Relationships between skeletal maturity estimated …kevinobrienorthoblog.com/.../02/Houston-Hand-wrist-radiographs.pdfRelationships between skeletal maturity estimated from hand-wrist

European Journal of Orthodontics 2 (1980) 81-93© 1980 European Orthodontic Society

0141-5387/8O/0O550081SO2.OO

Relationships between skeletal maturityestimated from hand-wrist radiographs andthe timing of the adolescent growth spurt

W. J. B. HoustonRoyal Dental Hospital, London, England

Summary. The roles of ossification events, bone stages and bone ages in the prediction of thetiming of the pubertal growth spurt are examined using data from the Harpenden growth study.In general, predictions made more than two years in advance of the average age of peakheight velocity (PHV) are of little clinical value. The timings of certain ossification events and ofPHV are related but the practical difficulties of obtaining reliable information on their timingsprecludes their use in most circumstances. Certain bone stages may be used to indicate thatgrowth is nearly completed. RUS bone age is more closely related to the timing of PHV than iscarpal age, and it is the most convenient and reliable way of estimating the age at PHV,although the confidence limits of such a prediction are appreciable. It may be very misleadingto assume that the growth spurt will be advanced or delayed to the same extent as ossificationevents or bone age and the appropriate regression equations must be used.

Certain aspects of orthodontic treatment,such as overbite reduction and the distalmovement of upper buccal segments, canmost readily be achieved while the face is stillgrowing and treatment designed to influencefacial growth can be successful only duringperiods of rapid growth. The velocity ofgrowth continually diminishes after birthexcept for two spurts, the first a small andinconsistent one at about 6 or 7 years of age,and the second at the time of puberty (Fig. 1).During the pubertal spurt, the velocity ofgrowth is greater than at any other time atwhich orthodontic treatment might be under-taken. Obvious benefits are to be gained if theaspects of treatment that depend on growthcan be undertaken during this period.

The timing of the growth spurt variesslightly in different parts of the body but inmost facial dimensions it seems to occur atabout the same time as in stature (Nanda,1955; Bergersen, 1972; Bjork, 1972). On

average, the peak of the growth spurt instature is at 12.0 years in girls and 14.0 yearsin boys with a standard deviation of nearly 1year for each sex. On a serially plotted curveit can be difficult to recognize the commence-ment of the growth spurt because of frequentirregularities resulting from various factorsthat include inherent variations in velocity andrandom errors in measurement. Deming,(1957) defined the start of the growth spurt^sthe point of inflection on a mathematicallyfitted Gompertz curve and Bergersen (1972)and Bowden (1976) tried to locate it from theraw data. However, most studies have con-centrated on peak height velocity (PHV)which is more readily identified on a seriallyplotted curve.

The uncertainty in the timing of theadolescent spurt makes it difficult for theclinician who wishes to take advantage of itto do so to maximal effect; and the irregularityof the serially plotted curve makes it hard to

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82 SKELETAL MATURITY AND THE GROWTH SPURT

CT1

OJ

9

Age (years)

12 15

Fig. 1. A smoothed height velocity curve. There is considerable variation in the size and timing of theadolescent growth spurt. In boys the peak is at 14.0 years (SD 0.9 years) and in girls it is at' 12.0 years(SD 0.9 years).

identify the growth spurt until it is well underway. The variability in the timing of thegrowth spurt reflects differences in the physicalmaturity of children of the same chronologicalage. It is well established that other matura-tional events are related to the growth curve.For example, menarche in girls occurs afterPHV while the appearance of various second-ary sex characteristics is related to earlier partsof the growth curve (Tanner et al., 1976). Skel-etal age derived from hand-wrist films (Fig. 2)is well established as a method of estimatingphysical maturity; and its value has been de-monstrated by the improvement in predictionof adult height when it is taken into account,particularly at about the time of puberty whenthe greatest variations in maturation are

found among children of the same chrono-logical age (Tanner, 1962). Thus the use ofinformation from hand-wrist films might helpestimation of the timing of the adolescentgrowth spurt. However, it should be notedthat while many studies have reported arelationship between maturity estimated fromhand-wrist films and the timing of the growthspurt, it still has to be shown that knowledgeof skeletal maturity improves by a clinicallyuseful amount the estimate of a child'sposition on his growth curve.

Information from hand-wrist films can beused in a number of ways to estimate theskeletal age of a child. In the atlas method ofGreulich and Pyle (1959) the radiograph in

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SKELETAL MATURITY AND THE GROWTH SPURT 83

Figure 2 Bones of the hand and wrist. The phalangesare labelled P with the prefix P (proximal), M (middle),or D (distal). The numbers refer to the digits, 1 beingthe thumb and 5 the little finger. S is the sesamoid.

question is compared with a standard series offilms, selected to be representative of normalchildren at different chronological ages. Theskeletal age is taken to be that of the standardfilm which the radiograph in question matchesmost closely. A practical difficulty is that therate of maturation in different bones may varyand so it may be difficult to decide whichstandard gives the closest overall match. Inthe Tanner and Whitehouse (TW2) method(Tanner et al., 1975a) a weighted score isallotted to the developmental stage of each of20 bones in the hand and wrist. The bone ageis determined by the total score for theradiograph. A full rating can be undertaken,

or the RUS (radius, ulna and short bones)and Carpal bone ages can be calculatedseparately.

In using hand-wrist films it is importantto distinguish bone stages from ossificationevents (Houston et al., 1979). Bone stages(Fig. 3) are arbitrary periods in the develop-ment of a bone that have been described in aparticular rating system (in the present studythe TW2 method as described by Tanner et al.,1975a). An ossification event occurs when onebone stage changes to the next. Its identifica-tion thus requires serial radiographs and thetiming of the ossification event is the midpointof the interval separating the two filmsbetween which the changeover of bone stagestook place (Fig. 3). In the present paper, anossification event and the immediatelyfollowing bone stage are identified by thesame letter, but the symbol + is added toidentify the stage. Thus the event that marksthe first appearance of an ossification centreis B and the subsequent stage is B + . MP3 (F)is an event and MP3 ( F + ) is the followingstage.

Bjork and Helm (1967), Helm et al.,(1971) and Grave and Brown (1976) reportedassociations between the timings of certainossification events and PHV ages but did notconsider whether this information allowed aclinically relevant improvement in the pre-diction of PHV age. Houston et al. (1979)investigated the association between PHVage and a large number of ossification eventsin the hand and wrist and showed that someevents could improve the prediction of PHVage although only to a limited extent.

Few studies have recommended singlebone stages as criteria of skeletal maturity.From the results of Helm et al. (1971) onossification events, Bjork (1972) discussed theuse of certain bone stages to indicate whetherthe growth spurt had passed or whethergrowth was complete. In certain circum-stances this is all that is required but, if thetiming of PHV is to be predicted, it must berecognized that data from ossification eventscannot be extrapolated directly to bone stagesbecause it is not possible to tell from a singlebone stage when the associated ossification

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E+ F+

S T A G E S

G+ H+

Figure 3 Bone stages and ossification events for the middle phalanx of the third finger (MP3). A detaileddescription of the bone stages in the TW2 system is given in Tanner et al. (1975b). In the ratings of Helmet al. (1971) 'MP3=* is equivalent to MP3(F+); 'MP3Cap' to MP3 (G+); and 'MP3U' to MP3 (!+)•

event occurred, except within very broadlimits. In the present context, a predictivemethod must be evaluated according to theexpected improvement in timing the growthspurt and the size of the confidence limitsassociated with the prediction. The demon-stration of an association between the timingsof the two variables does not by itself showthat the identification of one will be of anyclinical value in the estimation of the other.The clinician must decide, on the basis ofadequate evidence, whether the estimate isaccurate enough to be taken into account inplanning treatment.

Subjects and methods

The subjects were 68 boys and 58 girls ofEuropean origin who took part in theHarpenden growth study. They were asubsample of the group described by Tanneret al. (1976). Subjects were included in thepresent study only where it was possible tomake a reliable assessment of the age at PHV.Records, which had been obtained at six

monthly intervals until the first signs ofsecondary sex characteristics and then everythree months, included hand-wrist radio-graphs taken in a standardized fashion andmeasurements of stature as described byTanner (1962). The developmental stages ofthe bones of the left hand were rated accordingto the TW2 standards of Tanner et al. (1975a).The measurements of stature and the ratingsof the bone stages had all been undertaken bythe one auxologist, R. H. Whitehouse.

From the measurements of stature foreach child, height velocity was calculated anda curve was fitted to allow the age at peakheight velocity (PHV) to be calculated (Tanneret al., 1976). The methods of calculating thetimings of ossification events and bone stagesare described in the following sections. Thestatistical analyses were undertaken using theSPSS 6.5 computer package (Nie et al., 1975).First the distributions of all variables wereexamined for normality. A few ossificationevents had distributions that exhibited skew-ness or kurtosis but this was not a markedfeature (Houston et al., 1979). In the regressionequations, the residuals were plotted and

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examined (Anscombe and Tukey 1963) butthere was no evidence of departures fromlinearity or of inequality of variance.

Results and discussion

Ossification events

The date of each ossification event wascalculated as being halfway between the datesof the last radiograph showing the precedingbone stage and the first radiograph showingthe subsequent one. Over most of the periodcovered by this study, radiographs had beenobtained at least every three months and so,in most cases, the maximum error in theestimate of the age of an ossification event issix weeks.

The timings of ossification events relativeto PHV age in this study are broadly com-parable with those reported by Helm et al.

(1971) for Danish boys and by Grave andBrown (1976) for Australian aboriginalchildren (Table 1). There are some statisticallysignificant differences and this could reflectracial variation and socio-economic differ-ences. Magnusson (1979) has reported somestatistically significant differences in thetiming of certain ossification events betweenDanish, Greenlandic and Icelandic children.

As is evident from the standard devi-ations, the timing of PHV relative to theseossification events is rather variable. Indeed,it is only with events which on averageoccur after PHV that this variability isappreciably less than for the timing of PHVrelative to chronologic age (Table 2). Adetailed account of the relationships of 79ossification events to age at PHV has beenpublished by Houston et al. (1979). Data onthe timing of a number of ossification eventswith the highest correlations with age at PHVat different chronologic ages are presented in

Table 1 Differences in timing in years of certain ossification events and peak velocity in height from the presentstudy compared with other published results

MP3(F)

Ses (B)

MP3 (G)

DP3 (I)

PP3 (1)

MP3 (I)

(M)(F)

(M)(F)

(M)(F)

(M)(F)

(M)(F)

(M)(F)

Present study

Mean

-2 .0-1 .8

-1 .0-1 .0

-0.1-0 .4

1.81.7

2.42.4

2.83.0

S.D.

1.291.07

1.010.76

0.690.89

0.540.55

0.510.68

0.530.80

Grave & Brown 1976*

Mean

-2.4-2.0

-0 .3-0.5

0.30.6

1.61.5

2.32.4

2.32.8

S.D.

1.240.99

0.550.82

0.550.80

0.500.77

0.800.69

0.800.69

Helm et al.,

Mean

-1.2

-1.0

0.4

1.5

2.1

2.5

1971"

S.D.

1.15

0.92

0.56

0.58

0.66

0.64

A negative mean value indicates that the ossification event occurs on average in advance of PHV."The standard deviations have been calculated from the standard errors published in this paper. Due to roundingerrors, these figures can be regarded only as approximate. It should be noted that Grave and Brown took the timingof the ossification event to the midpoint of the year after the stage first appeared. In comparison with the other twostudies, the mean ages should be adjusted by subtracting 1 year.

•'These figures have been calculated from the frequencies published in this paper. A number of the distributionswere appreciably skewed but transformation to allow for this does not have an appreciable effect on the widthsof the confidence limits and so for simplicity, untransformed results are given in this table.

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Table 2 Ossification events with the highest correlations with age at PHV at various chronological ages

OssificationEvent

BoysUlna (D)Trapezium (E)Ulna (E)Scaphoid (E)Trapezium (F)Ulna (F)Trapezium (G)PP3 (F)Trapezium (H)Lunate (H)Scaphoid (H)MP3 (G)Ulna (G)MP5 (G)MCI (H)

GirlsDPI (F)Scaphoid (F)PP3 (F)Radius (G)MP3 (F)MCI (G)Sesamoid (B)DP3 (G)Trapezium (I)DPI (H)DP5 (H)MC3 (H)Radius (1)MC3 (I)

No

232833324645444849545558575635

2525303235393743453428272421

Age of AppearanceMean ± S.D.

(years)

8.58.99.29.7

10.110.611.111.612.212.913.213.914.014.515.3

8.28.89.39.7

10.310.911.111.712.213.313.714.414.715.3

1.571.681.351.661.431.361.311.451.091.150.980.971.000.901.05

1.030.981.160.821.120.980.930.980.811.030.960.881.111.02

Years toMean

-5 .5-5 .1-4 .8- 4 . 3-3 .9- 3 . 4- 2 . 9- 2 . 4-1 .8- 1 . 1-0 .8-0 .1

0.00.51.3

-3 .9-3 .3-2 .8- 2 . 4-1 .8- 1 . 2- 1 . 0- 0 . 4

0.11.21.62.32.63.2

PHV± S.D.

.411.511.201.561.361.36.25.42.07.11

0.840.690.740.650.49

.11

.141.110.751.070.910.760.770.750.620.550.600.660.81

Correlationr

0.440.470.460.360.360.300.400.330.410.390.580.720.690.740.89

0.300.180.370.580.440.520.660.670.610.820.840.800.810.67

Regressionb

0.18*0.14**0.27**0.18*0.20*0.180.26**0.19*0.32*0.27*0.50*0.66*0.62*1

0.74*0.81**

0.240.150.25*0.58*0.35*'0.47*'0.63*'0.63*'0.68*'0.82*"0.81**0.91**0.74**0.64**

ResidualS.D.

(years)

0.590.440.700.780.730.810.800.810.780.730.680.620.650.610.46

0.800.800.730.680.790.760.680.690.710.600.520.610.600.74

•Indicates significance at the 5 per cent level and **at the 1 per cent level

Table 2. These correlation coefficients are allstatistically significant and they tend to belarger for events close to PHV than for thoseoccurring several years in advance of it. Thisis hardly surprising because a child who isadvanced or retarded relative to his peers atone age will not necessarily be so at a later age.However, this means that the value of theearlier ossification events as predictors of ageat PHV is limited. For prediction, it isregression coefficients, not correlationcoefficients, that are of interest. The regressioncoefficients (Table 2) indicate the adjustmentswhich should be made to the expected age atPHV when the ossification event is taken intoaccount (e.g. see Fig. 4).

A number of points should be emphasized.1. The regression coefficients for boys and

girls differ and so separate figures must beused. For example, the regression onRadius (G) is highly significant in girls,but not at all significant in boys; and Ses(B) has a regression coefficient of 0.63 ingirls but only 0.39 in boys (Houston et al.,1979).

2. When the regression coefficient is small,even although it may be statisticallysignificant, the adjustment to the esti-mated time of PHV is trivial.

3. The highest regression (and correlation)coefficients are found at or after theaverage age of PHV but these are not of

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PP31F) PHV MCHH)

JO 11 12 13 14 15 16

Figure 4 The distribution of the timings of two ossification events relative to the age at peak height velocity inboys. (Left) the identification of PP3 (F) at the average age of its appearance indicates that in two such cases out ofthree, peak height velocity will occur between 10 years 9 months and 12 years 4 months. If the event occursearlier or later than average, the expected age of PHV should be adjusted according to the regression coefficientfor age of PHV on age of ossification event. (Right) in 97.5 per cent of cases, the occurrence of event MCI (H)indicates that PHV has occurred at least four months earlier.

predictive value. They could be used toindicate whether the growth spurt hadpassed or whether growth was nearlycompleted, but the subsequent bone stagescan be just as useful for this.

4. By taking account of regressioncoefficients for certain events which onaverage occur during the year or twobefore PHV, the prediction of the age ofPHV can be improved. It should be notedthat the residual standard deviations andthus the confidence limits of the predictionare quite large and so there is still con-siderable uncertainty in prediction. How-ever, because the prediction is moreefficient, they are slightly narrower thanthose obtained by using the meandifference. Compare for example Sesamoid(B) in girls where the standard deviation ofthe difference between the timing of theossification event and PHV is 0.76 yearswhile the residual standard deviation ofthe regression is only 0.68 years (Table 2).

5. It is important to note that when theregression coefficient is less than 0.5, theaddition of the mean difference to the ageof the ossification event in order toestimate age at PHV may well give aworse estimate of its timing than does

chronologic age alone. For example, if in aboy Ses (B) is 1 year late, it is quiteincorrect to estimate that PHV will becorrespondingly delayed. The regressioncoefficient in this case is 0.39 and so forevery year that SES (B) is advanced, orretarded, the expected age of PHV shouldbe adjusted by 0.39 years, not by 1 year.Thus it is essential to recognize that, evenif it is known that a particular ossificationevent has occurred early or late, it is notcorrect to assume that the age of PHV willbe affected to the same extent.

6. If clinical radiographs are taken lessfrequently than in this study, the timing ofthe ossification events will be less reliableand so, although the regression coefficientswill still apply, the confidence limits of theprediction will be wider. One of theproblems of using ossification events isthat serial radiographs may have to beobtained over quite extended periods oftime, indicated by the size of the standarddeviations of the timings of the ossificationevents (Table 2). In order to be confidentof identifying a particular ossificationevent in 95 per cent of children, it wouldbe necessary to obtain the first radiographtwo standard deviations in advance of the

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average age of its appearance and itmight be necessary to continue at regularintervals for as long as two standarddeviations after that. Clearly, in childrenwho were advanced, the event would beidentified rapidly and, in those who wereobviously delayed, the second radiographcould be postponed until the average ageof the event in question. In addition, otherevents that could be used might beidentified during the period of radio-graphic supervision. Nevertheless, thereliable timing of a particular event is notsimple unless hand-wrist radiographs areobtained at regular intervals, possiblyover an extended period of time. Althoughthe radiation dosage from a properlytaken hand-wrist film is small frequentradiographs may be undesirable.It might be expected that prediction couldbe improved by taking account of morethan one ossification event. However, thetimings of different ossification events arethemselves correlated and the contributionto the prediction of events after the first issmall and usually not of statisticalsignificance. (Houston et al., 1979).

Bone stages

Bone stages are identified from a singleradiograph. The duration of different stagesvaries considerably. For example, in boys,

MC3 stage F lasts on average for over 5.1years whereas Ulna stage D lasts for less than1 year. It is not possible from a singleradiograph to determine with any degree ofreliability whether a stage is early or late in itsdevelopment. Statistically, it is most efficientto assume that a stage is midway between itsdelimiting ossification events. Thus theexpected time of PHV is the average of thecorresponding figures for the ossificationevents. Clearly, because of the possible errorwhich is introduced by the assumption that astage is at its midpoint, the confidence limitsfor the timing of PHV will be greater thanthose for the ossification events. The meansand standard deviations of age at PHV werecalculated for each stage at each year of age,for boys and girls of the present sample.Table 3 is an extract of the resulting analysis,which is too extensive to publish in full. As isto be expected, the less mature a bone is in achild of a given age, the later is the averageage of PHV; and the latter also variesaccording to the chronologic age at which thestage was observed. When the data aresegregated in this fashion, the confidencelimits are smaller than would otherwise havebeen the case but at many points they are notappreciably less, and sometimes they aregreater, than for the estimations of PHV agefrom chronologic age alone. The differences inthe expected ages of PHV are mostly trivial.The dubious gain in predictive accuracy andthe cumbersome nature of the tables that

Table 3 Age at PHV for boys with the indicated bone stages at different chronologic ages (Boys)

Bone stage

PP3

MP3

DP3

E+F+G +E+F+G+E+F+G+

n

3810

462

2028

10.0

X

14.013.7

13.914.4

14.113.9

SD

0.830.79

0.830.88

0.710.90

n

3020

3911

1040

Chronologic age (years)

11.0

X

14.213.8

14.113.8

13.914.1

SD

0.681.02

0.791.04

0.810.86

n

1734

12823

13

481

12.0

X

14.313.715.014.113.713.814.113.913.0

SD

0.640.87

0.760.95

0.590.87

n

93713163211

4415

13.0

X

14.714.013.314.414.113.0

14.113.4

SD

0.470.631.100.680.650.88

0.750.89

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would be required, militate against the use ofsingle bone stages for the prediction of age atPHV.

As was indicated by Bjork (1972), singlebone stages can be used to indicate that thegrowth spurt has not yet started or that it haspassed, or that growth is nearly complete.The presence of a bone stage indicates thatthe prior ossification event has alreadyoccurred and the subsequent event has yet tocome. This could be of use if it is necessary toascertain that growth is nearly over beforeabandoning orthodontic retention or under-taking surgical correction of jaw malrelation-ships. In evaluating the probability that anevent such as PHV has passed, it is appropriateto use a 1 tailed test (see Fig. 4). However, thisapproach is of limited application because itcan indicate whether or not an event hasoccurred, but not its timing except within verybroad limits.

Bone age

RUS and Carpal bone ages at each birthdaywere estimated according to the TW2method (Tanner et al., 1975a). In some olderchildren these had reached maximum values(18.2 and 16.0 for RUS age in boys and girlsrespectively and 15.0 and 13.0 for Carpal age).Where this was the case, these children werenot included in the correlation and regressioncalculations for the relevant age groups, but

the age at PHV was calculated separately(Table 4). It is apparent that, in these cases,the variation is so great that the informationis of little value for predictive purposes.

Regressions and correlations of age atPHV on bone age and stature at each birthdaywere calculated. Taken singly, RUS bone age,Carpal bone age and present height all exhibitsignificant correlations with PHV age atcertain chronologic ages (Table 5). In general,the correlations with RUS bone age arehighest and those with Carpal bone age arelowest. In order to investigate the possiblebenefits of taking account of more than oneof these variables, multiple correlations wereevaluated, including the three independentvariables in different orders. It was found thatwhen RUS bone age was included first, thefurther contributions of Carpal bone age andof present height were generally trivial(Table 5). When RUS bone age was includedafter the other variables, it always made alarge and significant contribution to thecorrelation. Thus, the most efficient predictionof the age of PHV will be based on RUS boneage.

Regression coefficients of PHV age onRUS bone age at each birthday are given inTable 6. It will be noted that, in girls, these aresignificant at all the ages investigated but, inboys, it is only after 11 years of age that theregression coefficient becomes significant andeven at this age it is small. Separate standardsmust be used for the different ages and for

Table 4 Ages at PHV when RUS and carpal bone ages had reached maximum values

ChronologicAge in Years

11.012.013.014.015.016.017.0

n

423394535

Boys

Mean

12.813.413.814.014.1

Carpal age is maximum

±S.D.

1.40.90.70.81.0

n

4223841321915

Girls

Mean

10.811.111.912.012.112.112.2

± S.D.

0.90.71.01.11.11.11.1

RUS age is maximum

n

158

10

Girls

Mean

9.812.111.311.7

± S.D.

0.70.81.0

Each group contains all cases where RUS and Carpal bone age had reached maximum values, regardless of howlong this had been the case.

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Table 5 Correlation coefficients for bone ages and height with the timing of peak height velocity in children atdifferent chronological ages

ChronologicalAge

Boys8.09.0

10.011.012.013.014.015.016.017.0

Girls8.09.0

10.011.012.013.014.015.0

No

33384548525857554736

3235444951484127

RUS BoneAge1

-0.15-0.11-0.12-0.33*-0.40**-0.65**-0.78**-0.78**-0.78**-0.75**

-0.47**-0.51**-0.55**-0.71**-0.73**-0.71**-0.76**-0.76**

Height

-0.13-0.15-0.17-0.22-0.26-0.45**-0.51**-0.35**-0.13-0.10

-0.38*-0.45**-0.45**-0.57**-0.60**-0.48**-0.26-0.12

No

333845485254341621

32354445291010

Carpal BoneAge2

-0.17-0.11-0.09-0.26-0.37**-0.47**-0.43*-0.51*Too few

cases

-0.02-0.17-0.37*-0.66**-0.35-0.80Too few

case

Multiple Correlations3

RUS +

0.150.110.120.33*0.40**0.53**0.55**0.50*

Too fewcases

0.47**0.51**0.55**0.67**0.61**0.92**

Too fewcases

Carpal +

0.170.120.120.330.400.550.560.55

0.560.550.560.71*0.610.93

Height

0.180.160.170.340.410.550.560.55

0.600.610.590.730.620.93

"Indicates significance at the 1 per cent and *at the 5 per cent level.By the age of 16 years, most girls had reached adult values for both RUS bone age and for carpal bone age andso too few cases were left to allow the statistics to be calculated.

1 The negative signs of the correlation coefficients indicate that the more advanced a child of a given chronologicalage is for one of these variables, the earlier is the expected age of PHV.

2 In a number of older children, carpal bone age had reached the adult value and so they were not included inthe correlations involving it. For this reason there are sometimes fewer cases where carpal bone age is included and,in the multiple correlation, the coefficient for RUS bone age may differ from the simple correlation coefficient.

3 In the multiple correlation tables, signs have been suppressed. The first column is equivalent to the simplecorrelation coefficient and subsequent columns give the size of the multiple correlation coefficient when the variableis included. The asterisks indicate whether the correlation coefficient is increased by a significant amount when thatvariable in included.

each sex. At all ages the residual standarddeviations are still quite large and this mustbe taken into account if it is hoped to under-take treatment during a period of rapidgrowth.

As was the case with ossification events,gross errors in prediction may result if theexpected age of PHV is adjusted to correspondwith the bone age. In boys of 11 years forexample, the PHV age should be adjusted byonly three months for every year that RUSbone age differs from chronologic age.

Bergersen (1972) published a table for theprediction of the pubertal growth spurt inboys. This seems to have been based on the

assumption that the commencement of thegrowth spurt could be determined accordingto skeletal age. However, when skeletal age isused as a baseline, the variability of timing ofa number of maturational events is nearly asgreat as when chronological age is used. Forexample, Marshall (1974) reported that thestandard deviation of RUS bone age at thetime of PHV was 0.92 years in girls and 0.77years in boys compared with 1.06 and 0.96years for chronological age.- Thus in thepresent context, skeletal age does not offermajor advantages over chronological age.Only when both chronological age andskeletal age are taken into account, as was

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Table 6 Regression of PHV on RUS bone age

ChronologicAge

8.09.0

10.011.012.013.014.015.016.017.0

No

33384548525857554736

Boys

b

-0.15-0.10-0.09-0.25*-0.39*'-0.58*-0.72*'-0.84*'-0.62*'-0.63*'

ResidualS.D.

0.940.930.890.83

' 0.81• 0.66

0.57• 0.50

0.520.63

No

3235444951484127

Girls

b

-0.55*'-0.57*'-0.62*'-0.73*-0.82*'-1.07*-0.96*'-1.01*'

Too few cases" >» »»

ResidualS.D.

0.900.880.860.690.680.730.670.74

Average age at PHV: Boys 14.0 years (S.D. 0.9 years); Girls 12.1 years (S.D. 0.9 years)ExampleA boy aged 12.0 years has a RUS bone age of 11.0 years.Average age at PHV for boys = 14 years.Discrepancy between bone age and chronologic age = (11-12) years = — 1 year.Regression coefficient = —0.39Residual S.D. = 0.81

Expected age at PHV = 14 + (-0.39 x - 1 ) = 14.3968 per cent confidence limits are 14.39 ± 0.81 = 13.6 — 15.295 per cent confidence limits are 14.39 ± 2x 0.81 = 12.8 - 16.0

i.e. in 68 per cent of such cases, the true age at PHV will fall within the range 13.6-15.2 years and in 95 per centof cases, it will fall within the range 12.8-16.0 years. (Strictly speaking, the width of the confidence limits alsodepends on the distance of the estimate from the mean but in the present context such an adjustment is trivial andcan be ignored).

done in the present study, is there an effectivereduction in the uncertainty of the timing ofthe growth spurt.

The results of the present study arealmost identical with those of Liebgott (1967)for correlations between the age at PHV andskeletal age in boys from the Burlingtonstudy. Liebgott (1978) published correlationsbetween the peak of the mandibular growthspurt and skeletal age in boys from the samestudy. The figures are slightly higher thanthose for stature but the patterns of associa-tion are very similar and this lends support tothe assertion that the results of the presentstudy apply to facial growth as well as tostature.

Conclusions

It is clear that the information from hand-

wrist radiographs is of only limited value inpredicting the time of peak height velocityand thus of the growth spurt. With allmethods, the prediction improves as theaverage age of the growth spurt is approached.This is in accord with the finding of Tanneret al. (1975b) that bone age contributes littleto the prediction of adult stature in youngerchildren although it is helpful within a fewyears of the pubertal growth spurt.

The practical difficulties of timing ossifi-cation events and the need for serial observa-tions before an estimate of age at PHV can bemade, will preclude their use in most clinicalsituations. It should also be remembered thatif radiographs are obtained less frequentlythan in this study, predictions will be lessaccurate. Bone stages and bone ages have theover-riding advantage that they can beobtained from a single radiograph. Singlebone stages are not helpful in the prediction

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of PHV age although certain stages can beused to show that growth spurt has not yetcommenced or that it has passed.

Carpal bone age is generally less informa-tive than RUS bone age. It is also moredifficult to rate and reaches its adult valuebefore the age of PHV in some cases. Withexperience, the RUS bone age is not timeconsuming to calculate and this should bedone if an estimate of age at PHV is required.

The expected timing of PHV should beestimated using the appropriate regressioncoefficient and separate standards must beused for boys and for girls. Merely adjustingthe average age of PHV by the time that theskeletal maturity is advanced or retarded willgenerally give a poor estimate. Attentionshould also be paid to the size of the con-fidence limits of the prediction. Even underthe most favourable conditions these areappreciable and this must be allowed for iftreatment is to be timed to take advantage ofthe growth spurt.

The concern of this paper has been toexplore the contribution that informationfrom hand-wrist films might make to theprediction of the timing of the pubertalgrowth spurt. The advisability of attemptingto time orthodontic treatment to takeadvantage of the growth spurt will be dis-cussed in a separate paper.

Acknowledgement

I wish to record my thanks to ProfessorJ. M. Tanner for making available to medata from the Harpenden Growth Study andfor his advice and constructive criticism in thepreparation of this paper.

Address for correspondence

Professor W. J. B. Houston,Orthodontic Department,Royal Dental Hospital,Leicester Square,London WC2 H7LJ,England.

References

Anscombe, F. J. and Tukey, J. W. (1963). Theexamination and analysis of residuals.Technometrics, 5: 141-160.

Bergersen, E. O. (1972). The male adolescentfacial growth spurt: its prediction andrelation to skeletal maturation. AngleOrthodontist, 42: 319-338.

Bjork, A. (1972). Timing of interceptiveorthodontic measures based on stages ofmaturation. Transactions of the EuropeanOrthodontic Society, 1-14.

Bjork, A. and Helm, S. (1967). Prediction ofthe age of maximum pubertal growth inbody height. Angle Orthodontist, 37:134-143.

Bowden, B. D. (1976). Epiphysial changes inthe hand-wrist area as indicators ofadolescent stage. Australian OrthodonticJournal, 4: 87-104.

Deming, (1957). Application of the Gompertzcurve to the observed pattern of growth inlength of 48 individual boys and girls duringthe adolescent cycle of growth. HumanBiology, 29:83-122.

Grave, K. C. and Brown, T. (1976). Skeletalossification and the adolescent growthspurt. American Journal of Orthodontics,69: 611-619.

Greulich, W. and Pyle, S. (1959). Radio-graphic atlas of skeletal development ofthe hand and wrist. Second edn. StanfordUniversity Press.

Helm, S, Siersbaek-Nielsen, S, Skieller, V.and Bjork, A. (1971). Skeletal maturationof the hand in relation to maximumpuberal growth in body height. Tandlaege-bladet, 75:1223-1234.

Houston, W. J. B., Miller, J. C. and Tanner,J. M. (1979). Prediction of the timing of theadolescent growth spurt from ossificationevents in hand wrist films. British Journal ofOrthodontics, 6:145-152.

Liebgott, B. (1967). The usefulness of dentalage in determining the dental status of anindividual. M. Sc. D. Thesis, University ofToronto.

Liebgott, B. (1978). Dental age: its relationto skeletal age and the time of peak

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circumpuberal growth in length of themandible. Journal of Canadian DentalAssociation, 44: 223-227.

Magnusson, T. E. (1979). Skeletal maturationof the hand in Iceland. Act a OdontologicaScandinavica, 37:21-28.

Marshall, W. A. (1974). Inter relationships ofskeletal maturation, sexual developmentand somatic growth in man. Annals ofHuman Biology, 1: 29-40.

Nanda, R. S. (1955). The rates of growth ofseveral facial components measured fromserial cephalometric roentgenograms.American Journal of Orthodontics, 41:658-673.

Nie, N. H., Hull, C. H. Jenkins, J. G.Steinbrenner, K. and Bent, D. H. (1975).Statistical package for the Social Sciences.Second edn. McGraw Hill.

Tanner, J. M. (1962). Growth at Adolescence.Second edn. Blackwell: Oxford.

Tanner, J. M., Whitehouse, R. H., Marshall,W. A., Healy, M. J. R. and Goldstein, H.(1975a). Assessment of skeletal maturityand prediction of adult height: TW2method. Academic Press: London.

Tanner, J. M., Whitehouse, R. H., Marshall,W. A. and Carter, B. S. (1975b). Predictionof adult height from height, bone age andoccurrence of menarche at ages 4 to 16 withallowance for midparent height. Archives ofDisease in Childhood, 50: 14-26.

Tanner, J. M., Whitehouse, R. H. Marubini,E. and Resele. (1976). The adolescentgrowth spurt of boys and girls of theHarpenden growth study. Annals of HumanBiology, 3: 109-126.

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