Bayesian shape invariant model for longitudinal growth curve data

Growth curve modeling should ideally be flexible, computationally feasible and allow for the inclusion of co-variates for better predictability and mechanistic explanations. The original shape invariant growth curve model, motivated by epidemiological research on the evolution of pubertal heights over time, fits the underlying shape function for height over age and estimates subject-specific deviations from this curve in terms of size, tempo, and velocity using maximum likelihood. This approach is effective in subsequent applications but the estimation method does not provide uncertainty estimates for unknown parameters, and predictive ability has been largely unexplored. A more recent Bayesian implementation undertaken for multivariate SIM modeling and this approach requires multiple longitudinal outcomes and has added a computational burden. Modern growth curve studies of height measurements from children with attention-deficit hyperactivity disorder (ADHD) have gained importance in epidemiological research due to potentially adverse effects from stimulant medications. Motivated by a particular longitudinal study on the heights of 197 pediatric ADHD patients who began stimulant treatment at varying ages, we describe a Bayesian extension of the original SIM model. We incorporate co-variate effects, assess mixing properties and examine different spline formulations to model the underlying growth shape. As demonstrated by the real data application and simulation study, the Bayesian SIM approach provides a natural, computationally feasible way to generate uncertainty estimates for treatment-outcome associations. We discussed the future extensions to the approach.