Applied Mathematics, MAP5, UMR CNRS 8145, Université Paris Descartes, Paris, France.
Stat Med. 2012 Dec 30;31(30):4154-63. doi: 10.1002/sim.5392. Epub 2012 May 17.
Correcting for measurement error when estimating the density of a routinely collected biomedical variable is an important issue when describing reference values for both healthy and pathological states. The present work addresses the problem of estimating the density of a biomedical variable observed with measurement error without any a priori knowledge on the error density. Assuming the availability of a sample of replicate observations, either internal or external, which is generally easily obtained in clinical settings, we propose an estimator based on the non-parametric deconvolution theory with an adaptive procedure for cutoff selection, the replicates being used for an estimation of the error density. We illustrate this approach in two applicative examples: (i) the systolic blood pressure distribution density, using the Framingham Study data set, and (ii) the distribution of the timing of onset of pregnancy within the female cycle, using ultrasound measurements in the first trimester of pregnancy.
在描述健康和病理状态的参考值时，纠正医学学术文献中经常收集的生物医学变量的测量误差是一个重要问题。本工作解决了在没有关于误差密度的先验知识的情况下，估计具有测量误差的生物医学变量密度的问题。假设可以获得重复观测的样本，无论是内部的还是外部的，这在临床环境中通常很容易获得，我们提出了一种基于非参数解卷积理论的估计器，并采用自适应方法选择截止值，重复观测用于估计误差密度。我们在两个应用示例中说明了这种方法：（i）使用弗雷明汉研究数据集的收缩压分布密度，以及（ii）使用妊娠早期超声测量的女性周期中妊娠开始时间的分布。
