Division of Epidemiology, Statistics and Prevention Research, Eunice Kennedy Shriver National Institute of Child Health and Human Development, Bethesda, MD 20892-7510, USA.
Stat Med. 2011 May 30;30(12):1455-65. doi: 10.1002/sim.4189. Epub 2011 Jan 25.
Reference curves are commonly used to identify individuals with extreme values of clinically relevant variables or stages of progression which depend naturally on age or maturation. Estimation of reference curves can be complicated by a technical limit of detection (LOD) that censors the measurement from the left, as is the case in our study of reproductive hormone levels in boys around the time of the onset of puberty. We discuss issues with common approaches to the LOD problem in the context of our pubertal hormone study, and propose a two-part model that addresses these issues. One part of the proposed model specifies the probability of a measurement exceeding the LOD as a function of age. The other part of the model specifies the conditional distribution of a measurement given that it exceeds the LOD, again as a function of age. Information from the two parts can be combined to estimate the identifiable portion (i.e. above the LOD) of a reference curve and to calculate the relative standing of a given measurement above the LOD. Unlike some common approaches to LOD problems, the two-part model is free of untestable assumptions involving unobservable quantities, flexible for modeling the observable data, and easy to implement with existing software. The method is illustrated with hormone data from the Third National Health and Nutrition Examination Survey.
参考曲线通常用于识别具有临床相关变量或进展阶段极值的个体，这些变量或阶段的极值自然取决于年龄或成熟度。由于检测限（LOD）的技术限制，参考曲线的估计可能会变得复杂，因为在我们对青春期前男孩生殖激素水平的研究中，LOD 从左侧屏蔽了测量值。我们讨论了在青春期激素研究背景下，LOD 问题常见方法所存在的问题，并提出了一个两部分模型来解决这些问题。所提出模型的一部分将测量值超过 LOD 的概率指定为年龄的函数。模型的另一部分将给定测量值超过 LOD 时的条件分布指定为年龄的函数。可以结合这两部分信息来估计参考曲线的可识别部分（即超过 LOD 的部分），并计算给定测量值在 LOD 以上的相对位置。与 LOD 问题的一些常见方法不同，两部分模型没有涉及不可观测量的未经检验的假设，灵活适用于对可观测数据进行建模，并且易于使用现有软件实现。该方法通过第三次全国健康和营养调查的激素数据进行了说明。
