{'fraction_non_alphanumeric': 0.044608695652173916, 'fraction_numerical': 0.035260869565217394, 'mean_word_length': 4.554455445544554, 'pattern_counts': {'":': 0, '<': 7, '<?xml version=': 0, '>': 4, 'https://': 0, 'lorem ipsum': 0, 'www.': 1, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 13, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
BMI z-scores are a poor indicator of adiposity among 2- to 19-year-olds with very high BMIs, NHANES 1999-2000 to 2013-14

Objective Although the CDC growth charts are widely used, BMIz is known to be uninformative above the 97th percentile. We compared the relations of BMIz and other BMI metrics (%BMIp95, percent of 95th percentile, and ΔBMIp95, BMI minus 95th percentile) to circumferences, skinfolds and fat mass. We were particularly interested in the differences among children with severe obesity (%BMIp95 ≥ 120). Methods We used data from 30,003 2- to 19-year-olds who were examined from 1999-2000 through 2013-14 in NHANES. Results The theoretical maximum BMIz based on the growth charts varied by more than 3-fold across ages. The BMI metrics were strongly intercorrelated, but BMIz was less strongly related to the adiposity measures than were ΔBMIp95 and %BMIp95. Among children with severe obesity, circumferences and triceps skinfold showed almost no association with BMIz (r ≤ 0.10), whereas associations with %BMIp95 and ΔBMIp95 ranged from r=0.32 to 0.79. Corresponding associations with fat mass ÷ height2 ranged from r=0.40 (BMIz) to r=0.82 (%BMIp95) among 8- to 19-year-olds. Conclusions Among children with severe obesity, BMIz is only weakly associated with other measures of body fatness. Very high BMIs should be expressed relative to the CDC 95th percentile, particularly in studies that evaluate obesity interventions.


Introduction
The 2000 Centers for Disease Control and Prevention (CDC) growth charts (1,2) are widely used to classify obesity (BMI ≥ 95 th percentile for a child's sex and age) among 2-to 19year-olds. In these growth charts, 10 percentiles of BMI between the 3 rd and 97 th were estimated using various smoothing methods (1,3). These percentiles were then used to derive L (normality transformation for skewness), M (central tendency) and S (dispersion) parameters that allow for the estimation of z-scores and percentiles for any child (4).
The use of the LMS parameters in the CDC growth charts, however, is known to yield zscores for very high BMIs that can differ substantially from the estimates based on the data (3,5). This is, in part, because these parameters in the CDC growth charts were derived from already-smoothed percentiles ≤ 97 th (z-score of 1.88), rather than from the underlying data as originally proposed (4). In addition, it is difficult to accurately estimate extreme values. This has led to the use of 120% of the 95 th percentile of BMI rather than the LMSextrapolated 99 th percentile, to classify severe obesity (5,6).
Although the CDC growth charts were constructed as references for clinical care and in the estimation of prevalences, BMI-for-age z-scores (BMIz) have been widely used in all types of analyses, including obesity interventions (7)(8)(9)(10). This has occurred despite investigators having emphasized the limitations of very high BMIz values (11)(12)(13)(14)(15). A wide range of very high BMIs can map to similar z-scores, and BMIz values in the growth charts have a theoretical maximum (14,16). Further, when neither the baseline nor follow-up BMIz can be estimated accurately, an examination of ΔBMIz can lead to erroneous conclusions.
The objective of the current study is to describe the relationship of various BMI metrics to other anthropometric indices of obesity (arm and waist circumferences, and triceps skinfold thickness) and to fat mass assessed by dual X-ray absorptiometry (DXA). We were particularly interested in comparing the magnitudes of these associations among children with severe obesity.

Sample and Measurements
We used data from the National Health and Nutrition Examination Survey (NHANES) from 8 cycles conducted from 1999-2000 through 2013-2014 (17). NHANES employs a multistage, stratified, cluster sampling design to select a representative sample of the US civilian, non-institutionalized population. The surveys were approved by the ethics review board, and parental permission was obtained for subjects < 18 y of age.
We focus on 2-to 19-year-olds who had weight and height measurements, and after excluding pregnant girls, the resulting sample size was 30,003. Race and ethnicity were self-reported, and subjects were classified as white non-Hispanic, black non-Hispanic, Mexican-American, or other (which includes other Hispanics and multi-racial persons). Weight, height, waist circumference, and mid upper-arm circumference were measured in a standardized fashion (18). Triceps skinfold thickness was measured through the 2009-10 surveys, but not in more recent cycles.
DXA scans were acquired in NHANES 1999-2006 for boys and non-pregnant girls who were ≥ 8 y using a Hologic QDR 4500A fan-beam densitometer (Hologic Inc., Bedford MA) (19,20). The current analyses focus on fat mass (kg) and fat mass index (fat mass/ht 2 ). The 1999-2000 DXA data for girls are not available in the publicly released data and are not included in the current analyses.
We used the NHANES DXA Multiple Imputation Data Files (19) in the analyses. These imputations, which were performed by the National Center for Health Statistics, used sequential regression to impute (estimate) missing DXA values for 5 complete datasets from non-missing DXA measurements and characteristics such as sex, race-ethnicity, age, BMI and waist circumference (21).

BMI Transformations
Body mass index (BMI) was calculated as kg/m 2 . BMIz was calculated by expressing a child's BMI relative to children in the CDC growth charts (1). The L (power transformation for skewness) M (median), and S (dispersion) parameters in Cole's LMS method (4) allows for the estimation of a child's z-score with: Figure 1 show the L, M, and S estimates in the CDC growth charts (http://www.cdc.gov/ growthcharts/percentile_data_files.htm). Because L is large and negative, if a child's BMI is very large relative to the median BMI, (BMI ÷ M) L approaches 0 and the maximum BMIz value that is possible (−1) ÷ (L × S). An 8-year-old boy with a BMI of 80 kg/m 2 , for example, would have a (BMI ÷ M) L of 0.006 and a BMIz of 3.1.
Obesity is defined as a BMI ≥ 95 th percentile of the CDC growth charts (1,2). We refer to a BMI that is expressed as a percentage of the 95th percentile as %BMI p95 , and severe obesity as a %BMI p95 ≥ 120 (6). Several analyses also focus on children with %BMI p95 levels of 100 to <120; we refer to this category as moderate obesity.
We also examined other BMI metrics that account for sex and age. Because of the upper limit of BMIz, CDC proposed using 'modified' z-scores to identify extreme values; these were constructed by extrapolating ½ of the distance between 0 and 2 z-scores to more extreme values (16,22). In addition to %BMI p95 , which expresses a child's BMI as a percentage of the (sex-and age-specific) 95 th percentile, we also examine ΔBMI p95 (BMI -95 th percentile) which is the distance (in kg/m 2 ) from the 95 th percentile. For example, an 8year-old boy (95 th percentile, 20.5 kg/m 2 ) with a BMI of 25.3 kg/m 2 , would have a ΔBMI p95 of +4.8 kg/m 2 and a BMI p95 of 124%, whereas a similarly aged boy with a BMI of 18 kg/m 2 would have a ΔBMI p95 of -2.5 kg/m 2 (2.5 units below the 95 th percentile).
The CDC SAS program for the Growth Charts (23) calculates the 95 th percentile of BMI, %BMI p95 and ΔBMI p95 , as well as BMIz and the modified z-score for each child.

Statistical Methods
All analyses used the examination sample weights and accounted for the sample design using the survey package in R (24). About 3% to 4% of the 30,003 2-to 19-year-olds in the analyses were missing information on triceps skinfold thickness and waist circumference, and we imputed these missing values using the 'aregImpute' function in the Hmisc package (25). Because children who were missing information on these measures tended to have high BMIs, an analysis of only non-missing data would be biased, and multiple imputation replaces these missing values with estimates based on information from correlated variables (26). Predictors in these imputations included sex, race-ethnicity, age, BMI, DXA-calculated fat mass and fat mass index (kg of fat/m 2 ), leg length, circumferences, and survey cycle. One imputed data set was created for each of the 5 DXA data sets, and the 5 sets of results were combined (27).
Descriptive characteristics of various characteristics are contrasted across three categories (non-obese, moderate obesity and severe obesity) of BMI p95 . Before examining the relation of the various BMI metrics to levels of the circumferences, skinfolds and fat mass, we adjusted these other characteristics for sex and age by regressing each characteristic on sex, age (modeled with splines) and the sex × age interaction. The residuals from these models, referred to as 'adjusted levels', were then used in the correlational analyses. We also examined the correlations between the various BMI metrics and levels of circumferences, skinfolds and DXA measures within categories of sex, age (<12 y vs. ≥ 12 y) and BMI. We used lowess, a non-parametric smoother, to illustrate the relation of several of the examined characteristics to age. Table 1 shows levels of various characteristics among non-obese children, children with moderate obesity (BMI p95 , 100% to 119%), and children with severe obesity. About 11% of the children had a BMI ≥ 97 th percentile, and 5% had a %BMI p95 ≥ 120%. In the current study, 15 children had a %BMI p95 > 200%, with a maximum of 230% (BMI, 63 kg/m 2 ).

Results
Severe obesity tended to be more prevalent among boys than girls (p = 0.04) and among both black and Mexican-American children than among white children (p < 0.0001). Among children with severe obesity, the mean BMIz was 2.5 SDs and the mean ΔBMI p95 was 8.9 kg/m 2 . As compared to children without obesity, those with severe obesity had higher mean levels of both weight-for age and height-for-age, as well as higher levels of the of circumferences, triceps skinfolds and DXA-calculated body fat.
The bottom, right panel of Figure 1 shows the maximum values of BMIz that are theoretically possible at each age, based on the LMS values in the CDC growth charts; these values have been previously published (14). Among boys, the theoretical maximum BMIz is greater than 5 among 2-to 4-year-olds, but decreases to about 3 between ages of 6 and 12 y, and then increases to about 4 at age 18 y. Among girls, the maximum possible BMIz value decreases rapidly from > 11 (age 2 y) to about 3.5 (ages 6 to 15 y); this maximum further decreases to 2.8 at age 19 y. Figure 2 shows, for the CDC growth charts, BMIz values corresponding to levels of %BMI p95 between 100% (the CDC 95 th percentile) and 160%. As seen for the maximum possible BMIz (Figure 1), these very high BMIz values also vary by sex and age so that a constant %BMI p95 value is associated with substantially different z-scores. Among girls, zscores become more compressed at older ages, so that z-score differences (between constant %BMI p95 levels) become smaller. For example, a 2-year-old girl with a %BMI p95 of 140 would have a BMIz of about 4.5, whereas a 17-year-old girl with the same %BMI p95 would have a BMIz of 2.3. Among boys, the BMIz differences across %BMI p95 levels was more complex, and were most compressed at about age 10 y. A very similar pattern (data not shown) was seen if BMIz values were plotted against values of ΔBMI p95 that ranged from +6 to +18 kg/m 2 . Table 2 shows correlations among the BMI metrics, circumferences, skinfolds and fat mass among all children (top rows), those with moderate obesity (middle), and those with severe obesity (bottom). Overall, correlations among the BMI metrics were r ≥ 0.90 except for BMIz. For example, %BMI p95 (3 nd column) was very strongly correlated with modified BMIz (r=0.93) and ΔBMI p95 (r=0.98). In contrast, BMIz was less strongly associated with %BMI p95 and ΔBMI p95 (r=0.81 and 0.87). In addition, BMIz consistently showed weaker (about 0.05 to 0.10 lower) correlations with the other adiposity measures than did both %BMI p95 and ΔBMI p95 . Correlations with adjusted fat mass, for example, ranged from r=0.81 (BMIz) to 0.93 (%BMI p95 and ΔBMI p95 .) Although the magnitudes of the observed correlations were weaker among children with moderate obesity (middle) and those with severe obesity (bottom), due at least in part to the restricted ranges of BMI values, the decreases were most evident for BMIz. Among children with severe obesity, for example, correlations between BMIz and levels of both ΔBMI p95 and %BMI p95 were of r < 0.5. Further, among children with severe obesity, BMIz showed almost no association with adjusted levels of the two circumferences and triceps skinfold (r ≤ 0.10), and only a moderate (r=0.40) correlation with fat mass index, which was not available among 2-to 7-year-olds. In general, ΔBMI p95 showed the strongest associations with the other body size measures among children with either moderate or severe obesity. For example, correlations with waist to height among children with severe obesity were r=0.18 (BMIz), r=0.56 (%BMI p95 ) and r=0.62 (ΔBMI p95 ), while the comparable associations among children with moderate obesity ranged from r=0.26 (BMIz) to 0.52 (ΔBMI p95 ).
We then examined the relation of the various BMI metrics to the other adiposity measures within categories of BMI status and sex (Figure 3). For both boys (upper panels) and girls, associations with the other body size measures were generally stronger for %BMI p95 and ΔBMI p95 than for BMIz, and the magnitudes of the differences among the correlations were largest for children with severe obesity (right panels). Of the 36 sets of correlations (2 sexes × 3 obesity groups × 6 body size measures), 24 were strongest for ΔBMI p95 and 11 were strongest for %BMI p95 . Only for levels of fat mass index among non-obese girls, was the correlation with BMIz slightly higher than that with %BMI p95 (r = 0.77 vs 0.75). Among children with severe obesity, several of the associations between BMIz and adjusted levels of circumferences and skinfolds were < 0.30. The largest difference in the magnitudes of the 4 BMI metrics among children with severe obesity was seen for adjusted levels of arm circumference among girls, with correlations ranging from r=0.08 (BMIz) to r=0.79 (ΔBMI p95 ).
The relations of BMIz, %BMI p95 and ΔBMI p95 to adjusted levels of waist circumference are shown in Figure 4 among children with severe obesity. BMIz (left panels) showed a strong association with adjusted waist circumference among 12-to 19-year-olds, but almost no association with BMIz values above 2.5 among younger children (solid line). In contrast, both %BMI p95 and ΔBMI p95 showed strong associations with waist circumference over their entire ranges in both age groups.

Discussion
About 6% of 2-to 19-year-olds currently have a BMI that is greater than or equal to 120% of the CDC 95 th percentile (i.e., %BMI p95 ≥ 120) (28), and there is much interest in the evaluation and treatment of these children (6,29). Although the report accompanying the CDC growth charts (1) noted that extrapolation outside the 3 rd through 97 th percentiles (zscores of ± 1.88) should be interpreted cautiously, BMIz values remain widely used in crosssectional and longitudinal analyses of children with severe obesity (7,8,10,30,31). Our results emphasize that BMIz functions poorly as an indicator of adiposity among children with obesity, particularly among those with severe obesity. Among children with severe obesity, BMIz is, in general, much less strongly associated with circumferences, skinfolds and fat mass than are ΔBMI p95 and %BMI p95 . Because a wide range of very high BMI values can map to essentially the same z-score, which varies by sex and age, differences between children who have different levels of adiposity, as well as longitudinal BMIz changes (32), can be obscured. Many of the limitations of BMIz, particularly when based on the CDC growth charts, have been emphasized in previous studies (11)(12)(13)(14), and our results highlight the weak relationship of BMIz to levels of other measures of fatness among children who are severely obese.
Because of the LMS transformation, BMIz values can differ substantially among children who have similar levels of %BMI p95 , ΔBMI p95 and other measures of adiposity. For example, there were 2 boys (ages 3 and 9 y) in the current study who had a %BMI p95 of about 140, but the older boy had a markedly lower BMIz (2.5 vs 4.7). This BMIz difference resulted from the sex and age changes in the L and S parameters in the CDC growth charts which affect z-scores > 1.88 (97 th percentile). Previous studies (11)(12)(13)(14)(15) have concluded that LMS-based z-scores should not be used to assess BMI changes. Our results indicate that among children with severe obesity, even very large (e.g., >1 SD) BMIz differences may simply reflect differences in sex or age rather than body size.
The attenuation and confounding of very high BMIz values could influence the results of longitudinal studies that include a large proportion of children who have severe obesity. For example, a 17-year-old girl with a BMI of 50 kg/m 2 would have a BMIz of 2.6 based on the CDC LMS parameters (33). (The theoretical maximum BMIz for this sex/age is 3.1.) If this girl were to gain an additional 29 kg over 2 years, her BMI would increase by about 10 kg/m 2 , but her BMIz would remain constant. In contrast, there would be large increases in %BMI p95 (from 169% to 193%) and ΔBMI p95 (from +29 to +38 kg/m 2 ) reflecting her large weight increase.
The influence of the sex/age differences in the L and S parameters on very high BMIz levels may account for some of the conflicting results in the literature. For example, an intervention study (34) of children with severe obesity (mean BMI, 37 kg/m 2 ) reported a small, statistically significant decrease in BMIz (-0.03 SD) along with a statistically significant 1 kg/m 2 increase in BMI. These problems would be particularly relevant for intervention studies that contain a large proportion of children with severe obesity, and if analyses focused only on ΔBMIz (7,30,31,35), it is possible that the conclusions could be incorrect. Both cross-sectional and longitudinal studies that include a large proportion of children with severe obesity should express BMI levels relative to the CDC 95 th percentile.
In the current study, BMIz showed a moderate to strong association with both ΔBMI p95 and %BMI p95 (r=0.81 to 0.87) among all children, but much weaker associations (r < 0.50) among children with severe obesity. Although the relationships of %BMI p95 and ΔBMI p95 to the other measures of adiposity were generally similar, there are situations when 1 might be preferred. A 1-unit increase in ΔBMI p95 for example, would indicate that a child's BMI increased by 1 kg/m 2 more than expected based on sex and change in age, and this might be easier to interpret than a change in %BMI p95 . However, for comparisons of children across a wide range of ages over which BMI levels vary substantially, %BMI p95 might be preferred as a 1 unit BMI difference should likely be interpreted differently among 2-year-olds than among 18-year-olds. It is possible that neither ΔBMI p95 nor %BMI p95 would be best in all situations, and that both metrics could be investigated. It should also be noted that %BMI p95 and ΔBMI p95 resemble other BMI metrics that have been proposed, such as sympercents (11,12,36) and percent over BMI (12). Additional analyses (data not shown) of sympercents, defined in the current study as the difference, on the natural log scale, between a child's BMI and the 95th percentile of BMI, indicated that this metric was strongly associated (r=0.99) with %BMI p95 .
There are several limitations of the current study that should be considered when interpreting our results. Our results concerning the extrapolation of the LMS calculations apply to children with obesity, and particularly those with severe obesity. However, even in the entire sample of children, BMIz was less strongly correlated with the other adiposity measures than were ΔBMI p95 and %BMI p95 ( Table 2). It should also be realized that attenuation of the LMS-estimated z-scores in the CDC growth charts was recognized by CDC, and a set of modified z-score were developed to address this limitation (16). These modified z-scores are based on extrapolating the distance between 0 and 2 SDs to more extreme BMI values and therefore do not have an upper limit. However, the appropriateness of applying this fixed distance to very high BMI values is uncertain, and a somewhat different approach was used in the WHO growth standards (37). It should also be realized that all of the adiposity measures in the current study, including circumferences, triceps skinfold and DXA measurements, become increasingly difficult to accurately assess among children and adults with severe obesity (38,39). For example, about 27% of all children with severe obesity in the current study had a DXA measurement that was imputed from other characteristics (21). It should be also realized it would have been optimal to have examined differences between the BMI metrics using a gold-standard measure of adiposity rather than with indirect measures (e.g., circumferences) or with DXA measurements that were available for only a subset of the children.
Although LMS-extrapolated z-scores for children who have very high BMI levels are widely used (7,30,31,35), with some investigators specifically recommending the use of ΔBMIz among children with severe obesity (http://stokes.chop.edu/web/zscore), this approach is not optimal. BMIz levels among children with severe obesity (1) can differ substantially from the empirical estimates, (2) have an effective upper limit resulting in the mapping of very high BMIs to similar z-scores, and (3) can differ solely due to differences in sex and age. Investigators using the CDC growth charts to calculate BMIz values for analyses should be aware of these limitations. Although the drawbacks of BMIz would be unlikely to markedly influence the analysis of population-based studies, the results of studies that include a large proportion of children who have severe obesity should be verified using %BMI p95 or ΔBMI p95 . For studies that include many children with extreme BMI values, including those focused on obesity interventions, the analyses should likely emphasize %BMI p95 , ΔBMI p95 or another metric based on the 95 th percentile rather than BMIz.  Calculated BMIz values from the CDC growth charts associated with various levels of %BMI p95 and with the CDC 95 th percentile of BMI. Relation of BMIz, modified BMIz, %BMI p95 and ΔBMI p95 to other body size measures, by sex and BMI status. Values of arm circumference, waist circumference, triceps skinfold and fat mass were adjusted for sex and age.