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

Investigating early life growth dynamics is crucial for a more comprehensive understanding of the developmental origins of obesity. Spline methods based on basis splines (B-splines) provide excellent flexibility for modelling complex nonlinear growth patterns, but they are prone to overfitting. To ensure good fit and avoid overfitting, B-splines can be extended by adding a penalty term to control their flexibility, resulting in what are commonly known as penalized B-splines (P-splines). Despite their strengths, P-splines are not yet widely used in epidemiology, partly due to a lack of practical guidance. This paper provides an illustrative guide to using P-spline linear mixed effects models to examine early life growth trajectories and estimate key growth features in longitudinal studies. After detailing P-spline theory and model fitting, we apply the method to repeated measurements of height, weight, and body mass index (BMI) up to age 10 years in a Southeast Asian birth cohort. We estimated infant growth velocity, and magnitude and timing of infant peak BMI and childhood rebound BMI, and explored sex differences, intercorrelations, and associations with prenatal factors. In our cohort, infant peak growth velocity was higher in boys than girls, ages of peak and rebound BMI had a negligible correlation, and greater birth length was associated with lower infant height velocity and higher weight velocity. We discuss practical considerations, alternative modelling approaches and provide recommendations for research. P-splines simplify the knot selection process, making them a valuable approach for growth modelling. R library, code and datasets are provided to accelerate uptake.