# Integrating Multi-Omics Using Bayesian Ridge Regression with Iterative Similarity Bagging
###### Abstract  
Cancer research has increasingly utilized multi-omics analysis in recent decades to obtain biomolecular information from multiple layers, thereby gaining a better understanding of complex biological systems. However, the curse of dimensionality is one of the most significant challenges when handling omics or biological data. Additionally, integrating multi-omics by transforming different omics types into a new representation can reduce a model's interpretability, as the extracted features may lose the biological context. This paper proposes Iterative Similarity Bagging (ISB), assisted by Bayesian Ridge Regression (BRR). BRR serves as a domain-oriented supervised feature selection method, choosing essential features by calculating the coefficients for each feature. Despite this, the BRR output datasets contain many features, leading to complexity and high dimensionality. To address this, ISB was introduced to dynamically reduce dimensionality and complexity without losing the biological integrity of the omics data, which often occurs with transformation-based integration approaches. The evaluation measures employed were Root Mean Square Error (RMSE), the Pearson Correlation Coefficient (PCC), and the coefficient of determination (R\({}^{2}\)). The results demonstrate that the proposed method outperforms some current models in terms of regression performance, achieving an RMSE of 0.12, a PCC of 0.879, and an R\({}^{2}\) of 0.77 for the CCLE. For the GDSC, it achieved an RMSE of 0.029, a PCC of 0.90, and an R\({}^{2}\) of 0.80.  
anti-cancer; Bayesian Ridge Regression; deep learning; drug response prediction; multi-omics integration +
Footnote †: journal:  
predictions are significantly enhanced by multi-omics integration methods, which pool information across genomics, transcriptomics, proteomics, metabolomics, and other omics layers [8]. Utilizing diverse molecular data provides a robust basis for associating drug efficacy and toxicity with various biological processes and pathways. This comprehensive approach can identify new biomarkers that more accurately predict patient responses compared to single-omics analysis [1]. For example, multi-omics analysis has revealed complex gene-environment interactions and epigenetic alterations that affect drug metabolism and action. Consequently, multi-omics integration has become fundamental in developing personalized therapeutic strategies, minimizing unnecessary healthcare expenses, and improving patient outcomes [1]. Progress in cancer treatment using single-omics datasets, such as those produced by the Human Genome Project and early genomic profiling from the Cancer Genome Atlas (TCGA) studies [9], has been insufficient [6]. Multi-omics analysis, which has become increasingly important in cancer research in recent decades, is the only method to understand cancer behavior thoroughly and uncover previously unknown treatment vulnerabilities [1]. Integrating multi-omics data, which provide information on biomolecules from several layers, holds great promise for systematically and comprehensively understanding complicated biology [1]. Integrated techniques combine individual omics data either sequentially or simultaneously to elucidate the interactions between molecules [8]. The integration of multi-omics can be classified into three main approaches [6;7]: early integration (also called concatenation-based), mixed or middle integration (transformation-based), and late integration (model-based) [6;7]. Early integration involves combining all datasets into one large table or matrix, which leads to increased complexity, noise, and high dimensionality, making the learning process more difficult [7]. Additionally, varying sizes of omics datasets can lead to an imbalance in learning, as the algorithm may focus more on the omics with a greater number of variables and overlook the others [10]. The concatenation-based method is simple, easy to implement, and is performed early, before learning [7].