Back To Index Previous Article Next Article Full Text

Statistica Sinica 29 (2019), 1977-2005

TENSOR GENERALIZED ESTIMATING EQUATIONS
FOR LONGITUDINAL IMAGING ANALYSIS
Xiang Zhang, Lexin Li, Hua Zhou, Yeqing Zhou,
Dinggang Shen and ADNI
North Carolina State University, University of California, Berkeley,
University of California, Los Angeles, Shanghai University of Finance
and Economics, University of North Carolina, Chapel Hill
and the Alzheimer's Disease Neuroimaging Initiative

Abstract: Longitudinal neuroimaging studies are becoming increasingly prevalent, where brain images are collected on multiple subjects at multiple time points. Analyses of such data are scientifically important, but also challenging. Brain images are in the form of multidimensional arrays, or tensors, which are characterized by both ultrahigh dimensionality and a complex structure. Longitudinally repeated images and induced temporal correlations add a further layer of complexity. Despite some recent efforts, there exist very few solutions for longitudinal imaging analyses. In response to the increasing need to analyze longitudinal imaging data, we propose several tensor generalized estimating equations (GEEs). The proposed GEE approach accounts for intra-subject correlation, and an imposed low-rank structure on the coefficient tensor effectively reduces the dimensionality. We also propose a scalable estimation algorithm, establish the asymptotic properties of the solution to the tensor GEEs, and investigate sparsity regularization for the purpose of region selection. We demonstrate the proposed method using simulations and by analyzing a real data set from the Alzheimer's Disease Neuroimaging Initiative.

Key words and phrases: Generalized estimating equations, longitudinal imaging, low rank tensor decomposition, magnetic resonance imaging, multidimensional array, tensor regression.

Back To Index Previous Article Next Article Full Text