

*b*

_{ref}=3,590.1, and

*c*

_{ref}=0.537), which are also shown in Table 3. Fig. 1 shows the cumulative death rates with fitting curves for the reference case and dose category No. 17 as an example. The meaning of the IED is also indicated by blue arrows.

*a*and

*c*were fixed as mentioned above. As shown in Tables 1 and 2, since the number of subjects was very small for dose category No. 22, it was omitted in the following analysis. Table 3 also includes the value of

*b*and the resultant IED, respectively, obtained using Equations (2) and (3) for dose category No. 17 (1.25–1.5 Gy) as an example.

*x*-axis value is the arithmetic mean weighted colon dose for each dose category range (see Tables 1 and 2). Although the calculation is simple, the resultant shape of the dose–response curve and its tendency are quite similar to those of the dose–response curve of excess relative risk for all solid cancers in LSS-14 [7].

*y*-axis is IED and

*x*-axis is weighted colon dose, which intersects at the origin. The solid line indicates the result of fitting in the full dose range, while the broken line indicates that in the limited dose range of less than 1.5 Gy. As shown in the figure, the IED estimated to be approximately 4 years for an acute radiation exposure of 1 Gy regardless of the fitting dose range.

### 2. Cumulative Death Rates for All Solid Cancers and Circulatory Diseases

*y*-axis is IED and

*x*-axis is weighted colon dose, in the full dose range, while the broken line indicates that in the limited dose range of less than 1.5 Gy. For circulatory diseases, the slope of the simple linear regression was estimated to be 0.2 years at 1 Gy in the full dose range, while it was estimated to be −0.8 years at 1 Gy in the limited dose range of less than 1.5 Gy.

### 3. Dependences of Cumulative Death Rate on Age at Exposure and Sex

*y*-axis is IED and

*x*-axis is weighted colon dose, (full dose range) as before.