Bayesian Piecewise Linear Mixed Models With a Random Change Point: An Application to BMI Rebound in Childhood

Sam Brilleman, Laura Howe, Rory Wolfe, Kate Tilling

Research output: Contribution to journalArticle (Academic Journal)peer-review

9 Citations (Scopus)
231 Downloads (Pure)


Background Body mass index (BMI) rebound refers to the beginning of the second rise in BMI during childhood. Accurate estimation of an individual’s timing of BMI rebound is important since it is associated with health outcomes in later life.
Methods We estimated BMI trajectories for 6,545 children from the Avon Longitudinal Study of Parents and Children (ALSPAC). We used a novel Bayesian two-phase piecewise linear mixed model where the ‘change point’ was an individual-level random effect corresponding to the individual-specific timing of BMI rebound. The model’s individual-level random effects (intercept, pre-change slope, post-change slope, change point) were multivariate normally distributed with an unstructured variance-covariance matrix, thereby allowing for correlation between all random effects.
Results Average age at BMI rebound (mean change point) was 6.5 (95% credible interval: 6.4 to 6.6) years. The standard deviation of the individual-specific timing of BMI rebound (random effects) was 2.0 years for females and 1.6 years for males. Correlation between the pre-change slope and change point was 0.57, suggesting faster rates of decline in BMI prior to rebound were associated with rebound occurring at an earlier age. Simulations showed estimates from the
model were less biased than those from models assuming a common change point for all individuals or a non-linear trajectory based on fractional polynomials.
Conclusions Our model flexibly estimated the individual-specific timing of BMI rebound, whilst retaining parameters that are meaningful and easy to interpret. It is applicable in any situation where one wishes to estimate a change-point process which varies between individuals.
Original languageEnglish
Pages (from-to)827-833
Number of pages7
Issue number6
Early online date21 Sep 2017
Publication statusPublished - Nov 2017

Structured keywords

  • Jean Golding


  • splines
  • piecewise linear
  • change point
  • Bayesian
  • Stan


Dive into the research topics of 'Bayesian Piecewise Linear Mixed Models With a Random Change Point: An Application to BMI Rebound in Childhood'. Together they form a unique fingerprint.

Cite this