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.

中文翻译：

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纵向成像分析的张量广义估计方程


纵向神经影像研究变得越来越普遍，其中在多个时间点收集多个受试者的大脑图像。对此类数据的分析在科学上很重要，但也具有挑战性。大脑图像采用多维数组或张量的形式，具有超高维度和复杂结构的特点。纵向重复的图像和引起的时间相关性进一步增加了复杂性。尽管最近做出了一些努力，但纵向成像分析的解决方案仍然很少。为了满足分析纵向成像数据日益增长的需求，我们提出了几个张量广义估计方程（GEE）。所提出的 GEE 方法考虑了对象内相关性，并且对系数张量强加的低秩结构有效地降低了维度。我们还提出了一种可扩展的估计算法，建立了张量 GEE 解的渐近性质，并研究了用于区域选择的稀疏正则化。我们通过模拟和分析来自阿尔茨海默病神经影像计划的真实数据集来演示所提出的方法。