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Table 3 Two-phase 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 11.89 36.90 13.60
ca D φ > 0 1311 231 506
β c 0.46 1.43 0.44
σ 119.96 290.09 37.92
τ 82.67 76.82 4.47
LRT 2p-trans d 15.68 16.76 0.34
LRT 2p-lin 19.64 27.64 14.73
LRT 2p-con 21.19 34.87 16.04
ERR 0.025,φ 0.39 (0.08, 0.86) 1.10 (0.26, 2.37) 0.86 (0.14, 3.34)
ERR 1,φ 0.46 (0.11, 0.94) 1.43 (0.48, 2.95) 0.88 (0.12, 3.36)
Dmax e 0.01 0.01 0.23
ERR Dmax,φ 0.54 (0.17, 1.04) 1.41 (0.50, 2.86) 3.23 (0.09, 9.39)
Dev 1661.53 1234.35 1038.66
Chi-sq 3408.01 2447.95 2770.40
df 2990 2990 2990
R f 262.62 204.11 86.39
Excess 390.00 126.36 224.43
  Colon Uterus All Solid
gen M/F F M/F
φ m b 20.28 26.91 43.86
D φ > 0 184 127 365
β c -0.74 0.47 -0.62
σ 11.32 198.10 13.10
τ 2.66 81.12 2.32
LRT 2p-trans d 1.32 1.83 1.14
LRT 2p-lin 3.01 6.31 12.90
LRT 2p-con 3.54 6.31 17.93
ERR 0.025,φ 0.25 (-0.44, 1.46) 0.66 (-0.10, 2.44) 0.27 (0.05, 0.54)
ERR 1,φ 0.05 (-0.53, 1.15) 0.47 (-0.32, 2.12) 0.27 (-0.04, 0.66)
Dmax e 0.32 0.01 0.35
ERR Dmax,φ 1.31 (-0.71, 1.51) 0.90 (-0.17, 2.96) 1.59 (0.03, 2.54)
Dev 716.45 632.66 2120.13
Chi-sq 3339.24 1047.11 2759.48
df 2990 1511 2990
R f -14.36 425.41 -19.98
Excess 29.34 45.89 74.59
  1. a0 – 20 mSv subcohort, Excess Relative Risk ERR = βDφ + σDφ e ( τ D φ ) MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqqGLbqzdaahaaWcbeqaaiabcIcaOiabgkHiTiabes8a0jabbseaenaaBaaameaacqaHgpGzaeqaaSGaeiykaKcaaaaa@358E@ with τ ≥ 0 and β,σ,τ constrained by 1 + ERR 0 for all data cells; for Dφ see Table 1. The transient model is nested by β = 0; the linear model is nested by σ = 0 or by τ = 0; the control model is nested by β = σ = 0.
  2. bchosen in the range 5 – 44 years. to minimise two-phase model Deviance; where italicised φm minimises Dev subject to ERR0.025,φ ≥ 0, a weaker condition than β, σ ≥ 0.
  3. cAt φm, β, σ and τ are the fitted Maximum Likelihood Estimate parameter values.
  4. dAt φm, the likelihood ratio tests LRT2p-trans and LRT2p-lin compare the two-phase with the transient and linear models (χ2 on 1 df); and LRT2p-con compares the two-phase model with the control model (χ2 on 2 df)
  5. eAt φm, Dmax is the value of D giving a local maximum of ERRD,φ
  6. f R = 1 + σ/β
  7. Other definitions as in Table 2