Facility is the risk factor of primary interest and our evaluation is limited to white males for all causes of death. A detailed discussion of the potential for exposure to internal and external radiation and other related hazards at each facility is given in [2,3].
As a preliminary step in the comparison of the death rates of workers at the Oak Ridge plants an ADS was constructed based on birth cohort, age at risk, and facility. Each worker in a specified birth-cohort enters follow-up at the age of first hire, and subsequently contributes person-time at risk to appropriate five year age intervals until he dies or reaches the last day of follow-up. Poisson regression is used to estimate the age-specific death rates for each facility adjusted for birth cohort, and the 1915 birth cohort is used as the referent group. These estimated rates are shown in Fig. 1 for each of the Oak Ridge facility groups and the age-specific death rates for U.S. white males are also shown as the dotted lines. Fig. 1 shows that the log of the age-specific death rates increase linearly with age for all cause mortality, and that the rates for TEC, Y-12, K-25, and multiple facility workers are close to or above the U.S. rates, while X-10 rates are generally lower. To further evaluate the differences among the facilities a model is used to ''adjust" for age, using two different approaches.
In the first approach (internal
analysis) the age-specific death rates are assumed to increase
linearly with age at risk on a logarithmic scale
(see Fig. 1). The
regression function is
where is the rate for the ith age group for birth
cohort j and facility k, and represents the log of
the age-specific death rate for the jth birth cohort in facility k
at age 50 years.
where is the rate for the ith age group for birth cohort j and facility k, and represents the log of the age-specific death rate for the jth birth cohort in facility k at age 50 years.The maximum likelihood estimates of these "intercept terms" for this internal analysis are shown in panel A of Table II , and the corresponding estimated death rates (see the vertical axis in Fig.1 corresponding to age 50) are given in panel B. This approach uses the well known Gompertz law of mortality to ``adjust" for age. The maximum likelihood estimate of the ``slope" parameter is = 0.0794 (SE = 0.00069) and this, together with the can be used to estimate the median survival time, conditional on having reached age 50--see panel C of Table II .
Panels A-C of Table II are different ways to describe the all cause mortality experience of these facility/birth cohort groups. For statistical purposes the are the parameters of direct interest, whereas the estimated death rates exp() are more convenient for interpretation. For example, for the 1915 birth cohort at age 50 the estimated annual death rates for K-25 workers is 9.48/1000, which is 1.62 times higher than the X-10 rate of 5.85/1000. Another way to state this result is that the estimated relative risk for K-25 workers, with X-10 as the internal referent group is 1.62. The estimated median survival time at age 50 for the 1915 birth cohort is 24.15 years for K-25 workers which is 5.34 years less than that for X-10 workers (see panel C of Table II ) in the same birth cohort. The corresponding estimated median survival time for the 1915 birth cohort for U.S. white males at age 50 is 25.74 years.
In the second approach the external age-specific death rates
are used for each birthcohort and it is assumed that
the rates for each facility/birth cohort group are proportional to the
external rates. The regression function is
where the correspond to
the log of the SMR for each of the birth-cohort/facility groups.
where the correspond to the log of the SMR for each of the birth-cohort/facility groups.These estimates are given in panel D of Table II in logarithmic percent units (L%) , and the corresponding estimated SMRs---exp ---are given in panel E. For example, for K-25 workers in the 1915 birth cohort = 10.8L% and SMR = 1.11, i.e. their rates are 10.8 L% units higher than the U.S. white male rates which corresponds to an SMR that is elevated by 11%. The SMR can be interpreted as a relative risk with U.S. white males as the referent group. The estimates obtained using the external death rates can be used to make internal comparisons. For example, the relative risk for the 1915 birth cohort of K-25 workers with X-10 as the referent group in L% units is 10.8 - (-36.7) = 47.5L%, and the relative risk is exp(.475)= 1.61 which is in close agreement with the result obtained using the internal comparison approach. Table II shows that workers born after 1930 have much lower age-adjusted death rates than other Oak Ridge workers (see panel B) and than U. S. white males (see panels D and E). Further, X-10 workers have lower death rates than other Oak Ridge workers (panel B) and the U.S. white male comparison group (panels D and E). White males employed only at the K-25 site have the least favorable mortality experience with death rates that are higher than both other Oak Ridge workers and the U.S. except for those born after 1930.
This preliminary analysis illustrates two approaches to using Poisson regression methods to adjust for the effect of age at risk when comparing the mortality rates at the Oak Ridge facilities. To further describe the cause-specific mortality of Oak Ridge workers the analysis is extended to include the additional variables SES, length of employment, and calendar period and have adjusted for age by using the external rates. This leads to a four dimensional ADS for each race/gender group for each cause-of-death of interest. Results for white males and females are given in Table III, and results for nonwhite males and females are given in Table IV for selected disease categories. Table V presents result for white males for selected cancer causes. A detailed description of the data reduction procedure and of how to read these tables is given in the Appendix. The observed deaths (column 2 of Tables III-V) are slightly less than those given in Table I since only individuals with at least one year of follow-up were included in these analyses.