Multi-omics data integration using time-to event endpoint and supervised Cox penalized regression: a comprehensive review.

The integration of multi-omics data, encompassing genomics, transcriptomics, epigenomics, and proteomics, has revolutionized medical research by enabling a more comprehensive understanding of complex diseases like cancer. Multi-omics prognostic models facilitate improved patient stratification through personalized prognostication. However, the high dimensionality, heterogeneity, and correlations between omics layers pose significant challenges for predictive modelling building, particularly in time-to-event analyses. This review synthesizes current methodologies for variable selection and regularization in high-dimensional settings, focusing on their application to survival outcomes. We explore global penalty approaches, such as LASSO, Ridge, and Elastic Net, which apply uniform penalties to control model complexity and improve generalizability. Parallel regression methods, which independently analyse different omics layers before integrating results, offering robustness but potentially missing critical correlation. Group regularization techniques, including Group LASSO and OSCAR regression, address multicollinearity by clustering correlated predictors, enhancing interpretability in high-dimensional datasets. Hierarchical regression models, such as Priority LASSO and IPF-LASSO, leverage prior knowledge of omics relationships to improve integration and interpretability but may overlook platform interactions. Kernel-based methods like KEN-COX are also examined for their ability to handle nonlinear relationships and reduce dimensionality. Each method presents unique trade-offs between interpretability, computational efficiency, and predictive performance. This review highlights the need for tailored approaches that balance these factors, emphasizing the importance of model transparency and clinical applicability. Future research should focus on refining these techniques to better capture the complex interplay of omics data in disease progression and survival outcomes.