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Table 1 Linear 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
gender M/F M/F M/F
cases b 1482 540 524
φ m c 6.66 38.58 16.90
ca D φ > 0 d 1412 172 494
LRT lin-con e 2.09 11.21 2.26
ERR 1,φ fg 0.09 (-0.03, 0.22) 0.69 (0.25, 1.26) 0.16 (-0.05, 0.42)
Dev h 1680.64 1258.02 1052.43
Chi-sq i 3205.08 2389.85 2500.37
df j 2992 2992 2992
Excess k 38.13 27.17 23.20
  Colon Uterus All solid
gender M/F F M/F
cases b 214 263 4379
φ m c 43.91 6.12 43.86
ca D φ > 0 d 33 262 365
LRT lin-con e 0.19 0.51 5.03
ERR 1, φ fg 0.17 (-0.44, 1.17) 0.10 (-0.16, 0.44) 0.26 (0.03, 0.52)
Dev h 719.80 638.46 2133.03
Chi-sq i 3497.50 1010.56 2769.51
df j 2992 1513 2992
Excess k 1.51 8.88 25.01
  1. a0 – 20 mSv subcohort, Excess Relative Risk ERR = βDφ with β constrained by 1 + ERR 0 for all data cells. Dφ is the weighted adjusted colon dose (neutron RBE = 10), lagged by φ years, in 10 mSv units. The control model is nested by β = 0.
  2. bdeaths in the subcohort from the specified cancer
  3. cLatency φm is chosen in the range 5 – 44 years. to minimise linear model Deviance for the given cancer site and gender. Where italicised, φm minimises Dev subject to ERR ≥ 0, equivalent to β ≥ 0
  4. ddeaths in the subcohort from the specified cancer, for which Dφ > 0 where φ = φm
  5. eThe likelihood ratio test LRTlin-con compares the fitted linear model with the control model at φm and is χ2 distributed on 1 degree of freedom
  6. fERR1,φ is the Excess Relative Risk at Dφ = 1 with φ = φm
  7. g95% Profile Likelihood Confidence Intervals are calculated with φ fixed at φm
  8. hDeviance of the fitted model
  9. iPearson Chi-Square of the fitted model
  10. jDegrees of Freedom of the fitted model
  11. kdifference between Observed (= Expected) cases and the number expected if Dφ is set to 0 in every cell after fitting the model