Abstract
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 because it is associated with health outcomes in later life.Methods:We estimated BMI trajectories for 6545 children from the Avon Longitudinal Study of Parents and Children. 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, prechange slope, postchange 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 prechange slope and change point was 0.57, suggesting that faster rates of decline in BMI prior to rebound were associated with rebound occurring at an earlier age. Simulations showed that estimates from the model were less biased than those from models, assuming a common change point for all individuals or a nonlinear trajectory based on fractional polynomials.Conclusions:Our model flexibly estimated the individual-specific timing of BMI rebound, while 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.
Highlights
Body mass index (BMI) rebound refers to the beginning of the second rise in body mass index (BMI) during childhood
The timing of BMI rebound is a biologic characteristic known to vary between individuals
Through the use of a random change point, our model provided the flexibility required to estimate the individual-specific timing of BMI rebound for each child, while providing an estimate of the mean timing of BMI rebound and the variability around that mean
Summary
Body mass index (BMI) rebound refers to the beginning of the second rise in BMI during childhood. A number of authors have, extended the model to treat the change point as a random effect parameter, thereby, allowing individuals to have their own change point.[7,8,9,10,11,12] The use of a random change point has the advantage of increasing model flexibility and is, likely to improve model fit without major alteration of parameter interpretation Such models provide useful insights when the person-specific timing of the change point is of intrinsic interest, for example, estimating the onset of cognitive decline in the elderly[7,12,13] and disease progression in HIV patients.[9,10]. We compare our random change point model to an alternative model based on fractional polynomials, as well as simpler change point models that do not allow for between-individual variability in the timing of BMI rebound
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