Estimating peak height velocity in individuals: a comparison of statistical methods

Abstract

Background: Estimates pertaining to the timing of the adolescent growth spurt (e.g. peak height velocity; PHV), including age at peak height velocity (aPHV), play a critical role in the diagnosis, treatment, and management of skeletal growth and/or developmental disorders. Yet, distinct statistical methodologies often result in large estimate discrepancies.

Aim: The aim of the present study was to assess the advantages and disadvantages of three modelling methodologies for height as well as to determine how estimates derived from these methodologies may differ, particularly those that may be useful in paediatric clinical practice.

Subjects and methods: Height data from 686 individuals of the Fels Longitudinal Study were modelled using 5th order polynomials, natural cubic splines, and SuperImposition by Translation and Rotation (SITAR) to determine aPHV and PHV for all individuals together (i.e. population average) by sex and separately for each individual. Estimates within and between methodologies were calculated and compared.

Results: In general, mean aPHV was earlier, and PHV was greater for individuals when compared to estimates from population average models. Significant differences between mean aPHV and PHV for individuals were observed in all three methodologies, with SITAR exhibiting the latest aPHV and largest PHV estimates.

Conclusion: Each statistical methodology has a number of advantages when used for specific purposes. For modelling growth in individuals, as one would in paediatric clinical practice, we recommend the use of the 5th order polynomial methodology due to its parameter flexibility.

Keywords: Growth spurt; SITAR; growth trajectory; natural cubic spline; polynomial.

Figure 1.

Boys: individual (thin line) and population average (thick line) fitted models for growth in height (A) and rate of growth in height (B) for the 5th order polynomial, natural cubic spline, and SITAR (left to right) methodologies. The visualisation of SITAR growth trajectories is based on back-transformed chronological age, as per Cole (2017), despite modelling being performed on the logarithm of chronological age. This image is the property of the authors.

Figure 2.

Girls: individual (thin line) and population average (thick line) fitted models for growth in height (A) and rate of growth in height (B) for the 5th order polynomial, natural cubic spline, and SITAR (left to right) methodologies. The visualisation of SITAR growth trajectories is based on back-transformed chronological age, as per Cole (2017), despite modelling being performed on the logarithm of chronological age. This image is the property of the authors.

Figure 3.

aPHV: all pairwise estimate comparisons based on methodology for boys (A) and girls (B), where the trend line indicates a 1:1 relationship between methodology estimates. This image is the property of the authors.

Figure 4.

PHV: all pairwise estimate comparisons based on methodology for boys (A) and girls (B), where the trend line indicates a 1:1 relationship between methodology estimates. This image is the property of the authors.

Figure 5.

Comparison of growth in height (A) and rate of growth in height (B) trajectories for a single representative boy (left panel) and girl (right panel) for each of the following methodologies: 5th order polynomial (Poly), natural cubic splines (NCS), and SITAR where the black dots represent individual height observations. This image is the property of the authors.