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The Courteous Clauses Expedite an Expedition of Data

INTRODUCTION

We were summoned to this Data Expedition in response to a call for help from a place called Flatland which seems to have a problem with weightiness amongst its subjects, especially amongst the lower classes. The extra weight is threatening to "bend the plane" - whatever that means.

Our team, the Courteous Clauses, got off to what seemed a promising start. We made our introductions; set up a Google+ community and a Hackpad; and the programmers/developers/engineers established an organization on GitHub. One team member also put together a survey to get an idea of the mix of people on the team, and it looked like there was a good balance of experience and talent. After some initial confusion over interpretation of Flatland, we formed the general idea that we were to investigate some aspect of obesity in our world so that we might enlighten Flatland with our findings.

DATA GATHERING

Team members then set out in search of data - and we found plenty! A few examples are given below:

(The two data sets above were combined by a team member.)

PROBLEM IDENTIFICATION

We also found numerous studies on obesity - so numerous that we had trouble deciding on a direction. After soliciting suggestions and taking a vote, we decided to focus on obesity in urban areas, associations with urban density, and comparisons with rural areas. But almost immediately, team members started finding many articles suggesting that this aspect of the obesity problem had already been well covered, for example:

And then we found ourselves once again discussing where we should go with this expedition. Some team members felt we should find a problem that had not been tackled before - but others felt the pressure of time and the need to have something completed by February 5.  The team had already experienced attrition amongst the ranks - and we probably lost a few more team members at this stage.

WHERE NEXT?

A team member pointed out that the neighboring states of Colorado and Kansas present a comparison that might possibly be interesting. Figure 1 shows that Colorado stands out as the least obese state while Kansas ranks much more highly. A comparison of the two states using county-level BRFSS data is equally striking (Figure 2) - and it was suggested that we might compare the counties of eastern Colorado with those of western Kansas to possibly identify factors that might explain the difference. At this point, a couple of team members did express concern that the "state line effect" might be an artifact of the methods via which the data for these sparsely populated counties were compiled. And their concerns are probably justified, because Figures 3-6 do not suggest any sharp contrasts across the state line. (Data for Figures 2-6 are all from the USDA Food Environment Atlas, 2010).

Poverty levels (Figure 3) appear similar either side of the border, while Figure 4 suggests a somewhat older population in the counties of western Kansas compared with eastern Colorado. Accessibility to large grocery store is more variable in western Kansas (Figure 5), but not necessarily worse overall. Finally, the three counties of western Kansas that stand out in Figure 6 with regard to fast food restaurants just happen to be along the Interstate 70 corridor.

Before we went any further, one of the team members, concerned that the "state line effect" might not be what it appeared, investigated the data source more closely - and found there was good reason for concern.  A full account of how the county-level BMI values were estimated can be found at http://apps.nccd.cdc.gov/DDT_STRS2/FAQ.aspx#countylevelestimates. Basically, the estimates were derived from statistical models applied at the level of state and US Census Regions, with a separate model developed for each state and region. It happens that Colorado and Kansas are in different census regions, Mountain and West North Central, respectively (https://www.census.gov/geo/www/us_regdiv.pdf), making comparisons across the state line possibly invalid.

The team was then struck with what might be described as "analysis paralysis" and made little progress beyond that - and we probably lost a few more members. With time running short, those remaining considered some possible alternatives, one of which was to use the Flatland geometric shapes to explore possible problems with relying on the standard definition of BMI (weight/height^2) to determine obesity prevalence - and that is where we ended up.

However, before moving on, there was one more Colorado-Kansas comparison that was contributed as this was being compiled: Figure 7 compares prevalence of physical inactivity for the border counties of the two states. There is a suggestion of greater prevalence of inactivity on the Kansas side, and were more time available, this would definitely be worth examining further.

WHAT FLATLAND MIGHT TELL US ABOUT BMI

Flatland assesses the weight status of its inhabitants with their own version of our Body Mass Index (BMI). BMI is simply the weight divided by the square of the "height" of a shape measured perpendicularly from one of its sides. In Flatland's two-dimensional world, the shapes have no measurable thickness - and thus no measurable weight - so we are perhaps to assume that "weight" is simply proportional to area within the shape's perimeter. This raised immediate concerns about the validity of comparing BMI values across shapes, because the BMI definition only takes into consideration the "height" of the subject. Figure 8 compares BMI of different shapes of the same unit "height." An equilateral triangle of "height" 1.00 has a BMI of around 0.58. However, the son of this triangle will have a BMI of 1.00. The son of the square, a pentagon, will have a BMI of 0.73. So, a Flatland family of three generations of equal "height" can have a wide range of BMI values on account of geometry alone! ("Height" is placed within quotes because there is no "up" in Flatland and the very suggestion of it could land one in jail!)

Each successive generation will have a BMI bouncing back and forth around, until converging on, 0.78 = pi/4, the area of a circle of diameter 1.00. BMI values for the Isosceles triangles range from close to 0.58 down to almost zero - while the definition of BMI for females (who are just straight lines) is altogether meaningless!

So, we have a definition of BMI that is meaningless for a large segment of the population (all the females). And if we assume the value of 0.78 (pi/4) to be the ideal, then the definition is overstating BMI for the squares and understating it for the equilateral triangles.

Who might the squares represent in our world? Those who are going to be heavier at a given height on account of their underlying skeletal structure: those with wide shoulders, wide pelvis, thicker bones, denser bones, larger muscles, deep chests, long-body-with-short-legs stature - or combinations thereof. Such people can be heavy even when very lean and angular.

The triangles represent those with a tendency to weigh less for a given height on account of underlying skeletal structure: narrow shoulders, narrow pelvis, thin bones, less-dense bones, small muscles, puny chests, short-body-with-long-legs stature - or combinations thereof. Such people can be rounded and chubby without weighing as much.

The very wide range of healthy BMI values (18.5 - 24.99) probably does take much of these variations into account. But there is a possibility that many squares of healthy weight are erroneously classified as obese - while many lightweight triangles with BMI values in the healthy range might actually be obese. This has already been recognized to some degree, with different cutoff points of 23.0 for overweight and 25.0 for obesity being suggested for Asian people (http://blogs.nejm.org/now/index.php/bmi-in-asians/2011/02/25/).

A third measure is needed: one that can distinguish the triangles and the squares from the circles. But it needs to be simple to apply - and able to be measured as easily and accurately as height and weight. (Body fat percentage would probably be the best weight-related health measure, but getting accurate measurements is not exactly quick and easy.)

Flatlanders may want to reconsider their formula for BMI as reliable measure of obesity, one that takes into account the different shapes of inhabitants.  A hexagon, square, and triangle of the same mass and same geometric height would have the same BMI (Figure 9), even though their different areas and perimeters could suggest that their weight is distributed differently (Figure 10).

Figure 9

Figure 10

In Flatland, and in our own world, a possibility is to determine different cutoff BMI values for different population groups.

Or, one could just use some common sense instead of relying on a single number as a measure of weight-related health risk! Unlike Flatlanders, humans are irregular in shape!