A linear body fat formula

Title of article:

Limits of body mass index to detect obesity and predict body composition

Authors: Frankenfield DC, Rowe WA, Cooney RN, Smith JS, Becker D.
Journal: Nutrition, 2001 Jan;17(1):26-30

Abstract

Body mass index (BMI) is commonly used to identify obesity. In this study, we determined how accurately BMI could determine body composition and identify obese from non-obese individuals. Fat-free mass and body fat were determined with bioelectrical impedance. Adiposity was calculated as body fat per body mass and as body fat divided by body height (m2). Obesity was defined as a BMI of at least 30 kg/m2 or an amount of body fat of at least 25% of total body mass for men and at least 30% for women. Obesity as defined by percentage of body fat was always present with a BMI of at least 30 kg/m2. However, 30% of men and 46% of women with a BMI below 30 kg/m2 had obesity levels of body fat. The greatest variability in the prediction of percentage of body fat and body fat divided by height (m2) from regression equations using BMI was at a BMI below 30 kg/m2. In conclusion, using impedance-derived body-fat mass as the criterion, people with BMI of at least 30 kg/m2 are obese. However, significant numbers of people with a BMI below 30 kg/m2 are also obese and thus misclassified by BMI. Percent of body fat and body fat divided by height (m2) are predictable from BMI, but the accuracy of the prediction is lowest when the BMI is below 30 kg/m2. Therefore, measurement of body fat is a more appropriate way to assess obesity in people with a BMI below 30 kg/m2.

Comments and Key points

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 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.

There are some limitations of this study. Most importantly, they used impedence 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 formula

The article contains arithmetic formulas for this linear relationship.

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:

	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.

References

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