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}
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.
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