Optimal design for longitudinal studies to estimate pubertal height growth in individuals

The SITAR model expresses individual pubertal height growth in terms of mean size, peak height velocity (PHV) and age at PHV.

To use SITAR to identify the optimal time interval between measurements to summarise individual pubertal height growth.

Heights in 3172 boys aged 9-19 years from Christ's Hospital School measured on 128 679 occasions (a median of 42 heights per boy) were analysed using the SITAR (SuperImposition by Translation And Rotation) mixed effects growth curve model, which estimates a mean curve and three subject-specific random effects. Separate models were fitted to sub-sets of the data with measurement intervals of 2, 3, 4, 6, 12 and 24 months, and the different models were compared.

The models for intervals 2-12 months gave effectively identical results for the residual standard deviation (0.8 cm), mean spline curve (6 degrees of freedom) and random effects (correlations >0.9), showing there is no benefit in measuring height more often than annually. The model for 2-year intervals fitted slightly less well, but needed just four-to-five measurements per individual.

Height during puberty needs to be measured only annually and, with slightly lower precision, just four biennial measurements can be sufficient.