Physical Fitness and Blood Pressure
in School Children
GARY E. FRASER, M.B., CH.B., PH.D., M.P.H., ROLAND L. PHILLIPS, M.D., DR. P.H.,
AND RALPH HARRIS, M.B., CH.B.
SUMMARY We studied the relationship between physical fitness and blood pressure in 228 school
children. The data were collected as part of the Loma Linda Child-Adolescent Blood Pressure Study.
Systolic and diastolic blood pressures were lower in children above average fitness than in children below
average fitness among preadolescent and adolescent boys and girls. On multivariate analysis, adjusting for
skinfold thickness, an index of lean arm mass, height and age, the relationship between fitness and systolic
blood pressure was statistically significant for preadolescent boys and for adolescents of both sexes. The
multivariate relationship was not clearly seen for diastolic blood pressure. Multivariate techniques showed
that significant correlates of fitness were obesity in preadolescents, age in adolescent boys and height in
adolescent girls. Predicted pulse rates for stages 6-10 of a modified Balke treadmill protocol are given in
appendix 1 for preadolescent and adolescent boys and girls.
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graphic data were documented on about 8000 Southern
California children. Phase II documented dietary and
psychosocial variables in a subgroup of these children.
Phase III gathered similar data on the parents of a
sample of the phase II children. About 40% of the
phase II children were Seventh-day Adventist (SDA)
and 60% were not. Blood pressures did not differ significantly between SDA and non-SDA children.25
For the substudy reported in this article, we chose
300 white children from the phase I population who
lived within a reasonable driving distance of Loma
Linda University. One-half were SDAs. One-third
were randomly chosen from those who had blood pressures above the eighty-fifth percentile during the phase
I portion of the study. One-third were chosen with
blood pressures below the fifteenth percentile and the
final third were chosen with blood pressures between
the fifteenth and eighty-fifth percentiles.
A treadmill was chosen as the method of evaluating
physical fitness in the 270 children who responded to
the invitation to come to the testing center at Loma
Linda University. This has the advantage of individual
supervision and is superior to bicycle ergometry in that
there is less effect of muscular fatigue in the test performance. The test was usually submaximal, in that the
stopping rule was either maximal effort or a pulse rate
of 185, whichever came first. A modified Balke treadmill protocol was used. Depending on the size of the
child, the speed of the treadmill was either 2.6, 3.0 or
3.4 mph, so that smaller children did not have to run.
During the first stage of exercise, the treadmill was
level; the angulation of the treadmill was increased by
2° every minute.
The sequence of measurements and organization of
the testing were as follows. When the child arrived at
the testing center with the parents, simple demographic data were obtained; height, weight (shoes off)
and resting pulse were measured; a single resting blood
pressure was obtained with a standard mercury sphygmomanometer and an appropriate-sized cuff; a brief
physical examination was performed and medical history obtained to ensure the child's fitness to undergo
the stress test. The stress test was monitored by electrocardiograph. A physician was in attendance. During
BLOOD PRESSURE is a major determinant of health
in adult life, and is apparently determined by both
genetic'-' and lifestyle factors. Age and sex,4 race,5
body build,6'7 alcohol consumption,8,9 and probably
sodium and potassium consumption'0-3 all appear to
be important. Several sources of evidence suggest that
there is tracking of blood pressure levels from childhood to adult life.'4, 1' This phenomenon implies that
persons with blood pressure ranking high or low in the
blood pressure distribution of a childhood population
tend to retain that ranking during adult life. Therefore,
the determinants of blood pressure during childhood
may also be important predictors of adult blood pressure levels.
Several cross-sectional studies'6' 1' in adults have investigated the relationship between exercise and coronary risk factors, including blood pressure, in healthy
subjects. Other investigators have reported the effects
of exercise training as part of a rehabilitation program'8 19 or in men at high coronary disease risk.20'21
Montoye et al.'6 and Pickering2' reviewed these studies. There is evidence that exercise may lower blood
pressure in adults. Such evidence does not exist for
children.
In the present study, we investigated the relationship
between physical fitness and blood pressure in children
ages 7-17 years as part of the Loma Linda ChildAdolescent Blood Pressure Study. Although physical
fitness correlates with habitual exercise, other factors,
such as gender22 and probably genes,23 24 contribute to
fitness.
Methods
The Loma Linda Child-Adolescent Blood Pressure
Study is an epidemiologic study divided into three
phases. During phase I, blood pressure and demoFrom the Departments of Biostatistics and Epidemiology, Loma Linda University, Loma Linda, California.
Supported by NIH grant HL-20005.
Address for correspondence: Dr. G.E. Fraser, Department of Biostatistics and Epidemiology, Loma Linda University, Loma Linda, California 92350.
Received July 7, 1981; revision accepted September 9, 1982.
Circulation 67, No. 2, 1983.
405
406
CIRCULATION
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each stage of the test, an electrocardiographic strip was
obtained. About 15% of treadmill test results were
discarded because of noncooperation from the child,
because the protocol was not being correctly followed,
or because of technical difficulties with the equipment.
A technician was trained by a cardiologist to measure pulse rate using the ECG strips obtained at each
stage of the treadmill test. A sequence of six consecutive beats was chosen in each strip. These had to be
free from major artifact and not at the beginning or the
end of the strip. The RR distance was measured between the first and sixth beat to an accuracy of 0.5 mm.
Pulse rate for that stage was then calculated by the
formula 9000/X, where X is the number of millimeters
for six consecutive beats (paper speed 25 mm/sec).
The cardiologist checked a 20% sample and agreement
with the technician was excellent.
The blood pressures used in the Results section are
the resting blood pressures obtained on the day of the
treadmill stress test. These were chosen as having the
closest time proximity to the fitness testing. The blood
pressure was measured during the less anxiety-provoking preliminary phase of the day's activities, rather
than immediately before exercise, when anxiety might
have an effect.
Statistical Analysis
Maximal pulse rate is well defined for a given age.26
The rate of rise of pulse with exercise is linear until
near the maximum, when some plateau effect may
occur.26 This analysis takes advantage of these facts.
For each child, for each treadmill stage, work load per
kilogram of body weight (WTOT) was modeled on the
formnula WTOT = WO + W = WO + V(Sin 0), where
WO is the work per kilogram of body weight, while
walking at V miles per hour at no inclination, where V
is the treadmill speed and where 0 is the treadmill
angulation.27
W is actually a difference in work/kg performed,
representing the increment between the work/kg of
walking on the flat at V miles per hour and total work/
kg (WTOT) at the nominated treadmill stage. W is measured as vertical feet per minute per kg of body weight.
An accepted method of measuring fitness is the
pulse rate at a given work load,28 29 or, alternatively,
the work capacity at a fixed pulse rate. To obtain such
measures, we had to establish a relationship between
pulse rate and work capacity for each child.
Pulse rate (P) was plotted against W for each child.
For values of W less than 10 vertical feet per minute,
the relationship between P and W was nonlinear and
unpredictable, possibly because pulse rate is influenced substantially by apprehension or emotional factors. For values of W above 10 vertical feet per minute
(corresponding to stage 3 and above for all three treadmill speeds), a clear linearity was apparent in virtually
all individual plots. However, above 85% of the predicted maximal pulse, the relationship between P and
W is often nonlinear.26 Consequently, data points outside the linear range were excluded from analysis. Any
child with less than four valid data points in the re-
VOL 67, No 2, FEBRUARY 1983
maining range was also excluded. The mean of the
individual correlation coefficients (P vs W) of the remaining 228 plots was 0.97, showing excellent linearity for this relationship, in virtually all subjects.
For each child, the two related least-squares linear
relationships were found by computer.
P = a + 3W
(1)
W = a' + 13'P
(2)
In the remainder of this report, reference will be made
to two parameters derived from the above analyses:
W170 and P70. P70 is the predicted pulse rate when
the work increments/kg is 70 vertical feet per minute,
using regression equation 1. W170 is the predicted
increment in work/kg when the pulse rate is 170 beats/
min using equation 2. The values of 170 for W170 and
70 for P70, were chosen because nearly all children
achieved these values and they represent substantial
work effort. Thus, W170 and P70 represent individual
measures of fitness that are clearly interrelated. The
values of W170 are directly related to fitness and the
values of P70 are inversely related to fitness.
Stepwise regression analysis was then used to predict these fitness measures using triceps skinfold thickness, an index of arm lean mass (arm LMI), treadmill
speed, height and age as potential predictor variables
or covariates. These analyses were performed separately for preadolescent (- 12 years for girls and S
13 years for boys) and adolescent children of each sex.
Regression analyses also examine the relationship
between the fitness measures and blood pressure, adjusting for covariates such as treadmill speed, age,
height, skinfold thickness and arm LMI. Analyses
were again conducted for preadolescent and adolescent
children of each sex. All regressions were performed
with the SPSS programs.
Arm LMI is proportional to the cross-sectional area
of the muscle and bony tissue of the upper armn: (Cl
g - S)2, where S = triceps skinfold thickness (measured in mm but converted to cm for this calculation)
and C = arm circumference (cm). Triceps skinfold
thickness was measured midway between the acromion and olecranon processes using Harpenden calipers.
The results of regression 1, predicting pulse according to work, were used to form a model allowing
prediction of pulse rate for any given stage of the
treadmill (appendix 1). Only variables that were statistically significant predictors of fitness for a given sexadolescent group were used. Standard deviations for
the predictions are given. The method used to give
these predictions deals appropriately with the situation
of multiple observations on each of many subjects and
is described in appendix 2.
Results
The means and standard deviations for W170 and
P70, by age and treadmill speed are shown in table 1.
For a given treadmill speed, P70 decreases as age
increases only for the children younger than 11 years
of age. At the same age and treadmill speed, boys seem
FITNESS AND BLOOD PRESSURE/Fraser
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TABLE 1. Observed Fitness Variables by Treadmill Speed, Sex
and Age*
P70
W170
Age
Mean ± SD
Mean ± SD
(years) n
Speed 2.6 mph
172.8±17.9
M
64.3 ± 20.9
7-8
12
176.5 ±16.3
60.2±18.0
14
F
161.9±9.0
80.7 ± 14.2
M
9-10 11
76.5 ± 25.2
11
F
169.1±18.2
.Speed 3.0 mph
166.5± 18.2
78.7±30.8
M
9-11 25
59.5 ± 15.5
13
F
176.9±13.3
77.8±19.5
165.0± 16.0
M
12-14 17
16
F
179.2±10.2
58.9± 12.3
Speed 3.4 mph
163.8 ±17.5
M
79.5 ± 25.6
12-14 31
13
F
180.9± 16.4
55.8±17.9
168.4±13.4
M
71.6±15.7
15-17 31
179.7+21.7
60.4±27.1
12
F
*A few children who did not fit these categories are omitted from
this table.
Abbreviations: W170 = predicted increment in work/kg at a
pulse rate of 170 beats/min; P70 = predicted pulse rate when work
increment is 70 vertical feet per minute.
consistently fitter than girls. Although P70 and W170
are predicted values from regression lines fitted for
each child, they would be very close to observed values because of the excellent fit of the individual plots
to the fitted regression equations.
Multivariate linear regression showed that P70 and
W170 were significantly predicted by skinfold thickness in preadolescent children, by chronologic age in
adolescent boys and height in adolescent girls (table
2). These associations are further described in table 3,
where the observed W170 values are reported for subgroups below and above mean values of skinfold thickness, age and height.
With both sexes combined, separate analyses were
done for preadolescent and adolescent children with
sex as an independent variable. These results show that
sex is a powerful predictor of fitness (table 4). A com-
et
407
al.
parison of fitness between SDA and non-SDA children
showed no statistically significant difference. Similar
results were found if ponderal index replaced skinfold
thickness and arm LMI.
The relationship between blood pressure and fitness
was also explored. A comparison of blood pressures
was made between those above and below mean observed fitness levels (fig. 1). In a univariate sense for
all sex-adolescent status groupings, for both systolic
and diastolic pressures, the fitter group had lower pressures. This difference was statistically significant (p
< 0.05) for preadolescent boys (systolic and diastolic)
and adolescent girls (systolic only).
Tables 5 and 6 show the multivariate relationships
between systolic and diastolic blood pressure, fitness,
W170 and covariates representing adjustments for
height, skinfold thickness, arm LMI and age. These
regressions show that increasing fitness is associated
with lower systolic blood pressure in preadolescent
boys and in adolescents of both sexes. A significant
relationship between fitness and diastolic blood pressure cannot be shown in multivariate analyses. Again,
similar results were found if the ponderal index replaced skinfold and arm LMI as a covariate.
Detailed tables that may prove useful in assessing
physical fitness of individual children are shown in
appendix I.
Discussion
The use of submaximal exercise variables as indexes
of fitness (maximal oxygen uptake) has long been established in adults.30 Data for children are sparser, but
suggest that similar relationships hold between such
measures
and maximal oxygen uptake.31 32
Consequently, this study provides evidence that increased physical fitness in preadolescent and adolescent boys and adolescent girls is associated with lower
systolic blood pressure values. When comparing fit
(mean + 2 standard deviations of W170) and unfit
(mean 2 standard deviations of W170) children, the
magnitude of predicted differences of systolic blood
-
TABLE 2. Sex-specific Regression Coefficients from Stepwise Linear Regressions Predicting Fitness*
Adolescent
Adolescent
Preadolescent
Preadolescent
girls
boys
boys
girls
Dependent fitness
W170
P70
W170
P70
W170
P70
P70
W170
measure
Variable
Skinfold (mm)
Arm lean mass index
1.24t -1.44t
1.33t -1.34t
-
-
(cm2)
3.40t -5.15t
Age (years)
Height (inches)
Treadmill speed (mph) --21.53t
114.31 153.44
158.85 140.25
153.16 91.59
Constant
0.210
0.067
0.083
0.133
0.086
0.190
R2
statistical
for
variables
that
achieved
are
*Coefficients
significance.
reported only
tp < 0.05.
tp < 0.01.
Abbreviations: See table 1.
2.62t
-2.92t
9.47 249.17
0.108
0.121
VOL 67, No 2, FEBRUARY 1983
CIRCULATION
408
TABLE 3. Mean Values of W170 (Vertical feet/min) Within Subgroups Above and Below Mean Values* for Skinfold
Thickness, Age, and Height
Adolescent
Adolescent
Preadolescent
Preadolescent
girls
girls
boys
boys
High
Low
Low
High
Low
High
Low
High
77.6
73.9
60.5
68.7t
54.3t
58.9
68.8t
Skinfold
78.0t
57.4
57.7
82.0t
60.3
71.8t
67.0
75.2
74.4
Age
57.0
77.0
73.8
71.4
65.1
65.0'
76.3
54.61'
Height
*Mean values of skinfold thickness, age, and height computed separately for each sex-adolescent status group.
tSignificant difference in multivariate analysis (see table 2).
Abbreviation: W170 = predicted increment in work/kg at a pulse rate of 170 beats/min.
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pressure is approximately 16 mm Hg for each of the
three groups for whom evidence was found that fitness
related to blood pressure.
This study is a cross-sectional investigation and
does not provide proof that the relationship is dynamic
(that is, that in children and adolescents changes in
fitness produce changes in blood pressure). However,
this hypothesis seems reasonable and deserves further
investigation.
In view of the evidence that blood pressure tracks,
an intervention displacing an individual's track to a
lower rank within the population may produce a permanent change in rank, persisting into adult life. Miall
and Lovell,33 found that blood pressure "feeds on itself." In their longitudinal studies, higher baseline
pressures were associated with greater increases in
blood pressure over time. Again, the ability to influence this cycle in childhood and adolescence would be
very important. Physical activity may have potential as
one component of such an intervention.
The association of fitness with blood pressure was
not due to confounding by age, obesity or greater body
size. This possibility was eliminated by including the
skinfold measurement, arm LMI, height and age as
covariates in the regression procedures of tables 5 and
6. Consequently, physical fitness predicts systolic
blood pressure independently of these body build measures and age.
The relatively powerful effect of physical fitness on
blood pressure in adolescent girls and our inability to
detect such a relationship in preadolescent girls is an
interesting contrast. The lack of effect of fitness on
blood pressure in preadolescent girls in unexplained
TABLE 4. Regression Analysis Predicting W] 70 for Both Sexes
Combined*
Adolescent (n 93)
Preadolescent (n = 127)
CoeffiCoeffiVariable
cient t score
cient
t score
Variable
Sex
Sex
-16.98 3.93
-10.55 2.69
-3.36 1.74
Skinfold
-1.47 3.76
Age
143.46
102.45
Constant
Constant
R2= 0.16
R2 =0.16
*Males = 1, females = 2. Sex, skinfold thickness, arm lean
mass index, height, age and treadmill speed were available to the
stepwise program. Only variables with t scores corresponding to p
< 0.10 are reported.
Abbreviation: W170 = predicted increment in work/kg at a pulse
rate of 170 beats/min.
=
and needs to be confirmed by other data sets before
being accepted.
Previous data3437 and data from this study25 clearly
show that the relationship between blood pressure and
age changes during adolescence, particularly for boys.
For this reason we considered it important to separate
our analyses for preadolescents and adolescents. In an
epidemiologic study of this sort it was not feasible to
use an index of maturity (such as Tanner's index);
consequently, we are dependent on age alone. We
recognize that there will be some error in such a maturity dichotomization based on age. However, most girls
and boys ages 7-12 and 7-13 years, respectively, are
prepubertal and most ages 13-17 and 14-17 years are
postpubertal.
There is a constitutional component involved in fitness. However, there is evidence that fitness can be
improved commonly by up to 15-20%. 3140 Further,
the possible change depends on how sedentary the
subjects are before training. Some studies show gains
in fitness proportionately far greater than those reported above.41.42
SYSTOLIC
DIASTOLIC
LESiS FIT MORE FIT
LESS FIT MORE FIT
120
PRE-
ADOLESCENT
FEMALES
Hr_ i
65
60
70
65
1100
105
n
140
1a
-
Rn
a
a
a
60
m
a
135
130
130
125
120
115
80
75
70
_1
125
ADOLESCENT
FEMALES
70
115
a
ADOLESCENT
MALES
I
7
125 .ADOLESCENT 120
115
MALES
110
Hn-n
PRE-
U
m
p
In
75
HE Rnn
6
a
a
a
70
65
a
FIGURE 1. Univariate comparisons of systolic and diastolic
blood pressures in children above and below average observed
fitness. (Average fitness was calculated for each subgroup
separately.)
409
FITNESS AND BLOOD PRESSURE/Fraser et al.
TABLE 5. Regression Coefficients (b) from Multivariate Regressions Relating Fitness (W170) to Systolic Blood
Pressure*
Adolescent girls
Adolescent boys
Preadolescent girls
Preadolescent boys
Type of
R2
b
R2
R2
b
R2
b
b
coefficient
Variables
0.20
0.36
0.29
0.75
0.26
0.64
0.37
0.03
Skinfold
0.21
0.30
0.37t 0.19
0.30
0.47
0.68t 0.25
Arm lean mass index
0.22
-0.61
0.31
-0.42
0.30
-0.17
0.37
-0.63
Age
0.22
0.44
0.31
0.75
0.18
0.65
0.37
0.63
Height
- 0. 18t 0.15
0.30
-0.21t 0.26
-0.02
-0. 16t 0.35
W170
98.62
78.90
58.61
78.92
Constant
The order of
the
process.
which
it
entered
stepwise
in
for
the
step
variable
inde1endent
for
a
particular
*R2 is reported
entry can be found by ranking the R values in any particular regression.
tp < 0.05.
*p < 0.01.
Abbreviation: W170 = predicted increment in work/kg at a pulse rate of 170 beats/min.
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How this translates to possible changes in submaximal pulse rate can be estimated by, for instance, Astrand's equation.43 This equation shows that a decrease
of 17-20 beats/min at a work load originally producing
a heart rate of 170 beats/min represents about a 15%
increase in maximal oxygen uptake. All this suggests
the possibility that readily attainable increases in physical fitness may decrease systolic blood pressure by 45 mm Hg in children. In some instances, particularly
where the subject was initially quite sedentary,
changes may be greater.
Blood pressure is the result of two main hemodynamic influences: cardiac output and peripheral vascular resistance. The altered hemodynamics associated
with exercise could reset the controls determining vascular resistance and affect blood pressure levels. Alternatively, cardiac output at rest could be decreased in
physically fit people.
Some evidence suggests that resting cardiac output
in physically fit adults does not differ from that in unfit
adults.44 Little evidence is available on the relationship
between peripheral resistance and fitness. Pavlik et
al.'7 showed that highly trained adult athletes have
lower resting cardiac output and higher resting peripheral resistance than nonathletes. However, less well
trained athletes had lower resting peripheral resistance
and higher resting cardiac output than nonathletes.
Consequently, mechanisms whereby fitness may affect
blood pressure are not well understood.
Obese persons are generally more sedentary than
others.45 In this study, triceps skinfold thickness was
the most important predictor of physical fitness in both
preadolescent boys and girls. Part of the explanation
for the usual univariate relationship between obesity
and blood pressure in children may involve the decreased physical fitness of obese children.
Physical fitness in this data set was substantially and
significantly different in the two sexes. On average,
the pulse rates at a work load equivalent to raising
oneself 70 vertical feet per minute were 10 beats/min
faster in preadolescent girls than boys, and 14 beats/
min faster in adolescent girls than boys.
This sex difference has been described by others.26
Part of the explanation is probably that females have a
lower ratio of muscle to total body weight than males. 46
However, our data suggest that the effect is well established, but less pronounced, well before the usual age
of puberty.
As mentioned above, skinfold thickness is a predictor of fitness in preadolescents. Interestingly, for ado-
TABLE 6. Regression Coefficients (b) from Multivariate Regressions Relating Fitness (Wi70) to Diastolic Blood
Pressure*
Type of
coefficient
Variables
Skinfold
Arm lean mass index
Age
Height
W170
Preadolescent boys
b
R2
Preadolescent girls
b
R
Adolescent boys
R.
b
Adolescent girls
b
R2
0.14
0.09
0.12
0.15
0.99t 0.40
0.13
0.15
0.42
0.56
-0.45t 0.12
0.14
-0.43
0.06
5.37
5.53t 0.29
0.14
1.60t 0.08
0.79
0.45
-1.12
0.13
0.11
0.15
-0.11
0.45
-0.02
-40.72
32.77
48.52
Constant
variable for the step in which it entered the stepwise process. The order of
*R2 is reported for a particular
entry can be found by ranking the R values in any particular regression.
tp < 0.05.
:p < 0.01.
Abbreviation: W170 = predicted increment in work/kg at a pulse rate of 170 beats/min.
0.60
-0.07
1.54
0.28
-0.05
32.84
0.08
0.15
0.14
0.15
0.14
indeRendent
CIRCULATION
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VOL 67, No 2, FEBRUARY 1983
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lescent boys and girls, obesity is not a predictor of
fitness in either univariate or multivariate analyses;
rather, age in boys and height in girls are predictors as
fitness. This finding is not due to strong interrelationships between obesity and height or age. Height and
age are moderately correlated in adolescent boys (r
0.40), but neither the crude nor the partial correlation
coefficients between height and blood pressure are far
from zero. Thus, it is unlikely that age is a surrogate
for height in the analysis for adolescent boys. In adolescent girls, height and age are not correlated, making
it unlikely that height is a surrogate for age in this
analysis.
As adolescent boys grew older, fitness declined.
This maybe related to increasing preoccupation with
studies and vocational pursuits and less emphasis on
physical activity. However, this was not found for
adolescent girls, in whom the major relationship indicated that taller girls were less fit, as measured by
pulse rate at a standard exercise intensity. We are not
aware of any physiologic explanation for this relationship. We can only suggest that in this particular environmental setting, taller girls may have matured earlier, or may be physically less adroit and therefore less
likely to participate regularly in active sports.
Others have also related physical fitness to age, sex
and anthropometric measures. Matsui et al.47 found
increasing maximal oxygen uptake with age in adolescent boys, but no age trend for adolescent girls.
Krahenbuhl et al.'8 found a similar sex differential
favoring males in 8-year-old children. Mayhew and
Gifford49 related indexes of muscle mass and skinfold
thickness to maximal oxygen uptake during bicycle
exercise in preadolescent boys. Bonen et al.50 found
useful equations predicting maximal oxygen uptake
based on age, height and weight alone for boys 7-15
years old.
These data support the hypothesis that physical fitness is related to systolic blood pressure in preadolescent males and adolescents of both sexes. Because
high blood pressure may afflict as much as one-third of
the adult population,51 potential interventions in childhood merit further investigation.
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9. Harburg E, Ozgoven F, Hawthorne VM, Schork MA: Community
norms of alcohol usage and blood pressure: Tecumseh, Michigan.
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10. Joossens JV: Salt and hypertension, water hardness and cardiovascular death rate. Triangle 12: 9, 1973
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12. Morgan T, Gillies A, Morgan G, Adam W, Wilson M, CarneyS:
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Evans SJW, Ledingham JM: Blood pressure and hormonal changes
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APPENDIX 1. Predicted Pulse Rates in Children, by Treadmill
Stage and Other Significant Covariates of Fitness
Treadmill angulation
120
140
Covariate
100
160
Subgroup
Skinfold
Preadolescent boys
(mm)
(n = 78)
=
6
143
149
156
163
Treadmill speed 3.0 mph
145
165
8
152
159
10
13
20
Standard error of prediction (D)
Preadolescent girls
(n = 49)
Treadmill speed = 2.6 mph
Standard error of prediction (D)
Adolescent boys
(n = 56)
Treadmill speed = 3.4 mph
Skinfold
(mm)
7
9
12
14
20
Age
(years)
14
15
16
17
Standard error of prediction (D)
Adolescent girls
(n = 37)
Treadmill speed = 3.0 mph
Height
(inches)
59
61
63
65
67
error
169
172
147
150
158
14.0
154
157
165
14.8
161
165
173
15.7
168
171
180
16.7
175
178
146
148
151
153
160
12.4
151
154
157
163
166
169
172
179
13.6
169
171
175
178
166
12.7
157
160
163
166
173
13.1
148
151
155
158
13.7
156
159
163
166
14.1
164
167
171
174
14.7
171
175
178
179
183
146
153
157
162
167
172
15.7
159
164
170
175
180
166
171
177
182
130
155
160
164
14.8
159
17.8
14.3
182
15.5
16.8
18.3
of prediction (D)
*Predicted pulse rate is possibly above linear portion of the relationship between work and pulse rate.
Standard
180
16.8
173
178
184
20.0
CIRCULATION
412
Appendix 2.
Statistical Methods Used in Appendix 1 to
Calculate Predicted Pulse Rate by Treadmill Stage
The data collected in this study allow the prediction of pulse rates at
different levels of work and at different values of the relevant covariates.
The standard error of the prediction is also calculated (see below),
allowing the estimation of a prediction interval.
Splitting the observations to all reasonable combinations of these
different variables results in small numbers and loss of predictive accuracy. Consequently, it seemed most efficient to use the linear model
(which on inspection of residuals seemed satisfactory), and so allow the
use of all the data to predict pulse rates.
The standard errors of the predictions may seem rather large (see
appendix 1), but this is also in accord with the observed data. The
predictions of appendix 1 could be useful to assess the fitness of children, relative to the performance of similar children.
For the ith' individual at treadmill speed 1 and stage j (by regression 1):
P111 = ail + Iil1Wil
Two additional regressions were performed:
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atil =a+ (-Yk Xik)
Pi l + (8k Xik),
(3)
(4)
where X1, .
Xk are variables that are significant predictors of fitness
for that sex/adolescent status subgroup. In performing these regressions
we invoked the well-known normality of errors of estimated parameters
such as ail and il in regressions 1 and 2. In addition, plots of residuals
from regressions 3 and 4 did not indicate any deviations from
homoscedasity.
Then for each treadmill speed 1, and stage j:
VOL 67, NO 2, FEBRUARY 1983
Xik) + (1
+ 8k
k (yk
ail + /3il Wjl =a + (k
+
(8k
XiOWJw
Wil
Wjl) Xik
(5)
= rjl +
Xik).
Then this model allows prediction of the fitted regression 1 as dependent variable, according to the effect of other predictor variables. Confidence intervals (CI) (95%) for the variation of the corresponding points
calculated from the individual regressions (regression 1) about this
multivariate prediction can be calculated by standard formulas:
= a + 3
+
yj
CI = + t0?775 Si1 1 + U0 (XTX) U0
0 +7
= st07
0.975
-t.
*D,
where S2)J is the mean residual sum of squares from regression 5 for a
given work increment, W.. (Regression 5 was run for values of W.l
corresponding to each treadmill speed and stage, to find the corresponding values of S2.1 As expected, the values of rlji and g,kl were those
predicted from tle synthesis of regressions 3 and 4). X is the design
matrix corresponding to,regression 5, and U0 is the vector whose elements have the same form as a row of X, and specify the values of Xik
used to make the particular prediction of interest. The standard errors
(D) of the predictions are shown in appendix 1.
A close approximation to confidence intervals for actual measured
pulse rates about the prediction of regression 5 can be obtained by using
a value of D inflated by a factor of 1.03. This value was obtained by
adding a mean sum of squares to D2, resulting from variation of observed pulse rates about the regression lines corresponding to regression
1. This is a relatively insignificant addition, due to the very close fit of
observed points to the regressions corresponding to regression 1.
Physical fitness and blood pressure in school children.
G E Fraser, R L Phillips and R Harris
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Circulation. 1983;67:405-412
doi: 10.1161/01.CIR.67.2.405
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