We calculated the 95% CI of the RSE based on the maximum likelihood method described by Breslow and Day [10]. If the RSE significantly differs from 1, it implies that smoking is likely to be an effect modifier (e.g., if RSE.1, it suggests that the effect of silicosis on mortality among smokers was higher than the never smokers) and a separate report on the SAF-corrected SMR for the subgroup of smoking and never smoking silicotics should be delivered. Alternatively, if the RSE is not statistically significant, it suggests the absence of multiplicative interaction, and smoking in this context is likely to be a confounding factor which would have to be adjusted accordingly. We compared the smoking indirectly adjusted ‘‘SAF-corrected SMR’’ using the method proposed by Axelson [11] and the consistent findings (Supplement S2) suggested that
the methodology of this SAF method is valid. One advantage of using SAF method is that it could not only be used to evaluate the multiplicative interaction between smoking and silicosis but also to indirectly adjust for the potential confounding effect of smoking in studies of SMR.