MO-RiskVAE: A Multi-Omics Variational Autoencoder for Survival Risk Modeling in Multiple MyelomaMO-RiskVAE

The heterogeneity of multiple myeloma (MM) poses significant challenges for prognosis and personalized treatment. Traditional clinical staging systems like R-ISS provide limited insight into molecular complexity. Multi-omics data—such as gene expression, copy number variation, and mutational signatures—offer richer information for risk stratification. Deep generative models, especially variational autoencoders (VAEs), have gained prominence for their ability to fuse multimodal data into compact latent representations. The MyeVAE framework extended this by integrating multimodal data with Cox-based survival loss, enabling end-to-end risk prediction. Despite empirical success, the influence of latent space design—particularly regularization strength and structure—remained underexplored. This gap motivated a systematic investigation into how different regularization strategies and latent structures impact survival modeling performance, aiming to establish design principles for robust, interpretable prognostic models.

Existing multimodal survival models often rely on strong regularization, which can suppress critical prognostic signals, leading to unstable or overly constrained latent spaces. The challenge lies in balancing the regularization to preserve relevant variation while maintaining model stability. Additionally, the latent space's geometric and structural properties—whether continuous, discrete, or hybrid—affect the model’s ability to capture disease heterogeneity and risk gradients. Without a clear understanding of how these factors interact under survival supervision, models risk overfitting or failing to generalize. Addressing these issues is crucial for developing reliable, clinically applicable prognostic tools that can handle complex, high-dimensional multi-omics data.

This work introduces a comprehensive framework to analyze the impact of latent regularization scale and structure on survival prediction. Key innovations include: 1) Systematic control of the KL regularization strength (via β-ELBO), revealing that moderate relaxation enhances risk discrimination; 2) Comparative analysis of divergence measures—KL, MMD, HSIC—highlighting the importance of scale over formulation; 3) Design of a hybrid continuous-discrete latent space using Gumbel-Softmax, which improves global risk ordering and latent representation alignment. These contributions challenge the conventional emphasis on divergence choice alone, emphasizing the critical role of regularization tuning and latent structure in survival models.

• �� Utilize the MyeVAE architecture to encode multimodal data into a latent space, with an additional survival prediction head.
• �� Control regularization via β-ELBO, adjusting the KL divergence weight to modulate latent constraint strength.
• �� Incorporate alternative divergence measures—MMD for distributional alignment, HSIC for dependence control—to compare their effects.
• �� Implement a hybrid latent space combining continuous variables with Gumbel-Softmax-based discrete variables, enabling explicit modeling of disease subtypes.
• �� Train models on the CoMMpass dataset, tuning hyperparameters such as latent dimension (32), learning rate (5e-4), and batch size (1024).
• �� Evaluate performance using C-index and Kaplan-Meier curves, performing ablation studies to isolate the effects of regularization scale and latent structure.

The primary dataset is the MMRF CoMMpass cohort with 1,143 MM patients, with 628 having complete multi-omics data. External validation uses four independent microarray cohorts. Models are trained with identical protocols, varying only regularization parameters and latent structures. Performance is measured by C-index, with cross-validation and external validation to assess robustness. Ablation studies compare KL, MMD, HSIC regularizers, and different latent space configurations. Hyperparameters include latent dimension (32), learning rate (5e-4), batch size (1024). The experiments demonstrate that moderate KL relaxation and hybrid latent structures yield the best risk stratification results.

Adjusting the KL regularization weight (β) from 0 to 0.33 improves C-index from 0.7138 to 0.7419, confirming the importance of regularization tuning. MMD and HSIC regularizers, despite their theoretical appeal, only marginally improve performance, maxing out at 0.7140. The hybrid latent model with Gumbel-Softmax achieves a C-index of 0.7788, significantly better than continuous counterparts. Kaplan-Meier curves show clearer separation between risk groups, with hazard ratios up to 5.95. Latent space analysis reveals better alignment with survival risk gradients, validating the structural design's effectiveness. These results collectively emphasize the critical role of regularization scale and latent structure in survival modeling.

The proposed models can be directly applied to clinical risk stratification in MM, aiding personalized treatment planning. They require multi-omics and clinical data, providing risk scores and subgroup classifications. The framework can be extended to other cancers and complex diseases, supporting precision medicine initiatives. Integration into clinical decision support systems could improve prognosis accuracy and treatment outcomes.

Model performance depends on high-quality, comprehensive multi-omics data; missing or noisy data can impair accuracy. Increased model complexity, especially with hybrid latent spaces, raises computational costs and training difficulty. Stability issues in training discrete latent variables suggest the need for further optimization. Validation is primarily on MM datasets; generalization to other diseases remains to be demonstrated. Future work should address robustness, interpretability, and scalability challenges.