HySurvPred: Multimodal Hyperbolic Embedding with Angle-Aware Hierarchical Contrastive Learning and Uncertainty Constraints for Survival Prediction

Multimodal learning that integrates histopathology images and genomic data holds great promise for cancer survival prediction. However, existing methods face key limitations: 1) They rely on multimodal mapping and metrics in Euclidean space, which cannot fully capture the hierarchical structures in histopathology (among patches from different resolutions) and genomics data (from genes to pathways). 2) They discretize survival time into independent risk intervals, which ignores its continuous and ordinal nature and fails to achieve effective optimization. 3) They treat censorship as a binary indicator, excluding censored samples from model optimization and not making full use of them. To address these challenges, we propose HySurvPred, a novel framework for survival prediction that integrates three key modules: Multimodal Hyperbolic Mapping (MHM), Angle-aware Ranking-based Contrastive Loss (ARCL) and Censor-Conditioned Uncertainty Constraint (CUC). Instead of relying on Euclidean space, we design the MHM module to explore the inherent hierarchical structures within each modality in hyperbolic space. To better integrate multimodal features in hyperbolic space, we introduce the ARCL module, which uses ranking-based contrastive learning to preserve the ordinal nature of survival time, along with the CUC module to fully explore the censored data. Extensive experiments demonstrate that our method outperforms state-of-the-art methods on five benchmark datasets. The source code is to be released.