The Journal of Bone & Joint Surgery

The Journal of Bone & Joint Surgery, Volume 93, Issue 11

Scientific Articles | June 01, 2011

Comparison of the Paley Method Using Chronological Age with Use of Skeletal Maturity for Predicting Mature Limb Length in Children

James O. Sanders, MD¹; James Howell, MD²; Xing Qiu, PhD¹

¹ University of Rochester Medical Center, 601 Elmwood Avenue, Box 665 (J.O.S.) and Box 630 (X.Q.), Rochester, NY 14642. E-mail address for J.O. Sanders: James_sanders@urmc.rochester.edu
² Shriners Hospitals for Children, 1645 West 8th Street, Erie, PA 16505

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Disclosure: One or more of the authors received payments or services, either directly or indirectly (i.e., via his or her institution), from a third party in support of an aspect of this work. In addition, one or more of the authors, or his or her institution, has had a financial relationship, in the thirty-six months prior to submission of this work, with an entity in the biomedical arena that could be perceived to influence or have the potential to influence what is written in this work. Also, one or more of the authors has had another relationship, or has engaged in another activity, that could be perceived to influence or have the potential to influence what is written in this work. The complete Disclosures of Potential Conflicts of Interest submitted by the authors are always available with the online version of this article at jbjs.org.

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Investigation performed at Shriners Hospital for Children, Erie, Pennsylvania, and University of Rochester, Rochester, New York

J Bone Joint Surg Am, 2011 Jun 01;93(11):1051-1056. doi: 10.2106/JBJS.J.00384

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Abstract

Background:

Treating patients with congenital or acquired limb-length inequality requires accurate estimations of limb length at skeletal maturity. There is controversy over the best indicator of maturity to be used for limb-length calculations. Paley popularized the multiplier method, in which chronological age is used, which has the virtue of simplicity but does not account for the wide variance in timing of the adolescent growth spurt. The purpose of this study was to determine whether the use of chronological age or the level of skeletal maturity provides more accurate limb-length predictions.

Methods:

We identified patients with limb-length inequality, for whom scanograms had been obtained before and at maturity, and who had had no surgical procedures on their normal lower limb. Skeletal maturity was determined with use of the Greulich and Pyle atlas, Tanner-Whitehouse-3 method, and simplified stages described by Sanders et al. The length of the lower extremity was compared with the ultimate limb length and the actual multiplier (final limb length divided by current limb length) for each point in time. A linear model was used to determine the log-transformed multipliers for the level of skeletal maturity, and Paley's multipliers were used for chronological age. Residual standard errors were determined to compare the results of the methods. We also conducted piecewise linear regression on each of the methods and used the residual standard errors to rank their performance and cross-validated the results.

Results:

We identified twenty-four patients (twelve girls and twelve boys) who met the study criteria. Most subjects had had multiple scanograms along with skeletal age radiographs (average, 4.5) at different ages. When all ages are considered, the Paley method had the best overall performance, with residual standard errors that were typically =5 cm. However, the Paley method did not perform best for subjects at stage-2 skeletal maturity or above; in those cases, skeletal-maturity-based predictions had residual standard errors of <2 cm.

Conclusions:

While the Paley method, which is based on chronological age, provides reasonable estimates of ultimate limb length for most patients, use of skeletal-maturity determinations appears to provide better predictions of mature limb length during adolescence.

Figures in this Article

Introduction

Introduction | Materials and Methods | Results | Discussion | References

Children with limb-length inequality resulting from congenital discrepancies or physeal injury typically show proportional growth of the limbs, with the absolute difference increasing over time. Logically, more accurate measurements of skeletal maturity should yield better limb length predictions. A study by Anderson et al.¹ showed that the use of skeletal age was superior to the use of chronological age for predicting lower-extremity growth, and, until recently, their methods of limb length prediction remained a common technique for estimating mature limb length. Moseley² simplified the method of Anderson et al. by creating a straight-line graph in which only skeletal maturity is used. Paley et al.³, utilizing several large databases of limb lengths, introduced the multiplier technique, with which only chronological age is used and the degree of skeletal maturity is ignored completely. Since the two methods have not been directly compared, to our knowledge, it is uncertain whether the Paley method or skeletal-maturity-based determinations provide more accurate prediction of limb length, particularly for children who mature either early or late⁴. The issue of early or late maturation is important because the adolescent growth spurt is a time of very rapid growth that is not uniform among children. The growth spurt lasts about four years, with the midpoint at about age twelve in girls and age fourteen in boys, but normal pubertal timing can vary by as much as four years in children in similar environments⁵. The adolescent growth spurt should be the most difficult time for making reliable predictions based on chronological age.

The purpose of this study was to compare actual limb lengths with predicted limb lengths at various stages of skeletal maturity with use of both skeletal-maturity determinations and the Paley method.

Materials and Methods

Introduction | Materials and Methods | Results | Discussion | References

We performed a retrospective, institutional review board-approved study of patients treated at Shriners Hospitals for Children, Erie, Pennsylvania. The inclusion criteria were one normal limb that had not been operated on prior to physeal closure, limb-length studies done before and at maturity, and radiographs made to determine skeletal age at the time of the limb-length-inequality measurements. Patient charts and radiographs in the thirty years preceding the study were reviewed retrospectively to identify subjects for inclusion. Only the normal lower limb was used for the study. Exclusion criteria included both lower limbs affected by a disease process, surgery on the normal lower limb, or a lack of adequate available radiographs. The technique of obtaining the radiographs for measuring limb length was consistent at the hospital throughout the study period. The images were obtained with the patient supine, with a radiographic ruler aligned along the extremity. Individual images of the hip, knee, and ankle were made to avoid radiographic parallax. Posteroanterior radiographs of the left hand and wrist were made to determine skeletal age.

To minimize bias, separate investigators performed the three parts of this study: determination of limb length, determination of skeletal maturity, and statistical analysis. One investigator performed the limb-length measurements using a standardized method, with measurement of the femur from the top of the femoral head to the medial femoral condyle and measurement of the tibia from the medial femoral condyle to the tibial plafond. The sum of these measurements was defined as the limb length with the foot excluded. All limb-length studies for each patient who had corresponding skeletal age radiographs were utilized.

Skeletal age radiographs were reviewed by a separate investigator using the Greulich and Pyle method⁶, the Tanner-Whitehouse-3 RUS method⁷, and the method of Sanders et al.⁸. The length of the lower extremity was compared with the final limb length and the actual multiplier (the final limb length divided by the current limb length) for each point in time. The multipliers used for chronological age were determined from the data reported by Paley et al.³.

Statistical Methods

The boys and girls were analyzed separately. Curve fitting and statistical analyses were performed by a third investigator. Final length prediction was modeled as: FL = FL₀ exp[ß₀ + ß₁X_k + e], where FL represents the final limb length, FL₀ is the present (starting) length, ß₀ is a coefficient that is different for the two sexes, ß₁ is a coefficient that is assumed to be the same for the two sexes, X_k is one of the maturity indicators (determined with the Greulich and Pyle, Tanner-Whitehouse-3, or Sanders method), and e is the random error term, which is assumed to be normally distributed with mean zero and equal variance. This model can be reformulated as this linear model: log (M) = ß₀ + ß₁X_k + e, where M = FL/FL₀ is the true multiplier. The equation was used to determine the multipliers for the various maturity measures. The quality of the maturity indicators was assessed on the basis of the residual standard errors of the final length predicted with the use of each maturity indicator. We also calculated the residual standard error of the final length predicted by using Paley's multipliers. The multiple regression R² values are provided in Table II as a measurement of how much variance can be explained by each predictor in this model. We also conducted piecewise linear regression analysis to identify the break points of the maturity indicators between the various models, with validation performed with use of leave-one-out cross-validation apart from Paley's multipliers³.

Because the adolescent growth spurt begins at stage 2 in the Sanders system⁸, the results were also compared in individuals at stage 2 and above to separately compare the roles of skeletal maturity and chronological age in limb-length predictions during the adolescent growth spurt.

Source of Funding

No outside funding was received for this study.

Results

Introduction | Materials and Methods | Results | Discussion | References

We identified twenty-four patients (twelve girls and twelve boys) with limb-length inequality who had had scanograms made before and at maturity and had had no surgical procedures on the normal lower limb. Most subjects had had multiple scanograms and skeletal age radiographs (average, 4.5; range, two to nine) at different ages, and all of these images were used. The reasons for the short limbs are listed in Table I. We identified a recognizable stage in addition to those described by Sanders et al.⁸, by dividing their stage 3 into stages 3A and 3B on the basis of whether the distal part of the radius was covered (3A) or capped (3B). This corresponds to the Greulich and Pyle atlas female skeletal ages of eleven years for 3A and twelve years for 3B. The residual standard errors and multiple regression R² values are shown in Table II.

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TABLE I Etiologies of the Short-Limb Abnormalities of the Subjects in the Study

Etiology	Number
Idiopathic	3
Congenital deficiency or short femur	5
Hemiplegic cerebral palsy	4
Traumatic or septic	7
Developmental hip dislocation or Legg-Calvé-Perthes disease	2
Tibial congenital pseudarthrosis	2
Clubfoot	1

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TABLE I Etiologies of the Short-Limb Abnormalities of the Subjects in the Study

Etiology	Number
Idiopathic	3
Congenital deficiency or short femur	5
Hemiplegic cerebral palsy	4
Traumatic or septic	7
Developmental hip dislocation or Legg-Calvé-Perthes disease	2
Tibial congenital pseudarthrosis	2
Clubfoot	1

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TABLE II Multiple Regression R² Values and Residual Standard Errors for All Ages and for Subjects in Their Adolescent Growth Spurt (Stage 2 and Above)

	All Ages		Stage 2 and Above
Method	Multiple Regression R²*	Residual Standard Error (cm)	Multiple Regression R²*	Residual Standard Error
Paley	Not applic.	4.9	Not applic.	3.2
Greulich and Pyle	0.996	6.3	0.9993	2.2
Tanner-Whitehouse-3	0.995	7.1	0.9994	2.2
Sanders	0.984	12.7	0.9995	1.9

*Multiple regression R² values closer to 1.0 are better.

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TABLE II Multiple Regression R² Values and Residual Standard Errors for All Ages and for Subjects in Their Adolescent Growth Spurt (Stage 2 and Above)

	All Ages		Stage 2 and Above
Method	Multiple Regression R²*	Residual Standard Error (cm)	Multiple Regression R²*	Residual Standard Error
Paley	Not applic.	4.9	Not applic.	3.2
Greulich and Pyle	0.996	6.3	0.9993	2.2
Tanner-Whitehouse-3	0.995	7.1	0.9994	2.2
Sanders	0.984	12.7	0.9995	1.9

*Multiple regression R² values closer to 1.0 are better.

When using this specific model and considering all ages, we found that use of the chronological-age-based Paley method resulted in the best overall performance with residual standard errors typically =5 cm. However, when the analysis was restricted to subjects at stage 2 or above, the skeletal maturity measures provided more robust predictions than did chronological age. From stage 2 onward, the residual standard error of the Paley method estimates (3.2 cm) was greater than those of the various skeletal maturity methods (all about 2 cm).

Piecewise Regression Analysis

A linear growth model such as the one used in the analysis described above is a first-degree approximation of the complex, dynamic natural growth because it assumes constant relative growth velocity, which is defined as the growth velocity divided by height. We refit the linear model with three variables: age, sex, and the maturity score of interest. The results of the trivariate regressions were compatible with those of the bivariate regressions. The improvements achieved by adding one more predictor, age, into the regression model were not very large. All predictors were highly correlated, making the additional information provided by any one of them limited. A better way to capture the nonconstant nature of the relative growth velocity is through a piecewise linear model, under which the relative growth velocity can take (up to three) different values during different growth periods. The log of the true multiplier as compared with the predicted multiplier for the Paley method as compared with the commonly used Greulich and Pyle skeletal maturity prediction is shown in Figures 1-A (girls) and 1-B (boys). Figure 1 shows graphically that the piecewise linear regression curve fits better than does the Paley method for more mature patients but not as well for more immature patients. The breakpoints for the piecewise linear regression shown in Figure 1 were determined with use of the method described by Muggeo⁹ and limited to no more than two breakpoints to prevent overfitting in light of our limited sample size.

Fig. 1-A Fig. 1-B

Figs. 1-A and 1-B Graphs showing the natural log true multiplier (y axis) for each subject's multiplier with use of the Greulich and Pyle skeletal age (circles) compared with the Paley chronological age multiplier (triangles). The regression line is for the multiplier derived with use of the Greulich and Pyle skeletal age. The x axis indicates the skeletal maturity. The circles represent the true multiplier for the particular level of skeletal maturity while the triangles represent the multiplier predicted by the Paley method. Fig. 1-A Graph for females. Fig. 1-B Graph for males.

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Model Validation

Since piecewise linear regression is a more complex method than linear regression, we applied leave-out-one cross-validation to calculate the residual standard error and then ranked the different predictors performance accordingly. This approach removes the danger of model overfitting. The results of the piecewise regression analysis for each predictor are summarized in Table III.

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TABLE III Residual Standard Errors for Girls and Boys of All Ages and Those in Their Adolescent Growth Spurt (Stage 2 and Above) Calculated with Piecewise Linear Regression

	All Ages (cm)		Stage 2 and Above (cm)
	Girls	Boys	Girls	Boys
Paley	4.0	5.8	2.4	4.0
Greulich and Pyle	5.6	9.7	1.8	2.6
Tanner-Whitehouse-3	4.4	7.3	1.9	2.5
Sanders	9.3	15.3	1.9	2.2

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TABLE III Residual Standard Errors for Girls and Boys of All Ages and Those in Their Adolescent Growth Spurt (Stage 2 and Above) Calculated with Piecewise Linear Regression

	All Ages (cm)		Stage 2 and Above (cm)
	Girls	Boys	Girls	Boys
Paley	4.0	5.8	2.4	4.0
Greulich and Pyle	5.6	9.7	1.8	2.6
Tanner-Whitehouse-3	4.4	7.3	1.9	2.5
Sanders	9.3	15.3	1.9	2.2

From Table II, we can conclude that Paley's method is the best predictor when one is considering all ages for both boys and girls. However, when the analysis is limited to individuals in stage 2 and above, the conclusion is just the opposite: the Greulich and Pyle, Tanner-Whitehouse-3, and Sanders methods all perform better than the Paley method. This conclusion is consistent with the results of the linear regression analysis. The specific multipliers for the various methods can be found in Table IV.

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TABLE IV Multipliers for Different Levels of Skeletal Maturity with Use of the Various Methods

	Multiplier
	Sanders Method
	Girls	Boys	Greulich and Pyle Method	Tanner-Whitehouse-3 Method
Stage
2	1.11	1.11
3A	1.07	1.07
3B	1.06	1.06
4	1.05	1.05
5	1.03	1.03
6	1.01	1.01
7	1.00	1.00
Skeletal age, girls
10 yr			1.12	1.12
11 yr			1.09	1.08
12 yr			1.06	1.05
13 yr			1.04	1.03
13.5 yr			1.03	1.01
14 yr			1.02	1.00
15 yr			1.00	1.00
Skeletal age, boys
11 yr			1.13	1.13
11.5 yr			1.12	1.11
12.5 yr			1.09	1.08
13 yr			1.08	1.07
13.5 yr			1.07	1.06
14 yr			1.06	1.04
15 yr			1.04	1.02

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TABLE IV Multipliers for Different Levels of Skeletal Maturity with Use of the Various Methods

	Multiplier
	Sanders Method
	Girls	Boys	Greulich and Pyle Method	Tanner-Whitehouse-3 Method
Stage
2	1.11	1.11
3A	1.07	1.07
3B	1.06	1.06
4	1.05	1.05
5	1.03	1.03
6	1.01	1.01
7	1.00	1.00
Skeletal age, girls
10 yr			1.12	1.12
11 yr			1.09	1.08
12 yr			1.06	1.05
13 yr			1.04	1.03
13.5 yr			1.03	1.01
14 yr			1.02	1.00
15 yr			1.00	1.00
Skeletal age, boys
11 yr			1.13	1.13
11.5 yr			1.12	1.11
12.5 yr			1.09	1.08
13 yr			1.08	1.07
13.5 yr			1.07	1.06
14 yr			1.06	1.04
15 yr			1.04	1.02

Discussion

Introduction | Materials and Methods | Results | Discussion | References

Each of the major methods of estimating ultimate limb-length inequality begins with an estimation of the length of the longer lower limb at maturity. This is followed by determination of the rate of growth of the shorter limb compared with that of the longer limb and use of the difference in the rates to estimate the ultimate limb-length inequality. An accurate estimate of mature limb length requires a good estimation of the patient's current maturity. The two methods of maturity measurement involve use of chronological age or some physiological maturity measurement, with the most common being skeletal maturity. Errors in maturity determination result in unsatisfactory limb-length-inequality projections.

To our knowledge, only a few investigators^10-12, apart from Anderson et al.¹, have examined the error of prediction of various limb-length calculations. The values that we present are similar to those of the other authors. Aguilar et al.^10,11 evaluated limb-length predictions performed with the multiplier method, Green-Anderson method, and Moseley method but did so in a study of limbs that had undergone epiphyseodesis. Even so, their results mirror ours. The multiplier method demonstrated errors of up to 4.4 cm for boys and 2.6 cm for girls five years of age and younger; these errors decreased from ages five to nine and then increased again to a maximum of 2.3 cm for boys thirteen years of age and girls eleven years of age. Kasser and Jenkins¹² examined both chronological and skeletal-age-based limb-length estimates for patients younger than the age of ten years. Utilizing the Moseley graph, they found the absolute error in length prediction, for all children, to be 2.02 cm when they used chronological age and 2.8 cm when they used skeletal age. The length predictions for boys had an absolute accuracy of 3.8 cm (range, -3.6 to 9.6 cm) with use of skeletal age and 1.5 cm (range, -3.3 to 2.5 cm) with use of chronological age. For girls, the mean error of prediction of lower limb length was 2.46 cm (range, -2.9 to 12.4) with use of chronological age and 1.55 cm (range, -1.5 to 5.4 cm) with use of skeletal age.

The residual standard error can reasonably be considered the error expected for each of the various prediction methods. On the basis of our results, skeletal maturity is a better predictor of ultimate limb length for children going through their growth spurt while the Paley method works better for younger patients. This observation is consistent with those of both Anderson et al.¹ and Kasser and Jenkins¹². Of the various skeletal-maturity-determination methods, the Greulich and Pyle method and the Tanner-Whitehouse-3 methods are quite similar. The simplified method described by Sanders et al.⁸ is useful only for individuals in stage 2 and above, probably because stage 1 incorporates such a broad range. Radiographically, stage 2 corresponds to all of the epiphyses of the hand covering their metaphyses, meaning that they are all as wide as their respective metaphyses.

Our findings can be summarized as chronological age being superior to skeletal age for predicting ultimate limb length for children who have not begun their adolescent growth spurt but inferior once the early growth spurt begins. It is possible that the nearly linear lower-extremity growth pattern prior to the adolescent growth spurt makes the chronological age rather than the skeletal age more accurate for that younger age group. An alternative hypothesis is that longitudinal growth prior to the adolescent growth spurt occurs independently of mechanisms occurring during the growth spurt, with skeletal maturity and longitudinal growth being relatively uncoupled. However, once the hormonal mechanisms of the growth spurt begin, longitudinal growth becomes tightly coupled to skeletal maturity rather than chronological age. Hauspie et al.¹³ observed a similar phenomenon, finding that skeletal age was less associated with growth prior to the adolescent growth spurt but then quickly became closely related. They interpreted this as the adolescent growth spurt being able to start at any level of skeletal maturity. However, once the growth spurt starts, skeletal maturity quickly becomes tied to peripheral hormonal levels. Our findings support their hypothesis.

A second finding is that the multipliers are identical for boys and girls when the stages described by Sanders et al.⁸ are used. We believe that this indicates that the skeletal maturity of the hand in boys and girls during adolescence accurately reflects growth maturity independent of the subject's sex. This is not true of the Risser sign^1,14-16, and whether it is true for other skeletal maturity markers will have to be independently tested.

This study's primary weakness is the small number of subjects. However, the number of eligible patients was limited by the rarity of obtaining limb-length studies of patients who had no surgical procedure, particularly an epiphyseodesis, on their normal limb. The study by Anderson et al.¹ was based on fifty subjects with yearly data, and our study included half that number of subjects. The study by Anderson et al. is not reproducible today because of concerns about routine non-diagnostic studies involving radiation. If the original radiographs from their study or others are still available, they may be used to confirm or refute our findings. With regard to the statistical analysis, we are aware that repeated measurements from one subject are not independent. As a result, we may have overestimated the significance of every predictor. We have considered using a full longitudinal statistical model to allow the correlation between repeated measurements. However, our sample was not large enough to support a more complex statistical model. This is a known deficiency of this study, but it is unlikely to have affected the superiority of skeletal maturity to chronological age for subjects during their adolescent growth spurt or of chronological age to skeletal maturity prior to the growth spurt. Despite the small overall number of subjects, the fact that there were many data points lends strength to our findings, which clearly showed improvement in limb-length predictions when skeletal maturity rather than the Paley method was used for children undergoing their growth spurt. On the basis of our study, we cannot fully determine whether the superiority of using skeletal maturity for the predictions for patients in stage 2 and beyond was due to our hypothesis regarding chronological age versus skeletal maturity, that the regression model used in this study was superior to that used by Paley et al.³, or whether the model that we developed is specific to the subjects in this study and will not prove as robust in a prospective study.

Clinicians should be assured that using chronological age and the Paley multipliers will provide reasonable tentative predictions of ultimate limb length in preadolescent children, but once the patient is in adolescence, use of skeletal maturity provides more accurate prediction.

In conclusion, the Paley method, based on chronological age, provides reasonable estimates of ultimate limb lengths in children and is overall better than use of skeletal-maturity determinations for children who have not begun their growth spurt. However, once the growth spurt has begun, skeletal-maturity determinations provide better estimates. All of the methods of assessing skeletal maturity provided limb-length estimates within about 2 cm of the mature limb length when used for children who had begun the adolescent growth spurt.

References

Introduction | Materials and Methods | Results | Discussion | References

Anderson M; Green WT; Messner MB. Growth and predictions of growth in the lower extremities. J Bone Joint Surg Am. 1963;45:1-14.[PubMed]

Moseley CF. A straight-line graph for leg-length discrepancies. J Bone Joint Surg Am. 1977;59:174-9.[PubMed]

Paley D; Bhave A; Herzenberg JE; Bowen JR. Multiplier method for predicting limb-length discrepancy. J Bone Joint Surg Am. 2000;82:1432-46.[PubMed]

Moseley CF. Is it safe to use chronological age in leg length discrepancy?J Pediatr Orthop. 2005;25:408-9.[CrossRef][PubMed]

Parent AS; Teilmann G; Juul A; Skakkebaek NE; Toppari J; Bourguignon JP. The timing of normal puberty and the age limits of sexual precocity: variations around the world, secular trends, and changes after migration. Endocr Rev. 2003;24:668-93.[CrossRef][PubMed]

Greulich WW; Pyle SI. Radiographic atlas of skeletal development of the hand and wrist. 2nd ed.Stanford: Stanford University Press; 1959.

Tanner JM; Healy MJR; Goldstein H; Cameron N. Assessment of skeletal maturity and prediction of adult height (TW3) method. 3rd ed.London: WB Saunders; 2001.

Sanders JO; Khoury JG; Kishan S; Browne RH; Mooney JF 3rd; Arnold KD; McConnell SJ; Bauman JA; Finegold DN. Predicting scoliosis progression from skeletal maturity: a simplified classification during adolescence. J Bone Joint Surg Am. 2008;90:540-53.[CrossRef][PubMed]

Muggeo VM. Estimating regression models with unknown break-points. Stat Med. 2003;22:3055-71.[CrossRef][PubMed]

Aguilar JA; Paley D; Paley J; Santpure S; Patel M; Bhave A; Herzenberg JE. Clinical validation of the multiplier method for predicting limb length at maturity, part I. J Pediatr Orthop. 2005;25:186-91.[CrossRef][PubMed]

Aguilar JA; Paley D; Paley J; Santpure S; Patel M; Herzenberg JE; Bhave A. Clinical validation of the multiplier method for predicting limb length discrepancy and outcome of epiphysiodesis, part II. J Pediatr Orthop. 2005;25:192-6.[CrossRef][PubMed]

Kasser JR; Jenkins R. Accuracy of leg length prediction in children younger than 10 years of age. Clin Orthop Relat Res. 1997;338:9-13.[CrossRef][PubMed]

Hauspie R; Bielicki T; Koniarek J. Skeletal maturity at onset of the adolescent growth spurt and at peak velocity for growth in height: a threshold effect?Ann Hum Biol. 1991;18:23-9.[CrossRef][PubMed]

Little DG; Sussman MD. The Risser sign: a critical analysis. J Pediatr Orthop. 1994;14:569-75.[CrossRef][PubMed]

Shuren N; Kasser JR; Emans JB; Rand F. Reevaluation of the use of the Risser sign in idiopathic scoliosis. Spine (Phila Pa 1976). 1992;17:359-61.[CrossRef][PubMed]

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limb ; leg

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James O. Sanders, James Howell, Xing Qiu; Comparison of the Paley Method Using Chronological Age with Use of Skeletal Maturity for Predicting Mature Limb Length in Children. The Journal of Bone & Joint Surgery. 2011 Jun;93(11):1051-1056.

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