In the last sentence of the abstract of their paper, Lean and colleagues [1] state, "For the average patient each 1 kg weight loss was associated with 3-4 months prolonged survival." We appreciate Lean and Garthwaite's clarification that the "average overweight patient" in their study survived about 8 years, and we acknowledge that this is a technically correct interpretation of their data.

The crux of our disagreement with Lean and colleagues now centers on how best to interpret the "average effect" of weight loss on longevity given the statistical model they used for their analysis. In their statistical model, if survival is increased by 0.053^1/2 years with a weight loss of 1 kg, then a hypothetical average overweight person with diabetes, who would have survived 8 years without weight loss, will survive an additional (8^1/2 + 0.053)² – 8 years (0.34 years), or 3.6 months, if he or she loses 1 kg. The extra algebra is required because Lean and colleagues modeled survival time in terms of "square-root years" rather than years, presumably because the underlying association between weight loss and longevity was nonlinear.

Because Lean and colleagues restricted their analysis to diabetics who had already survived at least 1 year after diagnosis, the survival time for a person who died exactly 1 year after the date of diabetes diagnosis is assigned a value of 0 years. Thus, their model predicts that for this person, a weight loss of 1 kg increases survival time by only (0^1/2 + 0.053)² – 0 years (0.0028 years), or about 1 day. Therefore, the predicted increase in survival time attributable to weight loss depends on the point at which the person is on the longevity curve.

Our Figure 1 clarifies the association seen by Lean and coworkers between "expected survival" and "additional survival" attributable to 1-kg weight loss and gives 95% CIs around the trend. We estimated the CIs around "additional survival" from the 95% CIs reported for the slope coefficient of 0.053 (CI, 0.028 to 0.079) in Lean and coworkers' Table 4. The half width of the interval divided by 1.96 yields the estimate of the standard error (SE) of the slope coefficient, which is 0.013. For the example in which "expected survival" is 8 years, and by using a first-order Taylor series approximation (delta method) [2], the SE of the "additional survival" estimate of 3.6 months is the following:

View larger version (25K): [in this window] [in a new window]   Figure 1. The association between expected years of survival and additional years of survival attributable to a 1-kg weight loss in diabetics, based on the work of Lean and colleagues [1].

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The associated 95% CI is then 3.6 months ± 1.96 * 0.899, or 1.9 to 5.4 months.

According to Figure 1, Lean and colleagues' model suggests that weight loss is most useful for persons who need it least; for example, a 1-kg weight loss increases survival in a person who has survived 10 years by 4 months, but, in a person who has survived for 1 year, the increase is only 1.3 months. The larger the "average effect" of weight loss, the less precise the estimate. We believe that Figure 1 gives a more detailed view of the findings by Lean and colleagues because it appropriately incorporates the possible range of survival times for the diabetic in their study.