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The tabulations supplied by Professor Greenberg (1) clarify the procedures that he used in his previous article (2). He calculated the proportion of deaths attributable to obesity within a subgroup that he says had no serious illness. He then multiplied all the deaths in the whole sample by that same proportion to try to estimate the number of obesity-attributable deaths that would have occurred in the whole sample if there had been no serious illness in the whole sample. However, if there had been no serious illness in the whole sample, there would also have been far fewer total deaths (assuming that serious illness increases mortality). Greenberg is calculating deaths attributable to obesity for a hypothetical population that has no persons with serious illness but still has the same numbers of deaths as a population that includes people with serious illness. Thus, his procedure greatly over-estimates the number of obesity-attributable deaths that would occur if there was no serious illness. Although Greenberg calls these estimates the “maximum corrected values” of deaths attributable to obesity, these are not corrected values. His method makes no allowance for any impact of serious illness on mortality and does not correctly calculate the number of obesity-associated deaths that would be predicted if there was no serious illness in the whole sample. In addition, in order for the attributable fraction from the subgroup without serious illness to apply to Greenberg’s hypothetical population without serious illness, that hypothetical whole population would have to have not only BMI-specific hazard ratios identical to those in the subgroup but also a joint distribution of BMI and confounders that was identical to that in the subgroup.
Greenberg’s procedure is another variant of the incorrect, partially adjusted method in which relative risks or hazard ratios are adjusted (in this case by stratification) for a confounder (in this case, serious illness), but the effect of the confounder on mortality itself is ignored (3;4). As we noted previously (5), Greenberg’s procedures do not estimate the quantities of interest, cannot be recommended to estimate “corrected” attributable deaths, and have little bearing on the estimates by Flegal et al (6).
The findings and conclusions in this report are those of the authors and not necessarily of the agency.