TABLE 4.

Models for Excess Relative Risk (ERR) as a Function of Radiation Dose to the Thyroid Gland in the Childhood Cancer Survivor Study Cohort

Model number	Description	Equation	β1	β2	β3	Deviance	Referent model	P valuea
1	Baselineb	αc	_	_	_	1532.5
2	Linear	α[1 + β1d]	0.404	_	_	1469.9	1	<0.001
3	Quadratic	α[1 + β1d2]	0.00798	_	_	1515.0	1	<0.001
4	Linear exponential	α[1 + β1d × exp(β2d)]	2.420	−0.0665	_	1430.5	2	<0.001
5	Linear exponential quadratic model-1	α[1 + β1d × exp(β2d2)]	1.381	−0.00164	_	1419.2	2	<0.001
6	Linear exponential quadratic model-2	α[1 + β1d × exp(β2d + β3d2)]	0.670	0.0615	−0.00292	1417.1	5	0.1
7	Linear quadratic	α[1 + β1d + β2d2]	0.758	−0.0115	_	1441.8	2	<0.001
8	Linear quadratic exponential	α[1 + (β1d + β2d2) × exp(β3d)]	2.215	−0.0362	−0.0402	1426.7	7	<0.001
9	Linear quadratic exponential quadratic	α[1 + (β1d + β2d2) × exp(β3d2)]	0.433	0.0709	−0.00242	1416.6	5	0.1
10	Quadratic exponential quadratic	α[1 + β1d2 × exp(β2d2)]	0.0674	−0.00237	_	1417.5	3	<0.001

Note. Italics represent the most parsimonious models with the lowest deviance and compatibility with radiobiological theory.

^aLikelihood ratio test comparing to referent (nested) model (e.g. model 2 compared to model 1, model 5 compared to model 2).

^bBaseline function includes natural logarithm of attained age, sex and type of childhood cancer (Hodgkin lymphoma, leukemia or other).

^cα represents the baseline function as described in footnote b.