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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.