TABLE 12B-6 Comparison of Fits of Several Models (as Measured by the Deviance) Expressing the Dependence of Risk of Leukemia Mortality on Age at Exposure (e) and Time Since Exposure (t)a

Model Number

Age at Exposure (e), f(e)

Time Since Exposure (t) or Attained Age (a), g(t) or g(a)

Difference in Deviance for This Model and Model with No Modification by e or t (degrees of freedom)

Deviance

EAR Model

ERR Model

EAR Model

ERR Model

1

Categoricalb

log (t): full model

21.3 (5)

21.4 (5)

2254.9

2258.7

2

e − 30

log (t): full model

20.1 (3)

22.5 (3)

2256.1

2257.6

3

e − 30

log (t): main effect only ( = 0)

9.4 (2)

20.2 (2)

2266.8

2259.8

4

e − 30

log (t): interaction only (δ = 0)

19.5 (2)

13.3 (2)

2256.7

2266.8

5

e*c

log (t): full model

21.1 (3)

24.9 (3)

2255.1

2255.1

6

e*

log (t): main effect only ( = 0)

9.4 (2)

21.9 (2)

2266.9

2258.2

7

e*

log (t): interaction only (δ = 0)

20.4 (2)

22.9 (2)

2255.8

2257.2

8

Categorical

t

17.7 (5)

19.9 (5)

2258.5

2260.2

9

e − 30

t: full model

15.9 (3)

21.0 (3)

2260.3

2259.1

10

e*

t: full model

18.2 (3)

23.9 (3)

2258.1

2256.1

aBased on analyses of leukemia mortality (1950–2000) using models in which the EAR or ERR is given by βs(d + θd2) exp [γ f(e) + δ g(t) + iconid=pphi f(e) g(t)].

bSeparate estimates for e < 20, 20 e < 40, e 40.

ce* is min[(e − 30) / 10, 0], where e is age at exposure in years.

sure (p = .15). The total deviances for the preferred EAR and ERR leukemia models were nearly identical.

Thus, the committee’s preferred models for the EAR and the ERR are as follows, with δ = 0 for the EAR model:

(12B-11)

The parameter estimates for the committee’s preferred leukemia models are listed in Table 12-3 in the main chapter. Figure 12-2 shows both the ERR and the EAR as a function of time since exposure for exposure ages of 10, 20, and 30+ years. The ERR model is similar to that used for all leukemia by NIH (2003), although its leukemia model was based on e instead of e*, and on t instead of log (t), and did not allow for the dependence of the ERR on sex. Although there was no indication that the ERR depended on sex, this was included for compatibility with models for site-specific solid cancers.

ANNEX 12C: DETAILS OF LAR UNCERTAINTY ANALYSIS

Uncertainty Due to Sampling Variability

The approximate variance of the estimated LAR due to the uncertainty in LSS estimated linear models can be derived with the “delta method” (Feinberg 1988). As an example, the estimated LAR based on relative risk transport for solid cancer (for males or females) is calculated as

(12C-1)

where e* = e − 30 if e (exposure age) is less than 30 years and 0 otherwise; B(a) is the age-specific baseline rate at age a for the cancer of interest; S(a) is the probability of survival (in the 1999 U.S. population) to age a; and the Greek letters with hats represent the estimated coefficients in the excess relative risk model. The logarithm of Equation (12C-1) gives

where .

The result of a first-order Taylor’s approximation about is

so that the estimate of log (LAR) is a constant plus , where



The National Academies | 500 Fifth St. N.W. | Washington, D.C. 20001
Copyright © National Academy of Sciences. All rights reserved.
Terms of Use and Privacy Statement