Abstract

Recent advances in technology and artificial intelligence have driven the rapid expansion of medical imaging data, which contains crucial information for disease diagnosis and treatment outcomes. Inspired by recent developments in biomedical imaging analysis, we explore a class of functional regression models based on spatially varying coefficients for imaging responses and scalar predictors. We develop a scalable and communication-efficient distributed Image-on-Scalar Regression (DISR) method, utilizing trivariate spline smoothing over domain triangulation to achieve near-linear speedup. Leveraging the power of distributed learning, our method efficiently handles vast amounts of high-dimensional imaging data with a large number of voxels. We provide rigorous theoretical support for the distributed estimation framework, demonstrating that the distributed estimators of the coefficient functions attain the same root-n convergence rate as the global estimators derived from the entire dataset, and we derive the asymptotic distribution of the distributed estimators. Asymptotic confidence intervals and data-driven simultaneous confidence corridors (SCCs) are constructed for coefficient functions. Our method can simultaneously estimate and make inferences of the coefficient functions while incorporating spatial heterogeneity and spatial correlation. Monte Carlo simulation studies are conducted to examine the finite-sample performance of the proposed method. The proposed method is applied to the spatially normalized Positron Emission Tomography (PET) data of the Alzheimer's Disease Neuroimaging Initiative (ADNI).