Stützle W, Gasser T, Molinari L, Largo R H, Prader A, Huber P J
Ann Hum Biol. 1980 Nov-Dec;7(6):507-28. doi: 10.1080/03014468000004641.
A new approach to modelling human height growth is presented which is also suitable for other variables. In a mathematical algorithm, some guess about the functional form of this growth process is improved consistently using the data; the resulting shape-invariant model (SIM) allows an approximately bias-free fitting for longitudinal data from 1 to 20 years with six parameters assigned to each individual. The SIM approach and the use of velocities rather than distances proved to be suitable for biomathematical modelling in order to answer questions qualitative in nature. In comparison of an additive two-component SIM and one where the appearance of puberty inhibits further growth of the non-pubertal component ('switch-off model'), the latter proved to be superior in various aspects. Among the qualitative features found are notable: a pronounced midspurt, and a dip before the onset of puberty, as well as the asymmetry of the pubertal peak. A preliminary analysis of individual parameters confirmed some results found previously by other methods regarding sex differences and relations between parameters and with adult height.
本文提出了一种新的人类身高增长建模方法，该方法也适用于其他变量。在一种数学算法中，利用数据不断改进对这种增长过程函数形式的一些猜测；由此产生的形状不变模型（SIM）允许对1至20岁的纵向数据进行近似无偏差拟合，为每个个体分配六个参数。事实证明，SIM方法以及使用速度而非距离适用于生物数学建模，以便回答本质上定性的问题。在比较加法双组分SIM和青春期出现会抑制非青春期组分进一步生长的模型（“关闭模型”）时，后者在各个方面都表现更优。发现的定性特征包括：明显的中期快速增长、青春期开始前的下降，以及青春期峰值的不对称性。对个体参数的初步分析证实了之前其他方法在性别差异以及参数与成人身高之间关系方面的一些结果。
