Disentangling Latent Risk Pathways via Bayesian Hypergraph Inference

Electronic health records (EHR) pose large-scale multi-disease modeling problems in which many outcomes are rare and strongly influenced by shared risk factors. While modern approaches achieve strong predictive performance, they often treat diseases independently or rely on black-box architectures, offering limited insight into how risk factors organize disease risk and little principled uncertainty quantification. We introduce a Bayesian hypergraph inference framework that reframes multi-disease modeling around latent, risk-factor-modulated disease pathways. Risk factors act on hyperedges, latent disease subsets with shared risk patterns, allowing diseases to participate in multiple distinct pathways and enabling interpretable, higher-order structure beyond pairwise associations. A repulsion prior encourages parsimonious and identifiable structure, while posterior inference provides calibrated uncertainty over both disease groupings and risk-factor influence. To enable scalable inference on large EHR datasets, we develop a structured variational inference algorithm that preserves logical dependencies among hyperedge existence, disease membership, and pathway-level effects. Experiments on simulated data and UK Biobank demonstrate stable and interpretable disease pathway structure, well-calibrated uncertainty, improved estimation for rare diseases, and competitive predictive performance.

Problem. Across many chronic conditions, most of which are individually rare, patients typically have several diagnoses. A central scientific question is how different risk factors group diseases into shared patterns, and how confident we can be in each grouping. Standard prediction models either treat diseases separately or combine them under a single combined model, leaving open how distinct risk factors organise different subsets of diseases. Solution. Our model groups diseases into overlapping clusters we call pathways, where each pathway gathers conditions linked by the same risk factors. Smoking, for example, acts through one pathway covering asthma, emphysema, and bronchitis, and through a separate pathway covering stomach ulcers. A disease can belong to several pathways, reflecting its multiple causes. For every grouping the model also reports its own confidence. Impact. On records from 277,291 UK Biobank participants covering 66 chronic diseases, the model recovers a compact set of overlapping pathways and improves prediction for the rarest conditions. The recovered groupings match known comorbidity patterns, with one example being dementia's distinct routes through vascular disease, frailty, and metabolic conditions. The interpretable pathway structure can help researchers pinpoint co-occurring conditions and identify patients at higher multi-disease risk.