Abstract

We consider modeling and analysis of functional data arising in method comparison studies. The observed data consist of repeated measurements of a continuous variable obtained using multiple methods of measurement on a sample of subjects. The data are treated as multivariate functional data that are observed with noise at a common set of discrete time points which may vary from subject to subject. The proposed methodology uses functional principal components analysis within the framework of a mixed-effects model to represent the observations in terms of a small number of method-specific principal components. Two approaches for estimating the unknowns in the model, both adaptations of general techniques developed for multivariate functional principal components analysis, are presented. Bootstrapping is employed to get estimates of bias and covariance matrix of model parameter estimates. These in turn are used to compute confidence intervals for parameters and functions thereof, such as the measures of similarity and agreement between the measurement methods, that are necessary for data analysis. The estimation approaches are evaluated using simulation. The methodology is illustrated by analyzing two datasets.

摘要

我们考虑对方法比较研究中产生的功能数据进行建模和分析。观察到的数据包括对一个连续变量的重复测量，该变量是使用多种测量方法对受试者样本获得的。数据被视为多元函数数据，这些数据是在一组公共的离散时间点上用噪声观察到的，这些时间点可能因受试者而异。所提出的方法在混合效应模型的框架内使用功能主成分分析来表示根据少量特定于方法的主成分的观察结果。介绍了两种估计模型中未知数的方法，这两种方法都是对为多元函数主成分分析开发的通用技术的改编。Bootstrapping 用于获得模型参数估计的偏差和协方差矩阵的估计。这些又用于计算参数及其函数的置信区间，例如数据分析所必需的测量方法之间的相似性和一致性度量。使用模拟评估估计方法。通过分析两个数据集来说明该方法。