Bayesian scalar-on-image regression with spatial interactions for modeling Alzheimer's disease

There has been substantial progress in predictive modeling for cognitive impairment in neurodegenerative disorders such as Alzheimer's disease (AD), based on neuroimaging biomarkers. However, existing approaches typically do not incorporate heterogeneity that may potentially arise due to interactions between the spatially varying imaging features and supplementary demographic, clinical and genetic risk factors in AD. Unfortunately, ignoring such heterogeneity may potentially result in poor prediction and biased estimation. Building on existing scalar-on-image regression framework, we address this issue by incorporating spatially varying interactions between brain image and supplementary risk factors to model cognitive impairment in AD. The proposed Bayesian method tackles spatial interactions via hierarchical representation for the functional regression coefficients depending on supplementary risk factors, which is embedded in a scalar-on-function framework involving a multi-resolution wavelet decomposition. To address the curse of dimensionality, we induce simultaneous sparsity and clustering via a spike and slab mixture prior, where the slab component is characterized by a latent class distribution. We develop an efficient Markov chain Monte Carlo algorithm for posterior computation. Extensive simulations and application to the longitudinal Alzheimer's Disease Neuroimaging Initiative study illustrate significantly improved prediction of cognitive impairment in AD across multiple visits by our model in comparison with alternate approaches. The proposed approach also identifies key brain regions in AD that exhibit significant association with cognitive abilities, either directly or through interactions with risk factors.