Modeling and analysis of functional method comparison data

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.

Keywords:

• Agreement
• Bootstrap
• Functional principal component analysis
• Karhunen-Loeve expansion
• Mixed model
• PACE method

Acknowledgements

The authors thank an anonymous reviewer and the Associate Editor for a constructive review of our manuscript. Their comments have led to an improved article. They thank Prof. Vernon Chinchilli for providing the percentage body fat data and Profs. Runze Li and Mosuk Chow for providing the core body temperature data. They also thank the Texas Advanced Computing Center at The University of Texas at Austin for providing HPC resources for conducting the simulation studies.