',
C Macmillan Press Ltd 1994
lntemdonlll Journal of Obesity (1994) 18, ~12
Comparative .evaluation of body .
composition methods and predictions, and
calculation of density and hydration
fraction of fat-free mass, in obese women
N.J. Fuller, M.B. Sawyer and M. Elia
MRC Dunn Clinical Nutrition Centre, Hills Road, Cambridge CB2 2DH, UK
The objective of this study was to apply a three-component model of body composition to a group of obese women
In order tO (a) establish the relative value of a number of readily available prediction equations by comparison of the
extent of agreement between these predictions and body composition estimated by the model and other reference
methods and (b) evaluate density and hydration of fat-free mass.
·
Estimation of body composition was carried out by reference methods and prediction equations and the usefulness of these prediction equations for application speclflcally to obese women was evaluated. The subjects were 15
obese, otherwise healthy, Caucasian women (body mass Index> 30kg/m2 and body fat> 40% of body weight, as
orlglnally determined using densitometry).
Body composition was estimated using three established reference methods (deuterium dilution which primarily
measures total body water, densitometry for body fat and fat-free mass and total body potassium) and the three
component model constructed from deuterium dilution and densitometry. Density and hydration fraction of the fatfree mass were calculated from appropriate values obtained as Integral parts of the three-component model. In
addition, body composition was predicted from various prediction equations Incorporating weight and height (some
of which Include a factor for age), from a number of prediction equations utilizing different terms Involving the same
whole-body blo-electrlcal Impedance measurement and from measurements of sklnfold thickness and near Infrared lnteractance. The extent of agreement between methods was assessed using bias and 95% limits of agreemenL
Mean density of fat-free mass was found to be 1.104 kg/I (s.d. 0.006kg/I) with a range of 1.093 to 1.117 kg/I, and
mean hydration fraction was 0.712 (s.d. 0.016) with a range of hydration from 88.2% to 75.1% (all values were calculated from the three-component model).
In general, the reference methods (densitometry, deuterium dilution, the three-component model and total body
potassium) demonstrated better agreement with each other than with the prediction methods or equations. In these
obese women, sklnfold thickness measurements are apparently less reliable (large bias and 95% limits of agreement) than In the lean subjects of a variety of other studies. A majority of'lnterpretatlons of weight and height measurements and predictions Incorporating Impedance/resistance measurements are apparently not applicable to this
group of obese women, due to large values for both bias and 95% limits of agreemenL For body fat estimation
(% body weight), for example, the bias between reference methods and weight/height prediction equations ranged
from-12.5% to 8.4%, with 95% limits of agreement up to 15.8%; and the bias between reference methods and predictions incorporating whole-body bio-electrlcal Impedance ranged from -7.6% to 8.1%, with 95% limits of agreement up to 24.7%. The results of this study suggest that there Is no compelling reason, on ·the basis of the threecomponent model, to change the traditional value of 1.1 kg/I for use In densitometry with obese female lndlvlduals. It
fs also suggested that, there Is apparently a large and unacceptable variability In estimates of body composition
obtained by the various prediction equations applied here, and that there Is a particular risk Involved In applying
prediction equations, orlglnally derived In lean Individuals, to obese women.
Keywords: body fat, total body water, bias and 95% limits of agreement
Introduction
There are many different simple or convenient methods and
prediction equations available which claim to predict reference method assessments of body composition accurately
and reproducibly.' A series of body composition studies in
non-obese individuals carried out in our laboratory, have
shown that there is a large range of possible predictions of
body composition through the use of different methods, or
even different interpretations of the same measurements,
for example weight, height and whole-body bio-electrical
impedance. 1 ~ However, a comprehensive comparative
assessment of the extent of agreement between these predictions and reference methods or multi-component reference models has yet to be established. With few
exceptions7 there is also a paucity of information regarding
Correspondence to: N.J. Fuller.
Received 13 October 1993; accepted 12 January 1994
the relative value of these predictions in groups of obese
subjects.5 Moreover, since some measurements may be difficult to obtain accurately and precisely in the obese (e.g.
skinfold thicknesses), the application of the apparently
reproducible whole-body bio-electrical impedance measurement may prove to be more appropriate in this group.
However, since the numbers of overweight or obese individuals have been included to a varying extent in the
derivation of prediction equations, the use of those equations based on weight, height and bio-electrical impedance
may be inappropriate in the obese and lead to substantial
errors in assessment of body composition. In addition, there
is quite often a lack of basic information provided by the
manufacturers of certain commercially available bio-
504
electrical impedance instruments regarding their calibration
procedures and the origins of their equations. Furthermore,
' although some manufacturers claim that their particular
technique is applicable to a wide variety of individuals or
groups, including lean and obese adults, extending their use
beyond the range over which they were derived may be
inappropriate.
The primary aim of this study was to evaluate the validity and reproducibility of a large number of different prediction equations for body composition assessment in a specific group of obese, otherwise healthy, Caucasian women by
comparison with a three-component (fat, water, and protein
plus mineral 4) model and other traditional reference methods. These particular prediction equations incorporate
terms involving weight and height only or have additional
terms involving bio-electrical impedance/resistance mea~urements, and were assessed irrespective of whether or not
they were intended for use exclusively in females or in the
obese. Ultimately, it was intended to identify those that are
most suitable for use with obese women. The secondary
aim of the study was to establish both mean values and
extent of variation in the density and hydration fraction of
fat-free mass using the three-component model. These values have major implications for the interpretation of measurements obtained by two-component models of body
composition (densitometry and deuterium dilution) which
has been a matter for some debate in lean 4 •8 and, especially,
in obese subjects. 9•10
Weight and height
Body weight (Wt - kg) was determined using a Sauter Type
El210 electronic scale with digital readout, accurate to O.lg
(Todd Scales, Unit 4, Studlands Park Industrial Estate,
Newmarket, Suffolk, UK), and height was measured to the
nearest 0.5 cm using a wall mounted stadiometer (Holtain
Ltd., Crosswell, Crymych, Dyfed, Wales SA41 3UF).
Densitometry
Body volume (BV = body weight - under-water weight)
and body density (d = Wt I BV) were obtained using the
under-water weighing technique of Akers and Buskirk with
a modified helium dilution technique to account for lung
volume.2 Fat(% body weight) and fat-free mass (FFM - kg)
were calculated from body density using the equation of
Siri 11:
Fat (% body weight)
=4 ~ 5 -
450,
which assumes constant mean densities of these gross body
components (0.9kg/l and l.lkg/l, for fat and fat-free mass,
respectively).
Fat mass (kg) - %Fat x Wt
-
FEM (kg)
100
=Wt -
Fat mass
Total body water was calculated from the densitometric
estimate of fat-free mass by assuming that the hydration
fraction of fat-free mass is 0.72,1 1 or 72%.
Methods
Subjects
The characteristics (mean ± s.d.) of the fifteen obese, otherwise healthy, Caucasian female subjects who volunteered
for the study are shown in Table 1. The criterion for inclusion of subjects in the study were that each should be 40%
fat or more, as estimated bv densitometry (see below). All
measurements were performed on all subjects within about
a six hour period following an overnight fast. Approval for
the study was granted by the Ethical Committee of the
Dunn Clinical Nutrition Centre, and all subjects gave their
informed consent.
Deuterium dilution
Total body water (TBW) was measured using deuterium
dilution space.3 Fat-free mass was estimated by assuming
that the hydration fraction of fat-free mass is 0.72,1 1 and
body fat mass (kg) was determined by difference between
body weight and fat-free mass .
Fat mass (kg) = Wt (kg) - FEM (kg)
Fat (%Wt)
_ Eat mass 2!'. 100
Wt
Three-component model
Table 1 Characteristics of the subjects (mean, standard devia-
tion and range, unless otherwise stated)
Mean : s.d.
Age (years)
Weight (kg)
Height (mJ
Body density (kgll)
Total body water 0)
Total body potassium (mmol)
Lean body mass (leg)•
Body fat (% body weight)•
Whole bQdy impedane!! (Ohms)
43 Jmedlan)
11 2.2 :I: 29 .6
l.63:t 0.04
0.996 :t 0.01 4
41.3 :t 6.7
138.3 :t 1.S.O
.S6.6 :t 9.1
48.0 :I: 6.8
476± 45
•Estimated using the thru-component model.
Range
18 - 59
63..S - 16.S.6
1.55 -
l.(j!)
0.974 - I.Oil
30.6 - 49.S
107.8 - 160.6
39.8 - 69.4
37.3 - 58.1
40J - 5.S6
Body composition, in terms of body fat and fat-free mass,
was assessed using a three. component model,4 which
assumes that the body can be divided into fat, water and
fat·free dry mass (protein plus mineral), and that utilises
direct measurement$ of body weight (Wt), body volume
(BV - from densitometry) and totaJ body water (TBW •
from deuterium di lution pacQ);
Fat mass (kg) : : : 2.220BV (1 ) - 0.764TBW (1) - 1.465Wt (leg)
Fat(% Wt) and fat-free mass (kg) were calculated as above.
Calculation of the density of f at-free mass (Dffei):
Elements of the three-component model were combined to
505
enable a simple calculation of the density of fat-free mass4 :
Mass of body water (kg) + Mass of
fat-free dry matter (kg)
DITm (kg/I) =-v-o_l_u_m_e_o_f_b_o_d_y~w-a-te_r_(_l_)-+~V-o....,1-um-e
(5)
TBW (1) = 0;236Wt + 0.196Ht ~ 0.027A- 10.26
(derived from anti-pyrine distribution volume) 17
(6)
TBW (kg)= 0.24Wt + 0.20Ht- 0.03A-13.9
(tritiated water space) 18
(7)
FFM (kg) = O. l 50Wt + 0.224Ht - 0.092A + 1.31
of fat-free dry matter (1)
Calculation of the hydration fraction of fat-free mass
(HFffin): Hydration of the fat-free mass was calculated
from body water and fat-free mass 4 :
HF
_ Mass body water (kg)
ffm -
(rearrangement from equations derived from total body
potassium measurements reported by Boddy et al.) 19
Equations incorporating terms containing weight and height
only:-
Fat-Free mass (kg)
(8)
FFM (kg)= 0.035Wt + 0.629Ht- 63.78
Hrtm (%) = HFrtm x 100
(unpublished equation derived from data of Pullicino et
Total body potassium measurement
Total body potassium (TBK) was determined from whole
body measurement of radioactive potassium (4°K) in a
whole body counter (Department of Nuclear Medicine,
Addenbrooke's Hospital, Cambridge), by assuming a constant proportion (0.0012% 12 ) of 4°K existing in all naturally
occurring potassium. The effect of attenuation was accounted for by applying an (unpublished) equation, originally
derived in a sample consisting mainly of obese subjects
using 42 K. Fat-free mass was estimated from TBK assuming that the fat-free mass of women contains a constant
2.34g/kgFFM or 60mmol/kgFFM. 13 Total body water and
body fat (as % body weight) were calculated from fat-free
mass, as above.
Weight/height/age prediction equations
Body composition was estimated from a number of published prediction equations incorporating simple anthropometric measurements. Those equations incorporating a
measure of body mass index (Wt/Ht 2 - also known as
BMI or Quetelet's Index):(1)
% Fat= 1.48Wt
_ 7.0
Ht 2 (m)
(2)
% Fat = 71.3
(derived by T.P. Eddy 14 )
974Ht2 (m}_
Wt
(rearrangement of the equations relating body fat to a combination of density, deuterium dilution and total body
potassium estimations of fat, derived mainly from women
attending an obesity clinic reported by Garrow and
Webster) 15
·
(3)
% Fat = .L.20Wl
_ 0.23A - 5.4 16
Ht2 (m)
Those equations incorporating separate tenns involving
weight, height and age:·
(4)
FFM (kg)= 0.069Wt + 0.603Ht - 0.057A - 59.92
(unpublished equation derived from data of
Pullicino et al. )3
a/.)3
(9)
TBW
(I)
= O. l 84Wt + 0.345Ht - 35.27 20
( 10) TBW (I) = O. I07Ht + 0.247Wt - 2.097 2 1
And, an equation with weight and age terms only:(11) TBW (kg)= 0.698Wt- 0.0026Wt 2
-
0.0012A.Wt
(rearrangement of equations reported by Moore et a/.) 22
where; Ht = height (cm, unless otherwise indicated as m),
Wt= weight (kg) and A= age (years).
Assessment of gross body components was obtained
directly from these specific equations. However, where this
was not possible, fat (or fat-free mass) was obtained from
the difference between body weight and fat-free mass (or
fat); and body water was obtained from fat-free mass (or
vice versa) assuming that the hydration fraction of fat-free
mass is 0.72. 11 Wherever necessary, the appropriate conversion was applied to ensure consistency between the different estimates of total body water (equations use the units 1
or kg) assuming that the density of water is 0.9937 lkg/l at
36oC.4
Impedance/resistance
Whole body resistance (with a small correction to obtain
the appropriate impedance value, by accounting for reactance )2·23 was measured for all subjects in this study using a
Valhalla model l 990b instrument (Valhalla Scientific, 9955
Mesa Rim Road. San Diego Ca 92121 USA). The accuracy
and reproducibility of measurements obtained by this and
all other instruments used in this study, to measure both
standard resistors and whole-body resistance, had been
established previously.6 With the exception of Holtain Ltd ..
none of the manufacturers of instruments used here had
released details of their particular equations. Therefore,
body composition was assessed (according to manufacturers' instructions) using the E-Z Comp 1500 (Cranlea and
Co, The Sandpits, Acacia Road, Boumeville, Birmingham
B30 2AH) and the Maltron Model BT-905 (Maltron Ltd.;
PO Box 15, Rayleigh, Essex SS6 9SN) by effecting an
exact reproduction of the appropriate impedance/resistance
506
measurement (obtained from the Valhalla instrument) on
·the display of both these instruments, as described previously.6 In addition, the Bodystat-500 technique (Bodystat
Ltd., PO Box 50, Douglas, Isle of Man, British Isles)
enables whole-body impedance to be obtained manually,
before interpretation in terms of body composition by
means of a discrete computer program available on disk.
This same impedance/resistance value was incorporated
into a number of previously published equations. Those
equations which are specific for females:2
(12) FFM (kg)= 0.475Ht + 0.295Wt + 5.49
R
(Lohman, 1988; reported by Graves et al. 24 )
(13) FFM (kg)= 0.821Ht2 + 4.91725
R
2
(14) FFM (kg)= 5.091 + 0.6483Ht + 0.1699Wt
R
(RJL Systems Incorporated, Detroit, MI USA 26 )
(15) FFM (kg)= 0.00108Ht 2 - 0.0209R + 0.232Wt 0.0678A + 14.59
(Segal et al.27 - equation derivation included a
number of obese women)
2
( 16) FFM (kg) _ 0.698Ht + 9 4 2s
R
.
(17) FFM (kg)= 0.00151Ht2 - 0.0344R + 0.140Wt 0.158A + 20.387
(Gray et al.29 - equation for non-obese women)
( 18) FFM (kg) =
o. 3 ~Ht + 0.307Wt + 0.095 (Ht - 100)
2
+ 0.74!3°
(19) FFM (kg)= 17.79 + 0.000985Ht2 + 0.374Wt 0.0238R - 0.153A - 4 .2926
(20) TBW (l)
=0. 3 ~2Ht
2
+ 0.105Wt + 8._3 15 3 1
2
(21) TBW (kg) = il.24Ht + O. I 72Wt + O. I65Wt - 17 .58 32
Miscellaneous -equation_s, some of which are non-sex or
non-fat specific or were originally derived in men:2
(24) TBW (l) = o. 5 85 Ht + 1.825
z
(Holtain Ltd 2 )
2
(25) TBW (I)= 0. 587 Ht + 1.919
R
(calculated from data in men provided by Hoffer
et al. 33 )
2
(26) TBW (I) = Q,Qlli1 + 2.03
R
(Lukaski et al. 23 - equation derived in men)
34
R
(27) Body density (d) = 1.1113 - 0.0556 Wt.
Ht 2
and;
% Fat= fil - 450 11 •34
d
(28) % Fat= 4 1.52 CZ. WO - 30.027 35
Ht2
where; Z =impedance (Ohms), R =resistance (Ohms), Ht
=height (cm) and Wt= weight (kg).
Wherever possible, assessment of body composition was
obtained directly from available instruments or from specific equations. However, where this was not possible, fat (or
fat-free mass) was obtained from the difference between
body weight and fat-free mass (or fat); and total body water
was obtained from fat-free mass (or vice versa) assuming
that the hydration fraction of fat-free mass is 0.72. 11 Again,
the appropriate conversion was applied to ensure consistency between the different estimates of total body water
(equations use the units I or kg) assuming that the density
of water is 0.99371kg/I at 36 °C.4
Skinfold thickness measurements
Skinfold thicknesses were measured using standard calipers
(Holtain Ltd.) at four sites (biceps, triceps, supra-iliac and
subscapular) following the method of Durnin and
Womersley.36 Body density was predicted from the sum of
the four skinfolds, and body fat calculated from body density (as above).
R
Equations which are fat~specific for obese women:(22) FFM (kg)= 0.000912Ht 2 - 0.0147R + 0.3Wt 0.0701A + 9.38
27
(Segal et al. - equation for obese women)
(23) FFM (kg) = 0.000985Ht2 - 0.0387R + 0. 158Wt 0.124A + 29.612
(Gray et al. 29 - equation for obese women)
Near infra-red interactance
Body fat was estimated from measurement of near infra-red
interactance (NIRI) at the biceps, as previously described
by Elia et al. 37
Statistics
The biitii lilld 95% limit of 1agreement between
ferenc_
methods and the al ternative prediction technique or equations were calculated according to the method described by
Bland and Altman 38 - please note that this statistical
method indicates whether or not an alternative assessment
can acceptably repr-uduce estimates that would have been
507
obtained by using an existing assessment method; although,
in this study, reference methods were selected as the basis
for comparison, this statistical approach does not involve
any preconceived assumptions about which method is correct, neither does it assess potential relationships which
might exist between estimates obtained by different assessments. Possible relationships between the magnitude of the
estimate and the difference between methods were scrutinized.38
Results
Comparisons of methods (bias and 95% limits of agreement) for estimates of body fat (% body weight), fat-free
mass (kg) and total body water (l), are presented in Tables
2, 3 and 4 for reference methods, weight/height prediction
equations and whole body impedance/resistance prediction
instruments and equations and skinfold thickness and near
infra-red interactance measurements, respectively. In general, wherever there was a positive or a negative bias
between a particular reference method and its prediction
from specific measurements, this was also found to be true
for all the alternative reference methods and the same interpretation or prediction (see Tables). Reference methods
(three-component model, densitometry, deuterium dilution
and also total body potassium) provided better estimates of
the body composition assessments obtained by other reference methods than predictions based on alternative bedside
methods (equations incorporating weight and height,
whole-body bio-electrical impedance or resistance, skinfold
thicknesses and near infra-red interactance).
Tables 3 and 4 show the bias and 95% limits of agreement between the reference assessments of body composition and equations incorporating various combinations of
weight and height (Table 3), bio-electrical impedance/resistance measurements (Table 4) and skinfold thickness and
near-infra-red interactance measurements (Table 4). These
Tables also indicate which reference method was used to
derive the particular prediction equation and the sample
type or population on which it was originally based.
Clearly, application of the vast majority of these interpretations to the obese subjects in this study is associated with
substantial errors. This is demonstrated by large limits of
agreement between methods, irrespective of the magnitude
of the particular bias. In a majority of instances this poor
agreement was demonstrated despite the presence of very
good associations between estimates (correlation coefficients of associations between methods were all very high,
often in excess of 0.9 - not shown). In many instances
(indicated in the Tables by a superscript + or -) the difference between methods became more positive (+) or more
negative (-) with increasing magnitude of the estimate.
However, in no instance did the difference between methods become obviously larger or smaller with increasing
magnitude of the estimate and so the use of log plots was
not indicated.38
With the use of the three-component model, the density
of fat-free mass was found to be 1.104 ± 0.006 kg/I (mean
± standard deviation), with a range of 1.093 - 1.117 kg/I.
The hydration fraction of fat-free mass was 0.712 ± 0.016
(i.e. 71.2% ), with a range of 68.2 - 75. l %.
Discussion
The extent of variability in density and hydration fraction
of the fat-free mass of a specific group of obese, otherwise
healthy, Caucasian women was assessed using values
obtained with the three-component model. Because of the
nature of body composition calculations, the apparently
narrow ranges of results for the fat-free mass observed here
(mean density 1.104 kg/I, range 1.093 kg/I to 1.117 kg/I;
mean hydration 71.2%, range 68.2% to 75.l % ) outwardly
conceal major implications for individuals using multicomponent models. Small discrepancies in the density of
fat-free mass of about 0.005 kg/I, for example, will result in
body fat estimates being in error by about 2.5% fat as %
Table 2 Comparison of various body composition assessments obtained using reference methods (see text)*: bias and 95% (± 2 s.d.)
limits of agreement"*
Deuterium
dilution
Three-component
model
- 1.2 ± 6.2
-0.9 ± 3.1
1.8 ± 8.8
0.3 ± 3.1
2.3 ± 8.6
2.3 ± 8.4
1.2 ± 5.1
0.8 ± 2.6
- 1.4 ± 8.2•
- 0.4 ± 2.8
- 2.1 ± 8.s•
- 1.9 ± 7.9•
Densitometry
Reference methods
(a) Body fat{% body weight)
Deuterium dilution (n;: 15)
1bree-component model (n = 15)
Total body potassium (n 13)
=
(b) Fat-free mass (kg)
Deuterium dilution (n = 15)
1bree-component model (n 15)
Total body potassium (n = 13)
=
*Reference method/model assessment (top of Table) minus alternative method (left hand side of Table);
*To obtain equivalent figures for comparison of estimates of total body water. multiply the values for fat-free mass by a factor of 0. 72;
••Values for the bias forfat-free mass as % of body weight are equal and opposite to those for % fat. and the 95% limits of agreement are equal for both.
Those for bias for kg fat are equal and opposite to those for fat-fru mass, and the 95% limits of agreement are equal for both (see Bland and Altman.
1986);
•The differena between methods is significantly related to the magnitude of measurement (difference becomes more positive with increasing magnitude see Bland and Altman, 1986).
508
. Tllble 3 Comparison of various body composition assessments obtained using equations incol'.J)Oratlng weights and heights (with or
without a factor for age) against reference methods and three-component model (see text)*: bias and. 95% (:1: 2 s.d.) limits of agreement..; n = 15
··
Equation number.and source
(see text)
(a) Body fat(% body weight)
(I) Black et al. (1983)
(2) Garrow and Webster (1985)
(3) Deurenberg et al. (1991)
(4) Pullicino et al. (1990) - with age
(5) Dossing et al. (1982)
(6) Bruce et al. (1980)
(7) Boddy et al. (1972)
(8) Pullicino et al. (1990) - without age
(9) Hume and Weyers (1971)
(10) Watson et al. (1980)
(11) Moore et al. (1963)
(b) Fat-free mass (kg)
(I) Black et al. (1983)
(2) Garrow and Webster (1985)
(3) Deurenberg et al. ( 1991 )
(4) Pullicino et al. ( 1990) - with age
(5) Dossing et al. (1982)
(6) Bruce et al. (1980)
(7) Boddy et al. (1972)
(8) Pullicino et al. ( 1990) - without age
(9) Hume and Weyers (1971)
(10) Watson et al. (1980)
(I I) Moore et al. (1963)
Prediction equation derived against:
Densitometry
Deuterium
dilution
Three-component
model
Mainly lean/some obese
Mainly obese/some lean
Mainly lean/some obese
Mainly lean
Mainly lean
Mainly lean
Mainly lean
Mainly lean
Mainly lean/some obese
Lean and obese
Mainly lean
-9.1±14.70.5 ± 8.6
- 6.9 ± 11.3-11.7±9.7
7.3 ± 8.5
3.6± 8.1
-5 .4 ± 9.1
-12.5±11.4
0.5 ± 8.9
1.8 ± 8.4
- 3.0 :I: 10.2-
-8.0± 17.21.7 ± 7.2
- 5.8 ± 12.1- 10.6 ± 7.9
8.4 ± 7.2
4.8 ± 7.0
-4.3 ± 8.0
-11.3 ±9.51.6 ± 7.3
2.9 ± 7.5
- 1.9 :I: 11.3-
- 8.3 ± 15.81.4 ± 7.4
-6.1±11 .5-10.9 ± 8.5
8.1±7.3
4.5 ± 6.9
- 4.6 ± 8.2
-12.5 ± II.41.3 ± 7.7
2.6:1: 7.4
- 2.2 :t: I0.4-
Mainly lean/some obese
Mainly obese/some lean
Mainly lean/some obese
Mainl y lean
Mainly lean
Mainly lean
Mainly lean
Mainly lean
Mainly lean/some obese
Lean and obese
Mainly lean
12.0:t: 23.I
-0.7 ± 8.9
9.0±17.3+
13.5 :I: 11.9•
- 8.1±9.8
-4.3 :I: 10.0
6.5 ± 9.6•
14.6 :I: 14.o+
-0.4 :I: 8.7
-2.3 :t: IO. I
4.5 :I: 14.1+
10.8 ± 24.7
- 1.9 :I: 8.2
7.8 :I: 18.I+
12.3 :t: 11.?+
-9.3 ±9.1
-5.5±9.3
5.3 ± 9.3•
13.4 :I: 13.8•
-1.7±7.9
- 3.5 ± 9.4
3.2 :I: 14.8+
11.2 :I: 23.6
:I: 8.1
8.2 :I: 17.4•
12.7 :I: 11.4•
-8.9±9.1
-5.1 ±9.3
5.7 :I: 9.o+
13.8 ± 13.5+
- 1.3 :I: 7.8
- 3.1±9.4
3.7 ± 14. t•
Reference method
Population
d
TBW/d!fBK
d
TBW
TBW
TBW
TBK
TBW
TBW
TBW
TBW
d
TBW/d!fBK
d
TBW
TBW
TBW
TBK
TBW
TBW
TBW
TBW
- 1.5
*Reference method/model assessment (top of Table) minus weight and height prediction equation (left hand side of Table);
*To obtain eqUivalent figures for comparison of estimates of total body water, apply a factor of 0. 72 to the values shown for iat-free mass;
**Values for the bias for fat-free mass as % of body weight are equal and opposite to those for % fat. and the 95% limits of agreement are equal for both.
Those for the bias for Kg fat are equal and opposite to those for fat-free mass, and the 95% limits of agreement are equal for both (see Bland and Altman.
1986);
•The difference between methods is significantly related to the magnitude of measurement (difference becomes more positive with increasing magnitude see Bland and Altman, 1986).
-The difference between methods is significantly related to the magnitude of measurement (difference becomes more negative with increasing magnitude see Bland and Altman, 1986).
Abbreviations: d = densitometry
TBW = Total body water
TBK = Total body potassium
Table 4 Comparison of various body composition assessments obtained using alternative prediction methods incorporating bio-electrical impedance (with or without weights and heights), skinfold thickness and near infra-red interactance measurements against reference methods and three-component model (see text)*: bias and 95% (:1: 2 s.d.) limits of agreement*"; n = 15
Equation number and source
(see text)
Prediction equation derived against:
Reference method
Densitometry
Deuterium
dilution
Three -component
model
- 7.2 ± 24.5- l.9±7.6
-6.I ± 11.4
-5.2 ± 10.8
- 6.0± 24.7-0.7 :I: 6.8
-4.9 ± 9.2-4.0:t: 8.8
-6.3 ± 24.6-1.0± 6 Z
- 5.2 ± 10.0-4.3 ± 9.5-
6.9 ± 8.4
-4.9 :I: 11.3
3.2 :I: 9.4
-0.8±7.8
- 7.1:I:11.2
-3.4 ± 7.6
5.2 :I: 8.3
5.2 :I: 8.6•
0.8 :I: 9.9
I.I :I: 8.5
-0.4 :I: 7.9+
8.1:I:6.9
-3.7 :I: 9.24.3 :I: 7.4
0.4 :I: 6.5
-5.9 ±9.2-2.3 :I: 6.2
6.4 :I: 6.8•
6.4 :I: 8.s+
2.0± 8.1
2.3 :I: 6.5
0.7 :I: 7.1•
7.8 :I: 7.1
-4.0 :I: 10.04.0± 8.0
0.1:I:6.5
-6.2 :I: 9.9-2.6± 6.3
6.1 ±6.9
6.1:I:7.8•
1.7 :I: 8.6
2.0 :I: 7.0
0.4 :I: 6.8•
Population
(a) Body/at(% hotly weight)
Bio-electrical impedance instruments
(a) Valhalla I990B (see Elia, 1992)
Cbl Bodyst!t-500
(c) Maltron model BT-905
(d) E-Z comp 1500
Equation number and source
(see text)
Prediction equation derived against:
Reference method
(12) Lohman (see Graves et al. 1989)
d
(13) Lukaski et al. (1986)
d
(14) RJL (see Van Loan and Mayclin, 1987)
d
(15) Segal et al. (1988) for non-obese
d
(16) Deurenberg et al. (1989)
d
(17) Gray et al. (1989) for non-obese
d
(18) Hodgdon and Fitzgerald (1987)
d
(19) Van Loan and Mayclin (1987)
d
(20) Kushner and Schoeller (1986)
TBW
(21) Heitmann (1990)
TBW/TBK
(22) Segal et al. (1988) for obese
d
Population
Unreported
Mainly lean/some obese
Unreported
Lean
Unreported
Lean
Mainly lean/some obese
Mainly lean/few obese
Lean and obese
Lean and obese
Obese
509
Table 4 Continued
Prediction equation derived against:
Equation number and source
(see text)
Reference method
Population
d
TBW
TBW
d
d
d
Obese
Unreponed
Mainly lean/few obese
Mainly lean/few obese
Lean and obese
Mainly lean/few obese
Densitometry
Deuterium
dilution
Three-component
model
-6.7 ± 7.4
- 7.6 ± 10.4
-7.3 ± 10.5
-4.0± 11.3
3.2 ± 10.2-4.1±18.7-
-5.6 ± 6.5
-6.4 ± 8.3
- 6.2 ± 8.4
-2.9 ± 9. 14.3 ± 9.7- 3.0 ± 18. J-
- 5.9±6.3
-6.7 ± 9.0
- 6.5±9.1
-3.2 ± 10.04.0 ± 9.6- 3.3 ± 18.3-
= 11)
5.9 ± 10.J+
8.9 ± 7.7'
7.1 ± 11.3•
9.7 ± 9.8•
6.8 ± 10.2·
9.6±8.1•
Bio-electrical impedance instruments
(a) Valhalla 1990B (see Elia, 1992)
(b) Bodystat-500
(c) Maltron model BT-905
(d) E-Z comp 1500
11.4 ± 34.8
2.4 ± 7.9•
7.5 ± I t.8•
6.5 ± 10.9•
10.1 ± 35.4
1.2 ± 7.7•
6.3 ± 11.1·
5.3 ± I0.3·
10.5 ± 34.9
l.6 ± 7.2·
6.7 ± 11.1·
5.7 ± 10.2'
- 7.9 ± 10.6
6.2 ± 11.2·
-3.3 ± 8.3
0.8 ± 8.0
8.7 ± 12.0·
3.9 ± 7.8
-6. I ± 10.7
-6.6 ± 13.3- 0.4 ± 8.5
- l.4 ± 8.8
0.0 ± 9.4
7.4 ± 7.9
9.0 ± J J.3•
8.7 ± 11.3•
5.2 ± 10.9•
-2.6 ± 10.4
6.9 ± 24.4
-9.1±9.5
5.o ± 10.5•
-4.5±7.1
-0.5 ± 7.2
7.4 ± 11.5'
2.7 ± 7.1
- 7.3 ± 9.7-7.9± 12.6- l.7 ± 7.5•
- 2.6±7.6
- 1.2 ± 8.6
6.1±7.2
7.8 ± 10.s+
7.5 ± 10.5•
4.0± 10.1·
-3.9 ± 10.2·
5.6 ± 24.5
- 8.7 ± 9.75.4 ± 10.5•
-4.1 ±7.2
-0.0±7.1
7.8 ± I t.4•
3.1±6.9
-6.9 ± 9.8- 7.5 ± 12.7- 1.3 ± 7.5
-2.2 ± 7.7
-0.8 ± 8.5
6.5 ± 7.0
8.2 ± 10.5•
7.9 ± 10.s+
4.4± 10.1·
-3.5 ± 9.8
6.1±24.2
- 7.5 ± 15.0- 10.8 ± 14.9-
- 8.7 ± 14.8- 11.8 ± 15.9-
- 8.3 ± 14.5- 1 i.5 ± 15.2-
(23) Gray et al. ( 1989) for obese
(24) Holtain (see Fuller and Elia, 1989)
(25) Hoffer (data from Hoffer et al. 1969)
(26) Lukask.i et al. (1985)
(27) Segal et al. (1985)§
(28) Khaled (1988)
Miscellaneous methods
Sk.infold thickness (n = 15)
Near infra-red interactance (n
(b) Fatjree mass (kg)
Prediction equation derived against:
Equation number and source
(see text)
Reference method
d
(12) Lohman (see Graves et al. 1989)
d
(13) Lukask.i et al. (1986)
d
(14) RJL (sec Van Loan and Mayclin, 1987)
d
(15) Segal et al. (1988) for non-obese
d
(16) Deurenberg et al. (1989)
d
(17) Gray et al. (1989) for non-obese
(18) Hodgdon and Fitzgerald (1987)
d
(19) Van Loan and Mayclin (1987)
d
TBW
(20) Kushner and Schoeller ( 1986)
(21) Heitmann (1990)
TBWrrBK
(22) Segal et al. (l 988) for obese
d
(23) Gray et al. (l 989) for obese
d
TBW
(24) Holtain (see Fuller and Elia, 1989)
TBW
(25) Hoffer (data from Hoffer et al. 1969)
d
(26) Lukask.i et al. (l 985)
(27) Segal et al. (l 985)§
d
(28) Khaled (1988)
d
Miscellaneous methods
Sk.infold thickness (n = 15)
Near infra-red interactance (n
Population
Unreponed
Mainly lean/some obese
Unreponcd
Lean
Unreponed
Lean
Mainly lean/some obese
Mainly lean/few obese
Lean and obese
Lean and obese
Obese
Obese
Unreponed
Mainly lean/few obese
Mainly lean/few obese
Lean and obese
Mainly lean/few obese
= 11)
*Reference method/model assessment (top of Table) minus alternative method (left hand side of Table);
*To obtain equivalent figures for comparison of estimates of total body water, apply a factor ofO. 72 to the values shown for fat-free mass;
**Values for the bias for fat-free mass as % of body weight are equal and opposite to those for % fat, and the 95% limits of agreement are equal for both.
those for the bias for Kg fat are equal and opposite to those for fat-free mass, and the 95% limits of agreement are equal for both (see Bland and Altman,
1986);
•The difference between methods is significantly related to the magnitude of measurement (difference becomes more positive with increasing magnitude see Bland and Altman, 1986).
-The difference between methods is significantly related to the magnitude of measurement (difference becomes more negative with increasing magnitude see Bland and Altman, 1986).
§Interprets impedance in terms of body density and then to estimates of body composition.
Abbreviations: d = densitometry
1HW = Total body water
TBK =. Tota/body potassium
body weight (in a reference man of 15% fat as body weight,
this represents a relative error of about 17%). The ranges of
values obtained reflect, in part, biological variation and, in
part, precision of methodology (precision for the reference
methods used here has been reported previously4). In this
study, methodological imprecision4 in estimating the density
(s.d. 0.002 kg/I) and hydration (s.d. 0.7%) of fat-free mass
accounts for less than one half of the measured variability
(s.d. 0.006 kg/I and s.d. 1.6%, respectively). Therefore,
biological variation makes an important contribution to
variability in these estimates. However, despite this variability, the calculated mean value (1.104 kg/I) for the
density of fat-free mass is close to that constant (1.1 kg/I)
traditionally used in densitometry and also close to the
mean value (l.097 kg/I, s.d. 0.006 kg/I) obtained for a
group of non-obese women (calculated, using the threecomponent model, on the data of Fuller et al. 4 ) Therefore,
we feel that there is no compelling reason to change the
classic assumptions or calculations pertaining to estimation
of body composition in obese women by densitometry.
510
..
Deurenberg et al. 9 had previously proposed such a revision
based on the assumption that additional water (protein and
mineral is assumed to remain constant) associated with
excess adipose tissue deposition would increase the mean
hydration fraction of fat-free mass (not observed in this
study) and consequently decrease its density (also not
observed here). The hydration of fat-free mass obtained in
this study (71.2%) was close to that traditional value (72%)
proposed by Siri, 1 1 and that calculated from data presented
previously (73.0%) in lean women.4 However, the suggestion that there may be a need to change the traditional
assumptions and calculations used in the obese was not
based on actual estimates of the hydration fraction and density of the fat-free mass, but on speculative assumptions.
Fuller and Elia 10 argued that obesity is not only associated
with excess water, but it may also be associated with additional protein and mineral which would tend to increase the
density of fat-free mass and counteract the effect of the
extra water. (Despite the observed differences between
obese and lean women being apparently of little material
importance, it should be noted that the mean density of fatfree mass was significantly higher, P < 0.01, and the mean
hydration significantly lower, P < 0.01, in this group of
obese women: and, although small, this trend is in the
opposite direction to that proposed by Deurenberg et al.) 9
The outcome of any debate surrounding the extent of these
changes, and their concomitant effect on the density of the
fat-free mass, 10 is the apparent need for more detailed measurements using the four (or more) - component modeI 1.4
which incorporates direct measurements of total body bone
mineral. Although the four-component model is limited by
an assumed constant ratio of total body bone mineral to
total body mineral, its use negates the need for assuming a
constant ratio of protein to total body mineral (a central
assumption of the three-component model) which may not
be universally applicable and, in particular, this ratio may
differ between lean and obese women. Nevertheless, if the
ratio of protein to mineral was to change by about 20%, this
would only effect the estimated density of fat-free mass by
about 0.004 kg/l to 0.005 kg/l.
Of the body composition techniques that were not incorporated into the construction of the three-component
model, total body potassium appeared to provide the best
agreement with the established reference methods. This is
despite the poor precision (> 5% 39) associated with total
body potassium counting which may be due to the two relatively insensitive sodium iodide crystals used for detecting
40
K emissions. Furthermore, the extent of attenuation of
these emissions is probably greater in the obese than in lean
subjects, and so geometric considerations assume greater
significance in this group. The better agreement between
total body potassium and reference method estimates of
body composition obtained in this group of obese subjects,
compared to the non-obese group studied previously, 4 may
be explained, in part at least, by the fact that calibration of
the··AOK counter was achieved against 42 K in a group consisting predominantly of obese individuals. Furthermore,
there is some debate surrounding the most appropriate
value to apply as constant for the potassium content of fatfree mass (discussed by Burkinshaw and Cotes40 ) . In this
study, an assumed · constant value for females of 60
mmol/kgFFM 13 was applied. A slight discrepancy of only 2
mmol/kgFFM could contribute a mean systematic error of
2.1 % fat (as body weight) in this particular group of obese
women (mean weight 112kg and 48% fat). In contrast,
skinfold thicknesses are notoriously more difficult to obtain
and interpret in the grossly obese. There may be major
practical difficulties (limited size of_ calipers, site location
differences, variation in compressibility and so on) that
conspire to create poor reproducibility. The inter-observer
reproducibility for skinfold thickness measurements in nonobese subjects is known to be relatively poor in comparison
with some other bedside techniques, 41 and is probably more
so in the obese. In addition, relatively few grossly obese
subjects were involved in the original derivation of equations intended to interpret skinfold thickness measurements
in terms of body density and body composition, 36 and so
some of our subjects may have been outside the reliable
range (see Lohman, 42 for a comprehensive review of different interpretations of skinfold thickness measurements).
Of the anthropometric prediction equations incorporating
body mass index (Table 3), that of Garrow and Webster 15
apparently agrees most closely with body composition estimated by densitometry, deuterium dilution and the threecomponent model. This is not surprising since this equation
was derived from a sample population which consisted of a
number of women attending an obesity clinic. We are also
able to confirm the observation of Deurenberg et al. 16 that
their prediction equation actually overestimates body fat
when applied to the obese (Table 3), which supports the
view that prediction equations should only be applied to
appropriate populations. The other exclusively anthropometric prediction equations examined in this study contain
terms involving weights and heights as separate entities. In
general, those predictions that were derived against measures of total body water using isotope dilution techniques 18·20·21 are better predictors of reference methods and
the three-component model than those equations attempting
to predict fat-free mass and that were derived against densitometry. In fairness, few of these equations were derived
in sample groups containing obese subjects, nor was their
use in the obese necessarily advocated by these particular
authors. The Moore et al. 22 equation does not , involve
height, which might explain its lack of agreement with the
reference methods (although height in conjunction with
weight may provide an index of body fat, height alone
should not be considered to be an independent indicator of
adiposity). 15 •43 In addition, the equation of Dossing et al. 17
was regressed against antipyrine distribution space, which
may not accurately reflect either isotope dilution space or
total body water space.
Interpretation of bio-electrical impedance measurements
in terms of body composition has been advocated for both
lean and obese subjects. Previous studies from our laboratory have shown that use of only certain of the many available bio-electrical impedance ·predietions are valid in nonobese subjects, 2.4·6 but obese subjects were not always
included in these particular evaluations. In this study,
which does compare predictions of body composition in
obese females, the Bodystat-500 package appears to agree
511
better with the various reference methods, including the
three-component model, than other commercial bio-electrical impedance packages, some of which may result in
major inaccuracies (see Table 4). The bio-electrical impedance equations derived from studies in the obese (and,
. therefore, advocated for use in the obese) appear to be the
most promising.27 •29 Although the Gray et al. 29 obese specific equation has a relatively large bias, there is no obvious
trend with increasing magnitude of the estimate, and so the
bias could conceivably be removed to predict reference
method estimates more accurately.38 It should be noted that
the non-obese specific equations of these same authors 27 ·29
are almost as good predictors of body composition in this
particular group of obese females as are the obese-specific
equations. These comparative findings may reflect the relatively large numbers used in the comprehensive derivation
of the Segal et al. 27 prediction equations.
Wherever the use of particular prediction equations in
obese females has not been openly advocated, no criticism
of either the female specific, male specific or miscellaneous
predictions (or equations derived from published data) is
intended. However, if these non-specific equations were to
be applied to groups of obese females by extrapolation
(beyond the limits of their derivations), substantial errors
could occur. Furthermore, for non-obese subjects it has
been argued that no great advantage is gained with the
inclusion of bio-electrical impedance in prediction equations incorporating weight and height over those that incor-
porate weight and height (or body rnass index) only. 5•44 The
suggestion that this also appears to hold true for the
obese, 45 is supported by the results of this study (compare
results presented in Table 3 with the equivalent values in
Table 4).
Finally, because of the small number of measurements
involved, it may be inappropriate to generalise the implications of this study further than to those with characteristics
similar to this specific group of obese female subjects (e.g.
to men or to other obese populations). Furthermore, the
limited group size also prevents definition of the effects of
other variables, such as age or fat distribution. Nevertheless, in summary, estimates are presented of the density and
hydration of fat-free mass in a group of obese female subjects that are close to those obtained previously in nonobese subjects, and those constant values applied to traditional reference methods (densitometry and deuterium dilution). Attention is also drawn to the dangers of attempting
to estimate body composition in the obese using prediction
equations (e.g . based on bio-electrical impedance) originally derived in lean individuals.
Acknowledgements
The authors are indebted to Dr W.A. Coward, for discussions during this project, to Mr K. Szaz for the whole-body
potassium measurements and for very helpful advice, and
to Mr J. Ashford for help with the water measurements.
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