Evaluation of robust Bayesian mixed-effects models of longitudinal childhood BMI

This paper introduces Bayesian mixed-effects models (BMM) for characterizing childhood BMI trajectories from birth to 13 years of age and proposes a Bayesian marginal posterior sampling approach to decompose BMI variance into residuals, fixed, and random effects contributions. This is one of the first studies to rigorously evaluate Fractional Polynomials (FP), Reed2 (R2), and Breakpoint (BP) models using data from three longitudinal cohorts, assessing performance based on bias, heteroskedasticity, and Bayesian goodness-of-fit.Results indicate that model choice matters, as FP and Reed2 models generally outperform BP models in capturing the complex non-linearity of BMI trajectories, with residual errors accounting for less than 10% of BMI variance. Among five likelihoods considered, the Laplace distribution provided the most robust fit. The residual correlation structures were complex and non-stationary. A normal likelihood with a stationary correlation function improved fit, but less so than an independent Laplace likelihood. Most BMI variance was explained by random effects, underscoring the importance of personalized approaches in childhood obesity.This study rigorously evaluates competing BMI trajectory models and introduces a robust BMM library that improves modeling of abnormal trajectories. These results may inform early identification of children at risk, targeted intervention selection, and intervention efficacy monitoring.