Original

Reassessment KarlJ

Smalley,

Research

Communications-general

of body mass indices13

Anita

N Knerr,

Zebulon

V Kendrick,

Jerry

A Colliver,

and Oliver

E Owen

ABSTRACT The accuracy of body mass indices (BMls), such as Quetelet’s index, for the definition ofobesity was investigated in a large sample ofhealthy humans. Two hundred thirteen women and 1 50 men with a wide spectrum of weights, heights, and ages underwent densitometric analysis for the determination of percent body fat (%BF). %BF was then contrasted with various well-established BMIs. Although %BF was correlated with all the BMIs(r 0.60-0.82), applying objective definitions of obesity based on BMIs or %BF by densitometry

the weight-height indices provided and, thus, obesity. These findings

often

study were to reassess the agreement among the different weightheight indices in a general as opposed to an obese population and to assess the accuracy ofthe weight-height indices as predictors of body fat and fat mass determined by densitometry.

=

produced

conflicting

results.

It was

also

95% confidence intervals for predicting Quetelet’s index were very wide. Because for individuals between densitometrically and body fat as estimated by BMIs, we should be used with caution as indicators C/in

Nuir

KEY

found

that

the

%BF by using of the wide variation determined body fat conclude that BMIs of obesity. Am J

1990;52:405-8.

WORDS

Body

densitometry,

body

mass

index,

obesity,

weight,

height,

dwarves

raised

ateness

of

more

general

question

indices

for

more typical population of humans The present study was conducted commonly

used

weight-height

fat mass as determined to obese

humans

about

normal

appropri-

obesity

in

with normal stature. to assess the value

indices

as estimates

by densitometry

with

the

estimating

The

a

of six

of%BF

on a spectrum

stature.

fat

and

of lean

purposes

of the

Methods

Subjects women and 1 50 men served as volunwere studied at Temple University. This population included subjects with a wide range ofages, weights, heights, and body compositions. Caucasians, blacks, and orientals were studied. The subjects’ physical characteristics are summarized in Table 1. The nature and purpose ofthe investigations were fully explained to each subject before the study. The study was approved by the Human Institutional Review Board at Temple University. After an overnight fast, weight (kg) and height (m) were measured with the subjects barefooted and lightly clothed. UnderTwo

composition

the

weight-height

poor estimates of body with the achondroplastic

hundred

thirteen

teers. All participants

Introduction The

increasing

increased

incidence

the need

cal method

for

to identify

measuring

ofobesity

in the United

a clinically obesity

(1).

States

applicable Clinically,

and the

has

practipresence

is frequently assessed through one ofthe commonly used body mass indices (BMIs). These indices are defined as different combinations ofweight and height, such as weight divided by height, weight divided by height squared, and weight expressed as a percentage of mean weight for a given height and sex. The indices represent different attempts to adjust body weight for height to derive a height-free measure ofobesity. Although a number of weight-height indices are available, research has shown that different indices measure the same thing of obesity

in an obese patients indices

strated.

population;

almost for

the

that

is, the different

identically

(2).

estimation

of obesity

indices

However,

the has

order

obese

been

demon-

of the

National

Library

of

Medicine

(Bethesda,

that the terms BMI or Quetelet (a commonly used index) appeared in 252 journal article titles or abstracts between 1986 and 1988. These indices have been used in our research as well (3-7). In one of our recent studies of the obesity of achondroplastic dwarves (8), several commonly used weight-height indices as well as a newer index developed by Abdel-Malek et al (9) were related to percent body fat (%BF) by densitometry, a more direct method of assessing body fat (10). The results showed that A,n

J C/in Nuir

1990:52:405-8.

Printed

in USA.

repeated ues within lung

were

fat-free six or more

25

volume

(12). Body

determined

for

densitometric

mass (1 1). The consecutive

g were

obtained

was

determined

density

was

weighing

times for

until

each

used

three

to estimate

oxygen

%BF

of was

similar

individual.

by closed-circuit

then

analysis procedure

val-

Residual dilution

with

the

© 1990 American

Clinical Research Center, Temple University Philadelphia; the Biokinetics Research Laboratory, College of Health, Physical Education, Recreation and Dance, Temple University. Philadelphia: and the Division ofStatistics and Re. search Consulting and the Department oflnternal Medicine, Southern Illinois University School ofMedicine, Springfield, IL: 2 Supported in part by the US Public Health Service research grant MOl-RR 00349 (National Institutes of Health, General Clinical Research Centers Program). 3 Address reprint requests to OE Owen, Professor and Chairman, Department oflnternal Medicine, Southern Illinois University, School ofMedicine, P0 Box 19230, Springfield, IL 62794-9230. Receivediuly 10, 1989. Accepted for publication October 17, 1989. I

Nevertheless, the weight-height indices continue to be used. A literature search that used the Medlar database

widely MEDLINE MD) showed

weights

body fat and

of the

accuracy

not

water

Society

Downloaded from https://academic.oup.com/ajcn/article-abstract/52/3/405/4650856 by guest on 23 April 2018

From

the General

School of Medicine,

for Clinical

Nutrition

405

406

SMALLEY

TABLE Clinical

1 data5

ET

AL

indices.

The

advantage

generalized

Groups

Age

Weight

Percent body fat

Height

y

kg

m

%

34.6 ± 12.0 (15-82) 32.4 ± 12.0 (15-68) 37.7 ± 14.3 (18-82)

76.0 ± 18.9 (43.1-173.1) 69. 1 ± 16.5 (43.1-143.2) 85.8 ± 17.9 (59.8-171.3)

1.7 1 ± 0.09 (1.50-1.96) 1.66 ± 0.07 (1.50-1.88) 1.78 ± 0.07 (1.63-1.96)

24.0 ± 9.1 (5.0-55.2) 26.3 ± 9.4 (8.8-55.2) 20.9 ± 7.6 (5.0-52.9)

of using

indices

was

also

those used by Abdel-Malek

et al (9) were

our own estimates, the equation

women

for both

%BF All subjects (n = 363) Women (n = 213) Men (n = 150)

and statistical

Data

Pearson relationships sizes, such

i±

SD, range

sity was equation

by Brozek et al (10). Fat mass was calculated as

developed

(FATM)

etry

FATM

(%BF/lOO)

=

used

accuracy

X weight

weight-height

in estimating

indices

%BF

and

were

for indices,

evaluated

FATM.

The

based on different combinations ofweight (W, in kg)and height (H, in m), evaluated in this study were: W/H, W/H2 (Quetelet’s ( 13), W”3/H (ponderal index) ( 14), H/W”3 (Sheldon’s ( 1 5), cWt2/H33 (Abdel-Malek’s index, where c 4 x 106 for women and c 3 X 106 for men, and H is in cm) (9), and percent desirable body weight (%DBW, which is weight index) index)

more

similar

also

to develop

used

and men,

ofc,

m, and

to

k in

cWm/H(

%BF

BMIs.

W/H2 >

20%

or %DBW in men

and

to diagnose >

25%

obe-

in women

was used to determine obesity (7). Two commonly used weightheight measures ofobesity, W/H2 and %DBW, were compared with the densitometry standard. Obesity was indicated by a WI H2 27.3 in women and W/H2 27.8 in men (16) and by a

by densitom-

indices

Six commonly

their

the

(19) of using

determined.

120% in men

%DBW

Obesity

over

analyses

among

The validity

in parentheses.

=

indices

Methods

correlation coefficients ( 1 8) were used to assess the between all BMIs and measurements of body as %BF, FATM, weight, and height, as well as the

interrelationships S

sex-specific

evaluated.

and

women

(16).

Linear-regression analysis was also used to assess the utility of using W/H2 to predict %BF. The 95% confidence intervals for predicting %BF and for the mean %BF, given a W/H2, were calculated for the minimum, mean, and maximum W/H2 for both women and men. Regression analyses and confidence intervals were calculated by Minitab data-analysis software (version

6. 1, Minitab,

mc,

State

College,

PA).

=

=

expressed

as a percentage

andsex)(16, 17). Two of the indices,

TABLE 2 Intercorrelations

Allsubjects(n H W/H W/H2 W”3/H H/W”3 cW’2/H33 %DBW Women(n=

ofweight,

mean

weight

for a given

Results

height

The %DBW

and

height,

cW’2/H33,

are sex-specific

BMIs,

intercorrelated

both

generalized

(Table

and

sex specific,

2). The intercorrelations

were

strongly from

ranged

and BMIs5 W

H

W/H

W/H2

0.46 0.98 0.89 0.76 -0.75 0.52 0.91

0.26 0.02 -0.21 0.20 -0.43 0.07

0.97 0.88 -0.87 0.69 0.98

0.97 -0.96 0.82 0.99

0.02 -0.15 -0.31 0.32 -0.27 -0.06

0.98 0.94 -0.93 0.95 1.00

0.98 -0.97 0.99 1.00

0.14 -0.06 -0.26 0.26 -0.20 0.06

0.98 0.92 -0.90 0.94 1.00

0.97 -0.96 0.99 0.99

W”3/H

H/W”3

cW’2/H33

363)

=

-1.00 0.90 0.95

-0.88 -0.94

0.82

0.99 0.96

-0.98 -0.95

0.98

-0.99 0.99 0.94

-0.96 -0.93

0.96

213)

H

0.20

W/H W/H2 W”3/H H/W”3 cW’2/H33 %DBW Men(n= 150) H W/H W/H2 W”3/H

0.98 0.94 0.86 -0.85 0.88 0.96 0.33 0.98 0.92 0.82

-0.8 1

13

W’2/H33 %DBW S ,

ofthe

weight;

0.85 0.96 H, height:

BMI, body

mass

index;

% DBW,

percent

desirable

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body

weight.

-1.00

BODY TABLE 3 Correlations

ofdensitometric

data with weight,

height,

407

INDICES A

Men

0

Women

and BMIs5

Wo men

All su bjects

MASS

Men

o

0

A

E 0

%BF

FATM

%BF

FATM

%BF

FATM

w

0.47

0.79

0.76

0.92

0.61

0.85

H

-0.32

-0.04

4.)

m U

-0.21

-0.07

-0.13

0.13

W/H

0.60

0.88

0.82

0.95

0.67

0.89

W/H2

0.70

0.92

0.84

0.95

0.70

0.90

W”3/H

H/W”3 W’2/H33

0.77

0.89

0.86

0.92

0.70

0.85

-0.77 0.82

-0.87 0.84

-0.86 0.84

-0.91 0.93

-0.69 0.70

-0.82 0.88

0.70

0.92

0.83

0.96

0.69

0.90

%DBW

4.)

0 %BF, percent

S

body

fat by densitometry:

FATM,

fat mass

to

1 .00

in absolute

value

in the

group

20

composed

30

Quetelet’s

FIG 0.82

10

by densitometry.

of all

Within the sexes the intercorrelation among all the BMIs ranged from 0.92 to 1.00 in absolute value. All of the indices were strongly correlated with weight and weakly correlated with height. The correlations of all the BMIs with measures of body size

40

Index

50

60

(/2)

I. Scatter plot of percent body fat (%BF) vs Quetelet’s The solid line is the line ofidentity (y = x).

(W/H2).

index

subjects.

the

sensitivities

50.6% cated

obesity

are presented

in Table 3. The sex-specific BMIs (cW’2/H33 and %DBW) were not more strongly correlated with %BF than were

the generalized BMIs. Generally, all the BMIs were strongly correlated with %BF (r = 0.60-0.82, in absolute value) and FATM (r = 0.87-0.92, in absolute value) in all subjects. In the group composed ofwomen, the correlations between the BMIs and %BF were slightly stronger than in the group composed of men (r = 0.82-0.86 vs r = 0.67-0.70, in absolute value). The estimates ofthe power parameters in the function relating %BF to weight and height (BF = cWm/Ho) based on our sample were m = 1.38, k = 3.64, and c = 8.76 X 106 for women and 6.58

yses

106 for

men.

The

index

based

on

these

estimates

S displays

Table

of %BF

though the 95% confidence value for W/H2 are narrow, predicting

%BF

example,

ifa man

his %BF body

will

given

a value

be within

obesity.

in Figure

1.

Discussion

quite

for obesity

height

rather

insensi-

Malek

et al (9) created

related

to %BF

in the population

tive

to obesity

TABLE

and

studied,

height

were

as determined

the definitions

found

to be somewhat

by densitometry.

For

all subjects,

4

Most

ofthree

Group

quantitative

Sensitivity

definitions

of obesity

Specificityt

False

False

negatives

positives

All subjects

57.2

93.4

42.8

6.6

Women

60.4 53.2

98.2 85.9

39.6 46.8

1.8 14.1

50.6 55.4

95. 1 98.2

49.4 44.6

4.9 1.8

44.3

90.1

55.7

9.9

Proportion

t Proportion

diagnosed

obese

diagnosed

lean

j:

100%

-

sensitivity.

§

100%

-

specificity.

by the by the

BMI BMI

ifobese iflean

by the

anal-

of the

are

data.

Al-

%BF given a intervals for

quite

This

range

broad.

of%BF

borderline

variance

For reflects

malnutrition

is further

strongly

in obesity

as the ones

research

prior

area

with

than

by %BF. by %BF.

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here.

has

been

weight

and

directly

and

makes

presented

in this

correlated

to

demonstrated

thus

to obesity.

with

%BF than

method

is the most

quantitatively

will

it appears not

index.

accurately

However,

these

On

diagnose

indices

obesity,

at least

with

the correlation between W/H2 W/H2 was somewhat insensitive

as determined

true of %DBW. ered

a greater

would diseases

error

beneficial Although

is truly associated

density

by densitometry than

with

therapy. it has been

may obesity suggested

stud-

composition

(Table

4). This might

equal-magnitude

an individual obese,

alone

and that

this

was

also

be consid-

overprediction

as lean,

put

(19).

and %BF was strong to the detection of

of obesity

an

presented

in population

to body

Underprediction

be. Classifying

data

and height

validity of using weight-height be influenced by the 2.5% error

Although (r = 0.70),

body

this

for an individual.

may still have value

relating

more

for construct-

of the

on weight

not

indices,

method

associated

obesity

it was

the other

basis

is

with

body fat. Abdelthat is directly

Although

based

of the

that

correlated

with

were

the

ofmost

a BMI

weakly

direct

that an index

goal

to create

(cW’2/H33)

correlated

a weight-height

use of weight-height The

correlated

an index

strongly

individual S

obese

we can only be 95% certain

1 .7%.

ies. Our determinations of the indices to diagnose obesity may

%DBWvs%BF

Men

such

here,

%

Men W/H2 vs %BF All subjects Women

mdi-

linear-regression

W/H2

from

wide

of the research

indices

ing

Comparison

for

10.0-3

This

were

subgroup

of27,

ranging

moderate

that

and

W/H2

intervals for the man the 95% confidence

has a W/H2

compositions

men

in each

%DBW

for

of men,

ofsimple

W/H2

results (r = 0.8 1 between %BF and the index in all subjects) and, therefore, was not presented in tabular form. Weight was as strongly correlated with measures of body size as the BMls were with measures ofbody size within each sex. Table 4 demonstrates the validity of using W/H2 or %DBW to detect obesity. Although the specificity of each index was high

halfofthe

a summary

versus

57.2%

were

composed

produced

comparable

based on weight

indices

In the group

in less than

%BF criterion.

x

of the

for W/H2.

when

in fact the

individual

potentially sex-specific

at risk delay BMIs

for

possible would

SMALLEY

408 TABLES Linear-regression

analysis

of% BF vs Quetelet’s

ET AL

index5 95% confidence

Predicted

Group

95%

for mean

value(x)

Women(n = 213) [5.l]t Minimum Mean Maximum Men(n= l50)[5.5J

confidence

16.4 25.2 49.6

interval

%BFgiven

x

%

%BF

given

x

%

68 38

14.8 26.3 58.2

±

1.2

14.8 25.2

10.1

0.7

8 3

±

±

±

10. 1

± 2.9

5

58.2

± 10.4

18 77

Minimum

20.3

14.2

± 1.4

10

14.2

± 10.9

Mean Maximum

27.0 58.9

20.9 52.2

±

0.9 5.3

4 10

19.8 52.2

±

10.9

52

±

12.0

23

S

value

Predictions for the minimum, and an individual prediction.

t Root mean square f Interval expressed

mean,

and maximum

error given in brackets. as a percentage ofpredicted

±

of Quetelet’s

index

generalized

BMIs.

Garn

et al (21)

attributed

the

relationship

of

BMls to stature, lean body mass, and body frame or proportion as three limiting factors ofBMIs. These factors may be responsible for the inability of these indices to indicate obesity with greater accuracy. However, there may be other fundamental factors racy

that

have

not been

ofweight-height

different

identified

indices.

forms

Another

risks

in individuals,

W/H2