Longitudinal scalar-on-functions regression with application to tractography data

We propose a class of estimation techniques for scalar-on-function regression where both outcomes and functional predictors may be observed at multiple visits. Our methods are motivated by a longitudinal brain diffusion tensor imaging tractography study. One of the study's primary goals is to e...

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Bibliographic Details
Published in:Biostatistics (Oxford, England) England), 2013-07, Vol.14 (3), p.447-461
Main Authors: Gertheiss, Jan, Goldsmith, Jeff, Crainiceanu, Ciprian, Greven, Sonja
Format: Article
Language:English
Subjects:
Anisotropy
Biostatistics
Brain
Brain - pathology
Comparative analysis
Diffusion Tensor Imaging - statistics & numerical data
Estimating techniques
Humans
Linear Models
Medical imaging
Models, Statistical
Multiple Sclerosis - pathology
Normal distribution
Principal Component Analysis
Principal components analysis
Regression Analysis
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Summary:We propose a class of estimation techniques for scalar-on-function regression where both outcomes and functional predictors may be observed at multiple visits. Our methods are motivated by a longitudinal brain diffusion tensor imaging tractography study. One of the study's primary goals is to evaluate the contemporaneous association between human function and brain imaging over time. The complexity of the study requires the development of methods that can simultaneously incorporate: (1) multiple functional (and scalar) regressors; (2) longitudinal outcome and predictor measurements per patient; (3) Gaussian or non-Gaussian outcomes; and (4) missing values within functional predictors. We propose two versions of a new method, longitudinal functional principal components regression (PCR). These methods extend the well-known functional PCR and allow for different effects of subject-specific trends in curves and of visit-specific deviations from that trend. The new methods are compared with existing approaches, and the most promising techniques are used for analyzing the tractography data.
ISSN:1465-4644
1468-4357
DOI:10.1093/biostatistics/kxs051