Predicting
Adult
Stature
Without
Skeletal
Age and
Without
Paternal
Data
Howard Wainer, Ph.D., A. F. Roche, M.D., and Susan Bell, B.Sc.
Fronl the Department of Behauioral Sciences, The University of Chicago, and The Eels Research institute,
%Vright State LTniuersity School of Medicine, Yellow Springs, Ohio
ABSTRACT. The RWT method for predicting adult stature from childhood variables uses the current recumbent length and weight of the child, the stature of each parent, and the skeletal age of the child as predictor variables. There is only a small increase in the errors of prediction if population mean values are substituted in the prediction equations when the father’s stature, the skeletal age of the child, or both these variables are unknown. This modified method is more generally applicable than the original RWT method. Pediat-rics 61:569-572, 1978, stature, prediction, skeletal age.
The long duration of several serial growth
studies has allowed the development of systems
for the early prediction of adult stature from
childhood variables for individuals. These new
systems3 are considerably more accurate than
those previously i1 The RWT method
appears to be the most accurate prediction
method; it is also the most statistically rigorous
and robust. This method uses the present
recum-bent length of the child (or stature adjusted to be
approximately equivalent to recumbent length by
adding 1.25 cm), the weight of the child, the
stature of each parent, and the skeletal ag& of the
child. To obtain a prediction of adult stature
using the RWT method, a clinician must have
access to the prediction tables’2; use of an
elec-tronic calculator assists rapid computations.
A possible hindrance to the widespread use of
the RWT method is the need for skeletal age as a
predictor variable. The cost of taking and
assessing a suitably positioned hand-wrist
radio-graph may not be warranted for stature
predic-tions made in the context of periodic pediatric
examinations, although these assessments are
important in relation to the diagnosis of the
condition responsible for the variation from
normal in present stature. Additionally, the RWT
method uses mid-parent stature (the mean of the
statures of both parents) as a predictor variable.
Obviously, in many circumstances these two
variables (skeletal age and mid-parental stature)
are unavailable. It is unusual for both parents to
accompany a child for a routine pediatric exam
1-nation. Consequently, paternal stature is often
obtained from a report by the mother. The
possibility of error in such reporting is clear.
For widespread clinical use and for use by
educators and those in the child development
field, it would be helpful to modify the RWT
prediction method so that it could be used
effec-tively without one or the other or both of these
two predictor variables. This report shows that
this can be done without serious loss of
accuracy.
To achieve this, norms were used in the R\VT
method so that, in the absence of skeletal ages or
mid-parent statures, the mean of the predicted
statures would equal the mean of the actual
statures for the corresponding sex. This is a
standard statistical routine in regression schemes;
the mean is used as a default option and
addi-tional information from the predictor variables
Received February 7; revision accepted for publication June
28, 1977.
Supported in part by grant HD-04629 from the National Institutes of Health, Bethesda, Maryland.
ADDRESS FOR REPRINTS: (A.F.R.) The Fels Research
Institute, 800 Livermore Street, Yellow Springs, OH
90th 6 L) 4 3. 2 10 9. 8 7, 6’ 5, U 4, 3, 2
9----90th -8.909
. . .
-
-12.901570 PREDICTING ADULT STATURE iod’_
o
-
#{149}, , , U I I I U I U I U U 12 3 4 5 6 7 8 9 10 ii 12 13 14 15 16
AGE IN YEARS
Fn;. 1. Error bounds (50th and 9()th percentile) of adult stature predictions in children of The Fels Longitudinal
Sample when original RWT method is used.
leads to a prediction for the individual that differs
from the mean.
It is easy to modifv the RWT method so that it
can be applied when some of the predictor
variables are missing. If the person applying the
method lacks either the skeletal age of the child
or the stature of the child’s father, the population
mean for that measure can be substituted and the
original RWT prediction equations applied. The
nmjor question to be examined is the extent of the
loss of predictive accuracy.
This loss of accuracy has been established in
three realistic circumstances:
1. The lack of skeletal age. This was replaced
I)y chronological age and, as in the other
circum-stances to be considered, the standard RWT
prediction tables were applied. A direct transfer
is reasonable in the Fels population in which
mean Creulich-Pyle skeletal ages closely
approxi-mate mean chronological If a prediction
- 1 U U I I I I I I U I I I
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
AGE IN YEARS
FIG. 2. Error bounds (50th and 90th percentile) of adult
stature predictions in children of The Fels Longitudinal Sample when chronological age is substituted for skeletal
age.
were being made for an individual belonging to a
socioeconomic or pathological group known to be
divergent in skeletal maturation levels, an
“ad-justed” chronological age should be substituted.
2. The lack of father’s stature. This was
replaced with the mean for adult males in the Fels
population (176.3 cm). Again, if a prediction were
being made for a member of a group that is
divergent in adult stature, the mean adult stature
for men in this group should be substituted.
3. The lack of skeletal age and father’s stature.
Both the foregoing replacements were made.
In each of these hypothetical situations, RWT
predictions were made for the participants in The
Fels Longitudinal Study. The 50% and the 90%
error bounds were calculated from the differences
between the predicted and actual adult statures.
The 50% error bounds when added to and
subtracted from the estimates give the limits
within which 50% of the actual adult statures will
PREDICTION OF ADULT STATURE IN A HYPOTHETICAL BOY ASSUMING SKELETAL AcE Is UNAVAILABLE
\arial)le Value Weighting#{176} Pro
Positice
Iticts
.‘Vegaticc
Recumbent length (cm)
Weight (kg)
Mid-parent stature (cm) Skeletal age (yr)
Constant
108.7 1.143 124.244
17.4 -0.512 ...
169.0 0.389 65.741
6.25 0.123 0.769
Subtotals 190.754 -21.810 Prediction = 168.944 cm
#{176}Theweightings are the factors by which variables are multiplied in the RWT prediction method.
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9 8 7 6 U 4 3 2 9 8 7, 6 5, U 4, 3, 2
. I U I U I I T I I I I I I I
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
1o 01f 100*
AGE IN YEARS
Fn;. 3. Error bounds (50th and 90th percentile) of adult stature predictions in children of The Fels Longitudinal Sample when population mean is substituted for father’s
stature.
lie. Correspondingly, the 90% error bounds
provide the limits within which 90% of the actual
adult statures will lie.
The loss of predictive accuracy due to the
replacement of skeletal age is modest at all ages,
indicating that, for normal children, little
predic-tive information is provided by the Greulich-Pyle
skeletal age for the hand-wrist. A similar
conclu-sion would be expected if Tanner-Whitehouse
skeletal age had been used because this was
correlated significantly with the errors of the
complete RWT method at only one age in boys
and not at any age in the girls.’ Of course, for
children with markedly abnormal maturation
status, this may not be the case but, in such
circumstances, skeletal age assessments will
almost certainly be available. The errors of
prediction with this modification of the RWT
method are still substantially smaller than with
the Bayley-Pinneau method.4 This results from
the use of a superior statistical method to estimate
the prediction weightings and from the use of
additional predictor variables.
Consider a boy aged 6 years 3 months, with a
recumbent length of 108.7 cm, a nude weight of
17.4 kg, a mid-parent stature of 169.0 cm (mother
165
cm, father 173 cm), and a skeletal age of 5.4years. His predicted adult stature based on the
complete RWT method would be 168.82 cm with
90% error bounds of about 5.7 cm (Fig. 1). In all,
90% of such boys will have adult statures between
163.1 and 174.5 cm.
Substituting chronological age for skeletal age
(on the assumption that this is unavailable), the
calculations in the Table would be made yielding
a prediction of 168.944 cm. This prediction
1’
9----90th
50th
I I I I 1 1 I I I I I I I U
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
AGE IN YEARS
FIG. 4. Error bounds (50th and 90th percentile) of adult stature predictions in children of The Fels Longitudinal Sample when chronological age is substituted for skeletal age
and population mean is substituted for father’s stature.
should be rounded to one decimal place and its
limits of accuracy obtained from Figure 2. For
this boy, the predicted adult stature with the
modified method is 168.9 ± 5.8 cm for 90% error
bounds. This is, of course, very close to the
predic-tion with the complete method. This boy was
retarded skeletally. If his skeletal age had been
nearer his chronological age the effect of
substitu-tion would have been even smaller. Nevertheless,
the
two
predictions are similar, with the fullmodel having, quite naturally, a smaller error.
If this boy’s skeletal age were available lmt a
population mean were used instead of his father’s
stature, the predicted adult stature would I)e
169.5
± 6.0 cm for 90% error bounds (Fig. 3). Ifsubstitutions were made for both skeletal age and
father’s stature, the prediction would be
169.6
± 6.0 cm (Fig. 4). The data in Figures 2 to 4should be used to assist the interpretation of
predictions made with these modifications of the
RWT method.
The present findings indicate that the
uiiavail-ability of skeletal age or father’s stature or even
both of these, at many ages, has little effect on the
accuracy of RWT predictions of adult stature for
individuals, if population means for these
variables are used in the prediction equation. The
loss of accuracy is important only at ages when
the omitted predictor variables have relatively
large weightings in the prediction equation. In
general, these ages are before 5 years and after 14
years. The modifications described make the
RWT prediction method much more widely
applicable. It is important to stress, however, that
the assessment of skeletal age is helpful from a
devia-572 PREDICTING ADULT STATURE
tions from normal in rates of growth or in
pubertal status; in addition, these assessments are
important in growth prediction during the
pre-school period and after 14 years.
REFERENCES
I. Roche AF, Wainer H, Thissen D: Predicting adult
stature for individuals. .ionogr Paediatr 3, Basel, Switzerland, Karger. 1975.
2. Roche AF, Wainer H, Thissen D: The RWT method for
the prediction of adult stature. Pediatrics 56:1026, 1975.
3. Tanner JM, Whitehouse RH, Marshall WA, et al:
Assessmen t of Skeletal 4fatt1 ritq arl(l Prediction of
Adult Height (TW2 Method). London, Academic Press, 1975.
4. Bayley N, Pinneau SR: Tables for predicting adult height from skeletal age: Revised for use with Greulich-Pyle hand standards. I Pediatr 40:423,
1952.
5. Greulich WW, Pyle SI: Radiographic Atlas of’ Skeletal Deuelopment of the Hand and Wrist, ed 2. Stanford, Calif, Stanford University Press, 1959.
6. Wainer H, Thissen D: Multivariate semi-metric smoothing in multiple prediction. I Am Statist
As.s’oc 70:568, 1975.
THE EARLIEST RECORDED AUTOPSY IN AMERICA PERFORMED IN 1662 ON THE
8-YEAR-OLD ELIZABETH KELLEY
The parents of Elizabeth Kelley of Hartford, Connecticut, attributed her
death to witchcraft practiced on her by Goody Ayres, one of their
neigh-bors.
Elizabeth was suddenly taken with a violent attack of coughing and choking
during the evening of March 24, 1662. In her delirium she cried out: “Father,
father help me, help me Goodwife [Goody] Ayres is upon me, she chokes me,
she kneels on my belly, she will break my bowels, she pinches me, she will
make me black and blue.” Elizabeth died the next day. Following the
superstition of those times, both her parents and the townspeople thought that
her death was due to some preternatural cause, such as bewitchment. The
General Court of Connecticut accordingly ordered a postmortem examination
on Elizabeth to determine the cause of her death.
Mr. Bryan Rossiter, the prosector, described his findings in the following
1:
All these 6 particulars underwritten I judge preternatural:
Upon the opening of John Kelley’s child at the grave I observed,
1. The whole body, the musculous parts, nerves and joints were all pliable, without ally
stiffness or contraction, the gullet only excepted. Experience of dead bodies renders such
symptoms unusual.
2. From the costal ribs to the bottoni of the belly in the whole latitude of the womb, both the scarf skin and the whole skin with the enveloping or covering flesh had a deep blue tincture, when the inward part thereof was fresh, and the bowels under it in true order, without any discoverable peccancy to cause such an effect or symptom.
3. No (luantity or appearance of blood was in either venter or cavity as belly or breast, but in the throat only at the very swallow, where was a large quantity as that Part could well contain, 1)0th fresh and fluid, no way congealed or clodded, as it comes from a vein opened, that I stroke it out with my finger as water.
4. There was the appearance of pure fresh blood in the backside of the arni, affecting the skin
as 1)100(1 itself without bruising or congealing.
5. The bladder of gall was all broken and curded, without any tincture in the adjacent
1)arts.
6. The gullet or swallow was contracted, like a hard fish bone, that hardly a large pease could l)e forced through.
BR: ROSSETER
What became of Goody Ayres, the putative witch, is not known because she
and her husband fled, leaving all their possessions behind, as soon as they
learned of the court’s order.
Noted by T. E. C., Jr., M.D.
REFERENCE
1. badly CJ: Some early post-mortem examinations in New England. Proc Couit .‘iied Sue, centennial volume, 1892, p 207.
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1978;61;569
Pediatrics
Howard Wainer, A. F. Roche and Susan Bell
Predicting Adult Stature Without Skeletal Age and Without Paternal Data
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1978;61;569
Pediatrics
Howard Wainer, A. F. Roche and Susan Bell
Predicting Adult Stature Without Skeletal Age and Without Paternal Data
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