Penalized Cox Regression with Graph-Structured Distribution-Valued Predictors

We propose the Graph-Fused Distributional Cox Model (GFDCM), a penalized survival analysis framework for distribution-valued predictors organized on a known graph. Modern neuroimaging studies collect high-dimensional voxel-level measurements across multiple regions of interest (ROIs) with rich spatial dependency structures. Rather than reducing these to scalar summaries, GFDCM models the full distribution of voxel intensities within each ROI, retaining region-specific interpretability while exploiting spatial relationships among adjacent ROIs. The distributional associations are modeled using penalized splines. To achieve simultaneous predictor selection and graph-based fusion, we introduce a structured Graph-Fused Group LASSO (GFGL) penalty that combines a group-sparsity term for discarding irrelevant predictors with a fusion term that enforces coefficient functions for graph-adjacent predictors to be identical. A flexible alternating direction method of multipliers (ADMM) algorithm is employed to optimize the penalized partial likelihood. Numerical simulations illustrate satisfactory selection, fusion, and estimation performance of GFDCM compared with unpenalized functional Cox regression and selection-only alternatives. Finally, we apply GFDCM to baseline T1-weighted MRI data collected from 308 patients in the Alzheimer's Disease Neuroimaging Initiative (ADNI-1) to identify brain regions associated with AD conversion. The results provide clinically meaningful insights and exhibit superior predictive performance compared to traditional ROI-level summary-based approaches.