Buschang P H, Tanguay R, LaPalme L, Demirjian A
Department of Orthodontics, Baylor College of Dentistry, Dallas, TX 75246.
Eur J Orthod. 1990 Aug;12(3):290-6. doi: 10.1093/ejo/12.3.290.
The aim of this study was to compare growth predictions obtained by adding mean annual velocities with predictions derived from a polynomial model of the population's growth curve. Given the child's previous measures at 11, 12 and/or 13 years of age, the cephalometric distance sella-gnathion at 15 years was estimated. Based on a sample of 223 boys and girls, the root mean square error decreased from 0.28 cm (males) and 0.18 cm (females) at 11 years, to 0.19 cm (males) and 0.12 cm (females) at 13 years. Root mean square errors were similar between methods, which was due to high correlations between measures across ages. Significantly, predictions based on mean increments were biased. They often over or underestimate growth for children who are larger and smaller than average. The observed bias was due to expected changes of variance associated with growth, which unconditional methods of prediction cannot control for. Predictions derived from growth models are conditional upon the child's size and are, therefore, unbiased.
本研究的目的是比较通过添加年均生长速度得到的生长预测值与从人群生长曲线的多项式模型得出的预测值。根据儿童在11岁、12岁和/或13岁时的既往测量值，估算其15岁时蝶鞍-下颌平面的头影测量距离。基于223名男孩和女孩的样本，均方根误差从11岁时的0.28厘米（男性）和0.18厘米（女性）降至13岁时的0.19厘米（男性）和0.12厘米（女性）。两种方法的均方根误差相似，这是由于不同年龄测量值之间的高度相关性。值得注意的是，基于平均增量的预测存在偏差。对于高于或低于平均水平的儿童，它们常常高估或低估生长情况。观察到的偏差是由于与生长相关的预期方差变化所致，而无条件预测方法无法控制这种变化。从生长模型得出的预测取决于儿童的大小，因此是无偏差的。
