Estimating the Range of BMI Associated with Minimal Mortality

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Estimating the point of BMI associated with minimal mortality rate (i.e. the 'optimal' BMI) and the range around the point that still represents 'reasonable' BMIs for people is a challenging task involving empirical, statistical and conceptual issues. The empirical issue concerns the fact that the BMIs associated with minimal mortality seem to vary with subject characteristics such as age, sex, and race as described elsewhere in this chapter and may also vary as a function of other factors such as genotype. However, beyond the factors of age and sex, knowledge is very limited. Therefore, just as separate standards for BMI ranges associated with greater longevity are sometimes produced for men and women and people of different ages, perhaps the future will bring separate standards for people depending on other factors including ethnicity or genotype. Until greater information is available about genetic modifiers of the BMI-mortality relation, family history may be a useful proxy. For example, the optimal BMI for a person with a strong family history of osteoporosis and no family history of cardiovascular disease (CVD) may be substantially higher than the optimal BMI for a similar person with no family history of osteoporosis and a strong family history of CVD. This remains to be evaluated and is likely to be a fruitful area for future research.

The statistical issues are fairly straightforward. Although the most common approach is again to categorize BMI on the basis of sample quantiles and declare the category with the lowest sample risk or rate as the region of optimal BMI, this may not be an ideal approach. This is because, as stated above, the risk or hazard estimate for each bin is an estimate of the average risk or hazard for people in that bin. Therefore, there is no guarantee that the BMI bin with the lowest risk or hazard contains the BMI point with the lowest risk or hazard. Similarly, it is entirely possible that, if the bins are wide and the curvature of the BMI-mortality curve acute, then the range of the bin may be far greater than the range of BMI associated with reasonably low mortality rate. Of course, the converse is also true.

The alternative is to treat BMI as a continuous variable and estimate the minimum of a polynomial curve fitted to the data. It had been suggested that this would cause a systematic underestimation of the nadir of the curve (27). However, Allison and Faith (28) showed that, though either over- or underestimation could occur, there was no a priori reason to expect a particular bias. Thus, the calculus can be used to determine the BMI associated with minimum mortality rate and confidence intervals can be placed around such estimates using methods described elsewhere (29). In addition, Durazo-Arvizu et al. (30) demonstrated how change-point models can also be used to estimate the BMI associated with minimal mortality rate when the data may not be well characterized by a polynomial.

With respect to the conceptual issues, things are perhaps a bit trickier. Thus far, we have described methods for obtaining a point-estimate of the BMI associated with minimum mortality rate and, possibly, a confidence interval around that estimate. However, of equal importance is developing a range around that point-estimate. Without such a range, one would be left in the absurd position of stating, for example, that the optimal BMI for such-and-such a person is 24.65 and anything above (e.g. 24.7) or below (e.g. 24.6) is not good. So how does one declare such a range? One possibility would be to use the 95% (or other) confidence interval. However, this would conflate statistical precision of estimation with biological 'tolerability' of variation in BMI. That is, a wide interval could occur because nature truly tolerates a wide interval of BMIs for the class of individuals under study or because the sample size is small, or both. Conversely, a narrow interval could occur because nature only tolerates a narrow interval of BMIs for the class of individuals under study or because the sample size is large, or both. Alternatively, one might scale the relative risk, odds ratios, or hazard ratios to the average risk, odds, or hazard over the entire sample, find the points where the curve crosses a value of 1.0, and treat those points as the limits of the range. However, this essentially reifies the average and says 'your hazard of death is OK as long as it's not above average'. Who wants to be average when it comes to longevity?

The above methods of determining a range of BMIs associated with minimum mortality rate are flawed because they essentially try to take a judgement that is inherently a subjective value-based judgement and make it objective. Assuming the BMI-mortality curve is convex and differentiable (which seems likely), then the risk is always elevated once one moves off the nadir in either direction. Trying to find points where it is not elevated therefore seems unwise. In contrast, we suggest a simple two-stage approach where the first step is explicitly subjective and the second step involves objective quantification. The first step is to decide how big an increase in risk (either absolute or relative) one is willing to accept. Then, define the limits of the acceptable BMI range as the points on either side of the estimated nadir associated with that degree of elevation.

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