Using linear and natural cubic splines, SITAR, and latent trajectory models to characterise nonlinear longitudinal growth trajectories in cohort studies

Abstract

ABSTRACTLongitudinal data analysis can improve our understanding of the influences on health trajectories across the life-course. There are a variety of statistical models which can be used, and their fitting and interpretation can be complex, particularly where there is a nonlinear trajectory. This paper provides a guide to describing nonlinear growth trajectories for repeatedly measured continuous outcomes using linear mixed-effects (LME) models with linear splines and natural cubic splines, nonlinear mixed effects Super Imposition by Translation and Rotation (SITAR) models, and latent trajectory models. The underlying model for each of the four approaches, the similarities and differences between models, and their advantages and disadvantages are described. Their applications and correct interpretation are illustrated by analysing repeated bone mass measures across three cohort studies with 8,500 individuals and 37,000 measurements covering ages 5-40 years. Linear and natural cubic spline LME models and SITAR provided similar descriptions of the mean bone growth trajectory and growth velocity, and the sex differences in growth patterns. Latent trajectory models identified up to four subgroups of individuals with distinct trajectories during adolescence and similar trajectories in childhood and adulthood. Recommendations for choosing a modelling approach are provided along with a discussion and signposting on further modelling extensions for analysing trajectory exposures and outcomes, and multiple cohorts. In summary, we present a resource for characterising nonlinear longitudinal growth trajectories, that could be adapted for other complex traits. Scripts and synthetic datasets are provided so readers can replicate trajectory modelling and visualisation using the open-source R software.