2.1 Data

Transcriptomic RNA sequencing data from lung adenocarcinoma (LUAD) tissue samples from The Cancer Genome Atlas (TCGA) were used for omics analysis. The data were randomly split into a training set and a testing set in a 7:3 ratio, and the GSE115002 gene chip data were used as an external verification set. The LM22 immune cell gene signature in CIBERSORTx was used to calculate the abundance of each immune cell and perform a logarithmic transformation. Bayesian network parameter and structure learning were conducted based on the expression features of the two key genes.

2.2 Transcriptomics gene expression analysis

Differential gene expression refers to the variation in gene expression levels in different tissues caused by selective expression of genes in time or space. Differential expression genes are genes with significantly large fold changes in expression and statistical significance. Comparative analysis using gene expression data is performed to determine if there is differential expression of the same gene between two sets of samples (e.g., colon tumour tissue samples and normal tissue samples). The “limma” package⁸ in R language is used to analyze genes with differential expression levels between different tissues. The selection criteria include P < 0.01 and LogFC > 10.

The most challenging issue in gene data analysis is the curse of dimensionality, especially in small sample sizes with high-dimensional data. Traditional analysis methods are easily influenced by various confounding factors, and most studies only focus on the level of correlation analysis. Further data mining of publicly available databases can better utilize these databases. Moreover, by using Bayesian network algorithms, it is possible to learn causal relationships between different features, which can help researchers discover and improve the possible regulatory mechanisms within the entire disease process (e.g., which gene may have more research value in the occurrence of lung cancer). This provides a theoretical basis for further research. Therefore, in order to filter high-dimensional gene data, this study first employed lasso regression⁹ and enrichment analysis¹⁰ methods . Considering that different structural learning algorithms have different underlying assumptions, we used an ensemble approach to average the results from different algorithms to identify potential arc lists for the final learning of the directed acyclic graph (DAG). Subsequently, we combined these results using various structural learning algorithms to form the prior information of a Bayesian network, aiming to obtain more reliable estimation results. To avoid potential collinearity issues among genes, this study further screens differential expression genes using lasso regression models. Kegg pathway analysis and GO biological function enrichment analysis were used to preliminarily identify potential regulatory mechanisms of genes and select key genes for subsequent construction of the network model.

2.3 CIBERSORTx immune infiltration analysis

Tumor immune cell infiltration analysis.CIBERSORTx¹¹ is used to perform deconvolution calculations to obtain the immune cell content of the samples. Heatmaps, box plots, and other analyses are used to analyze the changes in different cell contents in different tissue samples. Furthermore, a comparison is made to determine if there are differences in the content of each immune cell type between the two groups, using the Wilcoxon rank-sum test for intergroup difference analysis.

2.4 Bayesian network model

Bayesian networks are directed acyclic graph methods that express probabilistic causal relationships between various indicators. With the development of Bayesian network algorithms, they have been used to model intracellular signaling pathways, such as identifying known DNA repair networks in Escherichia coli using microarray data or identifying simple phosphorylation cascades in T cells using flow cytometry data. However, there are also some issues in these studies, especially when the sample size is much smaller than the number of variables, both the computation and accuracy of the network will be adversely affected.^12-14 Transcriptomic data often have a large number of random variables and a small number of biological replicates, making inference of gene-level networks computationally challenging and introducing greater uncertainty into the inference.¹⁵ Therefore, variable selection methods often have significant importance in the early application of these studies.

2.5 Bayesian network structure learning

Bayesian network inference^{16, 17} involves inferring the structure of the network, capturing specific causal interactions or arcs between network nodes, and representing them as a DAG, followed by estimating the parameters of the conditional probability distribution from the dataset. First, use professional prior knowledge to determine the edges that are definitely not included in the network structure (‘blacklist’). Then, through various different structural learning algorithms, determine a set of possible edge relationships that consider the trade-off between regression accuracy and model complexity (‘whitelist’). Finally, use our initial prior information together with the results of the initial structural learning as a prior to learn the network structure. Seven different structure learning algorithms were used, including Incremental Association Markov Blanket (IAMB), IAMB with False Discovery Rate control (IAMB.FDR), PC.STABLE (Practical Constraint), Grow-Shrink, Hill-Climbing and Max-Min Hill-Climbing, Restricted Search Maximum (RSMAX2). The values of Bayesian information criterion (BIC) are calculated for the entire DAG and each node with respect to the inferred parent nodes (Table 1: parent node count / BIC). The ‘whitelist’ is determined based on the minimum BIC values. Additionally, we also note that if the inferred directions of arcs differ among algorithms, they are excluded from the ‘whitelist’ when exploring the impact of strength thresholds. While increasing the number of arcs in the DAG can better approximate the joint probability distribution, complex networks limit interpretability. We use BIC to quantify the trade-off between regression accuracy and model complexity, with the optimal balance at the minimum value.

The bootstrap resampling method, which involves replacing sampling from the dataset to generate synthetic datasets of similar size to the original dataset, was used. Each algorithm learned the inferred network structure using the synthetic datasets, resulting in 10 000 network structures. For each algorithm, the average network structure was computed from its set of network structures, and the threshold for including arcs in the average network was automatically determined by each algorithm.

2.6 Bayesian network parameter learning

The dataset was divided into a training set and a testing set in a 7:3 ratio, with the training set used for model parameter learning. The network structure learned from the final structure was imported into the software, and the maximum a posteriori estimate method was used to estimate the parameters of each node.

The Netica software allows us to obtain the conditional probability distribution of other nodes and model predictions by determining the node status. The validation set was used for model validation, and evaluation indices mainly included the area under the ROC curve and confusion matrix.

3.1 Mono-omics correlation analysis and dimensionality reduction processing

3.1.1 Transcriptomics gene expression differential analysis

First, a gene differential expression analysis was conducted, and 1294 genes that were differentially expressed between healthy and cancerous tissues were obtained (Figure 2). After that, to eliminate possible collinearity among variables, we used lasso regression to reduce the dimensionality of variables and selected the optimal λ value (0.002307535) through cross-validation (Figure 3), resulting in 227 genes in the model for KEGG pathway analysis and GO enrichment analysis. Finally, through these functional analyses, we could then identify the potential associations between transcriptomic gene expression and cellular functions. Genes that are significantly associated with cellular functions are of great significance for constructing gene-cell regulatory networks in subsequent studies.

3.2 Transcriptomics gene expression functional analysis

The KEGG pathway analysis revealed that various genes in non-small cell lung cancer patients may have abnormal expression in different pathways. For example, as shown in the Figure 4, five genes were up-regulated in the HEMATOPOIETIC_CELL_LINEAGE pathway. This suggests that these genes may influence the occurrence and development of the disease through these regulatory pathways. The GO biological enrichment analysis identified the main molecular functions, cellular components, or biological processes in which the genes are predominantly enriched. For example, as shown in the Figure 5, four genes were found to be enriched in the Angiotensin-activation signaling pathway. The genes that are identified in both analyses may be key genes that contribute to the development of the disease. Investigating the regulatory mechanisms of these genes may hold greater research value. Based on KEGG pathway analysis and GO enrichment analysis, we selected the genes ‘CD36’ and ‘ADRA1A’ for further analysis (See Table 2).

3.3 CIBERSORTx immune infiltration analysis

CIBERSORTx was used to calculate the content of immune cells in each sample and compare whether the content of each immune cell was different between healthy and cancerous tissues. The heatmap of cell abundance provides a rough display of the immune cell content in each sample. The Wilcoxon test is used to compare whether there are differences in cell abundance between different tissues.

In order to optimize the graph model and reduce computational complexity, we prioritize analyzing immune cell types with different abundance between different tissues. For example, in Figure 6, the abundance of plasma cells in normal tissues is significantly lower, so the high expression in cancer tissues may be caused by gene expression changes. Moreover, the differences between the two groups in Figure 7 are also statistically significant. Therefore, we further include this cell type data in subsequent analysis. Therefore, among the common 22 cell types provided by CIBERSORTx, we only selected 14 cell types (as shown in Figure 7).

3.4 Determination of network structure priors (consensus seed network) using multiple structure learning algorithms

Due to the different underlying assumptions of various structural learning algorithms, a single algorithm may perform poorly on a given dataset. Therefore, we utilized multiple diverse structural learning algorithms to obtain the initial structure of the network. When an edge is identified by multiple methods simultaneously, we have reasons to believe that the edge truly exists. Additionally, we pay attention to the BIC value. When a node has different numbers of parent nodes, we prioritize the case with the lowest BIC value. The cells highlighted in green indicate the minimum BIC values and corresponding arc counts included in the consensus whitelist.

3.5 Bayesian network

The final network structure of the dataset was generated using the IAMB algorithm based on the ‘blacklist’ specified by previous knowledge and the ‘whitelist’ corresponding to the consensus seed network (the average network was extracted after generating 10000 networks using bootstrap method, see Figure 8).

The probability distribution is marked in the Figure 8, such as the probability of the ‘normal’ state and ‘Cancer’ state of the event node being 10.8% and 89.2%, respectively, based on the current data.

3.6 Sensitivity and diagnostic analysis

Performing cause-oriented sensitivity analysis and result-oriented diagnostic analysis on the Bayesian network can effectively measure the influence relationships between factors in the model. Sensitivity analysis of the network involves observing the changes in probability parameters of output variables by varying the parameter values of input nodes, typically by comparing the magnitude of variance reduction or entropy reduction. The larger the variance reduction and entropy reduction values, the greater the influence of the respective indicators on the outcome. Diagnostic analysis, based on sensitivity analysis results, involves observing the changes in probability tables of influencing factors through Bayesian model inference. The larger the probability changes, the closer the relationship between the two.

3.7 Sensitivity analysis

Setting the analysis variable as the ‘event’ in the target variable (1 for cancer tissue), sensitivity analysis is performed on other factors using Netica software, and the results are shown in Table 3. The ‘entropy reduction value’ in Table 3 measures the interdependence between factors, and entropy reduction percentage and variance represent the degree of influence between factors.

From the table, it can be observed that ADRA1A has the most significant effect on the disease condition, with the highest entropy reduction percentage of 20.4%, while PM1 has an entropy reduction percentage of 0.00555, indicating the least impact on the disease condition.

3.8 Diagnostic analysis

For diagnostic analysis, we selected eight features that have a significant impact on the disease condition. Using the reverse inference of the Bayesian network model, we set the ‘event’ node to states ‘normal’ and ‘cancer’ representing the assumption of non-disease and disease conditions, respectively. We observed the changes in the probability parameter tables for each feature, and the results are shown in Figures 9 and 10.

By comparing the two graphs, it is not difficult to find that the probability of ADRA1A nodes varies significantly.

3.9 Model prediction

Model prediction evaluation was performed using a training set and a validation set, and the results are shown in Table 4. From the table, it can be observed that the model achieved an accuracy of around 96%, and the AUC values were around 0.98, indicating good predictive performance and generalizability of the model. The external validation dataset used in this study was randomly selected from the GEO public database, which may have different experimental designs that could result in prediction results that are not as good as the original data. However, the model still demonstrates high prediction accuracy (error = 28.85%, AUC = 0.8689), indicating that it has a certain degree of extrapolation capability.