International Journal of Obesity (2012) 36, 1135 -- 1140
& 2012 Macmillan Publishers Limited All rights reserved 0307-0565/12
www.nature.com/ijo
TECHNICAL REPORT
The current standard measure of cardiorespiratory fitness
introduces confounding by body mass: the DR’s EXTRA study
K Savonen1,2, B Krachler1,3, M Hassinen1, P Komulainen1, V Kiviniemi4, TA Lakka1,5 and R Rauramaa1,2
OBJECTIVE: Cardiorespiratory fitness is currently estimated by dividing maximal oxygen consumption (VO2max) by body weight
(per-weight standard). However, the statistically correct way to neutralize the effect of weight on VO2max in a given population
is adjustment for body weight by regression techniques (adjusted standard). Our objective is to quantify the bias introduced
by the per-weight standard in a population distributed across different categories of body mass.
DESIGN: This is a cross-sectional study.
SUBJECTS AND METHODS: Baseline measures from participants of the Dose-Responses to Exercise Training Study (DR’s EXTRA),
635 men (body mass index (BMI): 19--47 kg m2) and 638 women (BMI: 16--49 kg m2) aged 57--78 years who performed oral
glucose tolerance tests and maximal exercise stress tests with direct measurement of VO2max. We compare the increase in
VO2max implied by the per-weight standard with the real increase of VO2max per kg body weight. A linear logistic regression
model estimates odds for abnormal glucose metabolism (either impaired fasting glycemia or impaired glucose tolerance or
Type 2 diabetes) of the least-fit versus most-fit quartile according to both per-weight standard and adjusted standard.
RESULTS: The per-weight standard implies an increase of VO2max with 20.9 ml min1 in women and 26.4 ml min1 in men
per additional kg body weight. The true increase per kg is only 7.0 ml min1 (95% confidence interval: 5.3--8.8) and 8.0 ml min1
(95% confidence interval: 5.3--10.7), respectively. Risk for abnormal glucose metabolism in the least-fit quartile of the population
is overestimated by 52% if the per-weight standard is used.
CONCLUSIONS: In comparisons across different categories of body mass, the per-weight standard systematically underestimates
cardiorespiratory fitness in obese subjects. Use of the per-weight standard markedly inflates associations between poor fitness and
co-morbidities of obesity.
International Journal of Obesity (2012) 36, 1135 -- 1140; doi:10.1038/ijo.2011.212; published online 22 November 2011
Keywords: abnormal glucose metabolism; body mass; cardiorespiratory fitness; maximal oxygen uptake
INTRODUCTION
The original domain of measuring maximal oxygen uptake
(VO2max) was comparing fitness between athletes.1 More recently,
low VO2max was found to be an independent marker of
cardiovascular and metabolic risk in the general population.2,3
Comparisons of cardiorespiratory fitness can be based on
group-means of VO2max (mean standard) or by adjusting VO2max
for body weight (adjusted standard). However, dividing groups’
mean VO2max by mean body weight (per-weight standard) is the
most commonly used reference standard in research,4 and is used
in the current clinical guidelines.5
Problems arising from the use of a fixed ratio as standard were
described as early as 1949 by Tanner in his classical paper ‘Fallacy
of Per-Weight and Per-Surface Area Standards, and Their Relation to
Spurious Correlation’:6 Unless the regression line, representing the
true association between two variables in a population, passes
through the origin the per-weight standard introduces a bias.
Later, these principles were applied to fitness and body
size, claiming that the per-weight standard systematically underestimates fitness in heavy individuals.7,8 This has been shown for
athletes.9,10 Whether the per-weight standard is a better estimate
of the association between body mass and VO2max in today’s
increasingly obese populations is unknown.
1
The aim of the present study is to describe the association
between body weight and VO2max in a population-based sample
of middle aged and elderly men and women. Furthermore, we
intend to quantify any bias introduced by the per-weight standard
into models of fitness and morbidity. To demonstrate confounding by obesity we choose a common comorbidity of obesity
as outcome: abnormal glucose metabolism (AGM) defined as
either impaired fasting glycaemia or impaired glucose tolerance,
or Type 2 diabetes.
PATIENTS AND METHODS
We use baseline data of the Dose-Responses to Exercise Training Study
(DR’s EXTRA), which is an ongoing 4-year randomized controlled trial on
the health effects of regular physical exercise and diet; a detailed
description and flow chart have been published, elsewhere.11 Briefly, an
age-stratified sample of 1500 men and 1500 women aged 55 - 74 years was
randomly selected from the population register of the city of Kuopio, a
municipality of 93 000 inhabitants in Eastern Finland. In total, 1410
individuals completed baseline examinations in 2005 - 2006. After further
exclusions (three Type 1 diabetes, 134 incomplete data on VO2max or
glucose metabolism), we arrived at the present study population of 1273
individuals (635 men and 638 women) aged 57 - 79 years. (Supplementary
Kuopio Research Institute of Exercise Medicine, Kuopio, Finland; 2Department of Clinical Physiology and Nuclear Medicine, Kuopio University Hospital, Kuopio, Finland;
Occupational and Environmental Medicine, Department of Public Health and Clinical Medicine, Umeå University, Umeå, Sweden; 4Information Technology Centre, University of
Eastern Finland, Kuopio, Finland and 5Institute of Biomedicine/Physiology, University of Eastern Finland, Kuopio, Finland. Correspondence: Professor R Rauramaa, Kuopio
Research Institute of Exercise Medicine, Haapaniementie 16, Kuopio 70100, Finland.
E-mail: Rainer.Rauramaa@uef.fi
Received 13 April 2011; revised 23 September 2011; accepted 3 October 2011; published online 22 November 2011
3
Cardiorespiratory fitness and body mass
K Savonen et al
1136
Figure 1). The study protocol was approved by the Ethics Committee of
the University of Kuopio. All participants gave written informed consent.
Assessment of cardiorespiratory fitness
Cardiorespiratory fitness is assessed during a symptom-limited maximal
exercise stress test to exhaustion on an electrically braked cycle ergometer
(Ergoline, Bitz, Germany). The tests are supervised by physicians according
to a standardized test protocol with a warmup of 3 min at 20 W and a 20-W
increase of workload per minute. Participants are verbally encouraged
to maximal exertion. Oxygen consumption is measured directly by the
breath-by-breath method using the respiratory gas analyzer (Sensor
Medics, Yorba Linda, CA, USA). VO2max is defined as the mean of the
three highest values of the averaged oxygen consumption measured
consecutively over 20-s intervals. A total of 98% of the subjects achieved
the respiratory exchange ratio of X1.1.
Other assessments
Blood samples are taken after a 12-h fast. Fasting plasma glucose is
measured by the hexokinase method. A 2-h oral glucose tolerance test
with a 75-g glucose load is performed after a 12-h fast on all individuals
except for those with established diagnosis of diabetes. We classify
subjects according to the World Health Organization criteria, as having
normal glucose tolerance if the fasting glucose is o6.1 mmol l1 and the
2-h value on glucose tolerance test is o7.8 mmol l1. Type 2 diabetes
mellitus, impaired fasting glucose or impaired glucose tolerance from our
combined outcome of AGM. Individuals with known Type 1 diabetes are
excluded. Height and weight are measured by trained personnel.
Statistical analyses
To determine an individuals’ level of fitness, the measured VO2max is
compared with the gender-specific group results among participants with
a normal glucose metabolism. The three standards define differently the
VO2max at which an individual is considered to have a normal (i.e., neither
high nor low compared with the group) level of fitness ¼ expected normal
VO2max (compare Figures 1 and 2).
(i) An individual’s expected normal VO2max according to the per-weight
standard ¼ individual’s body weight multiplied with genderspecific
group mean VO2max in ml kg1 min1.
(ii) An individual’s expected normal VO2max according to the adjusted
standard ¼ individual’s body weight inserted as independent and
VO2max in ml min1 as dependent variable in gender-specific linear
regression equations.
(iii) An individual’s expected normal VO2max according to mean
standard ¼ Gender-specific group mean, irrespective of the individuals’ body weight.
Fitness is estimated based on the difference between actually
measured and expected normal VO2max for men and women
separately. Graphically, this corresponds to the vertical distance of
observed VO2max to lines (i), (ii) and (iii) in Figures 1 and 2.
Quartiles of actually measured VO2max as percentage of expected
normal VO2max are our quartiles of fitness.
The resulting quartiles are inserted into a logistic regression with AGM as
the outcome. We performed conditional logistic regression analysis stratified
for gender and adjusted for 5-year age groups. For additional adjustment we
used body mass index (BMI) as a continuous variable. The proportion of
excess risk explained by BMI is estimated according to the equation given by
Brotman:12 1(ln ORA/ln ORU), where ORA is the odds ratio for abnormal
glucose regulation conferred by low fitness after adjusting for BMI and ORU is
the unadjusted odds ratio. All reported P-values are two-sided. We use the
Statistical Analysis System (SAS for Windows, version 9.2, SAS Institute,
Cary, NC, USA) for all statistical evaluations.
RESULTS
Characteristics of subjects according to gender and BMI category
are shown in Table 1. Mean VO2max per kg body weight decreases
International Journal of Obesity (2012) 1135 - 1140
markedly with increasing BMI, whereas there is a slight increase in
the absolute values. There is a marked increase in the proportion
of subjects with abnormal glucose metabolism with increasing
BMI.
Associations between VO2max and body weight for women and
men are shown in Figures 1 and 2. The per-weight standard
implies an increase of VO2max with 21 ml min1 in women and
26.5 ml min1 in men per additional kg body weight. The true
increase per kg is only 7.0 (95% confidence interval: 5.3 -- 8.8) and
8.0 (95% confidence interval: 5.3 -- 10.7) ml min1, respectively,
(adjusted standard).
Residual analysis (lower panels) shows that the per-weight
standard is weight-neutral only in a narrow band of weight and
BMI. Mean residuals are positive in light individuals and negative
in heavier subjects. Average residuals for the weight-adjusted
standard of fitness are close to 0 across most of the range of
weight and body mass.
Distribution of Body mass categories within quartiles of fitness
and fitness-associated odds for AGM are shown in Table 2.
According to the per-weight standard, the quartile with lowest
fitness contains 46% obese individuals compared with 28% for the
adjusted and 21% for the mean standard. The quartile with
highest fitness according to the per-weight standard has only 1%
obese subjects compared with 18% for the adjusted and 30% for
the mean standard. On the basis of these quartiles, odds for AGM
are highest for the least fit according to the per-weight standard
and lower for those classified as least fit according to the adjusted
and mean standards. Additional adjustment for BMI eliminates
these differences.
DISCUSSION
In this population-based sample of 635 men and 638 women, the
group mean of dividing VO2max by total body weight (per-weight
standard) does not result in a body-mass independent standard of
cardiorespiratory fitness. The actual change in VO2max per kg body
weight is much lower than that implied by the per-weight
standard. For example, for equal fitness according to the perweight standard, the weight difference between a man weighing
100 kg and one weighing 70 kg would have to be compensated by
a 800 ml min1 higher VO2max in the former. The actual average
difference is only 240 ml min1. As body weight deviates from
group mean, the gap between expected and actual fitness
increases. In lighter individuals positive mean residuals indicate
systematic overestimation of fitness. Conversely, in heavier
individuals, residuals are negative, indicating a systematic underestimation of fitness. Thus, categories of fitness based on the perweight standard are confounded by body mass.
If lack of fitness, according to the per-weight standard, is
studied as risk factor for comorbidities of obesity the resulting
associations are partly spurious. Confounding by obesity causes
some of the risk attributed to lack of fitness. This is the
phenomenon described in 1949 by Tanner.6 In our population,
use of the per-weight standard inflates the risk for AGM by 52%.
In other studies investigating the association between poor
fitness, according to the per-weight standard and adverse
metabolic outcomes (diabetes, metabolic syndrome) confounding
by body mass, explains between 25 and 50% of the observed
risk.13 - 16 Thus, use of the per-weight standard markedly inflates
the associations between poor fitness and comorbidities of
obesity.
But is it correct to regard VO2max adjusted for body weight as a
‘true’ standard of cardiorespiratory fitness? It has been claimed
that adjusting for body weight may eliminate a possible mediator
between poor fitness and health outcomes.17 Body weight is
determined by both energy intake and energy expenditure. Thus,
claiming fitness as a causative factor of body weight would require
prior adjustment for energy intake. Moreover, there is evidence
& 2012 Macmillan Publishers Limited
Cardiorespiratory fitness and body mass
K Savonen et al
1137
Women
(i) per-weight
standard
2500
2250
VO2max ml/min
2000
(ii)adjusted
standard
1750
(iii) mean VO2max
1500
1250
1000
750
500
mean weight
250
0
0
10
20
30
40
50
60
70
weight kg
Residuals: Per-Weight
Standard
50
20
60
25
70
80
weight, kg
30
90
35
80
90
100
110
Residuals: Adjusted Standard
100
110
40
BMI, kg/m2
50
20
60
25
70
80
weight, kg
30
90
35
100
110
40
BMI, kg/m2
Figure 1. Maximal oxygen uptake (VO2max) and body weight in women: Expected normal VO2max according to per-weight standard (i),
adjusted standard (ii) and mean standard (iii). Residual distribution for per-weight standard and adjusted standard by body weight and
body mass. Per-weight equation: VO2max ¼ 20.91 weight; regression equation: VO2max ¼ 951 þ 7.03 weight.
that cardiorespiratory fitness and habitual physical activity are
separate entities with separate effects on metabolic outcomes.18,19
Consequently, energy expenditure should be attributed to
habitual physical activity rather than to cardiorespiratory fitness
at a given point of time. Therefore, we regard body weight
as a potential confounder of cardiorespiratory fitness rather than a
mediator of its health effects.
Given the shortcomings of the per-weight standard and the
need of a reference population for the adjusted standard, other
& 2012 Macmillan Publishers Limited
ways to account for body size have been explored. A ratio based
on fat-free mass compares favorably with the per-weight standard
in adolescents.20 Fat mass has been shown not to influence the
maximal aerobic capacity.21 Estimating fitness, independent from
obesity, has been shown to improve the accuracy of fitness as a
predictor of cardiac function.22 Further studies are necessary to
show whether dividing VO2max by fat-free mass, rather than by
total body mass, can avoid the bias against obese individuals that
is illustrated in our results.
International Journal of Obesity (2012) 1135 - 1140
Cardiorespiratory fitness and body mass
K Savonen et al
1138
Men
(i) per-weight
standard
3250
3000
2750
(ii) adjusted
standard
VO2max ml/min
2500
(iii) mean VO2max
2250
2000
1750
1500
1250
1000
750
mean weight
500
250
0
0
10
20
30
40
50
60
70
80
weight kg
Residuals: Per-Weight
Standard
60
20
70
80
90
100
weight, kg
25
30
110
35
90
100
110
120
130
Residuals: Adjusted Standard
120
40
BMI, kg/m2
60
20
70
80
90 100
weight, kg
25
30
110
35
120
40
BMI, kg/m2
Figure 2. Maximal oxygen uptake (VO2max) and body weight in men: expected normal VO2max according to per-weight standard (i), adjusted
standard (ii) and mean standard (iii). Residual distribution for per-weight standard and adjusted standard by body weight and body mass.
Per-weight equation: VO2max ¼ 26.44 weight; regression equation: VO2max ¼ 1508 þ 8.02 weight.
To our knowledge, this is the largest population-based sample with
objectively measured VO2max and glucose tolerance in the literature.
Direct measurement of oxygen consumption during an incremental
exercise stress test is the most accurate method to determine
VO2max.23,24 The use of a non-weightbearing form of exercise should
minimize the risk for confounding by body weight. We use an
electrically braked cycle ergometer, the preferred device for exercise
testing in clinical practice. It permits accurate quantification of
International Journal of Obesity (2012) 1135 - 1140
workload and monitoring of cardiac function with a minimum of
movement artefacts. Relating VO2max to muscle mass, lean mass and
fat mass separately would have added another dimension to our
study but we have no measure of body composition.
Our results indicate that categories of fitness based on the
per-weight standard are confounded by body mass. Use of the
per-weight standard markedly inflates the associations between
poor fitness and comorbidities of obesity.
& 2012 Macmillan Publishers Limited
Cardiorespiratory fitness and body mass
K Savonen et al
1139
Table 1.
Characteristics of the study population by BMI category
BMI (men)
o 18.5
(n ¼ 0)
18.5 - 25
(n ¼ 148)
mean
Mean age, years
VO2max,
ml min1 kg1
VO2max, ml min1
Weight, kg
Height, cm
Mean BMI, kg m2
AGM, %
BMI (women)
Mean age, years
VO2max,
ml min1 kg1
VO2max, ml min1
Weight, kg
Height, cm
Mean BMI, kg m2
AGM, %
o18.5
(n ¼ 5)
mean
S.d.
S.d.
25 - 30
(n ¼ 338)
mean
S.d.
30 - 35
(n ¼ 115)
mean
435
(n ¼ 34)
mean
S.d.
S.d.
All
(n ¼ 638)
mean
S.d.
Linear trend
b-Value
P-value
67
30
(6)
(6)
66
27
(5)
(6)
66
23
(6)
(5)
64
19
(5)
(4)
66
26
(5)
(6)
1.0
3.5
o0.001
o0.001
2066
70
173
23
25
(476)
(7)
(7)
(1)
2215
82
174
27
40
(494)
(6)
(6)
(1)
2227
97
174
32
57
(481)
(8)
(6)
(1)
2170
116
174
38
88
(396)
(12)
(6)
(3)
2180
84
174
28
42
(486)
(14)
(6)
(4)
54.3
14.5
0.7
4.6
18.4
0.026
o0.001
0.032
o0.001
o0.001
18.5 - 25
(n ¼ 205)
mean
S.d.
25 - 30
(n ¼ 263)
mean
S.d.
30 - 35
(n ¼ 118)
mean
S.d.
435
(n ¼ 47)
mean
S.d.
All
(n ¼ 635)
mean
S.d.
Linear trend
b-Value
P-value
66
25
(4)
(5)
66
24
(5)
(5)
67
21
(5)
(4)
67
18
(5)
(3)
66
16
(5)
(3)
67
21
(5)
(5)
0.1
2.6
0.558
o0.001
1194
47
163
18
0
(244)
(4)
(9)
(1)
1405
59
161
23
16
(314)
(6)
(6)
(2)
1449
70
160
27
24
(315)
(6)
(6)
(1)
1491
82
159
32
40
(300)
(7)
(6)
(1)
1555
98
159
39
64
(270)
(12)
(5)
(4)
1449
71
160
28
27
(311)
(13)
(6)
(5)
49.7
12.1
0.8
5.0
14.3
o0.001
o0.001
0.001
o0.001
o0.001
Abbreviations: AGM, abnormal glucose metabolism; BMI, body mass index; VO2max, maximal oxygen uptake. AGM ¼ either impaired fasting glycemia or
impaired glucose tolerance, or type 2 diabetes.
Table 2. Distribution of body mass categories within quartiles of fitness and fitness-associated risk for abnormal glucose metabolism (AGM)
according to per-weight standard, adjusted standard and mean standard
Per-weight standard ¼ weight indexed
BMI categories, %
o 18.5
18.5 - 25
25.1 - 30
30.1 - 35
435
Odds for AGM
Model 1a
95% CI
D Adj. Standardb
Model 2c
95% CI
BMI confoundingd
Adjusted standard ¼ weight adjusted
Mean standard ¼ weight ignored
Least fit
Q2
Q3
Q4
Least fit
Q2
Q3
Q4
Least fit
Q2
Q3
Q4
0
14
40
30
16
0
19
57
20
4
0
38
48
14
0
1
51
47
1
0
1
26
45
20
8
0
25
46
19
9
0
30
47
17
5
0
31
51
16
2
1
33
46
16
5
0
29
47
17
6
0
27
47
18
8
0
21
49
23
7
5.32
3.53 - 8.02
51%
2.22
1.40 - 3.51
52%
2.61
1.70 - 3.99
2.15
1.39 - 3.31
1.00
1.46
0.99 - 2.15
1.06
0.72 - 1.55
1.00
0.96
0.67 - 1.39
1.00
1.62
1.04 - 2.52
1.00
1.33
0.90 - 1.97
1.00
0.68 - 1.47
1.00
1.51
1.04 - 2.18
101%
1.96
1.32 - 2.91
63%
1.14
0.80 - 1.64
1.54
0.98 - 2.42
2.29
1.53 - 3.40
-1.94
1.29 - 2.92
20%
1.34
0.91-1.98
1.00
0.68 - 1.48
1.00
Abbreviations: Adj., adjusted; AGM, abnormal glucose metabolism; BMI, body mass index; CI, confidence interval; VO2max, maximal oxygen uptake.
AGM ¼ either impaired fasting glycemia or impaired glucose tolerance or type 2 diabetes. aStratified for gender, adjusted for 5-year age groups. bProportion of
excess risk compared to Adjusted standard according to Brotman:12 1(ln odds ratioA/ln odds ratioU) where odds ratio A is the odds ratio for abnormal
glucose regulation conferred by low cardiorespiratory fitness adjusted for body weight (adjusted standard), and odds ratio U are the weight-indexed and
weight ignored standards, respectively. cAs Model 1 with additional adjustment for body mass index. dProportion of risk explained by BMI
confounding ¼ excess risk in Model 1 compared with Model 2, calculated according to the formula given in footnote 2.
CONFLICT OF INTEREST
The authors declare no conflict of interest.
ACKNOWLEDGEMENTS
The DR’s EXTRA study was supported by grants from the Ministry of Education of
Finland (116/722/2004, 134/627/2005, 44/627/2006, 113/627/2007, 41/627/2008),
the Academy of Finland (104943, 211119, 123885), the European Commission FP6
Integrated Project (EXEGENESIS): LSHM-CT-2004-005272, the City of Kuopio, the
Finnish Diabetes Association, the Finnish Heart Association, Kuopio University
Hospital, Päivikki and Sakari Sohlberg Foundation and the Social Insurance Institution
of Finland. KS was supported by a grant from the Finnish Medical Foundation; BK was
supported by grants from Bruno Krachler and the Swedish Council for Working Life
& 2012 Macmillan Publishers Limited
and Social Research. The funding sources had no role in the collection, analysis and
interpretation of the data or in the decision to submit the manuscript for publication.
KS and BK contributed equally to data analysis and drafting of the manuscript.
MH and PK collected and assembled data, participated in revision of manuscript.
VK participated in data analysis. TL and RR are principal investigators of the DR’s
EXTRA study and participated in revision of manuscript.
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Supplementary Information accompanies the paper on International Journal of Obesity website (http://www.nature.com/ijo)
International Journal of Obesity (2012) 1135 - 1140
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