Is the BMI a Relic of the Past?

Wang-Sheng LeeSchool of Accounting, Economics and Finance

Deakin University

(joint work with David Johnston, Monash University)

Presentation at the Singapore Health Economics Association Conference17 April 2014

Preliminary work

How is obesity typically measured?• BMI = Weight/Height2

• BMI ≥ 30 is an indication of obesity

Short History of the BMI

• Created by Adolphe Quetelet in the 19th century.

• Based on observing that in young adults W/H2 is pretty stable with increasing height.

• The term “Body Mass Index” (BMI) coined by Keys et al. (1972).

• Empirical support for and against BMI as a measure of adiposity.

• Although shortcomings are known, still viewed to be a useful tool, especially for looking at trends in populations.

• Less useful for individual diagnosis of fatness, especially in the BMI < 30 range.

A Standard BMI Chart for Public Health Purposes

Why Does the Chart Look So Familiar?

Let y = weight.Let x = height.Then obesity using the BMI cutoff = weight/height2 = 30 is simply the graph of y = 30x2 for relevant values of weight and height.

Can we do better than using a graph of y = x2 for public health purposes?

Improving on the BMI

• Why weight/height2 and not weight/heightp where p is some value > 0?

• The “New BMI” formula proposed by an Oxford mathematician (Trefethen, 2013) :

New BMI = 1.3*weight(kg)/height(m)2.5

The New BMI Makes the News!

Source: The Daily Mail (UK), 21 Jan 2013.

Improving on the BMI (2)

• Using different BMI cutoffs to denote obesity

• Obesity cut-off points of 24 for females and 28 for males (Shah and Braverman, 2012)

• How about height2/weight? (Nevill and Holder, 1995)

• How about waist circumference? (e.g. Janssen et al., 2004)

• How about the waist to height ratio? (e.g. Ashwell et al., 1996)

Public Health Guidelines on Obesity

UK National Institute of Health, 2006

US National Institutes of Health, 1998

So…. does the BMI measure fatness well?

Well…. perhaps we can do better!

“Do you know your body fat percentage?”

Visualizing Fatness using Percent Body Fat (PBF)

Source:

BMI as an indicator of adiposity (1)

2

WeightPBFHeight

Suppose we believe that BMI is a key indicator of adiposity. We might write:

Let x = weight , y = height, z = PBF.We can then express the above equation as:

2

xzy

What does this graph look like in 3-D?

BMI as an indicator of adiposity (2)

Graph of 2

xzy

BMI as an indicator of adiposity (3)

Graph of 2

xzy

Restricted to weight (x) between 0 and 200 kg and height (y) between 0 and 2.0 meters.

BMI as an indicator of adiposity (4)

Graph of 2

xzy

Restricted to weight (x) between 30 and 200 kg and height (y) between 1.0 and 2.0 meters.

Scatter Plots of BMI and Percent Body Fat• How good a job does BMI do in detecting percent body fat (PBF)?• Use the NHANES III (1988-1994) data with PBF obtained from

bioelectrical impedance analysis.

Scatterplot of BMI vs Percent Body Fat, By Gender and Race

False negatives

False positives

010

2030

4050

60P

erce

nt B

ody

Fat

0 20 40 60 80BMI

White Male0

1020

3040

5060

Per

cent

Bod

y Fa

t

0 20 40 60 80BMI

White Female

010

2030

4050

60P

erce

nt B

ody

Fat

0 20 40 60 80BMI

Black Male

010

2030

4050

60P

erce

nt B

ody

Fat

0 20 40 60 80BMI

Black Female

Conditional Distribution of PBF at Different Levels of BMI

• At each level of BMI, PBF is a distribution and not a constant!

White Males White Females

Data: NHANES III

Can You Measure PBF Easily?

Skinfold Calipers Dual Energy X-ray

Hydrostatic Underwater Weighing

Bioelectrical Impedance Analysis

Introducing the Contour Plot: Recreating the BMI Chart

Estimated using the semi-parametric model:( , )BMI f height weight

Data: NHANES III, males and females combinedHeight(m)

Wei

ght(k

g)

0 10 20

30

40

50

60

70

1.4 1.5 1.6 1.7 1.8 1.9 2.0

5010

015

020

0BMI given height and weight is just over 30.

Weight, Height and PBF in a Contour Plot

Estimated using the semi-parametric model (by gender):( , )PBF f height weight

Data: NHANES III

Males

Height(m)

Wei

ght(k

g)

5 10 15

20

25

30

35

40

45

50

1.6 1.7 1.8 1.9 2.0

5010

015

020

0

Females

Height(m)W

eigh

t(kg)

20 25 30

35

40

45

50

55

60

65

1.4 1.5 1.6 1.7 1.8

4060

8010

012

014

016

018

0

Body fat ~ 28%

Body fat ~ 42%

• Information on height and weight alone (e.g. BMI) is likely to be insufficient for accurately measuring fatness.

• This combination suggested by the US and UK public health guidelines.

Let’s Focus on the Statistical Relationship Between PBF, BMI and

Waist Circumference

Using a combination of BMI and Waist Circumference (1)

BMI and waist circumference are positively correlated in 2D.

Data: NHANES III, white males

BMI

20

40

60 Waist_cm

50

100

150

PBF

0

20

40

60

Using a combination of BMI and Waist Circumference (2)

How BMI and waist circumference are associated with PBF in 3D.

Data: NHANES III, white males

BMI

20

40

60 Waist_cm

50

100

150

PBF

0

20

40

60

Using a combination of BMI and Waist Circumference (3)

How BMI and waist circumference are associated with PBF in 3D with a linear regression plane included.

Data: NHANES III, white males

BMI

20

40

60 Waist_cm

50

100

150

PBF

0

20

40

60

Is it Possible to Come up with a Easy to Use PBF Chart based on Height, Weight and Waist Circumference?

• Why use a linear model?

• Estimate a non-parametric model:

1 2( ) ( )PBF f bmi waist f age

• Age is important because PBF generally increases with age.

• Research also suggests that doing it separately by gender and ethnicity is also important.

3-D Plots for Percent Body Fat

Contour Plots for PBF

Are you sure these funky equations are doing a good job telling me how fat I am?

Prediction Equation for PBF (1)

• In the literature, there currently are several PBF prediction equations for adults. E.g. Deurenberg et al. (1991)

(1.20 ) (10.8 ) (0.23 ) 5.4PBF bmi male age

• We can also estimate a semi-parametric equation using the same covariates:

1 2(bmi) male ( )PBF f f age

• What happens when we compare the out of sample forecast ability?

Prediction Equation for PBF (2)

• We use a training sample of 5000 and an evaluation sample of 1676 from the NHANES III data.

Semiparametric model OLS model

1718

1920

2122

23

• From 500 simulations, the boxplot shows that the semi-parametric model clearly outperforms the linear model in the holdout sample (lower MSE).

Conclusion

• PBF is the key metric of interest so why not have charts that focus on it?

• Proposed a chart for public health purposes based on 3 inputs (height, weight and waist) that one can use to infer one’s PBF.

• Used BMI in its original form as an input for consistency with guidelines from the UK and US health authorities.

• Males and females have different body measurements to focus on if they are aiming to reduce body fat.