Formula body mass index trans-inverse-polarity disappointment

Comments and deriving a body fat percentage formula

This article uses the fairly standard definition of obesity, using body fat percentages of 25% for men, and 30% for women. It found the commonly seen curved relationship of body fat percentage versus Body Mass Index, as shown in the first chart below.

body fat percentage curve

I showed this chart because it has data from some super obese people. Most other studies don’t have subjects this heavy, which makes this study quite valuable.

OMG. A body mass index of over 50? That IS super fat.

There are some limitations of this study. Most importantly, they used impedance to estimate body fat percentage, but impedance measurements can be inaccurate in subjects in the super obesity range, so there is some doubt about whether the body fat measurements are "true". So, the curves (above) may not be as flat on top, as they appear to be.

This article found that a linear relationship between BMI and body fat could be achieved by plotting body fat divided by height squared, versus BMI. This is an interesting observation, shown below.

linear body fat percentage formula

The article contains arithmetic formulas for this linear relationship.

Why didn’t you show the formulas here?

I wish I had.

The article examined the Obesity thresholds using BMI, compared to body fat percentages as the gold standard. They reported their results in weird way, making it impossible to determine their sensitivity and specificity. But they did mention a similar study by Hortobagyi¹, which had these results for a BMI threshold of 30 kg/m²:

You were really hung up on thresholds back in 2002.

I was collecting evidence on proper cutoff levels, and was disappointed in the kinds of published articles available back then.

	BMI	sensitivity	specificity
Men	30	54.5%	91.8%
Women	30	26.9%	98.2%

Since I don’t know the ages of the Hortobagyi study, its not easy to interpret the data. The men’s threshold looks good, but the women’s threshold looks too high. If the threshold were lower than 30 in women, it would have higher sensitivity. But keep in mind that this is based on using an arbitrary body fat percentage standard of 30% for women. More likely, the 30% number should be raised.

I still agree with myself from 2002 with I first wrote this review. 30% body fat is still normal for women. They are not overweight at 30%. And the older a woman, the higher the cutoff must be.

References

Hortobagyi T, Israel RG, O’Brien KF. Sensitivity and specificity of the Quetelet index to assess obesity in men and women. Eur J Clin Nutr 1994: 48:369.