Vol. 84, Issue 6, 2163-2170, June 1998
MODELING IN PHYSIOLOGY
Predictors of age-associated decline in maximal aerobic capacity: a
comparison of four statistical models
Mitchell J.
Rosen1,
John D.
Sorkin1,2,
Andrew P.
Goldberg1,
James M.
Hagberg1,3, and
Leslie I.
Katzel1
1 Division of Gerontology,
Department of Medicine, University of Maryland, and Geriatric
Research, Education, and Clinical Center, Geriatrics Service,
Baltimore Veterans Affairs Medical Center, Baltimore 21201;
2 Laboratory of Clinical
Investigation, Metabolism Section, National Institute on Aging,
Baltimore 21224; and
3 Department of Kinesiology,
University of Maryland, College Park, Maryland 20742
 |
ABSTRACT |
Studies
assessing changes in maximal aerobic capacity
(
O2 max) associated
with aging have traditionally employed the ratio of
O2 max to body
weight. Log-linear, ordinary least-squares, and weighted least-squares
models may avoid some of the inherent weaknesses associated with the
use of ratios. In this study we used four different methods to examine
the age-associated decline in
O2 max in a
cross-sectional sample of 276 healthy men, aged 45-80 yr.
Sixty-one of the men were aerobically trained athletes, and the
remainder were sedentary. The model that accounted for the largest
proportion of variance was a weighted least-squares model that included
age, fat-free mass, and an indicator variable denoting exercise
training status. The model accounted for 66% of the variance in
O2 max and satisfied
all the important general linear model assumptions. The other
approaches failed to satisfy one or more of these assumptions. The
results indicated that
O2 max declines at
the same rate in athletic and sedentary men (0.24 l/min or 9%/decade)
and that 35% of this decline (0.08 l · min
1 · decade1) is due to the
age-associated loss of fat-free mass.
exercise; heteroscedasticity; weighted least squares; log-linear
model; ratio
| |
INTRODUCTION |
THERE IS AN AGE-ASSOCIATED decline in maximal aerobic
capacity (O2 max) in
trained and untrained men (6, 8, 10, 13, 22). This age-associated
decline in O2 max is
due to many factors, including decreases in maximum heart rate, stroke volume, arteriovenous O2
difference, and skeletal muscle mass and an increase in adiposity (10,
13, 22). Changes in physical activity habits, leading to a sedentary
lifestyle, also contribute to the age-associated decline in
O2 max (3, 12, 17, 22, 27). There is conflicting evidence on whether regular aerobic exercise
training attenuates the age-associated decline in
O2 max (13,
25, 28).
Different statistical models have been used to analyze the
relationships among the physiological variables associated with the
age-associated decline in
O2 max. The
statistical approach employed to adjust the
O2 max for body size
and composition must be considered carefully; the approach must be
statistically valid. All other factors being equal, a larger individual
would be expected to have a higher
O2 max than a smaller
individual. To account for differences in body habitus, the simple
ratio of O2 max to a
measure of body size [e.g.,
O2 max
ml · kg body wt1 · min1
or O2 max
ml · kg fat-free mass
(FFM)1 · min1]
is often used as the dependent variable in studies of the age-related decline in O2 max (3,
12, 27). We will refer to this model as the ratio standard (RS) model.
The use of ratios as dependent variables in regression models has been
criticized for a variety of reasons (2, 9, 20, 28, 30, 31, 33), but the main drawback is that the ratio Y/X is
correlated with X (21, 32, 33). In a
classic paper, Pearson (23) showed that if X,
Y, and Z are three
random variables and X, Y, and
Z are uncorrelated, X/Z and
Y/Z are correlated under minimally
restrictive assumptions (23). In the case of
O2 max, the
O2 max/body size ratio may not make O2 max
totally independent of body size. Given the physiological and
functional importance of the
O2 max-age relationship, it is important that this relationship is assessed in
valid statistical and mathematical terms to ensure appropriate interpretation of the results.
Two alternatives to the RS model have been used in the statistical
analysis of the age-related change in
O2 max:
ordinary least-squares (OLS) regression of
O2 max on a
measure of body size, such as FFM or weight (31), and log-linear (LL)
or allometric models (20, 21). OLS and LL models are not without
problems. OLS residuals in
O2 max models are often
heteroscedastic; i.e., they increase in variability as the measure of
body habitus increases (20, 33). Heteroscedasticity can affect the
standard errors of the parameter estimates and thus adversely affect
tests of significance (24). LL models have been criticized for their tendency to overfit biological data, modeling what is sometimes a
linear phenomenon with a nonlinear model (1). Additionally, LL models
assume a zero intercept, which usually involves extrapolation well
beyond the range of observed data (1). A variant of LL is the Box-Cox
transformation (4), in which the dependent variable is raised to the
power (i.e.,
O2 max
)
that maximizes the likelihood that the model residuals follow a normal
distribution. This method has not been widely used in studies that have
examined the age-associated decline in
O2 max.
In this paper an alternative method to modeling
O2 max is proposed:
weighted least squares (WLS). WLS models retain the advantages of OLS
models, producing "best linear unbiased estimates" (BLUE) and
overcoming the problem of heteroscedasticity (16, 24). Because of the
widespread use of the RS models in studies of
O2 max, the potential
errors caused by the failure of the RS to remove the effect of body
size on O2 max, and the
potential problems caused by the heteroscedasticity inherent in OLS
models of O2 max, we
believe that further analysis of the age-related decline in
O2 max is warranted.
Therefore, we compare the results obtained from RS, OLS, LL, and WLS
models of the age-associated decline in
O2 max. In each case we
examine how well the model satisfies the general linear model (GLM)
assumptions of normality and homoscedasticity.
| |
METHODS AND MATERIALS |
Subjects
This study was approved by the Institutional Review Boards of the
University of Maryland School of Medicine and Johns Hopkins University
Bayview Medical Center. All subjects provided informed consent before
participation. Over an 8-yr period, healthy nonsmoking men, ages
45-80 yr, with no prior history of cardiovascular disease and a
wide range of body mass index (BMI) and physical conditioning status,
were recruited to participate in exercise training and weight loss
studies (14, 35). Characteristics of the subjects are summarized in
Table 1. All subjects underwent a history
and physical examination and evaluation of fasting blood chemistries. Subjects were healthy and on no medications. Exclusion criteria included history of coronary artery disease (by clinical history and
electrocardiogram), pulmonary disease, hypertension (blood pressure
160/90 mmHg), hyperlipidemia, diabetes mellitus (fasting plasma
glucose 140 mg/dl), or any other significant medical problems that
would interfere with their ability to undergo maximal exercise treadmill testing. The study sample included a cohort of 61 healthy athletes recruited from participants of the Maryland Senior Olympics and athletic clubs in the Baltimore-Washington metropolitan area and
215 sedentary subjects (35). The sedentary subjects exercised <20 min
twice per week. The athletes exercised vigorously at least four times
per week and had <25% body fat by hydrodensitometry.
Measurement of Body Composition
Height and weight were measured, and BMI was computed as the ratio of
body weight in kilograms to height in meters squared. Body surface area
in meters squared was calculated as (height in
cm)0.718 × (weight in
kg)0.427 × 0.007449 (7).
Body density was determined by hydrostatic weighing, with percent body
fat calculated after correction for residual lung volume with use of
the Siri model (29). FFM was calculated as body weight minus fat mass.
Measurement of
O2 max
An exercise treadmill test to 85% of the predicted age-adjusted
heart rate (220 
age) was performed according to the protocol of
Bruce and Horsten (5) to exclude subjects with previously undiagnosed
heart disease. On a subsequent visit the
O2 max was determined
using a modified Balke protocol, as previously described (14). The
grade of the treadmill was increased every 2 min until the subject was
exhausted and could not continue (14). The
O2 max tests
fulfilled at least two of the three following criteria:
1) the heart rate at maximal
exercise was 85% of the age-adjusted maximal heart rate,
2) the respiratory exchange quotient was >1.10, and 3) there was a
plateau in O2 consumption defined as a change in O2 consumption of
<0.2 l/min during the final two collection periods. Absolute
O2 max, measured in
liters per minute, is used in the statistical modeling.
Statistical Analysis
All statistical analyses were performed using SAS version 6.11 run on
the Windows 3.1 operating system.
Statistical models of
O2 max.
Four statistical models were used to determine the age-associated
decline in O2 max.
1) The form of the RS model is
|
(1)
|
where
X1,
X2, etc., are
independent variables, 
0,
1, etc., are parameters, and
is a normally and independently distributed error term having equal
variance for all levels of the independent variable(s) in the target
population.
2) The form of the OLS regression is
|
(2)
|
where
FFM (= X1),
X2, etc., are
independent variables, 0,
1, etc., are parameters, and
is an error term with the same properties as in
Eq. 1. OLS estimation ensures that the
residuals of the model are uncorrelated with FFM,
X2, etc. (24).
3) The univariate form of the LL
model is
|
(3)
|
where
0 and
1 are parameters and 
is an
error term. Equation 3 is referred to
as an allometric model. The multivariable form is
|
(4)
|
where FFM (=
X1),
X2, etc., are
variables related in an LL manner to
O2 max,
W1,
W2, etc., are
variables related linearly to
O2 max,
0,
1, etc., are parameters, and
is an error term. For example, when age is used in the
multivariable model, Eq. 4 becomes
|
(5)
|
One
approach to estimating the parameters of the univariate or
multivariable models is to use OLS on the logarithmic transformation of
the model, e.g.
|
(6)
|
or
|
(7)
|
An
alternative approach is to estimate the coefficients in the original
scale by use of nonlinear regression methods. In this study the former
method was used.
When the univariate form of the LL model is used, it is usual practice
to verify that the variable
O2 max/FFM
1, which is proportional to the residuals of Eq. 3, has a correlation near zero with FFM (32, 33).
4) WLS regression is identical to
OLS regression, except each subject i
receives a weight
wi. The goal of
WLS is to minimize the sums of the squares
|
(8)
|
where
the first and second terms in parentheses are the observed and
predicted O2 max
values, respectively. In OLS,
wi = 1 (for all
i). For example, if the error
variance increases along with the values of a regressor (e.g., FFM),
observations that have higher values on the regressor receive lower
weights than observations that have lower values. The model then
reflects the greater uncertainty in the predicted values at higher
values of the regressor.
If the weights are chosen to be proportional to the reciprocal of the
error variance and the other GLM assumptions are met, the WLS model has
the desirable property of producing parameter estimates that are BLUE.
Moreover, the estimated variances of the parameters will be unbiased
and so will the t-tests on which these
variances are based. If heteroscedasticity exists, the estimates of the
variance of the parameters produced by OLS are not minimum variance
estimates, so OLS estimates will not, in general, be BLUE (24).
In this study, WLS weights took the form
wi = 1/FFM
i. When this form is
used, the following assumption, known as multiplicative
heteroscedasticity, is implied
|
(9)
|
In
Eq. 9,
2i is the error variance at
the level of FFM that equals
FFMi,
2 is the error variance from
the OLS model, and 
is the parameter related to the degree of
heteroscedasticity (homoscedasticity implies = 0).
Equation 9 suggests that the variation
of the residuals of model shown in Eq. 2 increases as FFM increases. This assumption is
usually examined by plotting the fitted residuals 
against
FFM. Harvey (11) provided a method for obtaining the maximum likelihood
(ML) estimator of . Other ways of obtaining the ML estimates of
2 and have been proposed
(16).
It is possible to demonstrate that using the weights
1/FFMi is equivalent to
transforming the linear model by dividing each term by
FFM/2i (24). For example,
if FFM is the only regressor, the transformed model is
|
(10)
|
The
model can be estimated by fitting the regression on the transformed
variables.
Equation 10 shows that the variance of
the transformed residuals is constant as long as the weights
wi are
proportional to the reciprocal of the error variance. Given the usual
regression assumption that the independent variables are fixed, we can
write the variance of the error term as
|
(11)
|
Now,
apply Eq. 9, setting
2i = var(i)
|
(12)
|
There
is another interesting consequence of Eq. 10. If = 2, Eq. 10
becomes
|
(13)
|
Then,
if 0 = 0 (zero intercept),
Eq. 13 is structurally identical to
the RS model (Eq. 1) with only an
intercept term. This suggests that if = 2 and
0 = 0, the RS model
(Eq. 13) will be homoscedastic.
Moreover, if the transformation does not greatly perturb the
correlation matrix, multivariable RS models should also have this
property, given the previous assumptions.
It is possible to extend Eq. 9 to
include multiple regressors, e.g.
|
(14)
|
The
weights for WLS derived from Eq. 10
are
1/(FFM1i)HEIGHT2i.
Note that the regressors in Eq. 9 or
14 need not necessarily be regressors in the OLS model (Eq. 2).
Factors related to the age-associated decline in
O2 max.
We initially examined models that included age, FFM, body weight, fat
mass, height, BMI, body surface area, and a dichotomous exercise
training variable (ET) that denoted whether the individual was an
athlete (0 = sedentary, 1 = athlete). Body weight, fat mass, BMI,
height, and body surface area were not significant predictors in any of
the models at the 0.05 level when FFM was included and were not
included in the analyses.
To determine whether the slopes of the age-related decline in
O2 max differed
between athletes and sedentary subjects, analyses were also performed
with RS, OLS, and WLS models that included interactions between age and
ET. For each model type we obtained estimates of the age-associated
decline and effect of ET on
O2 max. Because the
LL model is log linear, it does not permit a test of the hypothesis of
parallel linear declines in
O2 max.
Contribution of skeletal muscle loss to the age-associated decline
in O2 max.
We estimated the contribution of the loss of skeletal muscle to the
decline in O2 max as
|
(15)
|
where
AGE(adjusted) and
AGE(unadjusted) are the
regression coefficients for age in the models adjusted and unadjusted
for FFM, respectively
|
(16)
|
|
(17)
|
|
(18)
|
|
(19)
|
Tests of assumptions.
A key issue in the selection of an appropriate mathematical model for
describing a set of data is whether the model fulfills the appropriate
underlying statistical assumptions. It was therefore important to
examine the distribution of the residuals in the various models for
heteroscedasticity. For OLS models that contained FFM we used the
likelihood ratio test provided by Harvey (11) to determine the presence
of multiplicative heteroscedasticity (Eqs.
9 and 14). For LL
models we assessed multiplicative heteroscedasticity by computing the
correlation between the absolute value of the residuals and FFM (24).
Even if multiplicative heteroscedasticity is not present, other forms
of heteroscedasticity may exist. We used the method of White (34) to
test for the possibility of other forms of heteroscedasticity. This
test is sensitive to heteroscedasticity if it causes the
variance-covariance matrix of the OLS estimators to vary from its
asymptotic (large sample) form (15). Variation from the asymptotic form
can result if one or more of the linear model assumptions are not
satisfied. We used the Wilks-Shapiro test to test for violations of
normality. White's test and the Wilks-Shapiro test were obtained from
SAS proc reg and proc univariate, respectively. SAS proc IML was used
to obtain the ML estimate of and to compute the likelihood ratio
test for the hypothesis = 0. An ML grid search algorithm for
estimating is available in SPSS Professional Statistics 6.1 (WLS
procedure).
| |
RESULTS |
The correlations among selected measures of body size, age, and
O2 max are shown in
Table 2. All the body size variables correlated with O2 max
(P < 0.01). Regression results for
the unadjusted and adjusted RS, OLS, LL, and WLS models are shown in
Table 3. Only variables significant at
P < 0.05 in the regression are
listed.
View this table:
[in this window]
[in a new window]
|
Table 3.
Regression results for variables significant at P < 0.05 in models
unadjusted and adjusted for body habitus
|
|
Effect of Age Unadjusted for Body Habitus
All the parameter estimates of the OLS model
|
(20)
|
were
significant at P < 0.01 (Table 3).
This model accounted for 48% of the variance in
O2 max. There was no
evidence of lack of normality (Wilks-Shapiro test,
P > 0.10) or
heteroscedasticity due to lack of fit (White's test,
P > 0.7). However, it is of interest
that multiplicative heteroscedasticity with FFM was present [Harvey's test, 
2 (1) = 4.22, P < 0.05]. There was no
significant interaction between age and ET. Therefore, the absolute
age-associated rate of decline in
O2 max, 0.36 l/min, was
the same in athletes and sedentary men. The OLS estimate of the effect
of exercise training (the coefficient of ET) was 0.78 l/min (Table 3).
All the parameters of the LL model
|
(21)
|
were
significant at P < 0.01 (Table 3).
This model accounted for 46% of the variance in
O2 max. The residuals
were normally distributed, but there was evidence of heteroscedasticity
due to lack of fit (White's test, P < 0.05). Unlike the OLS and WLS models, in the LL model the percent
decline of O2 max per
decade is independent of the baseline value. The age-associated decline was proportional to exp(0.014 AGE) = 0.986 exp(AGE).
To obtain the WLS model, the OLS model
|
(22)
|
was
adjusted for multiplicative heteroscedasticity by using weights
1/FFM0.87. All the parameter
estimates were significant at P < 0.01 (Table 3). This model accounted for 49% of the variance in
O2 max. The WLS model
met all the GLM assumptions and yielded estimates of the training
effect and of the age-associated decline that were nearly identical to
the OLS model.
Effect of Age Adjusted for Body Habitus
The RS model was
|
(23)
|
The
ratio O2 max/FFM did
not completely remove the effects of FFM; the correlation between the
ratio and FFM was 0.17 (P < 0.01). All parameter estimates for the model (Eq. 23) were significant at
P < 0.01 (Table 3). The model
accounted for 60% of the variance in
O2 max. There
was no evidence of heteroscedasticity due to lack of fit and no
correlation between the absolute residuals and FFM
(r = 0.01). However, the residuals
were not normally distributed (P < 0.02). There was no significant interaction between age and ET. Thus
the age-associated rate of decline relative to FFM was the same in
athletes and sedentary men, ~0.0034 l · kg
FFM1 · min1 · decade1.
The estimate of the ET effect due to the difference in intercept was
0.016 l/min (Table 3).
For the OLS model
|
(24)
|
all
parameter estimates were significant at
P < 0.01. The OLS model accounted
for 64% of the variance in
O2 max. There was no evidence of lack of normality or heteroscedasticity due to lack
of fit. The absolute residuals correlated with FFM
(r = 0.18, P < 0.01). Harvey's test for
multiplicative heteroscedasticity confirmed this finding:
2 (1) = 7.52, P < 0.01. A plot of the residuals
vs. FFM, in which the heteroscedasticity is depicted, is shown in Fig.
1. As in the RS model, the rates of decline
were not significantly different in athletes and sedentary men. The
calculated decline in
O2 max was
0.24 l · min1 · decade1,
and the estimate of the exercise conditioning effect was 0.96 l/min.
View larger version (24K):
[in this window]
[in a new window]
|
Fig. 1.
Diagnostic scatter plot of ordinary least-squares (OLS) residuals vs.
fat-free mass (FFM). Residuals are derived from OLS model maximal
aerobic capacity
(O2 max) = 1.84 0.024 AGE + 0.96 ET + 0.035 FFM, where ET is exercise training.
|
|
For the LL model
|
(25)
|
all
parameter estimates were significant at
P < 0.01. The model accounted for
63% of the variance in
O2 max. However, there was evidence of lack of normality and of heteroscedasticity due to lack
of fit (Wilks-Shapiro and White's tests, both
P < 0.01). There was no evidence of
multiplicative heteroscedasticity; the absolute residuals were
uncorrelated with FFM (r = 0.01). For this model the age-associated decline was proportional to
exp(0.009 AGE) = 0.99 exp(AGE), suggesting an 8.4% decline in
O2 max per decade in
athletes and sedentary men.
WLS results were based on the OLS model (Eq. 21) using weights
1/FFM1.30. The WLS and OLS
estimates and standard errors were almost identical (Table 3). The WLS
model explained 66% of the variance in
O2 max compared with 64% for OLS. The residuals met all the important GLM
assumptions. As in the RS and OLS models, the rates of decline in
O2 max were the same in
trained and untrained men (i.e., there was no significant interaction
between age and ET). The WLS model yielded estimates of the training
effect and of the age-related declines in
O2 max that were
similar in athletes and sedentary men, as in the OLS model. A plot of
the decline in O2 max
with age based on the coefficients from the WLS model is shown in Fig.
2.
View larger version (20K):
[in this window]
[in a new window]
|
Fig. 2.
Scatter plot of O2 max
vs. age in athletes ( ) and sedentary men (+). Dashed and solid
lines, best-fit weighted least-squares regression for each group,
O2 max = 1.77 0.024 AGE + 0.96 ET + 0.036 FFM, at mean of FFM for entire sample.
|
|
Effect of Age Adjusted for FFM and Height
Nevill (19) suggested that height may be an important covariate in
LL models of O2 max. In
this study, height was not a significant predictor of
O2 max in any of the
models, and its inclusion had little effect on the estimates of the
age-associated decline. This may be due in part to the relatively small
variation in height (coefficient of variation of 4%) in these
subjects. Height also did not contribute when used in the model in
Eq. 10 with FFM as a predictor of
within-subject variance [Harvey's test 2 (1) = 2.64, P > 0.05].
Effect of Age Adjusted for FFM and Fat Mass
Toth et al. (30) suggested that the ratio of FFM to fat mass was an
important factor contributing to the age-associated decline in
O2 max. In this study
we found that neither fat mass nor the ratio of FFM to fat mass
contributed significantly to any of the models
(P > 0.05) when FFM was already
included.
Contribution of Loss of FFM to the Age-Associated Decline in
O2 max
The OLS, WLS, and LL models suggested that ~35% of the
age-associated decline in
O2 max was due to a
loss of skeletal muscle. Given that
O2 max declines 0.24 l · min1 · decade1,
the loss of skeletal muscle accounts for 0.08 l · min1 · decade1
of this quantity. Because FFM was not in the RS model as a predictor, the RS model cannot provide an estimate of the contribution of FFM to
the age-associated decline in
O2 max.
| |
DISCUSSION |
The WLS regression incorporating age, FFM, and a dichotomous indicator
of physical conditioning status yielded a model of O2 max that accounted
for the largest proportion of variance and met all the important GLM
assumptions. Absolute
R2 for the WLS
model was ~6% higher than for the RS model, 3% higher than for the
LL model, and 2% higher than for the OLS model (Table 3). These
results support the use of WLS models to examine the physiological
factors underlying the age-associated decline in O2 max.
Despite their failure to satisfy the underlying GLM assumptions, the RS
and OLS models incorporating age, FFM, and ET provided estimates
similar to the WLS model of the age-associated decline in athletes and
sedentary men. The RS model incorporating age, FFM, and ET produced
estimates that were ~10% lower than those produced by the OLS and
WLS models (the LL model suggested an exponential decay in
O2 max). The
OLS estimate was nearly identical to the WLS estimate, despite the
failure of the OLS model to satisfy the assumption of homoscedasticity.
This estimate (0.24 l · min1 · decade1)
suggests a 9% decline in
O2 max
between 60 and 70 yr of age, which is consistent with other studies
that indicate that the average healthy sedentary man >25 yr of age is
expected to lose 9-11% of his
O2 max per decade (10,
13, 30).
Because the WLS models satisfied all the important GLM assumptions, the
estimates produced by the WLS analysis were BLUE, and the
t-tests of the regression coefficients
were correct. All the other methods failed to satisfy one
or more of the assumptions.
Some investigators recommend verifying the assumption of
homoscedasticity when scaling for differences in body habitus (20, 33).
In this study the findings were generally robust to violation of this
assumption. Multiplicative heteroscedasticity did not significantly
affect the OLS standard errors, and the OLS model R2 increased
slightly compared with the (homoscedastic) RS model. We also found that
the estimates were virtually unchanged over the range = 0-2
(data not shown). This insensitivity of the WLS estimates may have been
due to the fact that the correlation between the absolute residuals and
FFM was only r = 0.18. It is possible
that WLS may have a greater impact on the estimates and standard errors
when the correlation is higher, e.g.,
r > 0.30. Higher correlations have
been reported elsewhere (33).
In the log-transformed LL models the residuals displayed lack of
normality and heteroscedasticity due to lack of fit. A post hoc
analysis (data not shown) determined that both problems were due to the
presence of an indicator variable in the analysis. When separate
analyses were carried out within the athlete and sedentary groups, the
residuals were normally distributed and homoscedastic.
Heteroscedasticity due to lack of fit is diagnostic of model
misspecification and suggests that the logarithmic transformation was
not the appropriate metric when the dichotomous training variable was
included in LL models.
The mechanisms underlying the age-associated change in
O2 max in healthy men
are multifactorial. Factors implicated in the age-associated decline in
O2 max
include decreases in maximum heart rate, stroke volume, arteriovenous
O2 difference, and skeletal muscle
mass, an increase in adiposity, and a decline in daily, regular
physical activity (3, 10, 12, 13, 17, 22, 27, 30). In the
present study the models adjusted for FFM accounted for more
variance than the unadjusted models (Table 3). The unadjusted models
yielded larger estimates of the percent decline in
O2 max in the athletes
and sedentary men than did models that included FFM. This difference
between unadjusted and adjusted models, which has been noted in RS
models that do not adjust for muscle mass (8), suggests that ~35% of
the decline in O2 max
is due to the age-associated decrease in skeletal muscle mass (OLS,
WLS, and LL estimate). This finding is consistent with that of Toth et
al. (30), who estimated the contribution to be 33%. Recent findings
suggest that the decrease in
O2 max that
is associated with the loss of skeletal muscle may be due, at least in
trained subjects, to reduced aerobic capacity per kilogram of active
muscle (26). Reduced aerobic capacity would result from age-associated
changes in maximal O2 delivery and be independent of any actual loss of muscle fibers.
In the present study the OLS and WLS models indicated that the athletes
and sedentary men decreased their
O2 max at the same
absolute rate, ~0.24
l · min1 · decade1.
However, the O2 max was
0.96 l/min higher in the athletes than in the sedentary men at all
ages. Although some cross-sectional studies report similar absolute
declines in O2 max over
time in athletes and in sedentary individuals (25), other longitudinal studies suggest that
O2 max declines at a
slower rate in athletes than in sedentary men (27). Hagberg (10)
estimated that the 5.5% decline in
O2 max per decade in
master athletes is ~50% of the rate of decline in age-matched
sedentary men. It is noteworthy that there is a correlation between the
change in training intensity and longitudinal changes in
O2 max (17). Possibly,
the attenuation of the rate of the age-associated decrease in
O2 max may be achievable only for a select group of elite older athletes who are able
to continue high-intensity training over an extended period of time and
also preserve their FFM. The athletes in the present study were
heterogeneous with respect to their
O2 max per kilogram of
FFM and the intensity and duration of their training. This
heterogeneity may have had an impact on the age-associated decline in
O2 max.
A strength of this study is that the athletes and untrained men
underwent a vigorous medical evaluation, and only those men with no
evidence of cardiovascular or other disease were enrolled. Also, the
athletes enrolled in this study were selected only if they were still
competitive in their age class. This reduced the potentially
confounding effects of disease on the age-associated declines in
cardiovascular fitness. Second, individuals with a wide range of
obesity and fitness levels were included in the study population.
Nevertheless, this study has several limitations. First, the subjects
were not randomly selected from the at-large older population, limiting
the generalizability of the study findings. The fact that several other
studies found similar rates of loss of fitness with age suggests that
any bias introduced by our subject-selection process is probably small.
Another limitation was the use of hydrodensitometry as the method of
assessing FFM. Hydrodensitometry does not yield a direct measurement of
skeletal muscle mass; muscle mass must be calculated from the observed
density. This calculation depends on several assumptions. In an aging
population, changes in bone density and residual lung volume may
confound the hydrodensitometric estimate of FFM and, hence, the
contribution of FFM and fat mass to the age-associated decline in
O2 max (18). More
direct measures of skeletal muscle mass, such as that provided by
magnetic resonance imaging or dual X-ray absorptiometry, may provide a more accurate quantification of muscle mass and prediction of the
age-associated decline in
O2 max. Third, younger
men were not included in this study, which has affected the estimates
of the intercept. Finally, training intensity was treated as a
dichotomous variable. This may not adequately account for the
heterogeneity in effects of exercise training and leisure time
activities in the sedentary and athletic populations. Toth et al. (30)
concluded that controlling for leisure time activity reduced the degree of decline in O2 max in
sedentary males.
In this study the OLS and WLS models possessed certain advantages over
the corresponding RS and LL models. First, OLS and WLS were able to
provide estimates of the contribution of the loss of FFM to the
age-associated decline in
O2 max, which the RS
model, without an explicit FFM term, could not. Another advantage of
OLS and WLS was their suitability for testing the hypothesis of
parallel linear declines in
O2 max in
athletic and sedentary individuals; the nonlinear LL model was not
appropriate for addressing this question. OLS or WLS should prove
useful in studies where these issues (or similar ones) comprise part of
the investigation, with WLS providing a slightly more efficient
analysis.
| |
ACKNOWLEDGEMENTS |
We acknowledge the contributions of Drs. E. Bleecker, P. Coon, J. Fleg, R. Pratley, M. J. Busby-Whitehead, and D. Drinkwater and the
research exercise physiologists who assisted in measuring O2 max and body
composition in the subjects in this study. In addition, we thank Drs.
A. Gardner, J. R. Hebel, and A. Yataco for helpful comments and
suggestions.
| |
FOOTNOTES |
This work was supported by National Institute on Aging (NIA) Grant
R01-AG-07660, The Johns Hopkins Academic Teaching Nursing Home Award
P01-AG-04402, Grant K07-AG-00608, the Department of Veterans Affairs
Geriatric Research, Education, and Clinical Center (GRECC), The Johns
Hopkins Bayview GCRC (Grant M01-RR-02719), the Claude D. Pepper Older
Americans Independence Center NIA Grant P60-AG-12583, and National
Institutes of Health Intramural Funds from the Gerontology Research
Center, Laboratory of Clinical Investigation, Metabolism Section, NIA.
Present address and address for reprint requests: M. J. Rosen, 42 Haymarket Ln., Bryn Mawr, PA 19010.
Received 29 May 1997; accepted in final form 5 February 1998.
| |
REFERENCES |
1.
Albrecht, G. H.,
B. R. Gelvin,
and
S. E. Hartman.
Ratios as a size adjustment in morphometrics.
Am. J. Phys. Anthropol.
91:
441-468,
1993[Medline].
2.
Allison, D. B.,
F. Paultre,
M. I. Goran,
E. T. Poehlman,
and
S. B. Heymsfield.
Statistical considerations regarding the use of ratios to adjust data.
Int. J. Obes. Relat. Metab. Disord.
19:
644-652,
1995[Medline].
3.
Badenhop, D. T.,
P. A. Cleary,
S. F. Schaal,
E. L. Fox,
and
R. L. Bartels.
Physiological adjustments to higher- and lower-intensity exercise in elders.
Med. Sci. Sports Exerc.
15:
496-502,
1983[Medline].
4.
Box, G. E. P.,
and
D. R. Cox.
An analysis of transformations.
J. R. Stat. Soc. B
26:
211-252,
1964.
5.
Bruce, R. A.,
and
T. R. Horsten.
Exercise testing in the evaluation of patients with ischemic heart disease.
Prog. Cardiovasc. Dis.
11:
371-390,
1969[Medline].
6.
Buskirk, E. R.,
and
J. L. Hodgson.
Age and aerobic power: the rate of change in men and women.
Federation Proc.
46:
1824-1829,
1987[Medline].
7.
Ewald, G. A.,
and
C. R. McKenzie
(Editors).
Manual of Medical Therapeutics (28th ed.). New York: Little, Brown, 1995, p. 577.
8.
Fleg, J. L.,
and
E. G. Lakatta.
Role of muscle loss in the age-associated reduction in O2 max.
J. Appl. Physiol.
65:
1147-1151,
1988[Abstract/Free Full Text].
9.
Goran, M. I.,
D. B. Allison,
and
E. T. Poehlman.
Issues relating to normalization of body fat content in men and women.
Int. J. Obes. Relat. Metab. Disord.
19:
638-643,
1985.
10.
Hagberg, J. M.
Effect of training on the decline of O2 max with aging.
Federation Proc.
46:
1830-1833,
1987[Medline].
11.
Harvey, A. C.
Estimating regression models with multiplicative heteroscedasticity.
Econometrica
44:
461-465,
1976.
12.
Heath, G. W.,
J. M. Hagberg,
A. A. Ehsani,
and
J. O. Holloszy.
A physiological comparison of young and older endurance athletes.
J. Appl. Physiol.
51:
634-640,
1981[Abstract/Free Full Text].
13.
Holloszy, J. O.,
and
W. M. Kohrt.
Exercise.
In: Handbook of Physiology. Aging. Bethesda, MD: Am. Physiol. Soc., 1995, chapt. 24, p. 633-666.
14.
Katzel, L. I.,
E. R. Bleecker,
E. G. Colman,
E. M. Rogus,
J. D. Sorkin,
and
A. P. Goldberg.
Effects of weight loss vs. aerobic exercise training on risk factors for coronary disease in healthy, obese, middle-aged and older men.
JAMA
274:
1915-1921,
1995[Abstract/Free Full Text].
15.
Kennedy, P.
A Guide to Econometrics (3rd ed.). Cambridge, MA: MIT Press, 1992, p. 90, 118-119, 130, 131.
16.
Kmenta, J.
Elements of Econometrics. New York: Macmillan, 1971, p. 263-264.
17.
Marti, B.,
and
H. Howald.
Long-term effects of physical training on aerobic capacity: controlled study of former elite athletes.
J. Appl. Physiol.
69:
1451-1459,
1990[Abstract/Free Full Text].
18.
Martin, A.,
and
D. Drinkwater.
Variability in the measures of body fat. Assumptions or techniques?
Sports Med.
11:
277-288,
1991[Medline].
19.
Nevill, A. M.
The need to scale for differences in body size and mass: an explanation of Kleiber's 0.75 mass exponent.
J. Appl. Physiol.
77:
2870-2873,
1994[Abstract/Free Full Text].
20.
Nevill, A. M.,
and
R. L. Holder.
Scaling, normalizing, and per ratio standards: an allometric modeling approach.
J. Appl. Physiol.
79:
1027-1031,
1995[Abstract/Free Full Text].
21.
Nevill, A. M.,
R. Ramsbottom,
and
C. Williams.
Scaling physiological measurements for individuals of different body size.
Eur. J. Appl. Physiol.
65:
110-117,
1992.
22.
Ogawa, T.,
R. Spina,
W. H. Martin III,
W. M. Kohrt,
K. B. Schechtman,
J. O. Holloszy,
and
A. A. Ehsani.
Effects of aging, sex, and physical training on cardiovascular responses to exercise.
Circulation
86:
494-503,
1992[Abstract/Free Full Text].
23.
Pearson, K.
Mathematical contributions to the theory of evolution on a form of spurious correlation which may arise when indices are used in the measurement of organs.
Proc. R. Soc. Lond. B Biol. Sci.
60:
489-497,
1987.
24.
Pindyck, R. S.,
and
D. L. Rubinfeld.
Econometric Models and Economic Forecasts. New York: McGraw-Hill, 1976, p. 139-142.
25.
Pollock, M. L.,
H. S. Miller,
and
J. Wilmore.
Physiological characteristics of champion American track athletes 40 to 75 years of age.
J. Gerontol. A Biol. Sci. Med. Sci.
29:
645-649,
1987.
26.
Proctor, D. N.,
and
M. J. Joyner.
Skeletal muscle mass and the reduction of O2 max in trained older subjects.
J. Appl. Physiol.
82:
1411-1415,
1997[Abstract/Free Full Text].
27.
Rogers, M. A.,
J. M. Hagberg,
W. H. Martin III,
A. A. Ehsani,
and
J. O. Holloszy.
Decline in O2 max with aging in master athletes and sedentary men.
J. Appl. Physiol.
68:
2195-2199,
1990[Abstract/Free Full Text].
28.
Rogers, D. M.,
B. L. Olson,
and
J. H. Wilmore.
Scaling for the O2-to-body size relationship among children and adults.
J. Appl. Physiol.
79:
958-967,
1995[Abstract/Free Full Text].
29.
Siri, W. E.
The gross composition of the body.
Adv. Biol. Med. Phys.
4:
239-240,
1956[Medline].
30.
Toth, M. J.,
A. W. Gardner,
P. A. Ades,
and
E. T. Poehlman.
Contribution of body composition and physical activity age-related decline in peak O2 in men and women.
J. Appl. Physiol.
77:
647-652,
1994[Abstract/Free Full Text].
31.
Toth, M. J.,
M. I. Goran,
P. A. Ades,
D. B. Howard,
and
E. T. Poehlman.
Examination of data normalization procedures for expressing peak O2 data.
J. Appl. Physiol.
75:
2288-2292,
1993[Abstract/Free Full Text].
32.
Vanderburgh, P. M.,
M. T. Mahar,
and
C. H. Chou.
Allometric scaling of grip strength by body mass in college-age men and women.
Res. Q. Exerc. Sport
66:
8-84,
1995.
33.
Welsman, J. R.,
N. Armstrong,
A. M. Nevill,
E. M. Winter,
and
B. J. Kirby.
Scaling peak O2 for differences in body size.
Med. Sci. Sports Exerc.
28:
259-265,
1996[Medline].
34.
White, H.
A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity.
Econometrics
48:
817-838,
1980.
35.
Yataco, A. R.,
J. Busby-Whitehead,
D. T. Drinkwater,
and
L. I. Katzel.
Relationship of body composition and cardiovascular fitness to lipoprotein lipid profiles in master athletes and sedentary men.
Aging Clin. Exp. Res.
9:
88-94,
1997.
J APPL PHYSIOL 84(6):2163-2170
Top
Abstract
Introduction
