7.17 - Body mass and diabetes risk

7.17 - BMI and waist-to-hip ratio

In type 2 diabetes, cells respond less strongly to insulin, so blood glucose can remain too high. Body fat, activity, genes and age can all affect risk. We can examine population evidence without treating body size as an individual diagnosis.

Body mass alone is difficult to compare between people of different heights. Body mass index (BMI) relates mass to height, while the waist-to-hip ratio compares two circumferences and gives information about body-fat distribution. Both are indicators rather than diagnoses.

BMI has the compound unit $\mathrm{kg}\,\mathrm{m}^{-2}$ (equivalently $\mathrm{kg}/\mathrm{m}^{2}$). Height must be in metres and must be squared before mass is divided by it.

Worked example: BMI

An adult has a mass of 78.4 kg and a height of 1.75 m. Find the BMI to 1 decimal place.

1. Requested quantity: BMI; mass is already in kilograms and height is already in metres.
2. Equation: BMI = mass / $\text{height}^{2}$.
3. Square the height: $1.75^{2} = 3.0625\,\mathrm{m}^{2}$.
4. Substitute: $\mathrm{BMI} = 78.4 / 3.0625 = 25.6\,\mathrm{kg}\,\mathrm{m}^{-2}$.
5. The value is positive and of a plausible human scale. It is a screening value, not proof that this person has or will develop diabetes.

Use the same unit for both measurements. The units cancel, so the ratio has no unit. Keep the direction as waist divided by hip.

Worked example: waist-to-hip ratio

An adult has a waist circumference of 84.0 cm and a hip circumference of 100.0 cm.

1. Equation: waist-to-hip ratio = waist / hip.
2. Substitute: $84.0\,\mathrm{cm} / 100.0\,\mathrm{cm} = 0.840$.
3. To 2 decimal places, the ratio is 0.84, with no unit. A value by itself estimates body shape; it does not diagnose type 2 diabetes.

To find a missing circumference, rearrange the ratio before substituting. If waist-to-hip ratio = waist / hip, then waist = ratio × hip. For a ratio of 0.90 and hips of 100 cm, waist = 0.90 × 100 = 90 cm. Check by dividing back: 90 / 100 = 0.90.

7.17 - Evaluating body mass evidence

Across populations, greater body mass and higher BMI are positively correlated with type 2 diabetes: as one tends to increase, the frequency or risk of the other tends to increase. Measures that include the waist can add information about central fat distribution. This evidence is useful, but it must be interpreted at population level rather than treated as a certain prediction for one person.