Estimating peak height velocity in individuals: a response to Cole (2020)

Abstract

Choosing a statistical methodology for modelling human growth is an important decision for researchers and clinicians alike. In Boeyer et al. (2020), we presented three common approaches for modelling childhood and adolescent growth (i.e. Natural Cubic Splines, SuperImposition by Translation and Rotation (SITAR), and Fifth Order Polynomials) with the primary aim to elucidate the advantages and disadvantages of each methodology. In a recent Letter to the Editor, Cole (2020) challenged two specific aspects of this work, including: (1) interpretations related to the derived "population average" and individual-level random effects in the SITAR methodology, and (2) our conclusions regarding the use of the polynomial methodology in paediatric clinical practice.Cole (2020) objects to our interpretation of the "population average" derived from the SITAR methodology, which we defined in our publication as the single curve derived from the data of all individuals combined. This definition is consistent with the documentation for the sitar () function, which states that "sitar is a methodology that summarises a set of growth curves with a mean growth curve as a regression spline." Given this language, the regression curve applied is approximating the mean or, using our terminology, "population" average trajectory.Cole (2020) also claims that Table 1 in Boeyer et al. ( 2020) "confirms that the SITAR mean curve is unbiased," because the values for PHV and aPHV derived from the "mean" or population average curve are the same as the mean estimate for all individuals included in our analyses. It is true that the average values we report for PHV and aPHV at both the population and individual level are not statistically different, but this specific comparison does not indicate the lack of "bias" within this methodology; instead, it highlights its shapeinvariant structure. To properly assess statistical bias, a cross-validation analysis is needed. In Boeyer et al. (2020), we performed a leave-one-out cross-validation analysis for each of