1. Is the BMI a Relic of the Past? Wang-Sheng Lee School of Accounting, Economics and Finance Deakin University (joint work with David Johnston, Monash University) Presentation at the Singapore Health Economics Association Conference 17 April 2014 Preliminary work

2. How is obesity typically measured? BMI = Weight/Height 2 BMI ≥ 30 is an indication of obesity

3. Short History of the BMI Created by Adolphe Quetelet in the 19 th century. Based on observing that in young adults W/H 2 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.

4. A Standard BMI Chart for Public Health Purposes

5. Why Does the Chart Look So Familiar? Let y = weight. Let x = height. Then obesity using the BMI cutoff = weight/height 2 = 30 is simply the graph of y = 30x 2 for relevant values of weight and height. Can we do better than using a graph of y = x 2 for public health purposes?

6. Improving on the BMI Why weight/height 2 and not weight/height p 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

7. The New BMI Makes the News! Source: The Daily Mail (UK), 21 Jan 2013.

8. 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 height 2 /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)

9. Public Health Guidelines on Obesity UK National Institute of Health, 2006 US National Institutes of Health, 1998

10. So…. does the BMI measure fatness well? Well…. perhaps we can do better!

11. “Do you know your body fat percentage?”

12. Visualizing Fatness using Percent Body Fat (PBF) Source:

13. BMI as an indicator of adiposity (1) 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: What does this graph look like in 3-D?

14. BMI as an indicator of adiposity (2) Graph of

15. BMI as an indicator of adiposity (3) Graph of Restricted to weight (x) between 0 and 200 kg and height (y) between 0 and 2.0 meters.

16. BMI as an indicator of adiposity (4) Graph of Restricted to weight (x) between 30 and 200 kg and height (y) between 1.0 and 2.0 meters.

17. 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

18. Conditional Distribution of PBF at Different Levels of BMI At each level of BMI, PBF is a distribution and not a constant! White MalesWhite Females Data: NHANES III

19. Can You Measure PBF Easily? Skinfold CalipersDual Energy X-ray Hydrostatic Underwater Weighing Bioelectrical Impedance Analysis

20. Introducing the Contour Plot: Recreating the BMI Chart Estimated using the semi-parametric model: Data: NHANES III, males and females combined BMI given height and weight is just over 30.

21. Weight, Height and PBF in a Contour Plot Estimated using the semi-parametric model (by gender): Data: NHANES III Body fat ~ 28% Body fat ~ 42%

22. 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

23. Using a combination of BMI and Waist Circumference (1) BMI and waist circumference are positively correlated in 2D. Data: NHANES III, white males

24. 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

25. 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

26. 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: Age is important because PBF generally increases with age. Research also suggests that doing it separately by gender and ethnicity is also important.

27. 3-D Plots for Percent Body Fat

28. Contour Plots for PBF

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

30. Prediction Equation for PBF (1) In the literature, there currently are several PBF prediction equations for adults. E.g. Deurenberg et al. (1991) We can also estimate a semi-parametric equation using the same covariates: What happens when we compare the out of sample forecast ability?

31. Prediction Equation for PBF (2) We use a training sample of 5000 and an evaluation sample of 1676 from the NHANES III data. From 500 simulations, the boxplot shows that the semi- parametric model clearly outperforms the linear model in the holdout sample (lower MSE).

32. 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.