Wellek Stefan
Department of Biostatistics, CIMH Mannheim, Mannheim Medical School of the University of Heidelberg, Mannheim, Germany.
Department of Medical Biostatistics, Epidemiology and Informatics, University Medical Center of the Johannes Gutenberg University Mainz, Mainz, Germany.
PLoS One. 2025 Aug 14;20(8):e0330330. doi: 10.1371/journal.pone.0330330. eCollection 2025.
The distribution-free approach to the construction of age-dependent reference centiles which has been originally published by this author in 1995 and applied since then in a multitude of large-scale studies has never been investigated from a sample-size planning perspective. In the present paper, this gap is filled using the precision criterion introduced by Jennen-Steinmetz and Wellek (2005) for the estimation of reference centiles for quantitative diagnostic markers being independent of other variables, and extended by Jennen-Steinmetz (2014) to the study of age-dependent markers. In the age-dependent case, that criterion does not admit an exact representation as a function of the sample size, even when interest is in estimating a one-sided reference limit. Hence, all sample-size results presented here are based on Monte Carlo simulation. The computations cover a broad range of conditional distributions of the marker at given age including both symmetric and positively skewed distributions. For the relationship between the conditional standard deviation and age, a linear function of different slopes was assumed. Except for the most extreme settings investigated, the sample sizes shown in the tables summarizing our numerical results do not exceed the order of magnitude which has been available for a recent, potentially very influential reference-value study of basic parameters making-up the normal fetal growth profile. Furthermore, our results suggest that in terms of sample-size requirements, the distribution-free approach of Wellek & Merz (1995) to the construction of age-dependent reference ranges is typically a good bit more efficient than reference-range determination by means of quantile regression.
本文作者于1995年首次发表的构建年龄依赖性参考百分位数的无分布方法，自那时起已应用于众多大规模研究中，但从未从样本量规划的角度进行过研究。在本文中，利用Jennen-Steinmetz和Wellek（2005）引入的精度标准填补了这一空白，该标准用于估计与其他变量无关的定量诊断标志物的参考百分位数，并由Jennen-Steinmetz（2014）扩展到年龄依赖性标志物的研究。在年龄依赖性情况下，即使感兴趣的是估计单侧参考限，该标准也不能精确表示为样本量的函数。因此，这里给出的所有样本量结果均基于蒙特卡罗模拟。计算涵盖了给定年龄下标志物的广泛条件分布，包括对称分布和正偏态分布。对于条件标准差与年龄之间的关系，假设了不同斜率的线性函数。除了所研究的最极端情况外，总结我们数值结果的表格中显示的样本量不超过最近一项关于构成正常胎儿生长曲线的基本参数的潜在非常有影响力的参考值研究可用的数量级。此外，我们的结果表明，就样本量要求而言，Wellek & Merz（1995）构建年龄依赖性参考范围的无分布方法通常比通过分位数回归确定参考范围效率高得多。
