### Introduction

### Materials and Methods

### 1. Part 1 (Estimation of Nonsmokers Baseline Risk)

*λ*

*, is lung cancer incidence baseline rates in all adults;*

_{m}*λ*

*, lung cancer incidence baseline rates in smokers;*

_{s}*λ*

*, lung cancer incidence baseline rates in nonsmokers; SR, smoking rates in both smokers and nonsmokers;*

_{n}*a*, attained age;

*b*, birth year (calendar year);

*c*, cigarettes per day; and

*g*, sex (male, female).

*b*representing birth effects among the parameters of the ERR model of smokers was fixed in 1915. This value of birth effects assumes that the age of the smokers was 30 years when the atomic bomb survivors were exposed. The impacts of the birth effects parameter on the baseline rate estimation in nonsmokers will be discussed in a sensitivity analysis session. In this paper, we assumed that smokers started smoking at the age of 20 years, as smoking is legalized in Japan at the age of 20 years.

*ERR*

*, is ERR model for smokers;*

_{s}*φ*

*, ERR per 50 pack-years (20 cigarettes per pack), 5.71 for male and 5.83 for female [10];*

_{g}*φ*

*, birth cohort (change per decade decrease in birth year), 0.09 [10];*

_{b}*μ*

_{1}, coefficient of log (duration/50), 1.09 [10];

*μ*

_{2}, coefficient of log (duration /50)

^{2}, −0.33 [10].

*c*” of the ERRs in Equation (4), the average value of each of the Japanese male and female smokers in Table 1 was used.

*ERR*, is ERR model for population that started smoking and radiation exposure;

*S*, probability of surviving at age

*a*;

*λ*, cancer incidence baseline rate for Japanese people per 10,000 persons; and

*D*, radiation dose (mGy per year).

*S*) were calculated using the latest Japanese life tables for the year 2017. Here, life tables indicate the probability that a person of that particular age will die before his or her next birthday for each age [15].

*LBR*is the cancer incidence LBR for nonsmokers, all adults, and smokers.

### 2. Part 2 (Risk Assessment Considering the Joint Effect of Radiation and Smoking)

#### 1) Radiation risk model

*ERR*

*) as a function of attained age, sex, and annual radiation dose [10]. In this study, the ERR model of single radiation exposure was extended to chronic radiation exposure to evaluate annual radiation exposure (*

_{Rs}*ERR*

*). In Equation (8), the duration of the radiation exposure was fixed between the ages of 20 and 60 as a hypothetical working duration. Equation (8) represents the case where attained age exceeds the age at exposure,*

_{Rc}*a>e*. If age at exposure exceeds attained age, there is no cancer risk due to radiation exposure. Therefore, the value of

*ERR*

*is zero in Equation (9). For the value of each parameter in Equations (7) and (8), the radiation parameters of the GM-ERR model [10] were used.*

_{Rc}*a>e*,

*e=>a*,

*ERR*

*, radiation ERR model for single exposure;*

_{Rs}*ERR*

*, radiation ERR model for chronic exposure;*

_{Rc}*D*, radiation dose (mGy per year);

*e*, age at exposure;

*β*

*, ERR per Gy at the age of 30 years and attained age of 70 years, 0.34 for male and 1.32 for female [10];*

_{g}*θ*, coefficient for effect modification by age at exposure, 16% [10]; and

*γ*, coefficient for the modification due to attained age, −2.11 [10].

#### 2) GM-ERR model

*φ*

*and age at which smoking was quit (*

_{b}*s*).

*ERR*

*, GM-ERR interaction model;*

_{GM}*ERR*

*, smoking ERR model;*

_{s}*ERR*

*, radiation ERR model;*

_{R}*c*, cigarettes per day;

*a*, attained age;

*g*, sex (male, female); and

*f*, function of smoking variables.

*c*).

### Results and Discussion

### 1. Part 1 (Estimation of Nonsmokers’ Baseline Risk)

#### 1) Estimation of nonsmokers’ baseline risk of Japanese population

#### 2) Sensitivity analysis: birth cohort effects

*b*in the smoking ERR model, Equation [3]) was considered. This implies that the ERR model was set in consideration of the age distribution of the population as of 2017. Next, the information of ex-smokers was used to define populations who smoked in the past but were not current smokers. This was considered to estimate the baseline risk for nonsmokers. For the ERR model of ex-smokers, the formula used in the study of Cahoon et al. [10] was used. The parameters of the ERR model for ex-smokers were set to be the same as the GM-ERR model (Table 3 of Cahoon et al. [10]).

*c*), age at which smoking was quit (

*s*), attained age (

*a*), birth year (

*b*), and sex (

*g*) [10].

##### (13)

*φ*

*, is ERR per 50 packs per year (20 cigarettes per pack), 5.71 for male and 5.83 for female [10];*

_{g}*φ*

*, birth cohort (change per decade decrease in birth year), 0.09 [10];*

_{b}*μ*

*, coefficient of log (duration/50), 1.09 [10];*

_{1}*μ*

*, coefficient of log (duration/50)*

_{2}^{2}, −0.33 [10];

*υ*, power of years post-quitting + 1, −0.18 [10];

*b*, birth year (calendar year); and

*s*, age at which smoking was quit.

*λ*

*, is lung cancer incidence baseline rates in ex-smokers;*

_{sq}*QR*, rates of quitting smoking for each age; and

*k*, birth cohort.

*c*” of the ERRs in Equation (13), the average value of each of the male and female smokers in Table 1 was used.

#### 3) Results of sensitivity analysis considering the birth cohort effects and ex-smokers

### 2. Part 2 (Risk Assessment Considering the Joint Effect of Radiation and Smoking)

#### 1) Results of radiation risk

*S(e)*, which decreases as the attained age increases, is taken into consideration; therefore, the value of radiation lung cancer LAR decreased around the age of 60 years.

#### 2) Results of radiation and smoking risk

*c*=10 lifetime lung cancer risk per 1,000 mGy in atomic bomb survivors in Hiroshima and Nagasaki. This is the first study to apply the GM model to a population different from the LSS cohort.

*c*<10. The LARs (300 mGy) were almost constant up to

*c*=20 and increased when

*c*>20. Moreover, the highest value was obtained at

*c*=10 due to the joint effect of exposed male smokers (500 mGy).

*c*=10.

#### 3) Results of LAR, AF, and PAF

*i*. In this paper, the exposed level

*i*implies the combination of smoking and radiation dose. RR is defined by dividing the LAR of nonsmoker’s baseline risk by the LAR of total.

*PAF*

*is the PAFs at exposure level*

_{i}*i*, and

*RR*

*is the RRs at radiation and smoking exposed level*

_{i}*i*.

#### 4) Sensitivity analysis: comparison between the GM-ERR model and other ERR models

*c*=10.

*ERR*

_{s}*×ERR*

*” in Equation (20). In the GA-ERR model, a peak was observed near*

_{R}*c*=10 when the radiation dose was 1,000 mGy. However, the magnitude of the peak was smaller than that in the GM-ERR model. This was because

*f*(

*c*) of the GA-ERR model affected only

*ERR*

*(Equation [19]), whereas*

_{R}*f*(

*c*) affected not only

*ERR*

*, but also*

_{R}*ERR*

*in Equation (11) of the GM-ERR model.*

_{s}#### 5) Discussion of the joint effect of smoking and radiation

#### 6) Overall discussion

*λ*used to calculate the LAR in Equation (5) is

*λ*

*of nonsmokers or*

_{n}*λ*

*of the mixed population.*

_{m}