. Author manuscript; available in PMC: 2014 Feb 1.

Published in final edited form as: Int J Radiat Oncol Biol Phys. 2012 Jun 9;85(2):451–459. doi: 10.1016/j.ijrobp.2012.04.029

Table 5.

Test of heterogeneity in dose response and its modification by age at exposure in various categories of cancer. The background model for each cancer subtype is cubic model in age, with adjustment for gender and smoking habit and quantity. Stomach dose is used for all cancer and stomach cancer, pancreatic dose is used for pancreatic cancer, (average of left and right lobe) lung dose is used for lung cancer, active bone marrow dose is used for leukemia, and stomach dose is used for all other cancers. All p-values relate to the improvement in fit over the model immediately above.

Panel	Model	p-value
A	Test of heterogeneity across five cancer endpoints (stomach, pancreas, lung, leukemia, all other cancers), linear dose response

	Background[1+ a D exp[τ (age at exposure − 41.32)]]^a	0.001^b
	Background[1+ a_i D exp[τ (age at exposure − 41.32)]]^a	0.004^c
	Background[1+ a_i D exp[τ_i (age at exposure − 41.32)]]^a	0.083^d

B	Test of heterogeneity across four cancer endpoints (stomach, pancreas, lung, leukemia), linear dose response

	Background[1+ a D exp[τ (age at exposure − 41.32)]]^a	<0.001^b
	Background[1+ a_i D exp[τ (age at exposure − 41.32)]]^a	0.037^c
	Background[1+ a_i D exp[τⁱ (age at exposure − 41.32)]]^a	0.071^d

C	Test of heterogeneity across five cancer endpoints (stomach, pancreas, lung, leukemia, all other cancers), linear-exponential dose response

	Background[1+ a D exp[γ D + τ (age at exposure − 41.32)]]^a	<0.001^b
	Background[1+ a_i D exp[γ D + τ (age at exposure − 41.32)]]^a	0.123^c
	Background[1+ a_i D exp[γ_iD + τ (age at exposure − 41.32)]]^a	0.682^e
	Background[1+ a_i D exp[γ_iD + τ_i (age at exposure − 41.32)]]^a	0.590^d

D	Test of heterogeneity across four cancer endpoints (stomach, pancreas, lung, leukemia), linear-exponential dose response

	Background[1+ a D exp[γ D + τ (age at exposure − 41.32)]]^a	<0.001^b
	Background[1+ a_i D exp[γ D + τ (age at exposure − 41.32)]]^a	0.774^c
	Background[1+ a_i D exp[γ_iD + τ (age at exposure − 41.32)]]^a	0.503^e
	Background[1+ a_i D exp[γ_iD + τ_i (age at exposure − 41.32)]]^a	0.463^d

age at exposure is approximately centered by subtracting off its person-year weighted mean (41.32 years) in the full cohort (exposed+unexposed), to stabilize parameter estimates.

p-value for improvement of fit over model without radiation dose response term.

p-value for improvement of fit over model with the same excess relative risk coefficient (α) for each endpoint.

p-value for improvement of fit over model with the same age at exposure trend in excess relative risk (τ) for each endpoint.

p-value for improvement of fit over model with the same exponential dose coefficient (γ) for each endpoint.