Modelling height in adolescence: a comparison of methods for estimating the age at peak height velocity

Abstract

Background: Controlling for maturational status and timing is crucial in lifecourse epidemiology. One popular non-invasive measure of maturity is the age at peak height velocity (PHV). There are several ways to estimate age at PHV, but it is unclear which of these to use in practice.

Aim: To find the optimal approach for estimating age at PHV.

Subjects and methods: Methods included the Preece & Baines non-linear growth model, multi-level models with fractional polynomials, SuperImposition by Translation And Rotation (SITAR) and functional data analysis. These were compared through a simulation study and using data from a large cohort of adolescent boys from the Christ's Hospital School.

Results: The SITAR model gave close to unbiased estimates of age at PHV, but convergence issues arose when measurement error was large. Preece & Baines achieved close to unbiased estimates, but shares similarity with the data generation model for our simulation study and was also computationally inefficient, taking 24 hours to fit the data from Christ's Hospital School. Functional data analysis consistently converged, but had higher mean bias than SITAR. Almost all methods demonstrated strong correlations (r > 0.9) between true and estimated age at PHV.

Conclusions: Both SITAR or the PBGM are useful models for adolescent growth and provide unbiased estimates of age at peak height velocity. Care should be taken as substantial bias and variance can occur with large measurement error.

Keywords: Age at peak height velocity; derivative estimation; lifecourse epidemiology; physical development; pubertal timing.

Figure 1.

True population mean height, velocity and acceleration.

Figure 2.

Mean bias with interquartile range and 95% range of bias for the Preece & Baines, multi-level models-fractional polynomial (MLM-FP), superimposition by translation and rotation (SITAR) and principal components analysis through conditional expectation (PACE) methods used to estimate age at PHV across different experimental scenarios.