Dear Sir,We appreciate the comment by Dr. Rundle concerning interpretation of the estimated association between the DNA adduct levels and the lung cancer rate. As pointed out by Dr. Rundle, the effect of adjustment for smoking on the risk estimate for DNA adducts in our study 1 is too modest to justify meaningful interpretations. Nevertheless, the discussion about interpretation of an association after adjustment for an antecedent variable within a complex biological system is of general interest. We can consider possible associations as depicted in Figure 1.We disagree with Dr. Rundle in the general view that statistical control for an antecedent variable such as smoking behavior does not provide information about the effect on lung cancer of other exposures that cause adducts. It is, however, evident that the part of the effect of such other exposures that is not mediated through the adduct measure cannot be captured by an analysis of the association between the adduct level and the lung cancer rate and so our statement only refers to effects mediated through the adduct level.In multiple regression analysis, the adjusted association estimates the association between the outcome and the variation in the exposure variable for fixed values of the adjustment variables. This is a general, mathematical-statistical result with no relation to whether or not the adjustment variable is antecedent. Since the smoking variables may be considered fixed in the adjusted analyses, the remaining variation in the adduct measure must be caused by other factors than the smoking variables adjusted for. Hence our interpretation that smokingadjusted risk estimates for adducts relate to variation in adducts caused by other factors than smoking. However, we acknowledge that the adjustment for smoking is not perfect and so part of the variation in adduct levels may still be caused by differences in the exact smoking history. We agree with Dr. Rundles previous demonstration that the presence of association between adduct level and risk of cancer after adjustment for exposure, smoking in this case, cannot be interpreted in terms of proof of modifying effects of genes.
2Considering a Cox regression model for the lung cancer rate including the smoking variables and the adduct measure as independent variables, the effect of the smoking variables adjusted for the adduct measure estimates the rate ratio related to pathways, unaccounted for by the adduct measure, through which the smoking behavior impacts the lung cancer rate. It is important to notice that this interpretation for the smoking variables does not mean that the rate ratio estimate for the adduct measure is only adjusted for the risk related to these other pathways.These understandings and interpretations correspond to those applied in nutritional epidemiology.3 A ''fat in diet-total energy consumption-cardiovascular disease'' model would (in a statistical sense) be similar to the ''smoking-adduct-lung cancer'' model. Also in the nutritional model, other factors (proteins, carbohyd...