Adiposity in Adolescents: Change in Actual BMI Works Better Than Change in BMI z Score for Longitudinal Studies

Purpose

Longitudinal epidemiologic studies often relate adiposity changes to suspected causal factors. In growing adolescents, this becomes complicated. Many investigators use within-child change in body mass index (BMI) z scores (Δz) from sex- and age-specific BMI charts developed by the Centers for Disease Control and Prevention (CDC). These charts, derived from cross-sectional data, may not represent BMI growth patterns of real children. Furthermore, because cross-sectional BMIs are not Gaussian, these z scores are from month-specific transformed distributions, with possible unintended consequences when used longitudinally. Alternatively, we can directly analyze BMI change (ΔBMI). We compare these two widely used measures of change in adiposity.

Methods and Results

With real adolescent data, we show that annual ΔBMIs have nonlinear peaks that are inconsistent with the CDC curves. We also show that a specified Δz represents a broad range of adiposity changes for children measured at the same two ages. To see how this affects power, we performed simulation studies confirming that analyzing ΔBMIs in models with hypothesized factors is more powerful than analyzing Δzs.

Conclusions

In longitudinal studies of adolescent adiposity, investigators should be encouraged to analyze ΔBMI rather than Δz because analyses using BMI are more powerful and findings presented in BMI units are more interpretable.

Introduction

Heightened concerns regarding childhood overweight follow disturbing increases in prevalence during recent decades (1). Even among children and adolescents, overweight is related to a broad range of chronic illnesses and premature mortality 2, 3. Longitudinal epidemiologic investigations and randomized controlled trials are underway to determine modifiable factors that may prevent excess weight gain or promote weight loss in youth.

Longitudinal changes in body mass index (BMI; weight/height²; kg/m²), a measure of adiposity, during childhood and adolescence show nonlinear patterns as part of normal growth and development 4, 5, 6. This complicates the analysis of factors thought to affect individuals' adiposity over time, particularly in cohorts with broad age ranges.

A popular analytic approach takes advantage of US population BMI growth curves, which provide sex- and age-specific percentiles and z scores. The outcome for longitudinal analysis, Δz, is the difference between a child's z scores at two ages a year apart (for example).

The Centers for Disease Control and Prevention (CDC) developed these BMI curves (www.cdc.gov/growthcharts) to help clinicians determine which children are underweight or overweight for sex, age, and height (7). These charts were created by using pooled BMI data from cross-sectional National Health and Nutrition Examination Survey data (8). Those age(month)-specific BMI distributions were skewed, and the CDC needed to implement slightly different normalizing transformations at each month; z scores correspond to these transformed distributions (8). Furthermore, because these charts were estimated from cross-sectional data, they may not reflect typical age-related patterns of BMI change (ΔBMI) among children. This is illustrated in Figure 1, which shows differences between BMI median values (50th percentiles) a year apart on the CDC curves for comparison with year-specific median ΔBMI from a large longitudinal cohort (Growing Up Today Study [GUTS]) (9). These adolescents have nonlinear peaks in ΔBMI curves similar to peaks in adolescent height growth (10) that are not reflected in the CDC 50th percentile curves.

Although the CDC never specifically recommended that their z scores be used longitudinally, journal reviewers often insist that Δz be analyzed, and these commonly are found in the childhood adiposity literature. We propose that using these z scores longitudinally may have unintended consequences. For example, Table 1 lists hypothetical boys, all aged 11 years, who are measured again at age 12, and hypothetical 15-year-old girls followed up to age 16, who experienced a change of one z score. Note that an increase of one z score during a year can represent a broad range of increases in BMI (2.2 to 8.9 kg/m² for 15-year-old girls) and weight (13.3 to 53.6 pounds for 15-year-old girls, assuming no height growth). Similarly, a one-z-score decrease may correspond to a broad range of BMI decreases (−0.9 to −5.1 kg/m² for 11-year-old boys) and weight changes (16.7-pound loss to 1.2-pound gain, assuming height growth fixed).

A second illustration of the unintended consequences of using BMI z scores longitudinally appears in Figure 2, which shows three boys and three girls who follow a Δz = 0 curve from ages 10 to 17 years. The boy and girl who grow along the CDC z = +1 curve are heavier than their peers at age 10 and become even heavier over time relative to their normal-weight (z = 0 curve) peers. Similarly, initially lean children who grow along the z = −1 curve are becoming thinner over time relative to normal-weight children (z = 0 curve). However, all six children have “normal changes in adiposity over time” according to Δz. For reasons shown in Table 1 and Figure 1, Figure 2, we believe that using Δz to study longitudinal adiposity change is inefficient.

An alternative involves directly regressing BMI changes (ΔBMI) on factors of interest, including nonlinear age terms in the model to adjust for normal BMI growth patterns (9). We believe this analysis is more efficient than analyzing Δz, it provides estimates that are more interpretable, and it is simpler for programmers to implement (CDC z scores not required). Because longitudinal studies seldom obtain all measurements at the intended times (e.g., 1 year apart), in practice, each observed ΔBMI is divided by the observed time interval to compute “annualized ΔBMI” (9).

To test our hypothesis that Δz analyses are less efficient than ΔBMI, we performed simulation studies to compare the power of these approaches. Our assumptions mirrored a published analysis (9) of adolescents who provided heights and weights 1 year apart and data for factors that we hypothesized were associated with changing adiposity. We also present three analyses of real data that use both ΔBMI and Δz to illustrate our conclusions.