Standard Analysis Procedure

A standard analysis procedure was used to evaluate the relative importance of the effect of each of the factors B, S, L, IG, F, and the dose variable D for each cause-of-death of interest. The multiplicative main effects model (see Eq. 3) was used for this screening procedure since in many situations the ERR model does not yield estimates of the dose related parameters.

1. Fit the main effects model Eq. 3 using external rates and compute the deviance and df (see Table AVI line 2).
2. Fit each of the models described in the first column of Table AVI, and compute the deviance, AIC, and LRT statistic with the main effects model as the referent model. The first line in Table AVI gives the deviance and other summary statistics for the ``minimal model", i.e., the model that has only one parameter which is the log of the SMR. For lines 3-8 in Table AVI the LRT test shows the effect of deleting terms not included in (see column one to identify the term that is deleted) the main effects model. For this example we see that birth cohort (B) and paycode (S) are strong predictors of cancer risk, and length of employment (L), internal exposure (IG) and facility (F) are not. This is consistent with the results (estimates and standard errors) given in Table AV . The last seven lines show the effect of adding additional parameters to the main effects model. Lines 9--13 evaluate possible interaction of each of the factors with radiation dose (i.e. effect modification). The likelihood ratio test statistics give no indication that the dose response estimate changes with levels of any of the other factors. The last line in the Table AVI contains a relative risk parameter for each dose group, and provides a ``lack-of-fit" test (FM) for the multiplicative dose-response. The relative risk estimates are shown graphically in Fig. 2A. Note that while the likelihood ratio test on line 14 of Table AVI does not indicate lack-of-fit of the linear dose-response model, the results in Table X and Fig. 2A suggest that the linear excess relative risk provides a ``better" description of the dose-response relation (see Results for further discussion of this point).

3. Fit a model which includes the main effects and all possible interaction term for the potential confounding variables A, B, S, and L. This is usually done by stratifying on these factors so that parameter estimates are not computed. The resulting estimates for the exposure variables (IG, F, and D) are then compared with those obtained from the main effects model to verify that there is no residual confounding associated with the interaction terms of the stratification variables. The results of this stratified analysis for the example are given in Table AVII.

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