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Research Reports |
SE Hanna, PhD, is Associate Professor, Department of Clinical Epidemiology and Biostatistics, and Investigator, CanChild Centre for Childhood Disability Research, School of Rehabilitation Science, McMaster University, IAHS 408, Hamilton, Ontario, Canada L8S 1C7
DJ Bartlett, PT, PhD, is Associate Professor, School of Physical Therapy, The University of Western Ontario, London, Ontario, Canada, and Co-Investigator, CanChild Centre for Childhood Disability Research, School of Rehabilitation Science, McMaster University
LM Rivard, PT, MSc, is Research Coordinator, CanChild Centre for Childhood Disability Research, School of Rehabilitation Science, McMaster University
DJ Russell, PhD, is Associate Professor, School of Rehabilitation Science, and Research Coordinator, CanChild Centre for Childhood Disability Research, School of Rehabilitation Science, McMaster University
Address all correspondence to Dr Hanna at: hannas{at}mcmaster.ca
Submitted October 12, 2007;
Accepted January 22, 2008
Subjects and Methods: A total of 1,940 motor measurements from 650 children with CP were used to develop percentiles. These observations were taken from a subsample, stratified by age and GMFCS, of those in a longitudinal cohort study reported in 2002. A standard LMS (skewness-median-coefficient of variation) method was used to develop cross-sectional reference percentiles.
Results: Reference curves were created for the GMFM-66 by age and GMFCS level, plotted at the 3rd, 5th, 10th, 25th, 50th, 75th, 90th, 95th, and 97th percentiles. The variability of change in children's percentiles over a 1-year interval also was investigated.
Discussion and Conclusion. The reference percentiles extend the clinical utility of the GMFM-66 and GMFCS by providing for appropriate normative interpretation of GMFM-66 scores within GMFCS levels. When interpreting change in percentiles over time, therapists must carefully consider the large variability in change that is typical among children with CP. The use of percentiles should be supplemented by interpretation of the raw scores to understand change in function as well as relative standing.
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In 2002, Rosenbaum and colleagues4 published a landmark longitudinal cohort study that dramatically improved knowledge of the development of gross motor function among children with CP. Rosenbaum et al4 used population-based sampling methods to conduct longitudinal assessments of the gross motor function of 657 children over approximately 4 years. Children were stratified by age and by the severity of the condition on the basis of the Gross Motor Function Classification System (GMFCS) for CP.5 The motor examinations were conducted with the 66-item version of the Gross Motor Function Measure (GMFM-66), an evaluative instrument for use with children with CP.6–9 The result was a set of 5 motor development curves, corresponding to each of 5 GMFCS levels of severity. The curves describe changes in GMFM-66 motor function scores within strata of severity, in terms of the rate of development and a presumed limit of functional ability (Fig. 1).
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Figure 1. Gross motor development curves representing average development predicted by the Gross Motor Classification System. The diamonds on the vertical axis identify 4 items of the 66-item Gross Motor Function Measure (GMFM-66) that predict when children are expected to have a 50% chance of completing that item successfully. The GMFM-66 item 21 (diamond A) assesses whether a child can lift and maintain his or her head in a vertical position with trunk support by a therapist while sitting, item 24 (diamond B) assesses whether a child can maintain a sitting position on a mat without support from his or her arms for 3 seconds, item 69 (diamond C) measures a child's ability to walk forward 10 steps without support, and item 87 (diamond D) assesses the task of walking down 4 steps by alternating feet with arms free. Reprinted with permission from Rosenbaum PL, Walter SD, Hanna SE, et al. Prognosis for gross motor function in cerebral palsy: creation of motor development curves. JAMA. 2002;288:1357–1363. Copyright 2002, American Medical Association. All rights reserved.
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With the curves provided by Rosenbaum et al,4 it is possible to crudely evaluate children's gross motor capability relative to the average for their age and GMFCS level. The user's manual for the GMFM-668 also provides item maps that aid in criterion-referenced interpretations of scores by relating total GMFM-66 ability scores to the probability of attaining motor tasks such as lying and rolling, sitting, crawling and kneeling, standing, walking, running, and jumping. However, it has been difficult for clinicians to make normative evaluations of children's motor capability within GMFCS levels because reference percentiles have not been available. In this article, we develop and present reference percentiles for GMFM-66 motor scores by age and GMFCS level. First, we review the clinical utility of the GMFM-66, the GMFCS, and the motor development curves as they pertain to examination, prediction, and intervention planning by using 3 case examples. After presenting the development of the reference percentiles, we revisit these examples to demonstrate how the percentiles can enhance assessment. We discuss the use of the percentiles both for understanding a single GMFM-66 assessment and for tracking a child's motor ability over time.
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Table 1. Description of Case Examplesa
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Table 2. Expected Functional Abilities for Children Aged 6 to 12 Years, According to the Gross Motor Function Classification System (GMFCS)
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Each of the 3 children selected as case examples had spastic diplegia. On the initial occasion of measurement, David, a boy who was 3 years 2 months old, was in GMFCS level I and had a GMFM-66 score of 57.6. Both Jennifer and Hardeep were older than David, had more severe limitations, and had lower GMFM-66 scores, 51.6 and 43.3, respectively. These scores, which are clearly not solely related to age, are useful for describing the current motor abilities of individual children, particularly when used with the item maps described earlier.8 For example, David was able to walk independently but probably could not achieve standing through either left or right half-kneeling, lower himself to sitting on a bench without hand support, pick up an object from the floor without hand support, or walk up or down stairs by holding onto a railing and alternating feet. Jennifer could pull herself to a standing position by using a surface and could cruise to left or right when holding on, but she could not stand without arm support.
Normative and predictive interpretations are facilitated by referencing a child's GMFM-66 score against the average developmental pattern for children in his or her GMFCS level. Such referencing can be done with the motor development curves4 shown in Figure 1. For instance, the average child in GMFCS level I is expected to achieve a GMFM-66 score of approximately 88 as he or she approaches adolescence. Rasch item maps from the user's manual for the GMFM-668 suggest that such a child has a high probability of being able to perform tasks such as independent walking on a level surface and walking down steps by alternating feet with arms free. However, there is considerable variability within GMFCS levels; therefore, it is clear that the average predicted capability is not the only factor. For instance, Rosenbaum et al4 reported variability in the ultimate limit of motor capability such that there is only a 50% chance of children in GMFCS level I achieving scores of between 80.1 and 92.3. In addition to the real variability in achievement, there is also measurement error, meaning that no one assessment falls exactly on the true developmental trajectory for a child.
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Clinicians are generally familiar with normative reference percentiles for answering the first question. Reference percentiles are commonly used for interpreting measurements in medicine, such as physical growth,15 and for defining the normal ranges for a wide variety of laboratory measurements.16 Many clinical measures in pediatric rehabilitation also provide percentiles to facilitate normative interpretation.17–19 Reference percentiles are constructed by selecting a clinically appropriate comparison group and developing a statistical summary of the distribution of scores for this group. This summary is transformed to a percentile scale, such that a child's percentile represents the percentage of children in the normative sample that he or she outperforms. Reference percentiles answer questions about function in terms of relative standing.
The question of whether David's motor ability will remain below average relates to issues of both prediction and longitudinal variability or tracking of measurements.20 It is common for therapists and families to assume that percentile rankings are stable, but in fact they can be highly variable over time.17 Thus, whenever therapists want to monitor function over time, it will be important to assess the likely degree of variation in percentiles over time. If clinicians do not consider this variation, it can be mistaken for evidence of clinically significant change.
In the present study, we used data from the sample of Rosenbaum et al4 to construct reference percentiles for GMFM-66 scores within GMFCS levels for children with CP. We also evaluated the degree to which percentile rankings are stable over time, and we discuss how this factor affects the appropriate use of percentiles for clinical monitoring of gross motor function. Our goal was to increase the clinical applicability of the GMFM-66 and GMFCS by providing reference curves in a form familiar to physical therapists and other service providers who work with children with CP.
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From 936 randomly selected children and families who were eligible and after refusals to participate (n=217; 23%), other losses of contact, and later exclusions because of reevaluation of eligibility, 657 children were included in the original motor development analyses. Children under 6 years of age were assessed every 6 months, and older children were assessed every 9 to 12 months. This protocol yielded a total of 2,632 GMFM-66 assessments, with an average of approximately 4 observations per child.
The method used to create percentiles (see section on data analysis below) required that the observations be treated as cross-sectional rather than longitudinal. To minimize the effects of the longitudinal design, while still including as many data as possible, we selected a subsample from the original 2,632 observations to avoid multiple observations from a child occurring close in time. To accomplish this, we established ten 1-year age bands from 2 years up to and including 12 years of age. Observations were selected so that there was no more than one observation per child per 1-year age band. As a result, statistical smoothing operations used to create the percentiles gave substantial weight to only one observation for each child at a given age. It is important to note that these age bands were used only for creating the subsample and were not used for fitting the percentiles. Observations were included only for ages from 2 to 12 years, restricting inferences to ages for which large amounts of data were available. This sampling also is consistent with the appropriate use of the GMFCS, which is currently applicable to children up to 12 years of age.
As a result of this subsampling, a total of 1,940 observations from 650 children were available for creating cross-sectional reference curves. The distribution and characteristics of this sample within 5 levels of GMFCS severity are shown in Table 3.
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Table 3. Description of the Sample Used to Create Reference Curvesa
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Gross motor function was examined with the GMFM-66.8 The validity of the GMFM-66 was established in several ways. Face validity was established by examining the hierarchy of items by use of Rasch analysis.7 Sensitivity to change was determined by demonstrating that children who were younger changed more than children who were older and that more change occurred in children in GMFCS levels I and II than in those in the other levels.7 Reliability was initially established with trained raters, who obtained intraclass correlation coefficients of .99 for both interrater reliability and test-retest reliability.7 In the study of Rosenbaum et al,4 all examining therapists were trained on the administration and scoring of the GMFM.
Data Analysis
The LMS method of Cole and Green21 was used to construct reference percentiles. The method summarizes the changing distribution of GMFM-66 scores as a function of age in terms of 3 curves representing the skewness (L), the median (M), and the coefficient of variation (S). Smooth, nonlinear fitting of the 3 LMS curves is accomplished with cubic splines by use of a penalized likelihood criterion. Assuming that the original data are skew-normal, the resulting curves approximate a standard normal distribution at any given age and thus can be combined to produce percentiles. The degree of smoothness for each of the 3 LMS functions is controlled by selecting smoothness parameters, often expressed as expected degrees of freedom (edf), for each curve. In turn, the smoothness of the resulting percentile curves depends on the smoothness of the LMS curves. Higher values for edf allow for more complexity and less smoothing with respect to each of the components of the curve—skewness (L), median (M), and variability (S)—with the goal being to select the simplest model (ie, with lower values for edf) that preserves clinically plausible details in the percentile curves. The LMS method is a standard method for constructing cross-sectional reference percentiles. Unlike many ad hoc methods, it produces smooth curves that incorporate the changing variability and skewness in the sample and does not require the arbitrary binning of subjects into crude age bands.
Determining the appropriate degree of smoothness for the LMS curves is necessarily a balance of smoothing out irregularities arising from sampling error without eliminating features of real clinical interest. For assistance in identifying the appropriate degree of smoothness, changes in edf were evaluated as likelihood ratio tests based on changes in the penalized likelihood.21 In a well-fitting model for the percentiles, the observations should conform to a standard normal distribution at any given age after LMS transformation. Thus, the goodness of fit for candidate models was evaluated by use of Kolmogorov-Smirnov tests of normality for the transformed data and by inspection of Q-Q plots of the estimated percentiles.21
The LMS percentiles were constructed separately for each GMFCS level by use of the statistical routines provided by Carey,22 implemented in the R statistical programming language.23 Separate curves were not considered for boys and girls because of sample size and because Rosenbaum et al4 found that gender was not a significant predictor of gross motor function trajectories in the sample studied.
To examine the degree of stability of GMFM-66 percentiles over time, we exploited the longitudinal aspect of the original data. A subsample of the observations used in constructing the reference percentiles was selected such that 2 GMFM-66 observations from each child were contributed to the sample. Children for whom only one observation was available were excluded. For children with more than 2 available measurements, the earliest 2 measurements were selected. The resulting sample contained pairs of measurements for 570 children. For each pair of observations, estimated percentiles were extracted, and the means and standard deviations of the differences were calculated for each GMFCS level.
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Figure 2. Gross Motor Function Classification System level I percentiles. GMFM-66=66-item Gross Motor Function Measure. Figure 2 may not be used or reproduced without written permission from the authors.
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Figure 3. Gross Motor Function Classification System level II percentiles. GMFM-66=66-item Gross Motor Function Measure. Figure 3 may not be used or reproduced without written permission from the authors.
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Figure 4. Gross Motor Function Classification System level III percentiles. GMFM-66=66-item Gross Motor Function Measure. Figure 4 may not be used or reproduced without written permission from the authors.
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Figure 5. Gross Motor Function Classification System level IV percentiles. GMFM-66=66-item Gross Motor Function Measure. Figure 5 may not be used or reproduced without written permission from the authors.
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Figure 6. Gross Motor Function Classification System level V percentiles. GMFM-66=66-item Gross Motor Function Measure. Figure 6 may not be used or reproduced without written permission from the authors.
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Kolmogorov-Smirnov tests of normality within each level were not significant, indicating that the percentiles conform to the expected normal distribution and that the model used in constructing the percentiles fits the data well. To assess fit at particular age ranges, the data for each level were split into 5 age bands of equal width, and Kolmogorov-Smirnov tests were applied within each age band. None of these tests were significant at any age band, within any GMFCS level, indicating a good fit at all ages. In addition, inspection of Q-Q plots yielded no evidence that the percentiles fit poorly at particular ages.
An approximate percentile can be obtained by consulting the figure for a child's GMFCS level and finding the percentile curve nearest the intersection of the child's age and the GMFM-66 score. For most clinical purposes, it will be sufficiently accurate to visually interpolate between adjacent percentile curves (eg, halfway between the 10th and the 5th percentiles). If greater accuracy is desirable, tabulated percentiles are available online24 or by contacting the corresponding author.
Longitudinal Stability of Percentiles
The means and standard deviations of the changes in percentiles by GMFCS level are shown in Table 4. The median time between observations for each child was 1.0 year for each level, and neither time difference nor baseline age was correlated significantly with the amount of change in percentiles.
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Table 4. Mean Changes in Percentiles Over 2 Assessments, With Probability Intervalsa
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The reference curves are straightforward for use in evaluating a child's relative capability at a single point in time. The percentiles for the case examples are shown in Table 5. They were obtained at this level of precision from the LMS output, but in a real application, tabulated percentiles or visual interpolation from Figures 2, 3, 4, 5, and 6 would normally be sufficient. On the first occasion of measurement (time 1), David, Jennifer, and Hardeep had percentile rankings of 14.9, 54.6, and 60.7 relative to other children in GMFCS levels I, III, and IV, respectively. David had the highest GMFM-66 score of the 3 children but, nonetheless, had a much lower percentile ranking. This inconsistency between capability and percentile rankings occurred because the 3 children were of different ages and in different GMFCS levels. In transforming scores to percentiles, the clinical meaning of original scores in relation to functional criteria is set aside in favor of relative ranking. Clinicians and families must adjust their interpretations accordingly. This is especially obvious for the GMFM-66 reference curves, because children's percentiles depend on both age and GMFCS level. As another example, a 6-year old child who scores 52 on the GMFM-66 is near the 95th percentile if she is in level IV but is near the 50th percentile if she is in level III. Her motor capability is the same in either case. Nonetheless, if expectations and intervention planning are being based on the GMFCS, it may be of interest to know that she is a very highly functioning child in level IV. In contrast to measures that derive their interpretation entirely from norm referencing, such as many intelligence tests, users of the GMFM-66 now have access to both functional and percentile interpretations; it is likely that many examinations will rely on both.
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Table 5. Changes in 66-Item Gross Motor Function Measure (GMFM-66) and Percentiles for Case Examples
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These percentiles are based on a large data set that, within GMFCS levels, is likely to be representative of the population of children with CP that most therapists in Europe and North America will serve. This is a key requirement for the effective interpretation of normative comparisons and is an important strength of the present study. Rosenbaum et al4 did not control therapeutic interventions during their study; therefore, the sample was representative of children who received a range of accepted medical, orthopedic, and developmental therapy services. Children receiving dorsal rhizotomy, botulinum toxin, and intrathecal baclofen prior to their study were excluded. At the time, these were newer therapies with largely unknown effects, and they were not readily available in Ontario. In any event, as Rosenbaum et al4 pointed out, these interventions are used only in highly selective subgroups of children and would have little effect on the estimated distribution of GMFM-66 scores as a whole.
Cross-sectional percentiles are most easily applied when therapists wish to evaluate relative standing at a single point in time. Therapists routinely use them to evaluate longitudinal change in standing as well, although this use is not strictly valid without consideration of the typical stability of percentiles. For example, a therapist who may be alarmed upon finding that a child in level I has dropped from the 50th percentile to the 40th percentile upon reexamination should consult Table 4 and consider that changes at least this large are quite common. For instance, for level I, 80% of reexaminations are expected to change by up to 20 percentile points in either direction, meaning that 20% of changes are larger than this. The reference curves require additional information to assist with the interpretation of change over time, as illustrated next.
Table 5 shows outcome data on David, Jennifer, and Hardeep after a period of approximately 1 year. For David, who was in GMFCS level I, the GMFM-66 score changed from 57.6 to 66.0, a change of 8.4 points. This change translates to a percentile ranking of 14.9 at the beginning of the year and a ranking of 19.6 at the end of the year, an increase of 4.7. An examination of Table 4 shows that this amount of change means that David is developing as might be expected; his change is well within the interval within which 80% of children change.
In contrast, for Jennifer, classified in level III, the GMFM-66 score changed from 51.6 to 49.9 (a decrease of 1.7 points). This change represents little or no loss of function but translates to a change in percentile ranking from 54.6 to 37.5 over 1 year, a decrease of 17.1. Table 4 shows that this amount of change is relatively uncommon in level III; there is an 80% chance that the percentile will remain within 15.9 points of the initial ranking on retesting 1 year later. Jennifer is not far outside this range, but the results may suggest that she is falling behind the developmental trajectory expected for children in level III.
The example for Jennifer shows how the percentiles can be helpful in revising goals and interventions over the subsequent time period to ensure that further unexpected changes do not occur. However, this example also illustrates that interpretations of changes in percentile rankings should be tempered by knowledge of the child's clinical situation, and we emphasize the hazards of overinterpreting longitudinal comparisons. For Jennifer, an uncommonly large decrease in percentile ranking resulted from a decrease of only 1.7 points in GMFM-66 scores, a finding that may have little importance in functional terms. Indeed, such a small raw score change may not be statistically significant given the standard error of the measure; if not, one cannot be confident that any functional change has occurred. A large downward percentile change arises nonetheless, because the distribution of scores is changing; Jennifer may not be changing, but other children are, and she is falling behind. However, "falling behind" is not the same as losing function. When large changes in percentiles occur, we encourage therapists to consider the functional meaning of the raw scores by using interpretative aids in the user's manual for the GMFM-66.8
Finally, for Hardeep, classified in level IV, the GMFM-66 score changed from 43.3 to 47.1, a modest increase of 3.8 points. This change translates to a change in percentile ranking from 60.7 to 77.8, an increase of 17.1. Table 4 shows that there is an 80% chance that percentiles for children in level IV will not change more than 15.1 points on retesting after 1 year. For Hardeep, one can conclude that his development was better than expected over the preceding year.
These examples illustrate how to use the reference curves to approximately interpret changes in percentiles. The results shown in Table 4 suggest that large changes in percentile rankings over 1 year are quite common at all levels of the GMFCS. This suggestion is consistent with the findings for gross motor development among children developing typically.17,26 Our approach to approximately quantifying the longitudinal stability of GMFM-66 percentiles will be useful for interpreting changes. We are presently developing a longitudinal approach that will further improve the prediction of changes in GMFM-66 percentiles. In the meantime, the cross-sectional percentiles presented here are important new tools for the clinical assessment of motor function among children with CP.
The study was approved by the Faculty of Health Sciences Research Ethics Board at McMaster University.
Collection of the original source data was supported by grants from the Canadian Institutes of Health (MT-13476) and the National Center for Medical Rehabilitation Research of the US National Institute of Child Health and Human Development (R01-HD-34947).
Dr Russell, as one of the authors of the Gross Motor Function Measure (GMFM-66 and GMFM-88) User's Manual, receives royalties, which are deposited into a research account and not taken for personal use.
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carey. Accessed January 2006.This article has been cited by other articles:
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R. L Craik Climbing Out of Our Silos to Improve Practice Physical Therapy, May 1, 2008; 88(5): 555 - 558. [Full Text] [PDF] |
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