# A Gene Ontology-Based Pipeline for Selecting Significant Gene Subsets in Biomedical Applications
## 2 Materials and Methods
### Gene Ontology-Based Pipeline for Identifying Statistically Significant Genes  
The step-by-step procedure for applying GO analysis to the preprocessed gene expression dataset is illustrated in Figure 3.  
The pipeline consists of the following stages:  
1. _Identification of Differentially Expressed Genes (DEGs)_. Statistical analysis is performed using the Kruskal-Wallis test, a non-parametric method suitable for comparing gene expression distributions across multiple independent groups. This test is particularly appropriate in the current study, as prior assessment revealed that the majority of gene expression profiles deviate from normality, often exhibiting skewed or multimodal distributions. Given the presence of 14 sample classes, the Kruskal-Wallis test enables the detection of genes with significant expression differences between groups. The  
Figure 3: Gene Ontology-based pipeline for identifying statistically significant genes. output is a vector of \(p\)-values, one for each gene, indicating the probability that the observed differences would arise by chance under the null hypothesis. 2. _Multiple Testing Correction Using the Benjamini-Hochberg (BH) Method_[23]. Due to the large number of simultaneous hypothesis tests (tens of thousands of genes), the probability of false-positive results increases. The BH procedure addresses this issue by controlling the false discovery rate (FDR), which reflects the expected proportion of incorrect rejections among all rejected hypotheses. The method consists of several steps. First, the \(p\)-values obtained from the tests are sorted in ascending order. Then, each sorted \(p_{i}\) is adjusted using the following formula: \[q_{i}=\frac{p_{i}\cdot m}{i}\] (1) where \(m\) is the total number of hypotheses tested, while \(i\) is the index of the sorted \(p\)-value. To ensure monotonicity, if \(q_{i+1}<q_{i}\), then \(q_{i+1}\) is set equal to \(q_{i}\). This step guarantees that the adjusted \(q\)-values do not decrease as the rank increases. Genes with adjusted \(q\)-values below a predefined threshold \(p_{\text{max}}\) are considered statistically significant. 3. _Threshold Initialization._ To determine which genes should be selected for further analysis, a significance threshold \(p_{\text{max}}\) is defined. In this study, the threshold was set to \(p_{\text{max}}=0.05\), which is a widely accepted value in statistical hypothesis testing. This value represents a 5% probability of committing a Type I error (false positive), balancing sensitivity and specificity in the identification of differentially expressed genes. The choice of this threshold was motivated by both statistical convention and practical considerations in high-dimensional biological data analysis. A more stringent threshold could exclude biologically relevant genes by increasing the false-negative rate, whereas a more lenient one might increase the risk of false discoveries. By applying \(p_{\text{max}}=0.05\) in conjunction with the Benjamini-Hochberg correction for multiple testing, the procedure effectively controls the FDR while maintaining adequate sensitivity. 4. _Gene Ranking._ Genes are ranked in ascending order based on their adjusted \(q\)-values to prioritize those with the strongest statistical significance. 5. _GO Enrichment Analysis._ To identify biologically meaningful functional groups among the differentially expressed genes, enrichment analysis is conducted using the topG0 package [[https://bioconductor.org/packages/release/bioc/html/topGO.html](https://bioconductor.org/packages/release/bioc/html/topGO.html)]([https://bioconductor.org/packages/release/bioc/html/topGO.html](https://bioconductor.org/packages/release/bioc/html/topGO.html)) (accessed on 29 October 2024)[24]. The analysis is performed separately for each of the three principal Gene Ontology (GO) categories: Biological Process (BP), Molecular Function (MF), and Cellular Component (CC).