Our main goal is to study and quantify the evolution of multiple sclerosis lesions observed longitudinally over many years in multi-sequence structural magnetic resonance imaging (sMRI). To achieve that, we propose a class of functional models for capturing the temporal dynamics and spatial distribution of the voxel-specific intensity trajectories in all sMRI sequences. To accommodate the hierarchical data structure (observations nested within voxels, which are nested within lesions, which, in turn, are nested within study participants), we use structured functional principal component analysis. We propose and evaluate the finite sample properties of hypothesis tests of therapeutic intervention effects on lesion evolution while accounting for the multilevel structure of the data. Using this novel testing strategy, we found statistically significant differences in lesion evolution between treatment groups.

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