Capturing infant and child growth dynamics with P-splines mixed effects models

BACKGROUND: Investigating early life growth dynamics is important for understanding the developmental origins of obesity. Basis splines (B-splines) provide excellent flexibility for modelling complex growth patterns, but they are prone to overfitting. Penalised B-splines (P-splines) extend B-splines by using a penalty to control their flexibility and avoid overfitting. Despite their advantages, P-splines remain underused in epidemiology, partly due to lack of guidance and accessible software. Our aim was to provide a guide on applying P-spline linear mixed effects models to analyse early life growth trajectories and extract key growth features. METHODS: We outline the theoretical foundation and fitting procedures for P-splines and illustrate their use on repeated height, weight, and body mass index (BMI) measures up to age 10 years from a Southeast Asian birth cohort (n = 1014). P-splines linear mixed effects models were fitted by reformulating P-splines as mixed models with sparse matrices for efficient estimation. From the fitted trajectories, we estimated infant peak growth velocity, magnitude and timing of infant peak BMI and childhood rebound BMI, and examined their sex differences, intercorrelations, and associations with prenatal factors. RESULTS: ), age at peak BMI (5.8 vs. 6.4 months), and age at rebound BMI (5.4 years) were comparable between sexes. Ages of peak and rebound BMI had a negligible correlation, higher maternal height was associated with higher peak growth velocity, higher maternal early-pregnancy weight was associated with higher and earlier rebound BMI, and higher birth weight was associated with higher and earlier peak BMI. CONCLUSIONS: P-splines simplify knot selection, making them a valuable approach for growth modelling. Software, code and datasets are provided to promote uptake of this method.