# Integrating Multi-Omics Using Bayesian Ridge Regression with Iterative Similarity Bagging
## 3 Materials and Methods
### Datasets  
The Genomics of Drug Sensitivity in Cancer (GDSC) and Cancer Cell Line Encyclopedia (CCLE) are comprehensive drug response datasets used to validate the proposed method, Bayesian Ridge Regression with Iterative Similarity Bagging (BRR-ISB). The (GDSC) project [50] tested 1000 cancer cell lines against 250 different chemicals for treatment sensitivity and identified genetic changes associated with drug efficacy. The TCGA's genomic data on 11,289 tumors were compared to cancer cell lines, highlighting \"cancer functional events\" (CFEs), key molecular abnormalities. Data from cell lines sharing similar CFEs are widely used to predict responsiveness to a specific pharmaceutical treatment. Mutation and copy number information predict drug responses in specific tissues, while gene expression predicts pan-cancer response [51]. The Cancer Cell Line Encyclopedia (CCLE) project is a collaborative effort to analyze the genetic and pharmacological characteristics of a vast collection of human cancer cell lines [52]. The main objective of the CCLE is to provide researchers with a comprehensive repository for understanding the molecular and genetic characteristics of various cancer types and their responses to distinct medications and treatments. By analyzing diverse cancer cell lines, the CCLE enables investigation into cancer heterogeneity and the discovery of possible targets for therapy and biomarkers [53]. The (CCLE) project characterized over 1000 human cancer cell lines at the molecular level [52]. Analysis identified 24 susceptibility profiles to anti-cancer drugs among a sample of 363 cell lines. The CCLE and GDSC [52; 54] datasets were utilized in this study. The IC50, representing drug responses for cell lines for different medications, was denoted as (yres,c) for a specific cell line c. Three omics were employed: single-nucleotide mutation (represented by xsnv,g) for gene g, gene expression (represented by xexp,g), and copy number alteration/variation (represented by xcnv,g). Gene expression and copy number alteration are continuous variables, while single-nucleotide mutation is binary. In the case of mutation, \"1\" is used to indicate the presence of mutation, while \"0\" represents the absence of mutation (wild type) [54]. The gene expression data do not contain any missing values. Rows containing more than 50% missing values were excluded from copy number alteration and single-nucleotide mutation analysis. The mean weight method was employed to compensate for the missing values in the remaining cell lines [54]. The distance was computed to get the closest \(k\), which was then utilized to fill in missing values for gene expression, as specified below:  
\[distance(c,k)=\left\|x_{exp,c}-x_{exp,k}\right\|_{2}^{2} \tag{1}\]  
where \(c\) represents the cell line, \(k\) represents the nearest cell line, and \(x\) is the gene expression value for each cell line. The missing value of cell line c in the copy number alteration of gene g was imputed using the mean value of the nearest cell lines. \[missingCNV(c,g)=\sum\limits_{k=1}^{K}\frac{distance(c,c_{k})}{\sum\limits_{k=1} ^{K}distance(c,c_{k})}missingCNV(c_{k},g) \tag{2}\]  
The single-nucleotide mutation features are represented by binary values, where a value of 1 indicates a mutation and a value of 0 indicates the wild type. The average feature value of cell line \(c\), calculated among the k-nearest cell lines, was utilized to adjust for the absence of the SNV (single-nucleotide mutation or variation) value of gene g in the following manner [54]:  
\[missingSNV(c,g)=\left\{ \begin{aligned} & 1\ if\ \left(\sum\limits_{k=1}^{K} missingSNV(c_{k},g)>\sum\limits_{k=1}^{K}(1-missingSNV(c_{k},g))\right)\\ & 0\ otherwise\end{aligned} \right. \tag{3}\]  
Similarly, the missing IC50 value was imputed using the same method as the copy number change. The missing value of cell line \(c\) was imputed using the average value of the closest cell lines.