Longitudinal Mixed Membership Image-on-Scalar Model

Magnetic resonance imaging (MRI) data has been extensively applied in diagnosing and predicting Alzheimer’s disease (AD). However, there has been a notable oversight in addressing individual heterogeneity within longitudinal MRI data. This article introduces a novel modeling framework to elucidate the diverse dynamic patterns inherent in longitudinal imaging data, thereby facilitating a better understanding of individualized AD progression. The framework commences with a basis expansion approach to approximate the longitudinal images. Subsequently, a vector of probability weights is introduced, delineating a subject’s partial membership across clusters. Such partial membership allows the subject’s repeatedly measured imaging data to belong to different clusters. Finally, a nonlinear trajectory model is employed to capture the typical normal aging process and the potential transition from normal to severe stages during the disease course. A Bayesian approach coupled with efficient MCMC algorithms is developed for statistical inference. Extensive simulation results demonstrate the efficacy of the proposed methods in parameter estimation and model selection. The framework is applied to the Alzheimer’s Disease Neuroimaging Initiative (ADNI) dataset, yielding insights into the evolving patterns of brain structures throughout AD progression. Supplementary materials for this article are available online.