Nonlinear association between body mass index and physical fitness in primary school children: a single-school...

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.

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).

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.

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.