Tensor generalized estimating equations for longitudinal imaging analysis

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 ap- proach 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 solu- tion 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.