To examine the associations among several BMI metrics (z-scores, percent of the 95^{th} percentile (%BMI_{p95}) and ΔBMIp95 (BMI minus 95^{th} percentile) as calculated in the CDC growth charts. It is known that the widely-used BMI z-scores and percentiles calculated from the growth charts can differ substantially from those that directly observed in the data for BMIs above the 97^{th} percentile (z = 1.88).

Study design Cross-sectional analyses of 8.7 million 2- to 4-year-olds who were examined from 2008 through 2011 in the CDC’s Pediatric Nutrition Surveillance System.

Because of the transformation used to calculate z-scores, the theoretical maximum BMIz varied by more than 3-fold across ages. This results in the conversion of very high BMIs into a narrow range of z-scores that varied by sex and age. Among children with severe obesity, levels of BMIz were only moderately correlated (r ~ 0.5) with %BMI_{p95} and ΔBMIp95. Among these children with severe obesity, BMIz levels could differ by more than 1 SD among children who had very similar levels of BMI, %BMI_{p95} and ΔBMIp95 due to differences in age or sex.

The effective upper limit of BMIz values calculated from the CDC growth charts, which varies by sex and age, strongly influences the calculation of z-scores for children with severe obesity. Expressing these very high BMIs relative to the CDC 95th percentile, either as a difference or percentage, would be preferable to using BMI-for-age, particularly when assessing the effectiveness of interventions.

The 2000 Centers for Disease Control and Prevention (CDC) growth charts are widely used to classify obesity (BMI ≥ 95^{th} percentile for a child’s sex and age) among children and adolescents (^{rd} and 97^{th}) of BMI for 2- to 19-year-olds (

However, the use of the LMS measures to calculate percentiles and z-scores above the CDC 97^{th} percentile yields values that do not agree with the estimates based on direct observation of the data (^{th} percentile of BMI (%BMIp95) for the classification of classify severe obesity among children (

Despite the limitations of very high BMIz values estimated from the CDC growth charts, these z-scores have been widely used as a continuous variable in various types of studies, including those focused on interventions (

The objective of the current study is to describe the interrelationships and differences among various BMI metrics (BMI, BMIz, and BMI expressed relative to the 95^{th} percentile) among 8.7 million 2- to 4-year-olds. These analyses extend our previous report concerning these BMI metrics among 2- to 19-year-olds in NHANES (

As previously described (

There were 14.4 million records (observations) in the database from children between 24.0 and 59.9 months of age from 2008 through 2011. The initial data cleaning excluded (1) 623,000 records that were missing data on weight or height, (2) 70,000 children for whom the date of birth or sex differed across records, and (4) 151,000 records that had an implausible weight, height or BMI based on the recommended cut-points of modified z-scores (

These exclusions resulted in a sample of 13.5 million records from 8,654,466 children. Based on the assigned ID and birthdate, we determined that 3.6 million had been examined multiple times, and we used data from only the first examination for these children.

Body mass index (BMI) was calculated as kg/m^{2}. BMIz was calculated by expressing a child’s BMI relative to children of the same sex and age in the CDC growth charts (

Because values of L are negative, when BMI is large relative to the median BMI, (BMI ÷ M)^{L} approaches 0 and the maximum BMIz that is possible at a specific sex/age is therefore (−1) ÷ (L × S). For example, a 2-year-old boy with a BMI of 30 would have a (BMI ÷ M)^{L} of ~0.3 and a BMIz of 5.1 SDs. Based on the values of L and S in the growth charts for this sex/age, the maximum possible BMIz for this child is 6.3 SDs irrespective of his BMI.

The difference between the LMS method proposed by Cole et al and the methods used in the CDC should also be appreciated (

Obesity is defined as a BMI-for-age ≥ 95th percentile (BMIz ≥ 1.645) of the CDC growth charts (^{th} percentile), moderately obese, and severely obese (%BMIp95 ≥ 120).

In addition to BMIz and %BMIp95, we the difference (in kg/m^{2}) of the child’s BMI from the 95^{th} percentile of BMI. This difference (ΔBMIp95), which assessed the distance from the 95^{th} percentile and does not represent change over time, was calculated by subtracting the sex- and age-specific CDC 95^{th} percentile from the child’s BMI. For example, an 8-year-old boy with a BMI of 22 kg/m^{2}, would have a ΔBMIp95 of +2 kg/m^{2} if the 95^{th} percentile were 20 kg/m^{2}. ΔBMIp95 values are somewhat like the residuals from a linear model in which BMI is regressed on sex and age, but expresses BMI relative to the 95^{th} percentile rather than to the mean.

BMIz, %BMIp95 and ΔBMIp95 each standardizes BMI values for the differences in BMI levels observed between boys and girls and across ages, but express these standardized BMI values on different scales. In addition to providing z-scores and percentiles, the output of the SAS program for the CDC growth charts (^{th} BMI percentile, ΔBMIp95 and %BMIp95.

Analyses were performed in R (

The relation of %BMIp95 to levels of BMI and the other BMI metrics are illustrated with violin plots (^{th}, 50^{th} and 90^{th} percentile for each characteristic.

^{th} percentile of BMI, and the theoretical maximum value of BMIz, in the CDC growth charts. Also shown are the observed, maximum values of BMIz in PedNSS (lower right). Between 24 and 59 months of age, the median BMI (M) decreased by about 1 kg/m^{2}, and except for small increases after about 50 months, the patterns for the CDC 95^{th} percentile were similar. In contrast, the theoretical maximum BMI-for-age, which is based solely on the L and S measures in the growth charts, showed a very different pattern (lower left), with the maximum possible BMIz decreasing from about 12 to 3.5 over the range of ages among girls. Among boys, the pattern was concave, with the maximum (10 SD) occurring at about 40 months of age. The maximum values of BMIz that were observed in PedNSS (lower right) show trends that were fairly similar to those for the theoretical maximums, but the values were lower. About 32,000 children in the current study had a BMIz ≥ 4 SDs; about two thirds of these children were boys between 30 and 54 months of age.

^{2}), along with higher levels of BMIz. As expected, children with severe obesity also had a higher (3.0 SDs) weight-for-age than did children without obesity, but they also had a 0.7 SD higher mean height-for-age.

^{2}. Apart from a ΔBMIp95 of 0 (the 95^{th} percentile), BMIz values for a given ΔBMIp95 varied substantially across ages and between sexes, with the shapes of the curves being somewhat similar to the theoretical maximums for BMIz (^{2} would have a BMIz of 5.5 SDs at 24 months, but a BMIz of 3.2 at 49 months. The extent of compression of these extreme BMIz values varied by sex, and older girls showed the most compression. For example, the BMIz difference between ΔBMIp95 values of +3 and +12 among girls was 2.5 SDs at 24 months, but only 0.8 SDs at 59 months.

BMIz was strongly correlated with levels of ΔBMIp95, and %BMIp95, but the magnitudes of the associations varied according to BMI status (

^{2} across the 6 categories of %BMIp95, and a similar trend was see for ΔBMIp95. In contrast, the pattern for BMIz (right panel) was curvilinear, with levels showing large differences across the 3 lowest %BMIp95 categories (< 140), but much smaller differences at higher %BMIp95 levels. BMIz levels for the 5832 children in the 2 highest %BMIp95 categories (≥ 150) were, on average, lower than those among children who had a %BMIp95 of 140 to 149 as a result of the strong influence of sex and age on very high BMIz levels. Children who had a %BMIp95 ≥ 150 tended to be older (mean, 46 months) and 75% were girls, characteristics associated with greater compression of very high BMIz values,

^{2} was about 1 SD higher than the corresponding value among girls, while among children with a BMI of 26.0 to 27.9 kg/m^{2}, the difference was 1.5 SDs. Furthermore, the decrease in the range of BMIz values with age among girls, as well as the lack of a sex difference among 2-year-olds, illustrate that BMIz cannot be used to standardize very high BMIs for sex and age.

These sex and age differences in the distributions of BMIz were due to differences in the L (power) and S (coefficient of variation) measures of the CDC growth charts. At 54 months of age, for example, the maximum possible BMIz is 6.5 among boys, but only 3.8 among girls, complicating the interpretation of very high BMIz levels between boys and girls. In contrast to these BMIz differences, the relation of BMI to %BMIp95 (bottom panels) and ΔBMIp95 (not shown) showed little difference between boys and girls with the exception of very high %BMIp95 values among 4-year-olds who had a BMI ≥ 28 (lower right panel). The maximum BMI in this subset of girls was 32 kg/m^{2} whereas the corresponding maximum BMI among boys was 28.4 kg/m^{2}. Despite this difference in BMI levels, values of BMIz in this subset were substantially higher among girls than boys (top right panel).

There is interest in the identification and treatment of children and adolescents who have high BMIs (^{rd} through 97^{th} percentiles, corresponding to z-scores of ±1.88), BMIz continues to be widely used for children who have extreme BMI values (

Several of the limitations of BMIz were most evident in the plots showing the relation of %BMIp95 to the other BMI metrics (

These findings in PedNSS extend our previous findings concerning the relation of various BMI metrics to skinfolds, circumferences and fat mass among 2- to 19-year-olds (

Because of the LMS transformation, extreme values of BMIz can differ substantially among children who have similar levels of BMI, %BMIp95 and ΔBMIp95. For example, the median BMIz among girls who had a BMI of ≥ 28 kg/m^{2} in the current study was 4.8 SDs at age 2 y, but 3.3 SDs at age 4y. This decrease in BMIz with age among these girls was seen despite age-related increases in both BMI and %BMIp95, and were due to differences in the L and S measures. Several investigators (

The attenuation and confounding of very high BMIz values could be particularly problematic in longitudinal studies that focus on children with obesity (^{th} percentile should express BMI relative to the to the 95^{th} percentile in the CDC growth charts as either %BMIp95 or ΔBMIp95. This would be particularly important when assessing BMI changes among children with severe obesity.

Several limitations of our analyses should be considered. The PedNSS dataset is extremely large, but the data were not collected for research purposes and we excluded over 800,000 (of 14.4 million) records that we identified as likely having errors or were missing data. Although it is very likely that errors remained in the data used in the current analyses, they would have influenced the calculations for all the BMI metrics, not only BMIz. It should also be realized that the prevalence of obesity among children in the current study was higher (14.7%) than that observed among 2 to 5-year-olds (12.1%) examined in NHANES 2009–2010 (^{2}. However, for analyses that include a wide range of ages over which the mean BMI would differ, the same ΔBMIp95 should likely be interpreted relative to the distribution of BMI values at that age and %BMIp95 might be preferred.

Investigators have continued to use LMS-extrapolated z-scores in analyses that include a high proportion of children who have a BMI ≥ 97^{th} percentile in the CDC growth charts (^{th} percentile. However, BMIz values calculated from the CDC growth charts for children who have a BMI ≥ 97^{th} percentile (z ~ 1.88) can differ substantially from the empirical estimates (^{th} percentile, and the distance of the BMI values above the 97^{th} percentile. In studies that include a large proportion of children with severe obesity, the analyses of BMIz values and changes in these values could result in incorrect conclusions. Rather than using z-scores, very high BMIs among children with severe obesity should be expressed relative to the CDC 95^{th} percentile, either as a difference or percentage.

Supported by the Centers for Disease Control and Prevention (RFA-DP-11-007 [to N.B. and E.T.] and U18DP003370 [to E.T.]) and by the National Institute of Diabetes and Digestive and Kidney Diseases (K24 DK10589 [to E.T.]).

None of the authors has any potential, perceived or real, conflict of interest.

DF wrote the first draft of the manuscript and received no form of payment of any type

The authors declare no conflicts of interest.

This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

body mass index

Centers for Disease Control and Prevention

Pediatric Surveillance Nutrition Surveillance System

Women, Infants and Children

Levels in the CDC growth charts of the 50^{th} percentile, the 95th percentile, and the theoretical maximum value of BMIz. Levels of the observed maximum BMI in the current study are shown in the lower right panel. Note that the scales and range of values on the y-axes differ across the 4 characteristics.

BMIz values associated with various levels of ΔBMIp95 by sex and age

Violin plots showing the distribution of levels of BMI and various transformation across categories of %BMIp95. The width of each violin is proportional to the density of the sample at that value, and the horizontal lines represent the 10^{th}, 50^{th}, and 90^{th} percentiles. Values below the 1^{st} percentile or greater than the 99^{th} percentile have been set to equal these percentiles.

Violin plots showing the distribution of levels of BMIz and %BMIp95 across categories of BMI, by sex and year of age. None of the 3-year-old boys had a BMI ≥ 28.0 kg/m^{2}.

Levels of various characteristics stratified by BMI status

Non-obese | Moderate Obesity (%BMIp95: 100 to 119) | Severe Obesity (%BMIp95 ≥ 120) | |
---|---|---|---|

| |||

N | 7,382,740 | 1,115,349 | 156,377 |

Age (months) | 37.0 (24, 58) | 37.8 (24, 58) | 41.9 (25, 59) |

Boys | 49.7% | 46.7% | 50.0% |

Girls | 50.3% | 53.3% | 50.0% |

White | 34.4% | 29.1% | 23.6% |

Black | 20.1% | 16.0% | 13.9% |

Hispanic | 37.4% | 47.2% | 54.7% |

Asian | 2.7% | 2.2% | 2.1% |

American Indian/Alaskan | 0.7% | 1.1% | 1.1% |

Unknown | 4.6% | 4.4% | 4.6% |

BMI (kg/m^{2}) | 16.2 (13.8, 18.4) | 19.5 (18.0, 21.8) | 23.8 (21.7, 27.9) |

BMI z-score (SDs) | 0.1 (−2.1, 1.6) | 2.2 (1.7, 3.1) | 3.6 (2.7, 4.7) |

ΔBMIp95 (kg/m^{2}) | −2.2 (−4.6, −0.2) | 1.1 (0.0, 3.3) | 5.5 (3.7, 9.6) |

%BMIp95 (% of 95th percentile) | 88.1 (75.1, 99.0) | 106.1 (100.2, 118.1) | 130.5 (120.3, 152.8) |

Weight-for-age z (SDs) | 0.08 (−2.14, 1.91) | 1.68 (−0.2, 3.31) | 3.1 (0.72, 4.75) |

Height-for-age z (SDs) | 0.04 (−2.27, 2.33) | 0.26 (−2.45, 2.65) | 0.73 (−3.83, 3.16) |

Values in parentheses represent the inner 95% of data

Percentages are column percents

Intercorrelations between age and the various BMI metrics

%BMIp95 Category | Age | BMI | BMIz | ΔBMIp95 | %BMIp95 | |
---|---|---|---|---|---|---|

< 100 (non-obese) | Age | 1 | −0.26 | 0.04 | 0.06 | 0.02 |

BMI | −0.26 | 1 | 0.94 | 0.93 | 0.95 | |

BMIz | 0.04 | 0.94 | 1 | 0.98 | 0.98 | |

ΔBMIp95 | 0.06 | 0.93 | 0.98 | 1 | 1 | |

%BMIp95 | 0.02 | 0.95 | 0.98 | 1 | 1 | |

100 –119 (moderate obesity) | Age | 1 | −0.33 | 0 | 0.05 | 0.08 |

BMI | −0.33 | 1 | 0.86 | 0.9 | 0.89 | |

BMIz | 0 | 0.86 | 1 | 0.96 | 0.96 | |

ΔBMIp95 | 0.05 | 0.90 | 0.96 | 1 | 1 | |

%BMIp95 | 0.08 | 0.89 | 0.96 | 1 | 1 | |

≥ 120 (severe obesity) | Age | 1 | −0.13 | −0.33 | 0.07 | 0.13 |

BMI | −0.13 | 1 | 0.55 | 0.97 | 0.95 | |

BMIz | −0.33 | 0.55 | 1 | 0.54 | 0.54 | |

ΔBMIp95 | 0.07 | 0.97 | 0.54 | 1 | 1 | |

%BMIp95 | 0.13 | 0.95 | 0.54 | 1 | 1 |