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Background <p>Body mass index (BMI) is associated with physical fitness in children, but the functional form of this relationship is debated. Using routinely collected fitness-monitoring data from a single primary school, this study examined whether BMI is nonlinearly associated with physical fitness in primary school children, treating the analysis as a methodological, single-school demonstration rather than a population-representative survey.</p> Methods <p>We analysed records from 1,572 students (808 boys, 764 girls; Grades 1–6) nested within 37 classes in one school in Tianfu New Area, Sichuan, China. BMI was calculated from measured height and weight. Four fitness indicators available for the whole sample—vital capacity, 50-m sprint, sit-and-reach, and 1-min rope skipping—were analysed as the primary outcomes; a composite index (mean of sex- and grade-standardised z-scores, with the 50-m sprint reverse-coded so that higher scores denote better fitness) was retained as a secondary descriptive summary. Quadratic regression and generalized additive models (GAMs; penalised cubic B-splines) adjusted for sex and grade were used to model BMI. Primary overall and sex-stratified models used cluster-robust standard errors at the class level; grade-stratified exploratory models, each based on only a few classes, were assessed with model-based smooth tests. Nonlinearity was quantified with the effective degrees of freedom (EDF) of the BMI smooth and a Wald test, and exploratory subgroup analyses were corrected for multiple comparisons (Benjamini–Hochberg false discovery rate, FDR).</p> Results <p>The class-level intraclass correlation was non-negligible for BMI (0.124) and the 50-m sprint (0.085), confirming the need to account for clustering. After cluster-robust adjustment, BMI showed a statistically supported nonlinear association with the 50-m sprint (EDF = 4.4, <i>P</i> &lt; 0.001), 1-min rope skipping (EDF = 5.1, <i>P</i> &lt; 0.001), and the composite index (EDF = 5.7, <i>P</i> &lt; 0.001), but not with vital capacity (EDF = 1.0, <i>P</i> = 0.44). For the 50-m sprint the best predicted performance was well localised at a BMI of about 16.2&#xa0;kg/m²; for 1-min rope skipping the optimum was less precisely located, and for the composite index the cluster bootstrap did not identify a stable interior optimum (it spread the maximum across ≈ 15.7–21.2&#xa0;kg/m², with a median of ≈ 19.7&#xa0;kg/m² well above the full-sample point estimate). Predicted performance declined at both lower and higher BMI. The quadratic turning point (~ 18.5&#xa0;kg/m²) was higher than the GAM peak and moved toward the GAM estimate when sparse BMI tails were trimmed, indicating sensitivity of the parabola to extreme values. In exploratory, FDR-corrected subgroup analyses, nonlinearity remained statistically supported in girls and in Grades 1 and 3 but not in boys or other grades; these subgroup findings are hypothesis-generating only.</p> Conclusions <p>In this single-school sample, the BMI–fitness association was nonlinear for speed- and coordination-related tasks; for the 50-m sprint the best predicted performance was well localised at an intermediate BMI (about 16.2&#xa0;kg/m²), whereas for the composite index no stable single optimum could be identified. Because the data come from one school and lack body-composition and physical-activity measures, the estimated optima are sample-specific descriptive features and should not be read as intervention targets. The study illustrates how routine school fitness data and GAMs can describe BMI–fitness patterns beyond categorical comparisons, and motivates multi-school, longitudinal confirmation.</p>

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Nonlinear association between body mass index and physical fitness in primary school children: a single-school cross-sectional study using generalized additive models

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  • 发表日期：

    2026年6月24日

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  • Junhui Zhu,
  • Mingling Zhao,
  • Meiling Zheng,
  • Ling Wang,
  • Qiuyue Li

摘要

Background

Body mass index (BMI) is associated with physical fitness in children, but the functional form of this relationship is debated. Using routinely collected fitness-monitoring data from a single primary school, this study examined whether BMI is nonlinearly associated with physical fitness in primary school children, treating the analysis as a methodological, single-school demonstration rather than a population-representative survey.

Methods

We analysed records from 1,572 students (808 boys, 764 girls; Grades 1–6) nested within 37 classes in one school in Tianfu New Area, Sichuan, China. BMI was calculated from measured height and weight. Four fitness indicators available for the whole sample—vital capacity, 50-m sprint, sit-and-reach, and 1-min rope skipping—were analysed as the primary outcomes; a composite index (mean of sex- and grade-standardised z-scores, with the 50-m sprint reverse-coded so that higher scores denote better fitness) was retained as a secondary descriptive summary. Quadratic regression and generalized additive models (GAMs; penalised cubic B-splines) adjusted for sex and grade were used to model BMI. Primary overall and sex-stratified models used cluster-robust standard errors at the class level; grade-stratified exploratory models, each based on only a few classes, were assessed with model-based smooth tests. Nonlinearity was quantified with the effective degrees of freedom (EDF) of the BMI smooth and a Wald test, and exploratory subgroup analyses were corrected for multiple comparisons (Benjamini–Hochberg false discovery rate, FDR).

Results

The class-level intraclass correlation was non-negligible for BMI (0.124) and the 50-m sprint (0.085), confirming the need to account for clustering. After cluster-robust adjustment, BMI showed a statistically supported nonlinear association with the 50-m sprint (EDF = 4.4, P < 0.001), 1-min rope skipping (EDF = 5.1, P < 0.001), and the composite index (EDF = 5.7, P < 0.001), but not with vital capacity (EDF = 1.0, P = 0.44). For the 50-m sprint the best predicted performance was well localised at a BMI of about 16.2 kg/m²; for 1-min rope skipping the optimum was less precisely located, and for the composite index the cluster bootstrap did not identify a stable interior optimum (it spread the maximum across ≈ 15.7–21.2 kg/m², with a median of ≈ 19.7 kg/m² well above the full-sample point estimate). Predicted performance declined at both lower and higher BMI. The quadratic turning point (~ 18.5 kg/m²) was higher than the GAM peak and moved toward the GAM estimate when sparse BMI tails were trimmed, indicating sensitivity of the parabola to extreme values. In exploratory, FDR-corrected subgroup analyses, nonlinearity remained statistically supported in girls and in Grades 1 and 3 but not in boys or other grades; these subgroup findings are hypothesis-generating only.

Conclusions

In this single-school sample, the BMI–fitness association was nonlinear for speed- and coordination-related tasks; for the 50-m sprint the best predicted performance was well localised at an intermediate BMI (about 16.2 kg/m²), whereas for the composite index no stable single optimum could be identified. Because the data come from one school and lack body-composition and physical-activity measures, the estimated optima are sample-specific descriptive features and should not be read as intervention targets. The study illustrates how routine school fitness data and GAMs can describe BMI–fitness patterns beyond categorical comparisons, and motivates multi-school, longitudinal confirmation.