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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

(2)

90th 6 L) 4 3. 2 10 9. 8 7, 6’ 5, U 4, 3, 2

9----90th -8.909

. . .

-

-12.901

570 PREDICTING ADULT STATURE iod’_

o

-

#{149}, , , U I I I U I U I U U 1

2 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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(3)

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 5.4

years. 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 full

model 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). If

substitutions 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 4

should 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

(4)

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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(5)

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

http://pediatrics.aappublications.org/content/61/4/569

the World Wide Web at:

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American Academy of Pediatrics. All rights reserved. Print ISSN: 1073-0397.

American Academy of Pediatrics, 345 Park Avenue, Itasca, Illinois, 60143. Copyright © 1978 by the

been published continuously since 1948. Pediatrics is owned, published, and trademarked by the

Pediatrics is the official journal of the American Academy of Pediatrics. A monthly publication, it has

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