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

TL;DR

HySurvPred addresses key obstacles in multimodal cancer survival analysis by embedding histopathology and genomics in hyperbolic space to capture hierarchical structures, employing a ranking-based contrastive loss to respect the continuous ordinal nature of survival time, and introducing a censor-conditioned uncertainty constraint to utilize censored data. The framework comprises three components: Multimodal Hyperbolic Mapping (MHM), Angle-aware Ranking-based Contrastive Loss (ARCL), and Censor-Conditioned Uncertainty Constraint (CUC), which jointly improve multimodal alignment and uncertainty handling. Evaluations on five TCGA cohorts demonstrate state-of-the-art performance in C-index and improved risk stratification via Kaplan-Meier analysis, validating the effectiveness of hierarchical, ordinal-aware, and censorship-aware learning. These advances offer more accurate prognostic predictions and better utilization of censored data, with potential clinical impact for individualized cancer management.

Abstract

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.

Figures (9)

• Figure 1: Our HySurvPred extracts original features from two highly structural modalities (i.e., histopathology slides and genomic data), and maps them into hyperbolic space for feature fusion.
• Figure 2: Overview of our HySurvPred, a novel framework for survival prediction, with a Multimodal Hyperbolic Mapping (MHM) to explore the inherent hierarchical structures within modality in hyperbolic space, an Angle-aware Ranking-based Contrastive Loss (ARCL) to preserve the ordinal nature of survival time and a Censor-Conditioned Uncertainty Constraint (CUC) to fully explore the censored data for optimization.
• Figure 3: Kaplan-Meier Analysis on five cancer datasets, where patient stratifications of low risk (green) and high risk (red) are presented. Shaded areas refer to the confidence intervals. P-value $<$ 0.05 means a significant statistical difference between two groups, and a lower P-value is better.
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