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

Table 3.

Parameter estimates (95% bootstrap confidence intervals) with additional factors added to the intercept of the nonlinear model

Parameter	Terms added to the basic four-parameter dose–response model
θ₁—intercept (%)	1.50 (0.94, 1.74)	1.33 (0.92, 1.71)	1.53 (0.94, 1.90)
θ₂—initial slope (%/mGy)	0.016 (0.0, 0.11)	0.027 (0.0, 0.136)	0.015 (0.0, 0.13)
θ₃—downturn (mGy⁻¹)	0.048 (0.027, 0.052)	0.038 (0.025, 0.061)	0.042 (0.032, 0.054)
θ₄—overall slope (%/Gy)	0.071 (0.0, 1.5)	0.32 (0.0, 1.55)	0.17 (0.0, 1.6)
θ₅—city (Δ%^b) (coded as ± 1)	0.094 (− 0.21, 0.40)	0.024 (− 0.18, 0.38)	0.13 (− 0.17, 0.36)
θ₆—distal (Δ%)	− 0.26 (− 0.48, 0.29)	− 0.15 (− 0.42, 0.36)	− 0.14 (− 0.52, 0.33)
θ₇—Nagasaki–distal interaction (Δ%)	0.17 (− 0.67, 0.91)	0.29 (− 0.55, 0.74)	0.024 (− 0.55, 0.80)
θ₈—mother’s age (Δ%/5 years)	–	0.022 (− 0.092, 0.13)	–
θ₉—1st trimester (Δ%)	–	–	− 0.10 (− 0.52, 0.30)
θ₁₀—2nd trimester (Δ%)	–	–	− 0.11 (− 0.49, 0.21)
Reference—3rd trimester	–	–	0

Parameter

Terms added to the basic four-parameter dose–response model

City and distance
Loglik^a = − 500.91

Mother’s age
Loglik = − 501.21

Trimester
Loglik = − 500.81

θ₁—intercept (%)

1.50

(0.94, 1.74)

1.33

(0.92, 1.71)

1.53

(0.94, 1.90)

θ₂—initial slope (%/mGy)

0.016

(0.0, 0.11)

0.027

(0.0, 0.136)

0.015

(0.0, 0.13)

θ₃—downturn (mGy⁻¹)

0.048

(0.027, 0.052)

0.038

(0.025, 0.061)

0.042

(0.032, 0.054)

θ₄—overall slope (%/Gy)

0.071

(0.0, 1.5)

0.32

(0.0, 1.55)

0.17

(0.0, 1.6)

θ₅—city (Δ%^b)

(coded as ± 1)

0.094

(− 0.21, 0.40)

0.024

(− 0.18, 0.38)

0.13

(− 0.17, 0.36)

θ₆—distal (Δ%)

− 0.26

(− 0.48, 0.29)

− 0.15

(− 0.42, 0.36)

− 0.14

(− 0.52, 0.33)

θ₇—Nagasaki–distal interaction (Δ%)

0.17

(− 0.67, 0.91)

0.29

(− 0.55, 0.74)

0.024

(− 0.55, 0.80)

θ₈—mother’s age (Δ%/5 years)

–

0.022

(− 0.092, 0.13)

–

θ₉—1st trimester (Δ%)

–

− 0.10

(− 0.52, 0.30)

θ₁₀—2nd trimester (Δ%)

–

− 0.11

(− 0.49, 0.21)

Reference—3rd trimester

–

The model is $p_{θ} = θ_{1} + [θ_{2} d e^{- θ_{3} d} + θ_{4} d] + θ_{5} c + θ_{6} g + θ_{7} (n \times g) + θ_{8} m + θ_{9} t_{1} + θ_{10} t_{2}$ , where d is mother’s uterus radiation dose, c is city (coded ± 1), g is distal ground distance (≥ 3 km), m is mother’s age at exposure (centered at the mean, 29.4 years), and t₁ and t₂ are indicators of first and second trimester, respectively (note that not all parameters were fit simultaneously)

^aLog-likelihood

^bΔ% is difference from overall mean translocation percentage; Hiroshima coded − 1, Nagasaki coded + 1