Insight into human pubertal growth by applying the QEPS growth model

BACKGROUND: Computerized mathematical models describing absolute and relative individual growth during puberty in both cm and standard deviation (SD)-scores are lacking. The present study aimed to fill this gap, by applying the QEPS-model that delineates mathematically the specific pubertal functions of the total growth curve. METHODS: Study population used was the individual growth curves of the longitudinally followed cohort GrowUp1974 Gothenburg (n = 2280). The QEPS-model describes total height as (T)otal-function: a combination of four shape-invariant growth functions, modified by time-scale and height-scale parameters: a (Q)uadratic-function for the continuous growth from fetal life to adulthood; a negative (E)xponential-function adds the rapid, declining fetal/infancy growth; a (P)ubertal-function the specific pubertal growth spurt; a (S)top-function the declining growth until adult height. A constructed variable, MathSelect, was developed for assessing data-quality. CIs and SD-scores for growth estimates were calculated for each individual. QEPS-model estimates used for pubertal growth; from the T-function: onset of puberty as minimal height velocity (AgeT (ONSET)); mid-puberty as peak height velocity (AgeT (PHV)); end of puberty as height velocity decreased to 1 cm/year (AgeT (END)); duration of different intervals and gain (AgeT (ONSET–END) and Tpubgain); from the P-function: onset of puberty, estimated as growth at 1% or 5% (AgeP1 (,) AgeP5); mid-puberty as 50% (AgeP50) and PHV (AgeP (PHV)); end of pubertal growth at 95 or 99% (AgeP95, AgeP99); duration of different intervals and pubertal gain (Ppubgain; P (max)); from the QES-function: gain (QESpubgain) (.) RESULTS: Application of these mathematical estimates for onset, middle and end of puberty of P-function, QES-function, and T-function during puberty showed: the later the onset of puberty, the greater the adult height; pubertal gain due to the P-function growth was independent of age at onset of puberty; boys had higher total gain during puberty due to P-function growth than to QES-function growth; for girls it was reversed. CONCLUSIONS: QEPS is the first growth model to provide individualized estimates of both the specific pubertal growth function and the total growth during puberty, with accompanying SD-scores and Cis for each individual. These QEPS-derived estimates enable more in-depth analysis of different aspects of pubertal growth than previously possible. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/s12887-017-0857-1) contains supplementary material, which is available to authorized users.