Using linear and natural cubic splines, SITAR, and latent trajectory models to characterise nonlinear longitudinal growth trajectories in cohort studies
Bibliographic record
Abstract
ABSTRACT Longitudinal 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.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.036 | 0.123 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.005 |
| Bibliometrics | 0.005 | 0.007 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.004 | 0.004 |
| Open science | 0.003 | 0.004 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.018 | 0.004 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".