All analyses were conducted using R language (version 4.3.3) or public databases. Prior to differential analysis, gene expression levels were standardized to z-scores using the scale() function, which performs the transformation (x-μ)/σ. Comparisons of discrete variables between groups (e.g., disease vs. healthy groups, binary classifications) were performed using the non-parametric Wilcoxon rank-sum test (via wilcox.test() function). The Kruskal-Wallis rank-sum test was employed for significance detection among multiple variables. For all boxplots, data distributions were visualized through violin plots with: Central line representing the median; Box boundaries indicating the third quartile (upper) and first quartile (lower); Whiskers extending to 1.5× the interquartile range (outliers beyond this range were displayed as integral components of the boxplot). Pearson correlation analysis (using cor.test(method='pearson')) was applied to normally distributed data or data with uniform dimensions, while Spearman correlation analysis (cor.test(method='spearman')) was used for non-normally distributed data or heterogeneous dimensions. Chi-square tests were performed using chisq.test().Pathway activity was evaluated through GSVA package with ssgsea parameter. Differential analysis was first conducted using limma package to obtain log2FC values for each gene, followed by gene set enrichment analysis using clusterProfiler package.All statistical tests were two-tailed, with p-values < 0.05 considered statistically significant and p-values < 0.0001 deemed highly significant. Statistical significance was denoted as: *P < 0.05, **P < 0.01, ***P < 0.001, and ****P < 0.0001.

Mainly used to compare whether there is a significant difference in means between two groups of data. It assumes that the data follows a normal distribution and is suitable for continuous variables. Common t-tests include independent sample t-tests and paired sample t-tests.

Used to compare whether there is a significant difference in medians between two groups of data. It does not require the data to follow a normal distribution and is suitable for non-parametric data or situations where the distribution is unknown. The rank sum test compares data by converting it into ranks, making it less sensitive to outliers.

It is a statistical method used to test the significance of differences between observed and expected values, commonly used for categorical data.

Null Hypothesis H0: The distributions of the populations are the same.
Alternative Hypothesis H1: The distributions of the populations are different.
If the chi-square value is greater than the critical value, reject H0; otherwise, do not reject H0.

p-value is the probability of observing the current data or more extreme data assuming the null hypothesis H0 is true. The smaller the p-value, the greater the deviation of the observed data from the null hypothesis. A p-value < 0.05 indicates statistical significance, leading to the rejection of the null hypothesis, meaning there is a significant difference in the distributions of the populations.

It is a statistical method used to handle binary dependent variable problems (e.g., "yes/no," "success/failure," "diseased/normal"). It fits a logistic function to predict the probability of an event occurring and analyzes the relationship between independent and dependent variables.

Coefficients: The regression coefficient (β) for each independent variable indicates the direction and strength of its impact on the dependent variable. A positive coefficient means an increase in the independent variable raises the probability of the event occurring, while a negative coefficient means it decreases the probability.
p-value: Used to test whether the regression coefficient is significant. Typically, a p-value < 0.05 indicates that the independent variable has a significant impact on the dependent variable.
OR (Odds Ratio): Derived by exponentiating the regression coefficient, it represents the ratio of the odds of the event occurring for a one-unit increase in the independent variable.
Confidence Interval (CI): If the confidence interval does not include 1, the OR is statistically significant. For example, if the OR for MKI67 is 1.5 with a 95% CI of [1.2, 1.8], it means we are 95% confident that for each one-unit increase in MKI67 expression level, the odds of tumor status increase by 20% to 80%.

Interpretation of OR:
OR > 1: An increase in the independent variable is associated with an increased probability of the event occurring. For example, if the OR for the gene MKI67 is 1.5, it means that for each one-unit increase in MKI67 expression level, the odds of tumor status increase by 50%.
OR = 1: The independent variable is unrelated to the probability of the event occurring.
OR < 1: An increase in the independent variable is associated with a decreased probability of the event occurring. For example, if the OR for the gene MKI67 is 0.7, it means that for each one-unit increase in MKI67 expression level, the odds of tumor status decrease by 30%.

It is a statistical method used to measure the strength and direction of the linear relationship between two continuous variables. It calculates the Pearson correlation coefficient (usually denoted as r), which ranges from -1 to 1.

r = 1: Perfect positive correlation, indicating that as one variable increases, the other increases linearly.
r = -1: Perfect negative correlation, indicating that as one variable increases, the other decreases linearly.
r = 0: No linear correlation, but this does not mean there is no other relationship between the variables.

Applicable Conditions:
Variable Type: Both variables should be continuous.
Linear Relationship: The relationship between the variables should be linear.
Normal Distribution: Both variables should approximately follow a normal distribution (especially in small sample sizes).
No Outliers: Outliers can significantly impact the correlation coefficient.

It is a non-parametric statistical method used to assess the monotonic relationship (not necessarily linear) between two variables. It is based on the ranks (order) of the variables rather than the raw data values, making it suitable for non-linear relationships or when the data does not follow a normal distribution.

r = 1: Perfect monotonic positive correlation, where the rank of one variable increases as the rank of the other variable increases.
r = -1: Perfect monotonic negative correlation, where the rank of one variable decreases as the rank of the other variable increases.
r = 0: No monotonic correlation.

Applicable Conditions:
Variable Type: Suitable for continuous variables or ordinal categorical variables.
Monotonic Relationship: Can detect monotonic relationships (whether linear or non-linear).
No Normal Distribution Requirement: No strict requirements on data distribution, suitable for non-parametric data.
Less Sensitive to Outliers: Since it is based on ranks, Spearman correlation analysis is less sensitive to outliers.

GSVA (Gene Set Variation Analysis) is a non-parametric method used to assess the enrichment of gene sets in samples. It converts gene expression data into gene set enrichment scores (GSVA scores), thereby evaluating the activity of gene sets at the sample level. The core function of GSVA is gsva(), which has four main method parameters:

"gsva": The default method, a non-parametric approach based on kernel density estimation.
"ssgsea": Single Sample GSEA, suitable for small sample data.
"zscore": A standardization method based on Z-scores.
"plage": A method based on PCA.

Selection of the kcdf parameter:
"Gaussian": Assumes that the expression data is continuous (e.g., log2-transformed data).
"Poisson": Assumes that the expression data is discrete (e.g., raw count data).

It is a statistical method used to evaluate the performance of classification models, widely applied in medical diagnosis, machine learning, bioinformatics, and other fields. ROC analysis assesses the discriminative ability of a model by plotting the ROC curve and calculating the area under the curve (AUC).

Classification Model: A model used to classify samples into two categories (e.g., positive/negative).
True Positive Rate (TPR): Also known as sensitivity, it represents the proportion of actual positive samples correctly classified.
False Positive Rate (FPR): The proportion of actual negative samples incorrectly classified as positive.
ROC Curve: A curve plotted with FPR on the x-axis and TPR on the y-axis, reflecting the classification performance of the model at different thresholds. The larger the AUC value, the better the model performance.

Interpretation of the ROC Curve:
Ideal Case: The ROC curve is close to the top-left corner, with an AUC value of 1, indicating that the model has perfect classification ability.
Random Guessing: The ROC curve is a diagonal line (AUC=0.5), indicating that the model has no classification ability.
Actual Case: The ROC curve lies between the diagonal line and the top-left corner, with the AUC value being closer to 1 indicating better model performance.

Significance of AUC Value:
AUC = 1: The model perfectly distinguishes between positive and negative classes.
AUC > 0.9: The model has excellent performance.
AUC > 0.8: The model has good performance.
AUC > 0.7: The model has acceptable performance.
AUC = 0.5: The model has no discriminative ability.