| Summary: | Abstract 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.
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