Many large-scale longitudinal imaging studies have been or are being widely conducted to better understand the progress of neuropsychiatric and neurodegenerative disorders and normal brain development. The goal of this article is to develop a multiscale adaptive generalized estimation equation (MAGEE) method for spatial and adaptive analysis of neuroimaging data from longitudinal studies. MAGEE is applicable to making statistical inference on regression coefficients in both balanced and unbalanced longitudinal designs and even in twin and familial studies, whereas standard software platforms have several major limitations in handling these complex studies. Specifically, conventional voxel-based analyses in these software platforms involve Gaussian smoothing imaging data and then independently fitting a statistical model at each voxel. However, the conventional smoothing methods suffer from the lack of spatial adaptivity to the shape and spatial extent of region of interest and the arbitrary choice of smoothing extent, while independently fitting statistical models across voxels does not account for the spatial properties of imaging observations and noise distribution. To address such drawbacks, we adapt a powerful propagation-separation (PS) procedure to sequentially incorporate the neighboring information of each voxel and develop a new novel strategy to solely update a set of parameters of interest, while fixing other nuisance parameters at their initial estimators. Simulation studies and real data analysis show that MAGEE significantly outperforms voxel-based analysis.
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