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KATZMARZYK ET AL.
years. The original CFS sample was selected by Statistics
Canada to be representative of the Canadian population and
contains information on individuals from urban and rural ar-
eas of every province (21). Data collection revolved around
households, and the first person to be contacted by the CFS
team was designated as the reference person. All individuals
in the household were then identified by their relationship to
the reference person. Thus, the family structures of the en-
tire sample could be reconstructed from this information.
The present sample is limited to nuclear families with at
least two biologically related individuals (mothers, fathers,
sons, or daughters), which yielded a total of 1264 people
cedures (23), as explained in detail elsewhere (24). Briefly,
each measure was regressed on BMI and up to a cubic poly-
2
3
nomial in age (age, age , age ) by using forward stepwise
regression (mean regression) retaining terms significant at
the 5% level, within sex-by-generation groups (mothers, fa-
thers, sons, and daughters). The change scores (ꢄ) were fur-
ther adjusted for the effects of ꢄBMI and the baseline level
of the phenotype. The residuals from the mean regressions
were retained and regressed on BMI and up to a cubic poly-
nomial in age (variance regression) in a forward stepwise
manner to test for heteroscedasticity. Heteroscedasticity
was present if any of the predictor variables entered the
variance regression at the 5% level of significance. In the
presence of significant heteroscedasticity, the final pheno-
type was calculated as the residual from the mean regres-
sion divided by the square root of the predicted score from
the variance regression. In the absence of heteroscedastic-
ity, the residual from the mean regression was used as the fi-
nal phenotype. The final phenotypes were standardized to a
mean of zero and unit variance within sex-by-generation
groups (mothers, fathers, sons, and daughters) prior to fur-
ther analysis.
(
635 males and 629 females) for whom measurements of
musculoskeletal fitness in 1981 (baseline) were available in
the Campbell’s Survey database. The sample was distrib-
uted among 502 nuclear families, with an average family
size of 2.75 people. A subsample of 834 people had mea-
surements of musculoskeletal fitness at both baseline and
follow-up, which was used for the longitudinal analyses.
The smaller sample size for the longitudinal analyses re-
sulted because many participants did not complete the mus-
culoskeletal measurements at the second visit; rather they
had only anthropometric or questionnaire data available.
This may introduce some bias into the change scores if it
was those people that decreased in fitness the most that did
not complete the second fitness assessment. Although this
question cannot be answered, there were no significant dif-
ferences between the two groups at baseline.
Familial Correlation Model
As a test of familial aggregation in the measures of mus-
culoskeletal fitness, an analysis of variance (ANOVA) was
used to compare the between-family to within-family vari-
ances, using the family identification number as the depen-
dent variable. Hypotheses regarding familial resemblance in
musculoskeletal fitness were then tested by using the com-
puter program SEGPATH (25). Familial correlation models
were fitted directly to the data under the assumption that the
family data follow a multivariate normal distribution. The
sex-specific correlation model was based on four types of
relatives: fathers (F), mothers (M), sons (S), and daughters
(D), giving rise to eight familial correlations (one spouse,
FM; four parent-offspring, FS, MS, FD, and MD; and three
sibling, SS, DD, SD). A series of nested (reduced) models
were compared with a general model in which all parame-
ters were estimated by using tests of the maximum-likeli-
hood ratio, defined as the difference in minus twice the log
likelihood (ꢅ2 ln L). Asymptotically, the log-likelihood ra-
Measurements
All measurements were made following the standardized
procedures of the CFS (22). Stature and body mass were
measured to the nearest millimeter and 0.1 kg, respectively,
2
and the body mass index (BMI; kg/m ) was calculated.
Hand-grip strength was measured with a Stoelting adjustable
dynamometer (C.H. Stoelting Co., Chicago, IL). Participants
held the dynamometer at the level of the thigh in line with
the forearm and were instructed to squeeze vigorously to ex-
ert maximum force. Maximal grip strengths of two trials for
the left and right hands were summed to provide a single
measure of grip strength (kg). The number of push-ups com-
pleted without time limit (n) and the number of sit-ups per-
formed in 60 seconds (n/min) were used as indicators of
muscular endurance. Participants performed sit-ups from the
supine position, with their fingers behind their ears, their an-
kles held, and their knees flexed 90ꢃ. A complete sit-up re-
quired touching the knees to the elbows. For push-ups, males
balanced from the toes, whereas females balanced from the
knees. Each push-up required a cycle of straightening of the
elbows to the chin touching the floor, with a straight back.
Finally, a sit-and-reach test was used to assess trunk flexibil-
ity. Participants reached toward their toes, with their knees
flat on the floor. The test was repeated twice, with the maxi-
mum value recorded to the nearest 0.5 cm. A trunk flexibility
score of 25 cm is equivalent to touching the floor.
2
tio follows a ꢆ distribution with degrees of freedom equal
to the difference in the number of parameters estimated un-
der the two hypotheses (26). Null hypotheses concerning
the strength of the familial resemblance included no familial
resemblance (FM ꢁ FS ꢁ FD ꢁ MS ꢁ MD ꢁ SD ꢁ SS ꢁ
DD ꢁ 0), no sibling resemblance (SD ꢁ SS ꢁ DD ꢁ 0), no
parent-offspring resemblance (FS ꢁ FD ꢁ MS ꢁ MD ꢁ 0),
and no spousal resemblance (FM ꢁ 0). A series of null hy-
potheses, including no sex differences in offspring (FS ꢁ
FD, MS ꢁ MD, SS ꢁ DD ꢁ SD), no sex differences in off-
spring or parents (FS ꢁ FD ꢁ MS ꢁ MD, SS ꢁ DD ꢁ SD),
and no sex or generation differences (FS ꢁ FD ꢁ MS ꢁ
MD ꢁ SS ꢁ DD ꢁ SD), and all correlations being equal
(
FM ꢁ FS ꢁ FD ꢁ MS ꢁ MD ꢁ SS ꢁ DD ꢁ SD) were
Data Adjustments
also tested.
Baseline values and changes in the musculoskeletal fit-
ness measures were adjusted for the effects of age and BMI
in both the mean and variance by using SAS regression pro-
Akaike’s information criterion (AIC), defined as ꢅ2 ln L
plus twice the number of parameters estimated, was used to
judge the fit of the models (27). The model with the lowest