Predicting body composition using simple measurement techniques

PREDICTING BODY COMPOSITION USING SIMPLE MEASUREMENT

TECHNIQUES

TIM JOHNSON, JAVIER NAVARRO, IDIONG IDONGESIT, MARK WEEKS

DATA • IN 1985 A STUDY ABOUT PREDICTING BODY FAT DISTRIBUTION

FROM EASILY OBTAINABLE MEASUREMENTS WAS UNDERTAKEN. 252 MALE SUBJECTS VOLUNTEERED FOR THE STUDY. OVER THE YEARS ONE INSTANCE WAS LOST.• RECORDS WERE RECORDED FOR THE FOLLOWING VITAL

STATISTICS:1. Density 6. Neck 11. Knee2. Percent Body Fat

7. Chest 12. Ankle

3. Age (years) 8. Abdomen 13. Biceps4. Weight (lbs) 9. Hip 14. Forearm5. Height (inches) 10. Thigh 15. WristItems 6-15 measured in

centimeters

CALCULATIONS

DENSITY 𝐷=

𝑊 𝑎𝑖𝑟

{[ (𝑊𝑎𝑖𝑟−𝑊𝑤𝑎𝑡𝑒𝑟 )𝑐 . 𝑓 . ]− 𝐿𝑢𝑛𝑔𝑣𝑜𝑙}

BODY FAT PERCENTAGE𝐷=

1

[( 𝐴𝑎 )+(𝐵𝑏 )]

where, W is weight in water or airc.f. is water temperature correction factor ~.997 at 76-78 degrees FahrenheitThis method of determining D, density, is considered the gold standard.

where, A= proportion of lean body tissuea= density of lean ~1.1 gm/cm3

B= proportion of fat body tissueb= density of fat ~0.90 gm/cm3

AND % Body Fat = 495/D – 400OR B = (1/D)*[ab/(a-b)]-[b/(a-b)]

EQUATION DEVELOPED FOR LEAN BODY WEIGHT

LBW=17.298 <numerical offset>+.89946(Weight)

-.2783(age) +.002617(age)2 <Age factor>

+17.819(Height) <Height factor>

-.6798(Waist-Wrist)Stepwise multiple regression techniques were used to develop this structural equation back in the 1980’s.

OVERVIEW OF THE DATA

HOW DOES AGE COMPARE TO DENSITY

HOW DOES HEIGHT COMPARE TO DENSITY?

AGE VS WEIGHT

HEIGHT VS WEIGHT

WEIGHT VS NECK

WEIGHT VS DENSITY

DENSITY VS WAIST

HOW DOES AGE COMPARE TO %BODY FAT

TRAINING SET DENSITY DISTRIBUTION

TRAINING SET %BODYFAT DISTRIBUTION

TEST SET’S %BODYFAT DISTRIBUTION

SIMPLE LINEAR REGRESSION

VISUALIZE ERRORS

HEALTH FREAK

CONSIDER THIS• THE PREVIOUS NEARLY PERFECT PREDICTION LOOSES THE EASE OF

PREDICTION USING SIMPLE MEASUREMENT TECHNIQUES. THE FORMULA ALSO USES THE GOLD STANDARD: DENSITY AS THE BASIS FOR THE PREDICTION.

• CAN SIMPLE MEASUREMENT TECHNIQUES PREDICTING %BODYFAT BE FOUND USING WEKA?

• THE FOLLOWING SLIDES CHECK OUT THAT POSSIBILITY• FIRST USING THE WAIST MEASUREMENT• THEN USING THE WAIST AND THE WRIST MEASUREMENTS • AND FINALLY USING ALL THE MEASUREMENTS BUT DENSITY

TRAINING SET WAIST

TRAINING SET WAIST & WRIST

TRAINING SET ALL BUT…

COULD WE DUPLICATE THE 1985 RESULTS?

ONE MEASUREMENT BODY FAT

TWO MEASUREMENT BODY FAT

ALL BUT PREDICT BODY FAT

1985

USING M5P RULES

Here we use machine learning to develop rules: Weka detects two using waist > or < 87.1 cm circumference. Overall accuracy is at a regression value of 85.33%

CLUSTERING—SIMPLE K MEANS

SUMMARY• THE FORMULA WITH THE BEST RESULTS BASED ITS PREDICTIVE

ABILITY UPON THE DENSITY OF THE INDIVIDUAL IN AIR AND WATER.• WE LOSE THE GOAL OF THE 1985 STUDY OF BEING ABLE TO

PREDICT THE PERCENT OF BODY FAT BASED ON EASILY ACCESSIBLE MEASUREMENTS. • BY ELIMINATING THE DENSITY CATEGORY THE CALCULATION

ENGINE IS FORCED TO UTILIZE THE REMAINING CATEGORIES. • THE RESULTING CORRELATION PROBABILITY SHOW THE

ACCURACY ATTAINED USING EASILY OBTAINABLE MEASUREMENTS WITHOUT OVER FITTING. • SOME EVIDENCE OF CLUSTERING WAS FOUND AND COMPARED

TO THE RULES.

REFERENCES

• “GENERALIZED BODY COMPOSITION PREDICTION EQUATION FOR MEN USING SIMPLE MEASUREMENT TECHNIQUES” K. W. PENROSE, ET AL. FACSM, HUMAN PERFORMANCE RESEARCH CENTER, BRIGHAM YOUNG UNIVERSITY, “MEDICINE AND SCIENCE IN SPORTS AND EXERCISE, V17, NO. 2, APRIL 1985, P. 189.

• “BODYFAT”, R.W.JOHNSON, DEPT OF MATHEMATICS & COMPUTER SCIENCE, SOUTH DAKOTA SCHOOL OF MINES AND TECHNOLOGY, HOSTED BY STATLIB, DEPARTMENT OF STATISTICS, CARNEGIE MELLON UNIVERSITY, HTTP://LIB.STAT.CMU.EDU/MODULES.PHP, ACCESSED 3/23/2014.