Characterizing extreme values of body mass index for-age by using the 2000 Centers for Disease Control and Prevention growth charts 1 3

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1 Characterizing extreme values of body mass index for-age by using the 2000 Centers for Disease Control and Prevention growth charts 1 3 Katherine M Flegal, Rong Wei, Cynthia L Ogden, David S Freedman, Clifford L Johnson, and Lester R Curtin ABSTRACT Background: The 2000 Centers for Disease Control and Prevention (CDC) growth charts included lambda-mu-sigma (LMS) parameters intended to calculate smoothed percentiles from only the 3rd to the 97th percentile. Objective: The objective was to evaluate different approaches to describing more extreme values of body mass index (BMI)-for-age by using simple functions of the CDC growth charts. Design: Empirical data for the 99th and the 1st percentiles of BMI-for-age were calculated from the data set used to construct the growth charts and were compared with estimates extrapolated from the CDC-supplied LMS parameters and to various functions of other smoothed percentiles. A set of reestimated LMS parameters that incorporated a smoothed 99th percentile were also evaluated. Results: Extreme percentiles extrapolated from the CDC-supplied LMS parameters did not match well to the empirical data for the 99th percentile. A better fit to the empirical data was obtained by using 120% of the smoothed 95th percentile. The empirical first percentile was reasonably well approximated by extrapolations from the LMS values. The reestimated LMS parameters had several drawbacks and no clear advantages. Conclusions: Several approximations can be used to describe extreme high values of BMI-for-age with the use of the CDC growth charts. Extrapolation from the CDC-supplied LMS parameters does not provide a good fit to the empirical 99th percentile values. Simple approximations to high values as percentages of the existing smoothed percentiles have some practical advantages over imputation of very high percentiles. The expression of high BMI values as a percentage of the 95th percentile can provide a flexible approach to describing and tracking heavier children. Am J Clin Nutr 2009;90: INTRODUCTION In 2000, the Centers for Disease Control and Prevention (CDC) released a set of reference growth charts for the United States (1 3), based primarily on data from the 1960s and 1970s from the National Health and Nutrition Examination Survey (NHANES) and the National Health Examination Survey (NHES). Each of the CDC growth charts included 9 selected smoothed percentiles: the 3rd, 5th, 10th 25th, 50th, 75th, 90th, 95th, and 97th percentiles. The body mass index (BMI; weight in kg/height squared in m) for age charts also included the 85th percentile. Smoothing methods for the selected percentiles included both parametric and nonparametric methods (4). After smoothing, age-specific lambda-mu-sigma (LMS) parameters were estimated to provide a normalizing Box-Cox transformation (3) to reproduce the selected smoothed percentiles and allow for calculation of other percentiles between the third and 97th percentiles. At each age or length/stature interval, a group of 9 equations (10 for BMI charts) was generated by specifying the LMS transformation equations for the previously smoothed percentiles. A simultaneous solution for the 3 parameters of L, M, and S from the group of specified equations was generated as the best solution to a system of equations rather than as likelihood-based estimates from empirical data. As noted in the technical report (4) Percentiles less than the 3rd or greater than the 97th are beyond the range of the data from which the LMS parameters were calculated. As in any statistical procedure, extrapolation beyond the range of the data should be done with caution. The CDC parameters for the normalizing Box-Cox transformation use the same designation as the LMS parameters calculated using Cole s LMS method (5, 6). However, the method used to arrive at the CDC LMS parameters was different from Cole s method (5, 6). The CDC LMS parameters are not derived directly from the underlying data, but rather only from the values of the 10 selected previously smoothed percentiles. Also in the CDC approach, the LMS method was not used to create smoothed percentiles. Instead the percentiles were smoothed by using other methods, and the LMS parameters were selected to match the already smoothed percentiles. The designation of the CDC procedure as a modified LMS procedure has resulted in some misunderstanding of the differences between the derivation of the parameters for the CDC growth charts and Cole s LMS method. At the time that the 2000 CDC growth charts were created, the use of the CDC LMS parameters to calculate more extreme values was not assessed by the CDC Growth Chart Working Group (4). Since the release of the 2000 CDC growth charts, 1 From the National Center for Health Statistics, Centers for Disease Control and Prevention, Hyattsville, MD (KMF, RW, CLO, CLJ, and LRC), and the National Center for Chronic Disease Prevention and Health Promotion, Centers for Disease Control and Prevention, Atlanta GA (DSF). 2 The findings and conclusions in this report are those of the authors and not necessarily those of the Centers for Disease Control and Prevention. 3 Address correspondence to KM Flegal, National Center for Health Statistics, Centers for Disease Control and Prevention, 3311 Toledo Road, Room 4201, Hyattsville, MD kmf2@cdc.gov. Received July 6, Accepted for publication August 26, First published online September 23, 2009; doi: /ajcn Am J Clin Nutr 2009;90: Printed in USA. Ó 2009 American Society for Nutrition

2 CHARACTERIZING EXTREME VALUES OF BMI-FOR-AGE 1315 additional interest has arisen in identifying more extreme BMI values, particularly high values. Despite the cautions in the CDC technical report about extrapolating beyond the range of the 97th percentile, several publications have used or recommended an extrapolated 99th percentile of BMI-for-age calculated from the CDC-supplied LMS parameters (7 13) or even higher percentiles (13 15). The objective of this report was to evaluate ways in which the existing CDC BMI-for-age growth charts can be used to quantify both high- and low-extreme BMI values beyond the range of the 10 selected smoothed percentiles. METHODS We used the data set of measured weight and height values from 5 national surveys for children and adolescents aged 2 through 20 y of age that was used to construct the 2000 CDC sexspecific BMI-for-age growth charts (4). Age was categorized into 6-mo intervals, and sex-specific empirical first and 99th percentile BMI values were calculated for each age group, as were empirical values for the 3rd, 5th, 95th, and 97th percentiles for comparative purposes. We used the CDC-supplied LMS values to calculate extrapolated 1st and 99th percentile values. We compared these extrapolated LMS-calculated values with the empirical values for the 1st and 99th percentiles. In addition, we re-estimated a complete set of new LMS parameters, using the CDC approach described above, which incorporated a smoothed version of the 99th percentile as part of the estimation procedure. We also investigated several functions of the previously smoothed 3rd, 5th, 95 th, and 97th percentiles as possible alternatives that could be used to approximate the empirical values of the more extreme percentiles (1st and 99th percentiles). For these comparisons, values of these functions were averaged over the point estimates of empirical and calculated values for 6-mo age groups, giving each 6-mo age group equal weight. Thus, these comparisons are not intended as population estimates. The purpose of these investigations was to find a simple function or functions of the existing smoothed percentiles that would provide an approximation to the empirical 1st and 99th percentile data. These functions were evaluated in terms of practical considerations. Desirable properties for a function were that it be similar between boys and girls, have relatively low variability, and have similar mean and median values, indicating a relative lack of skewness. We evaluated 3 different approaches to constructing functions of the existing percentiles that could be used to approximate the empirical 99th percentile values. One approach would be to approximate the empirical 99th percentile values by adding a constant value to an existing smoothed percentile. To evaluate this approach, we calculated the sex-specific mean BMI difference over age groups between the empirical 99th percentile values and the smoothed 97th percentile values. Another approach would be to approximate the empirical 99th percentile values by multiplying an existing smoothed percentile by a constant percentage. To evaluate this approach, we calculated the sex-specific mean ratio of the empirical 99th percentile values to the smoothed 97th percentile values over the age groups. Yet another possibility would be to use some multiple of the distance between the smoothed 97th and 95th percentiles to approximate the distance between the empirical 99th percentile and the smoothed 97th percentile at the same age. To evaluate this approach, we calculated the sex-specific mean ratio of these 2 distances over the age groups. The calculations for each of the 3 approaches were repeated with the 95th and 90th percentiles in place of the 97th and 95th percentiles. Corresponding calculations were carried out for the empirical first percentile values relative to the smoothed third and fifth percentiles. Prevalence of extreme BMI-for-age by using different approximations To examine the effect of different approximations on estimates of the prevalence of extreme BMI-for-age for children and adolescents, we used data from NHANES These data have been described in detail elsewhere (16 18). The data set included all examined children and adolescents aged 2 through 19 y of age. Pregnant girls were excluded. BMI was rounded to one decimal place. We estimated the prevalence of extreme BMI-forage using month-specific values of several different approximations to the first and 99th percentiles. Statistical methods Analyses were conducted with PC-SAS (version 9.1; SAS Institute, Cary, NC) and SUDAAN (version 9.03; Research Triangle Institute, NC). Except as noted for the averages over 6-mo age groups, analyses used sample weights and took into account the clustering and the sample design of the surveys. For prevalence estimates, statistical comparisons between estimates for boys and girls were made by using a 2-sample t test with statistical significance set at a P value of to account for multiple comparisons. RESULTS Extreme percentiles extrapolated from the CDC-supplied LMS values For boys, the extrapolated LMS-calculated values and the empirical 99th percentile BMI values are shown in the left panel of Figure 1; the smoothed and empirical BMI values for the FIGURE 1. Comparison of empirical to calculated 95th and extrapolated 99th BMI-for-age percentile data (left panel) and comparison of empirical 99th BMI-for-age percentile data to 120% of the 95th BMI-for-age percentile (right panel) in boys. LMS, lambda-mu-sigma parameters.

3 1316 FLEGAL ET AL 95th percentile are included in the figure for comparison. The data points in the figure are 6-mo averages. Similar results for girls are shown in the left panel of Figure 2. For both boys and girls, the empirical data points for the 99th percentile are more variable than the empirical data points for the 95th percentile, due in part to the sparseness of the data at the extremes as well as to the skewness and kurtosis of the distributions. As can be seen from these figures, the smoothed 95th percentile corresponds reasonably well to the empirical 95th percentile data, but the values extrapolated from the LMS parameters do not correspond well to the empirical data for the 99th percentile. For boys, the extrapolated LMS-calculated values tend to lie below the empirical 99th percentile values at younger ages and above at older ages. For girls, the differences are yet more extreme and at older ages the extrapolated LMS-calculated values tend to lie well above the empirical data, sometimes by 4 or 5 BMI units or more. For boys (left panel) and girls (right panel) similar data for the first percentile values extrapolated from the CDC LMS parameters are shown in Figure 3, which includes the smoothed and empirical fifth percentile values for comparison. As expected, the smoothed fifth percentile provides a reasonably good fit to the data points. The fit of the extrapolated first percentile from the CDC LMS parameters to the data are less good, with the extrapolated first percentile from the CDC LMS parameters tending to lie above the empirical data for boys and for younger girls. Functions of the existing 2000 CDC growth chart values We evaluated several simple functions of the existing smoothed growth chart values as possible approximations to the empirical 99th percentile. Some desirable properties for such a function would be that it had relatively small variability over age groups and was similar between boys and girls. First, we calculated the difference between the empirical 99th percentile values and the smoothed 97th percentile values (Table 1). This difference had a high CV (SD/mean). We also calculated ratios of the empirical 99th percentile values to the smoothed 97th and FIGURE 2. Comparison of empirical to calculated 95th and extrapolated 99th BMI-for-age percentile data (left panel) and comparison of empirical 99th BMI-for-age percentile data to 120% of the 95th BMI-for-age percentile (right panel) in girls. LMS, lambda-mu-sigma parameters. FIGURE 3. Comparison of empirical to calculated fifth and extrapolated first BMI-for-age percentile data for boys (left panel) and girls (right panel). LMS, lambda-mu-sigma parameters. smoothed 95th percentile data. The ratio of the empirical 99th percentile values to the smoothed 97th percentile data had a smaller CV (0.06 for both boys and girls) than the difference (0.48 for boys and 0.66 for girls). In addition the value of the ratio was similar between boys and girls. The ratio of the empirical 99th percentile values to the smoothed 95th percentile had similar properties. We also calculated the ratio of the distance between the smoothed 97th and the empirical 99th percentile to the distance between the 95th and 97th percentiles. This ratio was fairly variable and dissimilar between boys (3.14) and girls (2.50). We repeated the above calculations using the 90th percentile instead of the 95th percentile and obtained similar results. The comparable results for the low end of the percentile range are shown in Table 2. Differences between the first and third percentiles and first and fifth percentiles are shown along with the ratios corresponding to those done on the high end. These results paralleled the findings for the 99th percentile, with a percentage of the smoothed 3rd or 5th percentiles showing the smallest (0.03) CV. These results suggest that for practical purposes, either 120% of the smoothed 95th percentile or 112% of the smoothed 97th percentile might serve as a rough approximation to the empirical 99th percentile of BMI-for-age. In addition, either 94% of the smoothed fifth percentile or 96% of the smoothed third percentile might serve as approximations to the empirical first percentile data. These ratios have the desirable property of differing little or not at all between boys and girls. BMI differences between the empirical 99th percentile values and 4 possible approximations are shown in Table 3: the extrapolated LMS-calculated values, 112% of the smoothed 97th percentile, 120% of the smoothed 95th percentile and a 99th percentile calculated from the re-estimated LMS parameters. For boys, the average difference was relatively small for all approximations. The SD was higher for the LMS-calculated extrapolation than for the other approximations and the range of differences was wider. For girls, the average difference between the empirical percentile and the LMS-calculated extrapolation was fairly large (1.99 BMI units) compared with the mean difference of only 0.18 BMI units for the 120% approximation. As

4 CHARACTERIZING EXTREME VALUES OF BMI-FOR-AGE 1317 TABLE 1 Relation of empirical 99th percentile BMI values to smoothed BMI values within 6-mo age groupings, by sex Mean 6 SD CV Range Median Distance between empirical 99th percentile and smoothed percentiles in BMI units Empirical 99th 2 smoothed 97th Boys , Girls , Empirical 99th 2 smoothed 95th Boys , Girls , Ratio of empirical 99th percentile to smoothed percentiles Empirical 99th/smoothed 97th Boys , Girls , Empirical 99th/smoothed 95th Boys , Girls , Ratios of distances between percentiles (Empirical 99th 2 smoothed 97th)/(smoothed 97th 2 smoothed 95th) Boys , Girls , (Empirical 99th 2 smoothed 95th)/(smoothed 95th 2 smoothed 90th) Boys , Girls , was the case for boys, the range of differences was wider for the LMS-calculated extrapolation than for the other approximations. Similar data for the empirical first percentile are also shown in Table 3. For the first percentile, all approximations performed similarly and agreed fairly well with the empirical data. Thus, for the first percentile, extrapolation from the current CDCsupplied LMS parameters, although possibly inexact, may be adequate for most purposes. A comparison between the empirical 99th percentile values and a 99th percentile value based on re-estimating the LMS values is shown in Table 3. The re-estimated value did not agree with the empirical data as well as did the approximations based on the 95th or 97th percentile. In addition (data not shown), the re-estimated values changed the values of all the other smoothed percentiles, and, in most cases, particularly for girls, the reestimated percentiles agreed less well with the empirical data than did the original LMS values. The right panels of Figure 1 (boys) and Figure 2 (girls) show the empirical data points for the 99th percentile and the approximation of 120% of the smoothed 95th percentile. As can be seen, the smoothed 95th percentile approximations provide a better, although not perfect, fit to the empirical data points than do the extrapolations from the CDC-supplied LMS parameters (shown in the left panel in both figures), particularly for girls. Prevalence estimates We used data from NHANES to evaluate the effects of different approximations on the estimated prevalence of extremely high or extremely low BMI-for-age. It should be noted that none of these approximations are necessarily estimates of the true prevalences. The prevalence and SEs for BMI at or above the extrapolated LMS-calculated values, at or above 112% of the 97th percentile, at or above 120% of the 95th percentile, and at or above the values calculated from the re-estimated LMS parameters are shown in Table 4. Overall, the prevalence of extremely high BMI was higher when based on 120% of the 95th percentile or on 112% of the 97th percentile. In both cases, it was higher than when based on the extrapolation from the LMS parameters, particularly for girls. For girls aged 2 19 y, the prevalence of an extremely high BMI was 2.7% based on the extrapolated LMS parameters, but 4.3% based on 120% of the 95th percentile. The difference was particularly pronounced for girls in the age group y, in which the prevalence was more than doubled when the 120% of the 95th percentile definition was used than when the extrapolated LMS parameters were used (5.4% compared with 2.2%). Thus, these estimates are sensitive to the approximation used. For the definition based on the extrapolated LMS parameters, the prevalence of a very high BMI was significantly greater in boys than in girls overall (P, 0.01) and within y-olds (P, 0.01). For the definition based on 112% of the 97the percentile, the difference in prevalence between boys and girls was also significant overall (P, 0.01), but not within age groups. For the other 2 definitions, the difference was not statistically significant, and P values were Similar calculations were carried out for the prevalence of BMI-for-age values at or below the first percentile (data not shown). In this case, all estimates were similar, and differences were minimal. DISCUSSION The 2000 CDC growth charts, based on data from national samples of children who were measured from 1963 through 1994, include LMS parameters that allow for calculation of selected percentiles and interpolation between those percentiles. The

5 1318 FLEGAL ET AL TABLE 2 Relation of empirical first percentile BMI values to smoothed BMI values within 6-mo age groupings, by sex Mean 6 SD CV Range Median Differences between the empirical first percentile and smoothed percentiles in BMI units Empirical first 2 smoothed third Boys , Girls , Empirical first 2 smoothed fifth Boys , Girls , Ratio of empirical first percentile to smoothed percentiles Empirical first/smoothed third Boys , Girls , Empirical first/smoothed fifth Boys , Girls , Ratios of distances between percentiles (Empirical first 2 smoothed third)/(smoothed third 2 smoothed fifth) Boys , Girls , (Empirical first 2 smoothed 5th)/(smoothed 5th 2 smoothed 10th) Boys , Girls , lowest and highest smoothed percentiles of BMI-for-age available from these charts are the 3rd and 97th percentiles. The values of the LMS parameters supplied by CDC were not developed or evaluated for use to calculate higher or lower percentiles outside this range. The technical report on the CDC growth charts (4) includes cautions against such uses. We reiterate those cautions here. Recently, several publications have used 99th percentile values of BMI-for-age that were extrapolated from the CDC-supplied LMS values (7 13). A report from an expert committee convened by the American Medical Association included this 99th percentile as part of a treatment algorithm (13). The 99th percentile value calculated by extrapolation from the CDC-supplied LMS parameters does not correspond well to the empirical data. In particular, for older girls, the extrapolated LMS-calculated values are on average 2 BMI units higher than the empirical 99th percentile values and exceed a BMI of 40 at ages 17 and older. This can affect comparisons between boys and girls, with girls perhaps misleadingly seeming to have a much lower prevalence of very high BMI than boys, as shown in Table 3 and elsewhere (12). A related problem was noted at the time the growth charts were released, when it became evident that the CDC LMS parameters could not be used to calculate appropriately high z scores for biologically implausible outliers resulting from data entry or measurement errors (19). An alternative calculation based on SDs above and below the median values was recommended for the purpose of flagging implausible outliers. This problem was recently discussed elsewhere (20). The empirical 99th percentile values themselves are quite variable and are not necessarily an accurate estimate of the true 99th percentile. The CDC growth chart data set is too sparse to construct smoothed percentiles beyond the 97th percentile with adequate statistical reliability. Applying the same criteria to the 99th percentile that had been applied to the 97th percentile (21) showed that the sample size within age-sex groupings is not large enough to generate higher percentiles with adequate reliability. A much larger data set would be required to reliably estimate extreme values in the tails of the distribution. The lack of data alone does not preclude the LMS values calculated from the 3rd to the 97th percentiles from providing reasonable approximations to the empirical values of higher percentiles. The fact that the extrapolated LMS-calculated values are not a good approximation to the empirical 99th percentile points to a different issue, the behavior of the data in the very extreme tails of the distribution. BMI data are not normally distributed. Although a Box-Cox transformation can be found to yield an approximately normal distribution, the transformed data are not necessarily perfectly normally distributed. In particular, the tails of the distribution may not correspond to those of a normal distribution even after an approximate transformation to normality. Modeling the behavior in the tails is more difficult than modeling the central part of the distribution and would require strong assumptions. More complex statistical modeling of the tails of the distribution of BMI-for-age using the present data could be done (22), but it is limited by the sparseness of the data in the extremes of the distribution. Given the lack of data and the difficulties in modeling extreme tails of the distributions, various approximations to extreme percentiles that can be constructed do not necessarily represent an accurate assessment of the growth chart distribution of BMI-forage at the extremes. The 99th percentile cannot be estimated with adequate reliability, and the empirical values are not necessarily correct estimates. The use of the LMS parameters to estimate the

6 CHARACTERIZING EXTREME VALUES OF BMI-FOR-AGE 1319 TABLE 3 Differences in BMI units between the empirical 1st or 99th percentile of BMI-for-age and 3 approximations Mean 6 SD Range Median Empirical 99th 2 extrapolated LMS 99th Boys , Girls , Empirical 99th 2 112% of smoothed 97th Boys , Girls , Empirical 99th 2 120% of smoothed 95th Boys , Girls , Empirical 99th reestimated LMS 99th Boys , Girls , Empirical first 2 extrapolated LMS first Boys , Girls , Empirical first 2 96% of smoothed third Boys , Girls , Empirical first 2 94% of smoothed fifth Boys , Girls , Empirical first reestimated LMS first Boys , Girls , th percentile is an extrapolation beyond the range of the data from which they were calculated and does not appear to work well. The data are too sparse and the behavior of the data in the tails too variable to arrive at a reliable estimate of the 99th percentile. For practical purposes, there may be little need for an estimate of the 99th percentile. When the CDC growth charts were released, the 3rd and 97th percentiles were recommended as appropriate cutoffs for extreme low or high BMI-for-age values for children. Adequate data were available to estimate these percentiles. We found that 120% of the smoothed 95th percentile of BMI-for-age was similar to the unsmoothed 99th percentile of the growth chart data set, but it should be realized that this was an approximation. This should not be considered as an exact estimate of the true 99th percentile or as a new definition of severe obesity. It may be most useful as a model for an approach to TABLE 4 Prevalence of extremely high BMI-for-age calculated by using 4 different approximations: National Health and Nutrition Examination Survey (NHANES) Sex and age group 99th percentile extrapolated from CDC-supplied LMS values 112% of the 97th percentile 120% of the 95th percentile 99th percentile calculated from re-estimated LMS values Both 2 19 y 3.7 (0.24) 4.8 (0.30) 4.6 (0.29) 4.2 (0.27) 2 5 y 3.9 (0.41) 2.6 (0.39) 2.2 (0.37) 2.4 (0.38) 6 11 y 3.6 (0.37) 5.1 (0.40) 4.6 (0.37) 4.2 (0.34) y 3.7 (0.34) 5.6 (0.44) 5.8 (0.42) 5.0 (0.41) Boys 2 19 y 4.6 (0.35) 5.4 (0.39) 5.0 (0.40) 4.5 (0.36) 2 5 y 4.4 (0.60) 2.7 (0.50) 2.3 (0.47) 2.5 (0.50) 6 11 y 4.1 (0.54) 5.7 (0.62) 5.1 (0.65) 4.0 (0.51) y 5.1 (0.54) 6.3 (0.59) 6.1 (0.57) 5.9 (0.60) Girls 2 19 y 2.7 (0.22) 4.3 (0.34) 4.3 (0.33) 3.8 (0.31) 2 5 y 3.3 (0.58) 2.5 (0.55) 2.0 (0.50) 2.3 (0.50) 6 11 y 3.1 (0.39) 4.6 (0.50) 4.1 (0.46) 4.4 (0.52) y 2.2 (0.31) 4.9 (0.52) 5.4 (0.55) 4.1 (0.47) 1 Values in parentheses are SEs. CDC, Centers for Disease Control and Prevention; LMS, lambda-mu-sigma parameters.

7 1320 FLEGAL ET AL describing very high BMI values without the need to calculate exact percentiles. One of the reasons for interest in higher percentile values is to assess and track progress in extremely heavy children; for such purposes, a single 99th percentile value is not very useful. The BMI of very heavy children could be described as a percentage of the 95th percentile, without attempting to assign a precise percentile or z score to such values. For instance a child might move over time from 130% of the 95th percentile of BMI-for-age to 115% of the 95th percentile of BMI-for-age, which suggests improvement even though an exact percentile value or z score could not be readily assigned. It is not possible to assign values above the 97th percentile of BMI-for-age an exact place in the distribution of BMI-for-age in the growth chart data. In effect, there are upper and lower limits of detection, as is the case for many other types of variables (23, 24). For example, laboratory values may be below the lower limit of detection for a laboratory method, scales have an upper weight limit, and questions about income or education levels have openended top categories. Thus, this is not an uncommon situation. If needed, some imputation procedure could be used to assign a percentile or z score to extremely high or low values of BMIfor-age. For example, in the construction of the World Health Organization charts, z scores for values above a z score of 3 were imputed (14). However, with any imputation procedure, caution is advised, especially if such values make up.5% of the sample. Calculations of statistics such as means, SDs or regression coefficients can be affected by a large number of imputed high z scores (23, 24). There is no easy or obvious way to deal with this, because the true values are unknown and any assignments are of necessity somewhat arbitrary. Researchers need to be aware of this issue and use appropriate caution in data analysis and interpretation, particularly for analyses that are sensitive to the way in which high values have been imputed (23 26). The uncertainty introduced by the imputed values should be recognized. In the CDC growth chart data, percentiles of BMI-for-age beyond the 97th percentile cannot be well estimated because of sample size limitations and nonnormality of the data in the tails, even after transformations. Extrapolation from the CDC-supplied LMS parameters does not correspond well to empirical values of the 99th percentile. For many practical applications, expressing high BMI values as a percentage of the 95th percentile can provide a flexible approach to tracking and evaluating heavier children that obviates the need for the use of imputed z score values above the 97th percentile. The authors responsibilities were as follows KMF: designedthe study and wrote the first draft of the manuscript; and KMF, RW, and LRC: conducted the statistical analysis. All authors conducted the analysis and interpretation of the data and critically revised the manuscript for important intellectual content. None of the authors had a personal or financial conflict of interest. REFERENCES 1. Kuczmarski RJ, Ogden CL, Grummer-Strawn LM, et al. CDC growth charts: United States. Adv Data 2000;Jun 8: Ogden CL, Kuczmarski RJ, Flegal KM, et al. Centers for Disease Control and Prevention 2000 growth charts for the United States: improvements to the 1977 National Center for Health Statistics version. Pediatrics 2002;109: National Center for Health Statistics CDC growth charts: United States. Available from: (cited 31 July 2009) 4. Kuczmarski RJ, Ogden CL, Guo SS, et al CDC growth charts for the United States: methods and development. Vital Health Stat : Cole TJ. The LMS method for constructing normalized growth standards. Eur J Clin Nutr 1990;44: Cole TJ, Green PJ. Smoothing reference centile curves: the LMS method and penalized likelihood. Stat Med 1992;11: Barlow SE. Expert committee recommendations regarding the prevention, assessment, and treatment of child and adolescent overweight and obesity: summary report. Pediatrics 2007;120(suppl 4):S Freedman DS, Khan LK, Serdula MK, Ogden CL, Dietz WH. Racial and ethnic differences in secular trends for childhood BMI, weight, and height. Obesity (Silver Spring) 2006;14: Freedman DS, Mei Z, Srinivasan SR, Berenson GS, Dietz WH. Cardiovascular risk factors and excess adiposity among overweight children and adolescents: the Bogalusa Heart Study. J Pediatr 2007;150: Krebs NF, Himes JH, Jacobson D, Nicklas TA, Guilday P, Styne D. Assessment of child and adolescent overweight and obesity. Pediatrics 2007;120(suppl 4):S Lenders CM, Wright JA, Apovian CM, et al. Weight loss surgery eligibility according to various BMI criteria among adolescents. Obesity (Silver Spring) 2009;17: Skelton JA, Cook SR, Auinger P, Klein JD, Barlow SE. Prevalence and trends of severe obesity among US children and adolescents. Acad Pediatr (Epub ahead of print 26 June 2009). 13. Spear BA, Barlow SE, Ervin C, et al. Recommendations for treatment of child and adolescent overweight and obesity. Pediatrics 2007; 120(suppl 4):S WHO. WHO child growth standards: length/height-for-age, weightfor-age, weight-for-length, weight-forheight and body mass indexfor-age: methods and development. Geneva, Switzerland: World Health Organization, de Onis M, Garza C, Onyango AW, Borghi E. Comparison of the WHO child growth standards and the CDC 2000 growth charts. J Nutr 2007; 137: Hedley AA, Ogden CL, Johnson CL, Carroll MD, Curtin LR, Flegal KM. Prevalence of overweight and obesity among US children, adolescents, and adults, JAMA 2004;291: Ogden CL, Flegal KM, Carroll MD, Johnson CL. Prevalence and trends in overweight among US children and adolescents, JAMA 2002;288: Ogden CL, Carroll MD, Flegal KM. High body mass index for age among US children and adolescents, JAMA 2008;299: Cut-offs to define outliers in the 2000 CDC growth charts. Available from: (cited 11 March 2009). 20. Woo JG. Using body mass index Z-score among severely obese adolescents: a cautionary note. Int J Pediatr Obes 2009; (in press). 21. Guo SS, Roche AF, Chumlea WC, Johnson C, Kuczmarski RJ, Curtin R. Statistical effects of varying sample sizes on the precision of percentile estimates. Am J Hum Biol 2000;12: Rigby RA, Stasinopoulos DM. Smooth centile curves for skew and kurtotic data modelled using the Box-Cox power exponential distribution. Stat Med 2004;23: Lubin JH, Colt JS, Camann D, et al. Epidemiologic evaluation of measurement data in the presence of detection limits. Environ Health Perspect 2004;112: Schisterman EF, Vexler A, Whitcomb BW, Liu A. The limitations due to exposure detection limits for regression models. Am J Epidemiol 2006; 163: Little RJA, Rubin DB. Statistical analysis with missing data. Hoboken, NJ: John Wiley & Sons, Rubin DB. Multiple imputation for nonresponse in surveys. New York, NY: John Wiley, 1987.

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