Table 4.

Parameter estimates for esophageal cancer in multiplicative excess relative risk (ERR) models with smoking effects and alcohol effects

		Simple Linear ERRa	Quadratic ERR	Preferred model, adj. for smoking and alcohol
All esophageal cancer, n=486	ERR*/Gy	0.32 (−0.008, 0.80)b
	ERR/Gy2		0.27 (0.04, 0.61)	0.30c (0.05, 0.65)
	AICd	77.7	75.0	0
Upper and middle esophagus, n=240	ERR/Gy	0.09 (<−0.29, 0.89)		−0.0005c (−0.54e, 0.53e)
	AIC	46.8		0
Lower esophagus, n=70	ERR/Gy	0.91c (−0.58e, 2.86)		1.07 (<0.10, 3.63)
	AIC	3.2		0

^aExcess relative risk,

^b95% Confidence Interval,

^cRecommended model, esophageal cancer; $(1+\beta d^2*\mathrm{e}\mathrm{x}\mathrm{p}\left(\varphi I\left(K>4\right)\right))\left(1+{ERR}_{smk}\right)\left(1+{ERR}_{drk}\right)$ Cancers of upper and middle part of esophagus; $(1+\mathrm{\beta }d*\mathrm{e}\mathrm{x}\mathrm{p}\left(\varphi I\left(K>4\right)\right))\left(1+{ERR}_{smk}\right)\left(1+{ERR}_{drk}\right)$, Cancers of lower part of esophagus; $\left(1+\mathrm{\beta }\mathrm{d}\mathrm{*}\mathrm{e}\mathrm{x}\mathrm{p}\left(\varphi I\left(K>4\right)\right)\right)$, where $d$ is radiation dose, $I$ is an indication function, $K$ is total shielded kerma, $\mathrm{\beta }$ and $\varphi$ are regression coefficients.

^dAkaike Information Criterion (AIC) difference from model with lowest AIC,

^eWald-type confidence limit