Case Study: Prediction of Body Fat Composition

BIOST/STAT 579 - Autumn 2008

Analysis for Prediction




This chapter concerns the analysis of data from a study designed to derive
a predictive model. This goal is distinct from that of an experiment, which
estimates the effect of an intervention, and from an observational study
designed to estimate the association between a condition and an outcome.


Experiment: designed to assess the effect of an intervention (the
condition that is randomly assigned) on an outcome.

Observational association study: designed to assess the association
between an exposure (or treatment) and an outcome.

Predictive study: designed to derive a model for predicting an outcome
using a set of predictor variables.






A Contrast Between Predictive Studies and Experiments or Studies of
Associations


In experiments and studies of associations, the key quantity of
interest is the relationship between the treatment variable of interest
and the outcome. In a predictive study the key quantity of interest is
the prediction error.


Note: often studies of associations are loosely described to have as their
aim the "prediction" of an outcome using a set of explanatory variable,
when the real aim is to study the magnitudes of the associations between
these variables and the outcome. In this chapter, the term predictive study
is meant in the strict sense that the practical aim is to use the model
developed to predict future outcomes.

The Eight Data Analysis Issues Revisited:
Predictive Studies

I. Primary and secondary outcome variables: the choice of primary outcome
variable is usually clearly identified in a predictive study


II. Choice of test statistic: tests of hypotheses of statistical
significance of predictors are of less interest,


III. Modeling assumptions: assumptions generally less critical because the
goal is to achieve good prediction


IV. Multiplicity: not relevant


V. Power: still important but usually not addressed formally

VI. Missing data: critical for interpretation of results for all types of
studies


VII. Imbalance between treatment groups: not so relevant


VIII. Adherence/Implementation: like studies of associations, varying
exposure to treatments, exposure, etc, is the point of the study.



Case Study: Prediction of Body Fat Composition




Estimation of body fat percentage is one way to assess a person's level of
fitness. Assuming the body consists of just two components, lean body
tissue and fat tissue, then 1/D = A/a + B/b, where D = Body Density
(g/cm3), A = proportion of lean body tissue by weight, B = proportion of
fat tissue by weight (A+B=1), a = density of lean body tissue (g/cm3), b =
density of fat tissue (g/cm3). Using the estimates a=1.10 g/cm3 and b=0.90
g/cm3 and solving for B gives Siri's equation:

Percentage of Body Fat = 100B = 495/D - 450.

The technique of underwater weighing uses Archimedes' principle to
determine body volume: the loss of weight of a body submersed in water
(i.e., the difference between the body's weight measured in air and its
weight measured in water) is equal to the weight of the water the body
displaces, from which one gets the volume of the displaced water and hence
the volume of the body. At 39.2 deg F, one gram of water occupies exactly
one cm3, but at higher temperatures it occupies slightly less volume (e.g.,
0.997 cm3 at 76-78 deg F). Therefore, the density of the body can be
calculated as

Density = Wt in air/[(Wt in air - Wt in water)/c - Residual Lung Volume],

where the weight in air and weight in water are both measured in kg, c is
the correction factor for the water temperature (=1 at 39.2 deg F), and the
residual lung volume is measured in liters.

Of course, weighing yourself in water is no easy task so it is desirable to
have an easy inexpensive method of estimating body fat ...

References

1. Bailey, Covert (1994). Smart Exercise: Burning Fat, Getting Fit.
Houghton-Mifflin Co.

2. Behnke, A.R. and Wilmore, J.H. (1974). Evaluation and Regulation of
Body Build and Composition. Prentice-Hall.

3. Katch, F. and McArdle, W. (1977). Nutrition, Weight Control, and
Exercise, Houghton Mifflin Co.

4. Wilmore, J. (1976). Athletic Training and Physical Fitness:
Physiological Principles of the Conditioning Process. Allyn and Bacon, Inc.

5. Siri, W.E. (1956). Gross composition of the body. In Advances in
Biological and Medical Physics, vol. IV, (Eds. J.H. Lawrence and C.A.
Tobias), Academic Press, Inc.
A Predictive Study of Body Fat Percentage

A study was done to derive a prediction equation for body fat % in men
(n=252, age 22-81 years) from simple body measurements. Body density was
determined by the methods described above and body fat % determined from
Siri's equation. The data set includes the following variables (see Benhke
and Wilmore, 1974, pp. 45-48, for measurement techniques):

density: Density using underwater weighing (g/cm3)
bodyfat: Body fat percentage from Siri's (1956) equation
age: Age in years
weight: Weight in air in lbs (.4536 kg/lb)
height: Height in inches (2.54 cm/inch)
neck: Neck circumference (cm)
chest: Chest circumference (cm)
abdom: Abdomen 2 circumference (cm)
hip: Hip circumference (cm)
thigh: Thigh circumference (cm)
knee: Knee circumference (cm)
ankle: Ankle circumference (cm)
bicep: Biceps (extended) circumference (cm)
arm: Forearm circumference (cm)
wrist: Wrist circumference (cm)

The goals are:

1) to determine an equation for estimation of body fat percentage from age,
weight, height, and the circumference measurements, and

2) to assess the magnitude of the prediction error of the equation.


The published abstract reporting the results of this study is on the
following page.
Generalized body composition prediction equation for men using simple
measurement techniques

KW Penrose, AG Nelson, AG Fisher

MEDICINE AND SCIENCE IN SPORTS AND EXERCISE 17 (2): 189-189 1985

143 men ranging in age from 22 to 81 years and percent body fat of 3.7 to
40.1 were selected to establish a generalized body composition prediction
equation using simple measurement techniques. Subject selection was based
on a central composite rotatable design. The measurements consisted of
height (HT), weight (WT), age and 10 circumferences. The above measurements
were analyzed using stepwise multiple regression techniques and the
following equation was derived: LBW=17.298+.89946(Wt in kg)-.2783(age) +
.002617(age)^2+17.819(ht in m)-.6798(Ab-Wr in cm) (R=.924, SEE=3.27). where
LBW=lean body WT, Ab=abdominal circumference at the umbilicus and level
with the iliac crest, Wr=wrist circumference distal to the styloid
processes. A second group of 109 men (23-74 years, 0-47.5% fat) was used to
test the validity of this equation and similar equations derived by Hodgon
and Beckett (HB), Wright and Wilmore (WW), Wilmore and Behnke (WB), and
McArdle et al (MC). A paired t-test on the mean difference (D) between
actual and predicted percent fat showed that the present equation had a
mean difference of 0.6% plus/minus 0.45 which was not statistically
different from zero (p