Simple body measurements probably work about as well as a bioimpedance scale to inform health decisions and have better-characterized performance

Bioimpedance Scales and How They Work

Sometimes when I’m working out and trying to lose weight, a thought will occur to me: what if I’m actually doing much better at losing fat than the scale claims? What if my weight stubbornly refuses to go down not because losing weight is a slow and difficult process demanding tremendous consistency and a personalized approach but because I am an ALPHA MALE putting on EXTREME MUSCLE? This thought is so appealing that it will quickly be followed with something like, “you know, I should REALLY be measuring body fat percentage, not weight.” And then the inevitable: “I should get one of those bioimpedance scales!”

A bioimpedance scale works by sending an electrical current (an AC current) through your body to measure the impedance (resistance) of your body. Muscle tends to have a lot more electrolytes and ionic solutions than fat, so muscle tissue will conduct electricity better. Your overall body conductivity will depend on a number of factors, including but very much not limited to:

You might notice that if you only have one measure (impedance), this problem is inherently underspecified. The most common approach to this problem is to combine the bioimpedance monitor with a scale and an app that asks users for their height and age, so you can cheat by using variables other than impedance. Some fancy scales will also use multi-frequency bioimpedance, changing the frequency of the AC current and measuring the impedance at different frequencies. The advantage of this is that low-frequency AC is effectively blocked by cell membranes (the membrane acts as a capacitor, and at low frequencies the current is blocked by the membrane most of the time), but high-frequency current is not. This allows you to distinguish between extracellular water content (measured by low-frequency AC) and total water content (high-frequency AC). This allows you to infer intracellular water content. Fat has low intracellular water, while muscle has high intracellular water, so you can infer (modulo overall hydration levels!) the percentage of the body that’s bone vs muscle, especially if you can also factor in things like weight and height. But only very fancy scales have this functionality!

I did not do enough research to figure this out before buying a $20 bioimpedance scale on Amazon.

Digression: Skinfold Calipers

You can use a skinfold technique to measure subcutaneous fat and then infer body composition with some formulas. However, performing this test accurately requires you to have an expert check multiple sites (usually at least the triceps, the “subscapular region” on your back, and the back of the calf, but sometimes up to seven sites) with the calipers. This technique has fairly high test-retest variability even for skilled practitioners (especially if they’re not doing as many sites), so even though it’s quite accurate, it’s not always very precise, and it will be less accurate and precise for you than it is for people with training. I don’t think it makes sense for normal people to use skinfold calipers.

We Have Body Composition at Home

You can find a huge number of calculators online that will tell you what your body composition is from simple measurements that require no special equipment. But few of these calculators will tell you the margin of error in their outputs. I downloaded the 2005-2006 NHANES demographic and body measurement data and used it to check out a few techniques.

Inferring Body Composition in NHANES

A quick caveat: I filtered the NHANES data down to 20-40 year old men to do all of the calculations below. Coefficients typically change across age groups and genders.

NHANES doesn’t include body composition directly, but does include skinfold measurements. I used the regression coefficients on page 10 of “Body fat assessed from total body density and its estimation from skinfold thickness: measurements on 481 men and women aged from 16 to 72 years” to estimate body density from the tricep and subscapular measurements:

$$D = 1.1525 - 0.0687 \log (F_{tri} + F_{sub})$$

Body density can be converted to percent body fat by means of the Siri equation:

$$\texttt{% fat} = 100 * \left(\dfrac{4.95}{D} - 4.5\right)$$

Relative Fat Mass and Height-Waist Ratio

Height-Waist Ratio (HWR) is supposed to be a reasonable proxy for body composition. It is converted to body fat percent with the Relative Fat Mass (RFM) formula:

Where waist circumference is measured at the top of the iliac crest. Based on the NHANES data, there is a linear relationship between these variables, with an R-squared of 10.90

BMI

BMI is often criticized as an imperfect measure that doesn’t account for different body types. Let’s see how it stacks up to HWR! I included age in the regression because I found a random website that gave a BMI-Body Fat conversion that included an age term, but in my regression age had a coefficient of 0.04, so basically no effect. The R-squared of this model was 11.35.

Model: rfm = 0.04 age + 0.96 bmi + -6.07

BMI-HWR

OK let’s just throw everything into a regression now. Age still had a near-zero coefficient (0.02 this time), so I removed it and just did a BMI-HWR regression. This has an R-squared of 9.99:

Model: y = 0.462 bmi + -9.512 hwr + 26.707

Using both BMI and HWR gives a larger improvement in $R^2$ over HWR than switching from BMI to HWR! I think it would be really interesting to look at more complex models here - my intuition for why this would be an improvement over HWR is that some people store fat in places that aren’t their waist, but this seems like it would suit itself well to some ensemble model. At some point I may try this as an exploration of the Akaike Information Criterion?

Error

In this model, 50% of cases have absolute error of less than 2 percentage points body fat percent, and 75% have error <3.2 percentage points. And not only that, but it seems extremely likely to be a good directional indicator (if body fat percent as imputed by this formula goes down, you probably really are losing body fat, not just putting on muscle)

Conclusion

I’ve been pretty convinced by this exploration that bioimpedance scales don’t offer very much marginal accuracy over simpler measurements, with the possible exception of the fancy multifrequency ones. A probable error of 3pp is, in one sense, not great in that it’s ~13% of the 5%-30% range of body fat percentage that’s interesting to me, but it’s dirt-cheap to gather and directionally useful. And it’s being compared to a system whose performance characteristics are completely unknown to me. I recommend that you do not buy a bioimpedance scale (and if you really want one - get a multifrequency option).