Information bottleneck-driven Gaussian PID enables modality-level interpretability in multimodal survival prediction

Multimodal survival analysis is essential for precision oncology, yet existing interpretability methods cannot distinguish whether modalities provide shared, modality-specific, or jointly emergent prognostic information. Partial Information Decomposition (PID) offers a theoretical basis for this question, but remains difficult to apply to continuous, high-dimensional survival data. This study introduces an information bottleneck-driven Gaussian PID framework (IB-GPID) for modality-level interpretation in multimodal survival prediction.

IB-GPID integrates information bottleneck-driven multimodal feature selection, continuous survival-target construction with Gaussianization, and bias-corrected Gaussian PID to decompose survival-predictive information into redundancy, uniqueness, and synergy. The framework is benchmarked on TCGA-BRCA and TCGA-LUSC and further applied across 17 TCGA cohorts spanning four molecular modality pairs.

IB-GPID achieved competitive survival prediction performance while producing stable and biologically interpretable PID profiles. Across the expanded analysis, redundancy and synergy dominated over modality-unique information, indicating that prognosis is mainly encoded through shared or jointly emergent molecular programs. RNA-methylation and RNA-miRNA pairs tended to be synergy-leaning, consistent with cross-layer regulatory coordination, whereas RNA-RPPA and methylation-RPPA pairs tended to be redundancy-leaning, consistent with shared pathway-level activity.

IB-GPID provides a principled and biologically interpretable framework for quantifying shared, unique, and synergistic molecular mechanisms underlying cancer prognosis.