For the past several months, we’ve been working with Fit3D to create a cardiovascular risk score based on anthropomorphic measurements (waist-hip ratio, thigh circumference, torso-to-leg volume ratios, etc.) obtained from Fit3D scans. Our overall goal was to produce a single score that (a) was easy to interpret, (b) was backed by the scientific literature, and (c) was composed of simpler disease-specific scores so users could see exactly where their risks were coming from and feel motivated to improve. The project has been interesting and challenging from several angles, so I’m including some technical details about our process and calculations in this post.

The Literature

We began by scouring the literature for any papers that related anthropomorphic measurements to heart disease, stroke, diabetes, or their associated risk factors (e.g. high blood pressure, metabolic syndrome). We arrived at a set of ten papers that represented a wide breadth of topics. Some investigated more than one outcome and all reported results from multiple models. Our general feeling was that more numbers were better, so we included all available outcomes from each paper (technical note: ignoring the correlations between different outcomes appears not to be too big a deal). We stuck to the models that controlled for the most potential confounders, since these tended to produce the most conservative risk estimates.

Here is our list of papers:

  1. Wilson, J. P., Kanaya, A. M., Fan, B., & Shepherd, J. A. (2013). Ratio of trunk to leg volume as a new body shape metric for diabetes and mortality. PLoS One, 8(7), e68716.
  2. Heitmann, B. L., & Frederiksen, P. (2009). Thigh circumference and risk of heart disease and premature death: prospective cohort study. Brit. Med. J., 339, b3292.
  3. Hu, G., et al (2007). Body mass index, waist circumference, and waist-hip ratio on the risk of total and type-specific stroke. Archives of internal medicine, 167(13), 1420-1427.
  4. Vazquez, G., Duval, S., Jacobs Jr, D. R., & Silventoinen, K. (2007). Comparison of body mass index, waist circumference, and waist/hip ratio in predicting incident diabetes: a meta-analysis. Epidemiologic Reviews, 29(1), 115-128.
  5. Snijder, M. B. et al (2003). Associations of hip and thigh circumferences independent of waist circumference with the incidence of type 2 diabetes: the Hoorn Study. The American Journal of Clinical Nutrition, 77(5), 1192-1197.
  6. Onat, A., et al (2009). Neck circumference as a measure of central obesity: associations with metabolic syndrome and obstructive sleep apnea syndrome beyond waist circumference. Clinical Nutrition, 28(1), 46-51.
  7. Stabe, C., et al (2013). Neck circumference as a simple tool for identifying the metabolic syndrome and insulin resistance: results from the Brazilian Metabolic Syndrome Study. Clinical Endocrinology, 78(6), 874-881.
  8. Zhou, J. Y., et al (2013). Neck circumference as an independent predictive contributor to cardio-metabolic syndrome. Cardiovascular Diabetology, 12(1), 76.
  9. Suk, S. H., et al (2003). Abdominal obesity and risk of ischemic stroke. Stroke, 34(7), 1586-1592.
  10. Dey, D. K., et al (2002). Waist circumference, body mass index, and risk for stroke in older people. Journal of the American Geriatrics Society, 50(9), 1510-1518.

In the end, we decided to eliminate #2; it is an excellent paper, but the study population had thigh circumferences that were well outside those of the Fit3D population, so we would have had to extrapolate. In a broader sense this is a problem for clinical research in general - all studies are all performed in people of a certain age or ethnic group, and so their results are not necessarily translatable to other populations.

What relationships are out there?

Based on our literature review, the main anthropometric measurements people have investigated include: waist circumference, waist-hip ratio, neck circumference, thigh circumference, trunk-to-leg volume ratio, BMI, and hip circumference. We were hoping for a paper that found a substantial correlation between “ratio of left ring finger length to fourth toe circumference on the right foot” and “heart disease” but surprisingly no one has investigated that yet.

Outcomes of interest include “diabetes”, “high blood pressure”, “high triglycerides”, “low HDL”, “metabolic syndrome”, “ischemic stroke”, “total stroke”, “insulin resistance”, and “obstructive sleep apnea” (which has a very interesting correlation with neck circumference, it turns out). There is a complex web of causal and non-causal relationships among all of these various outcomes. Differences in ease of data collection, patient recruitment, and disease prevalence also make some conditions more popular than others - nine separate papers investigated correlations between anthropometric measurements and diabetes, for example, compared to only three for ischemic stroke.

Making Comparisons

People tend to think in terms of absolute risk - “How likely am I to die of a heart attack this year, given my age, BMI, etc.?” - whereas most research papers report relative risks - “If a patient’s waist circumference increases by 1 cm, how much does his risk of diabetes change?” The reason for this is that reporting absolute risk requires an estimate of disease prevalence - how frequent the disease is - which constrains the type of study design a researcher can use. If you do a classic case-control study (take 50 people with diabetes, compare them to 50 controls without diabetes) you don’t get an estimate of prevalence, so you can’t report absolute risk.

Figure 1 Figure 1: Predicted distribution of thigh circumferences for women of age 44 years and height 5’6”, based on Fit3D’s data, with our user’s thigh circumference denoted by the red line.

The upshot of this is that when you’re dealing with ratios, you need something to compare against. We decided that our score would be based on comparisons with “an average person of your same age, gender, and height”. For example, the graph above shows a predicted distribution of thigh circumferences, based on Fit3D’s population level data, for a 44-year-old woman of height 5’6” (a real user). The red line shows her actual thigh circumference, which is above average for a woman of her same age and height. If stroke risk increases with thigh circumference, for example, we would expect her risk to be elevated.

From Measurement to Risk Percentile

By comparing a person to a fictitious “comparator individual” with thigh circumference, waist circumference, etc. all at the 50th percentile, we can calculate a risk ratio for that person reflecting their risk relative to Mr./Ms. Average. We can also transform the distributions of measurements to distributions of risks and find our individual’s percentile score within the overall risk distribution for each disease. This requires some math, but for all of the risk relationships we looked at, the calculations can be done analytically.

The percentile score can be interpreted as “our estimate of the percent of people of your same age, gender, and height who are worse off than you” on the basis of a given disease risk.

The table below shows the estimated risk ratios and percentile scores for various disease outcomes for the woman whose thigh circumference is shown above (based on that plus all of her other measurements). Note that some papers are listed multiple times because the same paper could contain multiple models.

The first thing you’ll notice is that the risk ratios and percentiles for the same outcome are often quite different. For example, one paper that used waist circumference said this woman was doing better than 45.5% of women like her in terms of ischemic stroke risk, while another that used waist-hip ratio said she was only in the 14.5% percentile. This is often true even for multiple models from the same paper that use the same anthropometric measurements. All we can say to that is: this is science, folks. The effects we’re looking at here are often only marginally significant, there are differences due to modeling choices, measurement accuracy, and study population, and myriad other factors impacting these results. For now, these are the best estimates we’ve got.

Table 1 Table 1: Risk ratios and percentile scores for our user.

One additional technical note: most of these papers use models from survival analysis and report something called a hazard ratio, not all do. Others may use risk ratios or odds ratios instead. In the limit of “low disease prevalence” and “a risk that doesn’t change much over time”, they are all similar measures, but statisticians will be the first to point out the differences. This is part of why we average the percentiles and not the raw ratios.

Creating a Composite Score

In the end, we wanted to create a single number for each user that would reflect his or her cardiovascular risk relative to people of similar age, height, and gender. We began by averaging the percentile scores for each outcome, then created a weighted average of outcomes based on a “badness coefficient” related to the number of deaths caused per year by the disease. Stroke had a weight of 140, and diabetes 80. The rest, which were risk factors rather than proximate causes of death, were given a generic weight of 50. A more elaborate model might use Quality-Adjusted Life Years (QALYs) or some kind of weighting scheme that includes age and gender, but we elected to keep things simple and instead provide users with the opportunity to drill down into the finer-grained scores.

Take-Home Points

There is no one “right way” to create a composite score for something like cardiovascular risk. We like our score because people are fairly good at interpreting percentiles - we are used to them on things like standardized tests - because no one paper has massively inflated influence, and because users can see where all the numbers come from.

In case you were wondering, the composite score for the woman whose data we’ve been analyzing so far is 35.0. Hopefully through the right combination of diet and exercise, and by monitoring her progress through repeated Fit3D scans, she can find ways to reduce her cardiovascular disease risk over time.