Holmgren Anton, Niklasson Aimon, Gelander Lars, Aronson A Stefan, Nierop Andreas F M, Albertsson-Wikland Kerstin
Göteborg Pediatric Growth Research Center, Department of Pediatrics, Institute of Clinical Sciences, Sahlgrenska Academy at University of Gothenburg, SE-41685, Gothenburg, Sweden.
Hallands Hospital Halmstad, Halmstad, Sweden.
BMC Pediatr. 2017 Apr 19;17(1):107. doi: 10.1186/s12887-017-0857-1.
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.
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 ); mid-puberty as peak height velocity (AgeT ); end of puberty as height velocity decreased to 1 cm/year (AgeT ); duration of different intervals and gain (AgeT 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 ); end of pubertal growth at 95 or 99% (AgeP95, AgeP99); duration of different intervals and pubertal gain (Ppubgain; P ); 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.
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.
缺乏描述青春期绝对和相对个体生长（以厘米和标准差（SD）分数表示）的计算机化数学模型。本研究旨在通过应用QEPS模型填补这一空白，该模型从数学上描绘了总生长曲线的特定青春期功能。
所使用的研究人群是纵向跟踪的哥德堡GrowUp1974队列的个体生长曲线（n = 2280）。QEPS模型将总身高描述为（T）总函数：四个形状不变的生长函数的组合，由时间尺度和身高尺度参数修改：一个（Q）二次函数用于从胎儿期到成年期的持续生长；一个负（E）指数函数增加了快速下降的胎儿/婴儿期生长；一个（P）青春期函数用于特定的青春期生长突增；一个（S）停止函数用于生长下降直至成年身高。开发了一个构建变量MathSelect来评估数据质量。为每个个体计算生长估计值的置信区间（CIs）和标准差分数。QEPS模型估计值用于青春期生长；从T函数：青春期开始为最小身高速度（AgeT ）；青春期中期为身高速度峰值（AgeT ）；青春期结束为身高速度降至1厘米/年（AgeT ）；不同时间段的持续时间和增长（AgeT 和Tpubgain）；从P函数：青春期开始，估计为1%或5%时的生长（AgeP1 ，AgeP5）；青春期中期为50%（AgeP50）和身高速度峰值（AgeP ）；青春期生长结束时为95%或99%（AgeP95，AgeP99）；不同时间段的持续时间和青春期增长（Ppubgain；P ）；从QES函数：增长（QESpubgain） 结果：在青春期应用这些针对P函数、QES函数和T函数的青春期开始、中期和结束的数学估计值显示：青春期开始越晚，成年身高越高；由于P函数生长导致的青春期增长与青春期开始时的年龄无关；男孩由于P函数生长在青春期的总增长高于QES函数生长；女孩则相反。
QEPS是第一个能够提供特定青春期生长功能和青春期总生长的个体化估计值的生长模型，同时为每个个体提供伴随的标准差分数和置信区间。这些源自QEPS的估计值能够比以前更深入地分析青春期生长的不同方面。
