next up previous
Next: Dose-Response Analyses (DRA) Up: Facility Comparison Analyses Previous: FCP Step 2-

FCP Step 3- Fit Main Effects Model

The third step was to fit a main effects model (see Eq. 2) for each race and gender group for each cause of death of interest---the results are given in Tables III--V. Consider, as an example of how to read these tables, diseases of the respiratory system (ICD 460--619) for white males---see line 5 in Table III. Table AII (see first five rows) shows the parameter estimates for each facility in log percentage (L%) units in column 2 and the corresponding estimates of the SMRs (adjusted for S and L) at the mid-point of the 1965--69 interval of follow up. These facility effect estimates estimates are listed in columns 4 through 8 or row 5 in Table III. The estimated relative risk (adjusted for L and F) for monthly compared to nonmonthly workers is exp (-78.6/100) = 0.46 with 95% confidence interval of (.35, .59) indicating a substantial 5% difference in respiratory system disease rates between monthly (white collar) and nonmonthly (blue collar) workers. The estimated relative risk (adjusted for F and S) for short term workers (< 1 year) relative to those who worked one year or longer is 1.30 with 95% CI = (1.17, 1.44). The period trend parameter estimate 0.97 ( see the last line of Table AII ) represents the yearly change in the log SMR in L% units over the forty years of follow-up. The parameter estimates for each cause of death in Tables III--V can be combined to estimate the SMR for each facility, at the mid-point of each follow-up interval for each level of S and L:

log (SMR) = log (facility SMR in 1965--69)
          + (effect due to  L)
          + (effect due to  S)
          + (Interval-Midpoint--1967.5) * 0.97.

For example, for long term nonmonthly workers at K-25, during the last interval of follow-up (1980-84), with mid-point = 1982.5, the log(SRM) is

log(SMR)= 6.7 + 0 + 0 + (1982.5-1967.5)*0.97 = 21.3L% 
so that the estimated SMR is exp(0.213) = 1.24.

The lowest estimated SMR was exp(-1.41)= 0.24 and occurs for:

   X-10    Monthly  Long-Term   1945--49 
  -43.0 +   -78.6 +    0.0    +  -19.4   =  -141.0 L%.
The largest estimated SMR is 1.69 and occurs for:
  K-25  Non-Monthly Short-Term  1980--84  
   6.7 +    0.0    +    26.1   +  14.    =  47.4 L%.

The likelihood ratio statistic (see column 9 of Table III) for the null hypothesis of no differences among facilities was 24.4 with 4 df ( p<.01). Table AII indicates that the risk of respiratory disease was much higher for TEC, K-25 and multiple facility workers than for X-10 or Y-12 workers. For example, the estimated relative risk for K-25 with X-10 as the reference facility is exp[(6.7-(-4.0))/100] = 1.64. A large value for the LRT statistic (in column 9 of Tables III--V) indicates that there were differences among facilities in the death rates for that cause of death after adjusting for S, L, period of follow-up, and age through use of external rates.

next up previous
Next: Dose-Response Analyses (DRA) Up: Facility Comparison Analyses Previous: FCP Step 2-