Monday, February 3, 2020

A network of life expectancy and body mass index

At my advanced age, the concept of Life Expectancy (the average age at which people of my generation die) becomes of some practical importance. Perhaps more importantly, the concept of Healthy Life Expectancy rears its head, this being the average age at which one's health starts to notably deteriorate.

Both of these human attributes are related to many things, but in the modern world Obesity is one of the most important contributors to lack of health. This is frequently measured as the Body Mass Index (BMI), defined as the body mass (kilograms) divided by the square of the body height (meters). A BMI > 30 is classified as Obese, and this is definitely considered to represent lomg-term poor health.

So, let's look at some data, to see how the USA currently fares with regard to these characteristics. The US Burden of Disease Collaborators recently released some up-to-date data (The state of US health, 1990-2016. Burden of diseases, injuries, and risk factors among US states. Journal of the American Medical Association 319: 1444-1472). You can consult their Table 1 if you want to consider the major recent causes of death in the USA.

However, we will focus on the positive side, instead — how long do people live? The first graph here shows the relationship between the two Life Expectancy variables for the year 2016, with each point representing one state of the USA, plus DC. The line shown on the graph represents the national average.

Life expectabcy versus healthy life expectancy

As expected, there is a high correlation between the two variables, although there is a 6-year difference in Expectancy among the various states. The top states include Hawaii, California, Connecticut, Minnesota, New York, Massachusetts, Colorado, New Jersey and Washington; while the bottom states are Mississippi, West Virginia, Alabama, Louisiana, Oklahoma, Arkansas, Kentucky, Tennessee and South Carolina. The social and economic differences between those two groups should be clear to everyone, and this is well-known to relate to life-length.

The national average for Life Expectancy is 78.9 years, while the Healthy Life Expectancy is 67.7 years (ie. 11.2 years less). This probably doesn't surprise you — the last 11 years of your life is likely to be spent dealing with ill health. The points on the graph are scattered around the national-average line except at the lowest Expectancies — this implies a shorter period of unhealth at the end of life for those with a poor Life Expectancy. Notably, Mississippi has the lowest Life Expectancy but only the 5th lowest Healthy LE.

We can now turn to look at Body Mass Index (BMI) and how it relates to Healthy Life Expectancy. This is shown in the next graph, where the BMI data refer to the percentage of people who are obese (BMI > 30). Once again, each point refers to a single state. Clearly, as Obesity increases then Healthy LE decreases. The medical people have been telling us this for decades.

Body mass index versus healthy life expectancy

Note, however, the big difference in obesity levels between the states (15.5 percentage points) — there are nearly two-thirds more obese people in some states than in others. The states with the highest Obesity levels include West Virginia, Mississippi, Oklahoma, Iowa, Alabama, Louisiana and Arkansas, while the other extreme includes Colorado, DC, Hawaii, California, Montana, Utah, New York and Massachusetts.

Also, note that the relationship between the Obesity and Life Expectancy variables is not linear. Below 26% population obesity there is little change in average Life Expectancy, whereas above 30% obesity levels Life Expectancy declines rapidly. For every 1% increase in average Obesity the average LE is reduced by 0.3 years.

Two of the territories are labeled in the graph, as showing unusual patterns. The people of the District of Columbia are clearly not "fat cats", as often depicted, but their lives are apparently not all that healthy. On the other hand, the people of Iowa somehow manage to remain healthy for longer than average, even though they have one of the highest Obesity levels.

Finally, we can put all of this together in a single network, depicting the data patterns. As usual in this blog, one of the simplest ways to get a pictorial overview of the data is to use a phylogenetic network, as a form of exploratory data analysis. For this analysis, I first calculated the similarity of the states using the manhattan distance, based on the three variables listed above. A Neighbor-net analysis was then used to display the between-territory similarities.

The resulting network is shown in the final graph. Territories that are closely connected in the network are similar to each other based on their two Life Expectancies and BMI levels, and those that are further apart are progressively more different from each other.

Network of life expectancy and body mass index

In this case, the network displays states with decreasing Life Expectancies from top to bottom, and decreasing Obesity from left to right. It makes visually clear that those states with the shortest Life Expectancies are almost always associated with high Obesity levels (ie. they are at the bottom-left of the network).

For longer Life Expectancies, some states have high Obesity levels (top-left of the network) while some have lower levels (top-right). Iowa is shown as quite distinct from the other states (it has a long edge of its own), since it has longer LE than would be expected for its population Obesity level.

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