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Table 2 Transient modela

From: Low dose radiation and cancer in A-bomb survivors: latency and non-linear dose-response in the 1950–90 mortality cohort

 

Stomach

Liver

Lung

gen

M/F

M/F

M/F

φ m b

11.85

36.90

13.60

ca D φ > 0

1323

231

506

σ c

77.56

33.51

34.72

τ

129.19

3.56

3.78

LRT trans-lin d

4.49

10.89

14.39

LRT trans-con

5.91

18.12

15.70

ERR 0.025,φ e

0.08 (-0.11, 0.23)

0.77 (0.18, 1.67)

0.79 (0.20, 2.01)

ERR 1,φ

0.00 (-0.06, 0.16)

0.95 (0.28, 1.99)

0.80 (0.19, 1.99)

Dmax f

0.01

0.28

0.27

ERR Dmax,φ

0.22 (-0.04, 0.61)

3.46 (1.00, 7.11)

3.38 (0.90, 8.43)

Dev

1676.81

1251.10

1039.00

Chi-sq

3397.32

2436.33

2728.08

df

2991

2991

2991

Excess

91.23

95.89

214.39

 

Colon

Uterus

All solid

gen

M/F

F

M/F

φ m b

43.98

26.91

43.86

ca D φ > 0

28

127

365

σ c

26.69

275.88

11.89

τ

5.98

132.36

3.68

LRT trans-lin d

3.17

4.48

11.75

LRT trans-con

3.20

4.48

16.78

ERR 0.025,φ e

0.58 (-0.25, 1.85)

0.25 (-0.09, 1.13)

0.27 (0.07, 0.51)

ERR 1,φ

0.07 (-0.49, 1.71)

0.00 (-0.23, 1.06)

0.30 (0.03, 0.63)

Dmax f

0.17

0.01

0.27

ERR Dmax,φ

1.64 (-0.60, 6.10)

0.77 (-0.54, 5.35)

1.19 (0.41, 2.06)

Dev

716.79

634.49

2121.27

Chi-sq

3473.93

1051.37

2765.95

df

2991

1512

2991

Excess

8.24

19.99

78.00

  1. a0 – 20 mSv subcohort, Excess Relative Risk ERR = σDφ e ( τ D φ ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqqGLbqzdaahaaWcbeqaaiabcIcaOiabgkHiTiabes8a0jabbseaenaaBaaameaacqaHgpGzaeqaaSGaeiykaKcaaaaa@358E@ with τ 0 and σ,τ constrained by 1 + ERR ≥ 0 for all data cells; for Dφ see Table 1. The linear model is nested by τ = 0; the control model is nested by σ = 0.
  2. bchosen in the range 5 – 44 years. to minimise transient model Deviance; where italicised φm minimises Dev subject to ERR ≥ 0, equivalent to σ ≥ 0.
  3. cAt φm, σ and τ are the fitted Maximum Likelihood Estimate parameter values.
  4. dAt φm, the likelihood ratio test LRTtrans-lin compares the transient with the linear model and LRTtrans-con compares the transient model with the control model. Each LRT is χ2 distributed on 1 degree of freedom.
  5. eAt φm, ERRD,φ is the Excess Relative Risk at Dφ = D, with 95% Profile Likelihood Confidence Interval.
  6. fAt φm, Dmax = 1/τ is the value of D which maximises ERRD,φ
  7. gn/a indicates no lower limit could be calculated with 1 + ERR ≥ 0
  8. Other definitions and total cases as Table 1.