Table 3.

Two-phase model^a

	Stomach	Liver	Lung
gen	M/F	M/F	M/F
φmb	11.89	36.90	13.60
ca Dφ > 0	1311	231	506
βc	0.46	1.43	0.44
σ	119.96	290.09	37.92
τ	82.67	76.82	4.47
LRT2p-transd	15.68	16.76	0.34
LRT2p-lin	19.64	27.64	14.73
LRT2p-con	21.19	34.87	16.04
ERR0.025,φ	0.39 (0.08, 0.86)	1.10 (0.26, 2.37)	0.86 (0.14, 3.34)
ERR1,φ	0.46 (0.11, 0.94)	1.43 (0.48, 2.95)	0.88 (0.12, 3.36)
Dmaxe	0.01	0.01	0.23
ERRDmax,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
Rf	262.62	204.11	86.39
Excess	390.00	126.36	224.43
	Colon	Uterus	All Solid
gen	M/F	F	M/F
φmb	20.28	26.91	43.86
Dφ > 0	184	127	365
βc	-0.74	0.47	-0.62
σ	11.32	198.10	13.10
τ	2.66	81.12	2.32
LRT2p-transd	1.32	1.83	1.14
LRT2p-lin	3.01	6.31	12.90
LRT2p-con	3.54	6.31	17.93
ERR0.025,φ	0.25 (-0.44, 1.46)	0.66 (-0.10, 2.44)	0.27 (0.05, 0.54)
ERR1,φ	0.05 (-0.53, 1.15)	0.47 (-0.32, 2.12)	0.27 (-0.04, 0.66)
Dmaxe	0.32	0.01	0.35
ERRDmax,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
Rf	-14.36	425.41	-19.98
Excess	29.34	45.89	74.59

^a 0 – 20 mSv subcohort, Excess Relative Risk ERR = βD_φ + σD_φ ${\text{e}}^{(-\tau {\text{D}}_{\phi })}$ with τ ≥ 0 and β,σ,τ constrained by 1 + ERR ≥ 0 for all data cells; for D_φ 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.

^b chosen in the range 5 – 44 years. to minimise two-phase model Deviance; where italicised φ_m minimises Dev subject to ERR_0.025,φ ≥ 0, a weaker condition than β, σ ≥ 0.

^c At φ_m, β, σ and τ are the fitted Maximum Likelihood Estimate parameter values.

^d At φ_m, the likelihood ratio tests LRT_2p-trans and LRT_2p-lin compare the two-phase with the transient and linear models (χ² on 1 df); and LRT_2p-con compares the two-phase model with the control model (χ² on 2 df)

^e At φ_m, Dmax is the value of D giving a local maximum of ERR_D,φ

^f R = 1 + σ/β

Other definitions as in Table 2