A Numerical Method for Estimating the Variance of Age at Maximum Growth Rate in Growth Models.
A Numerical Method for Estimating the Variance of Age at Maximum Growth Rate in Growth Models.
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DOI：
10.1080/03610926.2011.588368
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发表时间：
2013-01-01
期刊：
影响因子：
--
通讯作者：
Ramakrishnan V
中科院分区：
文献类型：
--
作者：
Beyene S;Ramakrishnan V
关于成熟和身体成分的研究提到，峰值身高速度 (PHV) 年龄是预测成年结果的重要指标。 PHV 的年龄通常源自生长模型，例如拟合身材（身高）数据的三重逻辑。理论上，对于表现良好的生长函数，可以通过将生长函数的二阶导数设置为零并求解年龄来获得 PHV 时的年龄。这样的解决方案显然取决于增长函数的参数。因此，由于生长模型估计的不确定性而导致 PHV 年龄估计的不确定性，需要在将其用作预测变量的模型中加以考虑。对于一些常用的非线性增长函数（例如三重逻辑函数），不存在 PHV 年龄的显式表达式以及因此 PHV 年龄估计的方差。一旦获得了方差的估计，就可以通过测量误差模型或使用方差作为权重将其纳入后续建模中。实施了估计方差的数值方法。通过比较存在方差显式解的模型来证明该方法的准确性。通过应用于 Fels 研究中的生长数据来说明估计方差的方法，并随后将其用作对同一研究中的两个成年结果进行建模的权重。
Studies on maturation and body composition mention age at peak height velocity (PHV) as an important measure that could predict adulthood outcome. The age at PHV is often derived from growth models such as the triple logistic fitted to the stature (height) data. Theoretically, for a well behaved growth function, age at PHV could be obtained by setting the second derivative of the growth function to zero and solving for age. Such a solution obviously depends on the parameters of the growth function. Therefore, the uncertainty in the estimation of age at PHV resulting from the uncertainty in the estimation of the growth model, need to be accounted for in the models in which it is used as a predictor. Explicit expressions for the age at PHV and consequently the variance of the estimate of the age at PHV do not exist for some of the commonly used non-linear growth functions, such as the triple logistic function. Once an estimate of this variance is obtained, it could be incorporated in subsequent modeling either through measurement error models or by using the variances as weights. A numerical method for estimating the variance is implemented. The accuracy of this method is demonstrated through comparisons in models where explicit solution for the variance exists. The method of estimating the variance is illustrated by applying to growth data from the Fels study and subsequently used as weights in modeling two adulthood outcomes from the same study.
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影响因子：
2.9
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