Multimodal time-to-event prediction often requires integrating sensitive data distributed across multiple parties, making centralized model training impractical due to privacy constraints. At the same time, most existing multimodal survival models produce single deterministic predictions without indicating how confident the model is in its estimates, which can limit their reliability in real-world decision making. To address these challenges, we propose BVFLMSP, a Bayesian Vertical Federated Learning (VFL) framework for multimodal time-to-event analysis based on a Split Neural Network architecture. In BVFLMSP, each client independently models a specific data modality using a Bayesian neural network, while a central server aggregates intermediate representations to perform survival risk prediction. To enhance privacy, we integrate differential privacy mechanisms by perturbing client side representations before transmission, providing formal privacy guarantees against information leakage during federated training. We first evaluate our Bayesian multimodal survival model against widely used single modality survival baselines and the centralized multimodal baseline MultiSurv. Across multimodal settings, the proposed method shows consistent improvements in discrimination performance, with up to 0.02 higher C-index compared to MultiSurv. We then compare federated and centralized learning under varying privacy budgets across different modality combinations, highlighting the tradeoff between predictive performance and privacy. Experimental results show that BVFLMSP effectively includes multimodal data, improves survival prediction over existing baselines, and remains robust under strict privacy constraints while providing uncertainty estimates.

翻译：多模态时间-事件预测通常需要整合分布在多方之间的敏感数据，由于隐私约束，集中式模型训练变得不可行。同时，现有的大多数多模态生存模型仅能产生单一的确定性预测，无法指示模型对其估计结果的置信程度，这限制了其在真实世界决策中的可靠性。为应对这些挑战，我们提出了BVFLMSP，一种基于分割神经网络架构的用于多模态时间-事件分析的贝叶斯纵向联邦学习（VFL）框架。在BVFLMSP中，每个客户端使用贝叶斯神经网络独立建模一种特定的数据模态，而中央服务器则聚合中间表示以进行生存风险预测。为增强隐私保护，我们在传输前对客户端侧的表示施加扰动，整合了差分隐私机制，从而在联邦训练过程中为信息泄露提供形式化的隐私保障。我们首先将所提出的贝叶斯多模态生存模型与广泛使用的单模态生存基线模型以及集中式多模态基线模型MultiSurv进行了对比。在多模态设置下，所提方法在判别性能上呈现出一致的提升，与MultiSurv相比，C-index最高提高了0.02。随后，我们在不同模态组合及不同隐私预算下，比较了联邦学习与集中式学习，突显了预测性能与隐私之间的权衡。实验结果表明，BVFLMSP能够有效整合多模态数据，相较于现有基线模型改进了生存预测，并且在严格的隐私约束下依然保持鲁棒性，同时能够提供不确定性估计。