Table 3. Modifiers of dose response for various categories of circulatory disease, among full cohort (exposed + unexposed) and among exposed group only. Parameter estimates (all Gy⁻¹) with 95% profile likelihood CI, unless otherwise indicated.

Background model is quartic model in age, with adjustment for gender, smoking habit and quantity, alcohol habit and quantity, and calendar year period treated (year of entry).

Model no.	Model/parameters		Exposed and unexposed				Exposed only
			All circulatory disease	IHD	Stroke	Other circulatory	All circulatory disease	IHD
1		α (Gy−1)	0.082 (0.031, 0.140)	0.102 (0.039, 0.174)	0.028 (−0.085, 0.186)	0.050 (−0.053, 0.194)	0.194 (0.014, 0.648)	0.376 (0.060, 1.735)
	Background[1+ α D]	p-valuesa	0.001	0.001	0.665	0.384	0.028	0.007
2		α (Gy−1)	0.104 (0.026, 0.287)	0.107 (0.025, 0.296)	1.604 (−404.3, 807.5)	0.035 (−0143b, 14.12)	0.441 (0.042, 1.767b)	1.043 (−0.657, 4.356b)
	Background[1+ α D exp[γ D]]	γ (Gy−1)	−0.074 (−0.468, 0.197)	−0.016 (−0.391, 0.262)	−1.242 (−157.1, 0.852b)	0.105 (−0.987b, 1.196b)	−0.162 (−0.675, 0.140b)	−0.155 (−0.355, 0.086b)
		p-valuesc	0.599	0.920	0.123	0.834	0.212	0.152
3		α (Gy−1)	0.089 (0.034, 0.151)	0.123 (0.054, 0.204)	0.004 (−0.120b, 0.128b)	0.051 (−0.056, 0.203)	0.248 (0.035, 0.935)	0.403 (0.060, 2.154)
	Background[1+ α D exp[κ1sex=female]]	κ	−0.625 (−54.32, 0.877)	−1124 (NA, NA)	3.532 (<−104, 35.56b)	−0.123 (−5.647, 6.135b)	−8.049 (−3469b, 1.108)	−0.535 (−71.30, 3.233b)
		p-valuesc	0.501	0.092	0.114	0.964	0.236	0.762
4	Background[1+ α D exp[τ (age at exposure – 41.32)]]d	α (Gy−1)	0.062 (0.023, 0.113)	0.078 (0.028, 0.143)	0.016 (−0.050b, 0.137)	0.046 (−0.063, 0.190)	0.236 (0.067, 0.698)	0.453 (0.118, 2.047)
		τ (y−1)	0.051 (0.025, 0.082)	0.050 (0.023, 0.082)	0.097 (−0.034b, 0.228b)	0.021 (−0.115b, 0.157b)	0.040 (0.023, 0.066)	0.035 (0.020, 0.059)
		p-valuesc	<0.001	<0.001	0.064	0.677	<0.001	<0.001
5		α (Gy−1)	0.115 (0.054, 0.181)	0.140 (0.067, 0.223)	0.107 (−0.085b, 0.299)	0.004 (−0.048b, 0.195)	0.318 (0.115, 0.794)	0.596 (0.195, 2.250)
	Background[1+ α D exp[δ (time since exposure – 20.78)]]d	δ (y−1)	−0.075 (−0.126, −0.045)	−0.066 (−0.113, −0.036)	−0.118 (−0.395, −0.044)	−0.299 (−1.487b, 0.889b)	−0.048 (−0.086, −0.027)	−0.039 (−0.068, −0.021)
		p-valuesc	<0.001	<0.001	0.003	0.270	<0.001	<0.001
		p-valuese	<0.001	<0.001	0.009	0.372	<0.001	<0.001
6	Background[1+ α D exp[τ (age at exposure – 41.32) + δ (time since exposure – 20.78)]]d	α (Gy−1)	0.115 (0.053, 0.193)	0.133 (0.060, 0.229)	0.150 (−0.125b, 0.554)	0.001 (−0.020b, 0.022b)	0.367 (0.112, 1.270)	0.602 (0.150, 3.409)
		τ (y−1)	−0.001 (−0.035, 0.033)	0.006 (−0.031, 0.044)	−0.024 (−0.124, 0.079)	−0.044 (−0.217b, 0.128b)	−0.013 (−0.076, 0.044)	−0.001 (−0.074, 0.076)
		δ (y−1)	−0.076 (−0.139, −0.036)	−0.061 (−0.119, −0.020)	−0.132 (−0.392, −0.035)	−0.434 (−1.723b, 0.856b)	−0.060 (−0.129, −0.000)	−0.040 (−0.112, 0.043)
		p-valuesf	<0.001	0.004	0.014	0.111	0.050	0.286
		p-valuesg	0.964	0.738	0.575	0.222	0.652	0.964

^ap-value for improvement of fit over model without linear term in dose

^bWald-based confidence limit

^cp-value for improvement of fit over model with (unadjusted) linear term in dose

^dage at exposure and time since exposure are approximately centered by subtracting off their person-year weighted means (41.32 years, 20.78 years respectively) in the full cohort (exposed+unexposed), to stabilize parameter estimates.

^ep-value for 2 degrees of freedom test of improvement of fit over model with no dose-response terms

^fp-value for improvement of fit over linear model in dose with adjustment for age at exposure.

^gp-value for improvement of fit over linear model in dose with adjustment for time since exposure