. 2022 Feb 17;61(1):59–72. doi: 10.1007/s00411-021-00960-4

Table 4.

Parameter estimates (95% confidence intervals) for smoking and sex in the intercept as well as interactions with the overall slope for radiation

Parameter	Smoking	Sex	Trimester
θ₁—Intercept (%)	0.96 (0.77, 1.62)	1.27 (0.82, 1.51)	1.47 (0.93, 1.70)	1.14 (0.84, 1.58)	1.21 (0.91, 1.53)
θ₂—Initial slope (%/mGy)	0.079 (0.002, 0.13)	0.041 (0.0, 0.080)	0.011 (0.0, 0.12)	0.064 (0.0, 0.13)	0.026 (0.0, 0.11)
θ₃—Downturn (mGy⁻¹)	0.040 (0.033, 0.056)	0.031 (0.024, 0.036)	0.046 (0.035, 0.047)	0.041 (0.035, 0.050)	0.044 (0.034, 0.050)
θ₄—Overall slope (%/Gy) (with interactions, overall slope for non-smoker, average of sex, or 3^rd trimester)	1.1 (0.00005, 1.9)	0.43 (0.0, 2.0)	0.10 (0.0, 1.5)	0.90 (0.00008, 1.85)	0.000005 (0.0, 1.25)
θ₅—city (Δ%) (coded as ± 1)	0.10 (− 0.15, 0.47)	0.12 (− 0.15, 0.36)	0.13 (− 0.11, 0.40)	0.11 (− 0.12, 0.41)	0.04 (− 0.17, 0.39)
θ₆—distal (Δ%)	0.24 (− 0.17, 0.41)	0.08 (− 0.23, 0.35)	− 0.25 (− 0.47, 0.28)	0.14 (− 0.28, 0.39)	− 0.14 (− 0.41, 0.30)
θ₇—Nagasaki–distal interaction (Δ%)	0.17 (− 0.76, 0.64)	0.07 (− 0.46, 0.72)	0.13 (− 0.49, 0.63)	0.09 (− 0.54, 0.76)	0.26 (− 0.48, 0.86)
Smoking (Δ%) (non-smoker is the reference)	θ₁₁—current θ₁₂—former	0.15 (− 0.15, 0.47) 0.05 (− 0.42, 0.51)	− 0.086 (− 0.16, 0.54) − 0.19 (− 0.53, 0.31)	0.13 (− 0.19, 0.45) − 0.02 (− 0.22, 0.33)	0.029 (− 0.22, 0.43) − 0.069 (− 0.43, 0.43)	0.27 (− 0.060, 0.47) 0.14 (− 0.34, 0.58)
θ₁₃—Sex (Δ%; sex coded as − 1 for males, + 1 for females)	–	− 0.052 (− 0.22 0.12)	− 0.14 (− 0.30 0.096)	–
Smoking–radiation interaction (Δ%/Gy) (non-smoker is the reference)	θ₁₄—current θ₁₅—former	–	− 0.18 (− 2.4, 0.99) 2.3 (− 1.3, 4.6)	–	–
θ₁₆—Sex–radiation interaction (Δ%/Gy; sex coded as − 1 for males, + 1 for females)	–	–	0.42 (− 0.46 1.2)	–
Trimester–radiation interaction (Δ%/Gy)	–	–	0.000001 (0.0, 2.18)
θ₁₇—1st trimester (3rd trimester is the reference)			0.70 (0.0, 1.56)
θ₁₈—2nd trimester

Parameter

Smoking

Sex

Trimester

No interaction
(− 502.98)

With interaction
(− 501.08)

No interaction
(− 499.57)

With interaction
(− 500.84)

With interaction
(− 500.09)

θ₁—Intercept (%)

0.96

(0.77, 1.62)

1.27

(0.82, 1.51)

1.47

(0.93, 1.70)

1.14

(0.84, 1.58)

1.21

(0.91, 1.53)

θ₂—Initial slope (%/mGy)

0.079

(0.002, 0.13)

0.041

(0.0, 0.080)

0.011

(0.0, 0.12)

0.064

(0.0, 0.13)

0.026

(0.0, 0.11)

θ₃—Downturn (mGy⁻¹)

0.040

(0.033, 0.056)

0.031

(0.024, 0.036)

0.046

(0.035, 0.047)

0.041

(0.035, 0.050)

0.044

(0.034, 0.050)

θ₄—Overall slope (%/Gy) (with interactions, overall slope for non-smoker, average of sex, or 3^rd trimester)

1.1

(0.00005, 1.9)

0.43

(0.0, 2.0)

0.10

(0.0, 1.5)

0.90

(0.00008, 1.85)

0.000005

(0.0, 1.25)

θ₅—city (Δ%) (coded as ± 1)

0.10

(− 0.15, 0.47)

0.12

(− 0.15, 0.36)

0.13

(− 0.11, 0.40)

0.11

(− 0.12, 0.41)

0.04

(− 0.17, 0.39)

θ₆—distal (Δ%)

0.24

(− 0.17, 0.41)

0.08

(− 0.23, 0.35)

− 0.25

(− 0.47, 0.28)

0.14

(− 0.28, 0.39)

− 0.14

(− 0.41, 0.30)

θ₇—Nagasaki–distal interaction (Δ%)

0.17

(− 0.76, 0.64)

0.07

(− 0.46, 0.72)

0.13

(− 0.49, 0.63)

0.09

(− 0.54, 0.76)

0.26

(− 0.48, 0.86)

Smoking (Δ%)

(non-smoker is the reference)

θ₁₁—current

θ₁₂—former

0.15

(− 0.15, 0.47)

0.05

(− 0.42, 0.51)

− 0.086

(− 0.16, 0.54)

− 0.19

(− 0.53, 0.31)

0.13

(− 0.19, 0.45)

− 0.02

(− 0.22, 0.33)

0.029

(− 0.22, 0.43)

− 0.069

(− 0.43, 0.43)

0.27

(− 0.060, 0.47)

0.14

(− 0.34, 0.58)

θ₁₃—Sex (Δ%; sex coded as − 1 for males, + 1 for females)

–

− 0.052

(− 0.22 0.12)

− 0.14

(− 0.30 0.096)

–

Smoking–radiation interaction (Δ%/Gy)

(non-smoker is the reference)

θ₁₄—current

θ₁₅—former

–

− 0.18

(− 2.4, 0.99)

2.3

(− 1.3, 4.6)

–

θ₁₆—Sex–radiation interaction (Δ%/Gy; sex coded as − 1 for males, + 1 for females)

–

0.42

(− 0.46 1.2)

–

Trimester–radiation interaction (Δ%/Gy)

–

0.000001

(0.0, 2.18)

θ₁₇—1st trimester

(3rd trimester is the reference)

0.70

(0.0, 1.56)

θ₁₈—2nd trimester

^aThe model is $p_{θ} = θ_{1} + [θ_{2} d e^{- θ_{3} d} + θ_{4} d] + θ_{5} c + θ_{6} g + θ_{7} (n \times g) + θ_{11} s_{C} + θ_{12} s_{F} + θ_{13} x + θ_{14} (s_{C} \times d) + θ_{15} (s_{F} \times d) + θ_{16} (x \times d) + θ_{17} (t_{1} \times d) + θ_{18} (t_{2} \times d)$ , where in addition to variables defined in the model for Table 3, s_C indicates current smoker, s_F indicates former smoker, and x is sex (males coded − 1, females coded + 1) (note that not all parameters were fit simultaneously)