Table 3.

Estimates of 50^th percentiles and 90% CIs of LDEF based on analyses of curvature in dose-responses (ERRs or EARs) for mortality from all solid cancers in LSS cohort assuming linear-quadratic models^a

Reference	Dose range (Gy)	Follow-up period	Method of calculation	LDEFb
Little et al. (2008)	0–4c	1950–2000	[1 + (β/α)]d (ERR model)e	1.34 (1.01, 2.53)f
			[1 + (β/α)]d (EAR model)e	1.51 (1.07, 3.26)g
Ozasa et al. (2012)	0–2h	1950–2003	[1 + (β/α)]d (ERR model)i	3.2 (1.2, 8.3)j
			αL/αLQk (ERR model)i	2.0 (1.0, 6.8)m
	0–4n		[1 + (β/α)]d (ERR model)i	1.11 (0.94, 1.48)o
			αL/αLQk (ERR model)i	1.16 (0.77, 1.90)p

^aERRs and EARs estimated using DS02 dosimetry were sex-averaged. LDEFs were included in our analysis to estimate DDREF for solid cancers induced by low-LET radiation.

^bEstimates are based on assumption that reported MLEs and CIs of risk coefficients or ratios of risk coefficients can be represented by Weibull distributions with modes at MLEs.

^cRange of shielded kerma free-in-air from photons and neutrons. Members of LSS cohort with shielded kerma >4 Gy were omitted. Range of neutron-weighted doses to colon, calculated assuming biological effectiveness of neutrons at Hiroshima and Nagasaki relative to high-energy photons of 10, over which ERRs or EARs were modeled to estimate LDEF was slightly less than range of shielded kerma (Egbert 2005; RERF 2007).

^dα (Gy⁻¹) and β (Gy⁻²) are coefficients of linear and quadratic terms, respectively, in linear-quadratic fit to dose-response, and β/α (Gy⁻¹) is curvature parameter. LDEF is estimate at dose of 1 Gy.

^eERRs and EARs were modified by time since exposure and attained age.

^fEstimate based on reported MLEs and 90% CIs of α [0.347 (0.161, 0.566) Gy⁻¹] and β [0.121 (0.004, 0.246) Gy⁻²] and assumption that α and β are negatively correlated (correlation coefficient of −1). Assumed parameter correlation should result in slight overestimate of uncertainty in LDEF.

^gEstimate based on reported MLEs and 90% CIs of α [5.58 (2.31, 9.40) Gy⁻¹] and β [2.86 (0.66, 5.22) Gy⁻²] and assumption that α and β are negatively correlated (correlation coefficient of −1). Assumed parameter correlation should result in slight overestimate of uncertainty in LDEF.

^hRange of neutron-weighted doses to colon, calculated assuming biological effectiveness of neutrons at Hiroshima and Nagasaki relative to high-energy photons of 10, over which ERRs were modeled to estimate LDEF.

ⁱERRs were modified by age at exposure and attained age.

^jEstimate based on reported MLE and 95% CI of β/α [0.81 (0.08, 8.6) Gy⁻¹]. Reported β/α is estimate of curvature in dose-response preferred by Ozasa et al. (2012).

^kα_L is ERR per Gy obtained from linear fit to dose-response, and α_LQ (Gy⁻¹) is coefficient of linear term in linear-quadratic fit.

^mEstimate based on reported MLEs of α_L (0.44 Gy⁻¹) and α_LQ (0.22 Gy⁻¹), estimated 95% CIs of α_L [(0.33, 0.56) Gy⁻¹] and α_LQ [(0.036, 0.43) Gy⁻¹] (D. Preston, personal communication, November 6, 2016), and assumption that α_L and α_LQ are uncorrelated.

ⁿRange of shielded kerma free-in-air from photons and neutrons, with estimates of shielded kerma >4 Gy truncated to 4 Gy. Range of neutron-weighted dose to colon, calculated assuming biological effectiveness of neutrons at Hiroshima and Nagasaki relative to high-energy photons of 10, over which ERRs were modeled to estimate LDEF was slightly less than range of shielded kerma (Egbert 2005; RERF 2007).

^oEstimate based on reported MLEs of α (0.36 Gy⁻¹) and β (0.038 Gy⁻²), estimated 95% CIs of α [(0.21, 0.53) Gy⁻¹] and β [(−0.043, 0.123) Gy⁻²] (D. Preston, personal communication, November 6, 2016), and assumption that α and β are negatively correlated (correlation coefficient of −1). Assumed parameter correlation should result in slight overestimate of uncertainty in LDEF.

^pEstimate based on reported MLE and 95% CI of α_L [0.42 (0.32, 0.53) Gy⁻¹)], reported MLE of α_LQ (0.36 Gy⁻¹), estimated 95% CI of α_LQ [(0.21, 0.53) Gy⁻¹] (D. Preston, personal communication, November 6, 2016), and assumption that α_L and α_LQ are uncorrelated.