Table 7.

Analysis of effect modification for the effects of thyroid and pituitary radiation doses on the incidence of hypothyroidism^a: Childhood Cancer Survivor Study.

Modifier	Cases	PYR/10000	Exp(δj)	Pb	Pc
Time since exposure, years
<10	228	5.4	1.00d	<0.01	0.41
10–14	202	4.5	0.90
15–19	139	3.7	0.63
20–24	106	2.8	0.33
≥25	85	2.1	0.21
Age at exposure, years
<5	238	7.1	1.00d	0.01	0.16
5–9	154	4.5	0.60
≥10	368	6.9	0.56
Attained age, years
<25	383	11.0	1.00d	0.01	0.55
25–29	133	3.2	0.54
30–39	184	3.4	0.33
≥40	60	0.8	0.30
Sex
Male	308	9.7	1.00d	<0.01	0.45
Female	452	8.7	0.41
Type of cancere
Other cancers	193	8.1	1.00d	0.08	0.53
Leukemia	194	6.5	0.07
CNS cancer	127	2.0	0.46
HL	246	1.8	0.33
Chemotherapyf
No	190	3.5	1.00d	0.96	0.18
Yes	570	14.9	0.98
CCNU
No	704	18.0	1.00d	0.33	<0.01g
Yes	55	0.4	1.39g
Cyclophosphamide
No	450	10.3	1.00d	0.88	0.63
Yes	309	8.1	1.01
Bleomycin
No	690	17.6	1.00d	<0.01	0.12
Yes	69	0.8	1.77

^a

Fitted model had the form:

$$\text{RR}\left(d_t, d_p, c\right)=1+ {\text{G}}_t\left(d_t\right)\times \text{H}\left(d_p\right)+ {\text{G}}_p\left(d_p\right)+\theta c$$

where ${\text{G}}_t(d_t)={\beta }_t{d}_t{e}^{{\gamma }_1{d}_t+}{}^{{\gamma }_2{d}_t{}^2}$,${\text{G}}_p(d_p)={\beta }_p{d}_p{e}^{\phi d_p}$ and $\text{H}(d_p)=e^{{\gamma }_3{d}_p+}{}^{{\gamma }_{4}In(d_p)}$ and where d_t, d_p and c were radiation dose to the thyroid, radiation dose to the pituitary and chemotherapy (yes=1/no=0), respectively. See text equation 1 for additional specification. For effect modification of variable z with J levels, β_t exp{Σ_jδ_t,jZ_j} replaced β_t and β_p exp{Σ_jδ_p,jZ_j} replaced β_p, where z_j, j=1, …, J was an indicator variable and exp(δ_t,j) and exp(δ_p,j) represented the relative changes in the linear slope parameters for the j^th category in relation to level 1, where δ_t,1=0 and δ_p,1=0 for identifiability. Model includes 2×(J-1) distinct δ_t,jand δ_p,j parameters; however, the relative changes in across levels of a modifier were statistically homogeneous for thyroid dose and for pituitary dose, i.e., δ_t,j= δ_p,j for all j. Entries are homogeneous relative effect estimates.

^bP-value for test of homogeneity across levels of modifier; δ_{2= =δj=0.}

^cP-value for test of homogeneity of modifying effects for thyroid radiation dose and pituitary radiation dose, i.e., , i.e., δ_{t,j =} δ_p,j for all j.

^dReferent category.

^eModel includes additional terms for the interaction of type of cancer and chemotherapy, θ_k, k=1, …, 4.

^fModel includes additional terms for the interaction of CNS cancer and chemotherapy, θ_k, k=1, 2.

^gThe relative effects for thyroid dose and pituitary dose differed significantly. Among persons treated with CCNU, exp(δ_j) was 4.5 (95% CI: 2.4–8.6) for pituitary dose and 0.82 (95% CI: 0.36–1.9) for thyroid dose relative to those not treated with CCNU. The value of 1.39 is based on a model in which relative effects for thyroid dose and pituitary dose were constrained to be the same.

Abbreviations: CCNU=cyclohexyl-chloroethyl-nitrosourea; CNS=central nervous system; HL= Hodgkin lymphoma); PYR=person-years