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This study demonstrates the relationship between short and medium term mortality in the population studied and not long term mortality or life expectancy. It is large enough to do so, but misses the opportunity of stratifying by age and height. Besides the obvious ones of the contribution of the different types of muscle and fat to BMI there are several other possible confounding and explanatory variables, amongst which are the relatively absolute contribution of the head to body bulk, and possible advantage of greater body bulk in the short and elderly. Stratification might have revealed differences between different age groups.
Unlike a true index, BMI essentially has the dimension of length and so is proportional to height. A person of 2m height with the same bulk as a person of 1.6m and a BMI of 25 has one of 31.5. It is counter-intuitive to believe the medium term risk of death is 50% higher in the former just because they are taller. Stratification by height would solve this problem.