We introduce a class of dynamic regression models designed to predict the future of growth curves based on their historical dynamics. This class of models incorporates both baseline and time-dependent covariates, start with simple regression models and build up to dynamic function-on-function regressions. We compare the performance of the dynamic prediction models in a variety of signal-to-noise scenarios and provide practical solutions for model selection. We conclude that (a) prediction performance increases substantially when using the entire growth history relative to using only the last and first observation; (b) smoothing incorporated using functional regression approaches increases prediction performance; and (c) the interpretation of model parameters is substantially improved using functional regression approaches. Because many growth curve datasets exhibit missing and noisy data, we propose a bootstrap of subjects approach to account for the variability associated with the missing data imputation and smoothing. Methods are motivated by and applied to the CONTENT dataset, a study that collected monthly child growth data on 197 children from birth until month 15. R code describing the fitting approaches is provided in a supplementary file.
- Function-on-function regression
- functional data
- functional regression
- longitudinal data