Abstract
Background
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. Our aim was to provide an accessible guide along with applied examples to using four sophisticated modelling procedures for describing nonlinear growth trajectories.
Methods
This expository paper provides an illustrative guide to summarising nonlinear growth trajectories for repeatedly measured continuous outcomes using (i) linear spline and (ii) natural cubic spline linear mixed-effects (LME) models, (iii) Super Imposition by Translation and Rotation (SITAR) nonlinear mixed effects models, and (iv) latent trajectory models. The underlying model for each approach, their similarities and differences, and their advantages and disadvantages are described. Their application and correct interpretation of their results is illustrated by analysing repeated bone mass measures to characterise bone growth patterns and their sex differences in three cohort studies from the UK, USA, and Canada comprising 8500 individuals and 37,000 measurements from ages 5–40 years. 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.
Results
Linear and natural cubic spline LME models and SITAR provided similar summary of the mean bone growth trajectory and growth velocity, and the sex differences in growth patterns. Growth velocity (in grams/year) peaked during adolescence, and peaked earlier in females than males e.g., mean age at peak bone mineral content accrual from multicohort SITAR models was 12.2 years in females and 13.9 years in males. Latent trajectory models (with trajectory shapes estimated using a natural cubic spline) identified up to four subgroups of individuals with distinct trajectories throughout adolescence.
Conclusions
LME models with linear and natural cubic splines, SITAR, and latent trajectory models are useful for describing nonlinear growth trajectories, and these methods can be adapted for other complex traits. Choice of method depends on the research aims, complexity of the trajectory, and available data. Scripts and synthetic datasets are provided for readers to replicate trajectory modelling and visualisation using the R statistical computing software.
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. Our aim was to provide an accessible guide along with applied examples to using four sophisticated modelling procedures for describing nonlinear growth trajectories.
Methods
This expository paper provides an illustrative guide to summarising nonlinear growth trajectories for repeatedly measured continuous outcomes using (i) linear spline and (ii) natural cubic spline linear mixed-effects (LME) models, (iii) Super Imposition by Translation and Rotation (SITAR) nonlinear mixed effects models, and (iv) latent trajectory models. The underlying model for each approach, their similarities and differences, and their advantages and disadvantages are described. Their application and correct interpretation of their results is illustrated by analysing repeated bone mass measures to characterise bone growth patterns and their sex differences in three cohort studies from the UK, USA, and Canada comprising 8500 individuals and 37,000 measurements from ages 5–40 years. 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.
Results
Linear and natural cubic spline LME models and SITAR provided similar summary of the mean bone growth trajectory and growth velocity, and the sex differences in growth patterns. Growth velocity (in grams/year) peaked during adolescence, and peaked earlier in females than males e.g., mean age at peak bone mineral content accrual from multicohort SITAR models was 12.2 years in females and 13.9 years in males. Latent trajectory models (with trajectory shapes estimated using a natural cubic spline) identified up to four subgroups of individuals with distinct trajectories throughout adolescence.
Conclusions
LME models with linear and natural cubic splines, SITAR, and latent trajectory models are useful for describing nonlinear growth trajectories, and these methods can be adapted for other complex traits. Choice of method depends on the research aims, complexity of the trajectory, and available data. Scripts and synthetic datasets are provided for readers to replicate trajectory modelling and visualisation using the R statistical computing software.
| Original language | English |
|---|---|
| Article number | 68 |
| Number of pages | 20 |
| Journal | BMC Medical Research Methodology |
| Volume | 22 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 15 Mar 2022 |
Bibliographical note
Funding Information:This project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreements No. 874739 (LongITools) and No. 733206 (LifeCycle). AE, KMT, RAH and DAL work in a unit that is supported by the University of Bristol and UK Medical Research Council (MC_UU_00011/3 & MC_UU_00011/3). RAH is supported by a Sir Henry Dale Fellowship jointly funded by the Wellcome Trust and the Royal Society (Grant Number 215408/Z/19/Z). ASFK is supported by an Economic Social Research Council Postdoctoral Fellowship (Grant ref.: ES/V011650/1). The UK Medical Research Council and Wellcome (Grant Ref: 102215/2/13/2) and the University of Bristol provide core support for ALSPAC. A comprehensive list of grant funding is available on the ALSPAC website ( http://www.bristol.ac.uk/alspac/external/documents/grant-acknowledgements.pdf ). PBMAS was supported in part by funding from the Canadian Institutes of Health Research, the Saskatchewan Health Research Foundation (SHRF), The Dairy Farmers of Canada and the University of Saskatchewan. This research reflects only the authors’ view, and the European Commission is not responsible for any use that may be made of the information it contains. The funders had no role in the design or conduct of the study, nor management, analysis, and interpretation of the data, or the decision to submit the manuscript for publication.
Funding Information:
We thank the study participants from each cohort who took part in this study and the scientific and data collection teams from the ALSPAC, BMDCS and PBMAS cohorts. We are extremely grateful to all the families who took part in the ALSPAC study, the midwives for their help in recruiting them, and the whole ALSPAC team, which includes interviewers, computer and laboratory technicians, clerical workers, research scientists, volunteers, managers, receptionists and nurses. We acknowledge the BMDCS Principal Investigators: Vicente Gilsanz, MD, PhD, Heidi Kalkwarf, PhD, Joan Lappe, PhD, Sharon Oberfield, MD, John Shepherd, PhD, and the National Institute of Child Health and Human Development (NICHD) Data and Specimen Hub (DASH) for providing the BMDCS data that was used for this research.
Publisher Copyright:
© 2022, The Author(s).
Keywords
- ALSPAC
- Bone mineral content
- BMDCS
- Growth models
- Life-course
- Mixed-effects
- PBMAS
- Tutorial