Comprehensive review of Bayesian network applications in gastrointestinal cancers

Abstract

Gastrointestinal cancers, including esophageal, gastric, colorectal, liver, gallbladder, cholangiocarcinoma, and pancreatic cancers, pose a significant global health challenge due to their high mortality rates and poor prognosis, particularly when diagnosed at advanced stages. These malignancies, characterized by diverse clinical presentations and etiologies, require innovative approaches for improved management. Bayesian networks (BN) have emerged as a powerful tool in this field, offering the ability to manage uncertainty, integrate heterogeneous data sources, and support clinical decision-making. This review explores the application of BN in addressing critical challenges in gastrointestinal cancers, including the identification of risk factors, early detection, treatment optimization, and prognosis prediction. By integrating genetic predispositions, lifestyle factors, and clinical data, BN hold the potential to enhance survival rates and improve quality of life through personalized treatment strategies. Despite their promise, the widespread adoption of BN is hindered by challenges such as data quality limitations, computational complexities, and the need for greater clinical acceptance. The review concludes with future research directions, emphasizing the development of advanced BN algorithms, the integration of multi-omics data, and strategies to ensure clinical applicability, aiming to fully realize the potential of BN in personalized medicine for gastrointestinal cancers.

Key Words: Gastrointestinal cancers; Bayesian networks; Heterogeneous data integration; Early detection; Risk prediction; Prognosis; Personalized medicine

Core Tip: Bayesian networks (BN) provide a powerful framework for managing the complexity and uncertainty in gastrointestinal cancer research and clinical practice. By integrating diverse data types and modeling causal relationships, BN facilitate personalized treatment strategies. However, challenges such as data availability, computational demands, and clinical adoption must be addressed to fully unlock their potential for improving patient outcomes and quality of life.

INTRODUCTION

Gastrointestinal cancers are among the most prevalent and deadly malignancies worldwide, posing a major public health challenge[1]. These cancers, including but not limited to esophageal, gastric, colorectal, liver, gallbladder, cholangiocarcinoma, and pancreatic cancers, collectively contribute substantially to cancer-related morbidity and mortality[2,3]. Each of these cancers presents unique clinical characteristics and etiological factors, ranging from genetic predispositions and environmental exposures to lifestyle influences such as diet, alcohol consumption, and smoking[4]. Despite advances in cancer biology, diagnostic technologies, and therapeutic interventions, many gastrointestinal cancers continue to exhibit poor outcomes, especially when diagnosed at late stages. This underscores the critical need for improved methods for early detection, risk stratification, and personalized treatment to enhance survival rates and quality of life for affected individuals[5].

Gastrointestinal cancers typically involve complex interactions between genetic, molecular, and environmental factors, making it challenging to identify clear patterns or causal relationships[6]. Moreover, the data generated in cancer research and clinical practice are diverse, spanning epidemiological datasets, clinical observations, imaging studies, and molecular profiles[7]. To address these challenges, computational models have gained prominence as powerful tools for synthesizing and interpreting complex data. Among these models, Bayesian network (BN) has emerged as a particularly promising approach for their ability to handle uncertainty, integrate heterogeneous data, and support decision-making[8]. BN is probabilistic graphical models that represent variables as nodes and their conditional dependencies as directed edges. They provide a framework for modeling causal relationships, enabling researchers and clinicians to infer probabilities and predict outcomes even in the presence of incomplete or uncertain data. By incorporating prior knowledge and learning from data, BN can uncover hidden patterns, facilitate diagnostic decision-making, and improve the accuracy of predictions in complex systems such as cancer biology[9].

In the context of gastrointestinal cancers, BN has been applied to address a wide range of challenges. For example, they have been used to identify risk factors and predict individual cancer risk, integrating genetic predispositions, lifestyle behaviors, and environmental exposures. In diagnosis, BN has shown potential in early detection by combining biomarkers, imaging data, and clinical symptoms[10]. For treatment planning, they offer decision support by weighing the probabilities of different outcomes based on patient-specific data, helping to optimize therapeutic strategies[11]. Additionally, BN has been employed in prognosis, enabling the prediction of survival probabilities and disease progression by analyzing patient-specific characteristics and treatment responses.

Despite their significant promise, the adoption of BN in gastrointestinal oncology is not without challenges. One major limitation is the quality and availability of data, as high-quality, large-scale datasets are often difficult to obtain[12], particularly for rare cancers such as gallbladder and pancreatic cancers. Moreover, the computational complexity of constructing and analyzing large BN can be a barrier, especially when dealing with high-dimensional datasets. The interpretability of the models and their acceptance among clinicians also remain critical issues, as healthcare professionals require intuitive tools that can seamlessly integrate into clinical workflows[13].

This review aims to provide a comprehensive exploration of the applications of BN in gastrointestinal cancers. It begins by introducing the foundational concepts and content of BN, followed by an exploration of their applications across various types of gastrointestinal cancers. It highlights specific use cases such as risk prediction, early diagnosis, treatment decision-making, and survival analysis. The review critically examines challenges and limitations, including data-related issues, computational demands, and the gap between research and clinical implementation, and concludes by identifying promising directions for future research.

FUNDAMENTALS OF BN

BN is a class of probabilistic graphical models that represent a set of variables and their conditional dependencies through a directed acyclic graph (DAG)[14]. These models are uniquely suited for applications in complex systems such as medicine, where uncertainty, interdependence, and incomplete data are prevalent. A BN consists of nodes, representing random variables, and directed edges, denoting the causal or probabilistic relationships between these variables[15]. Each node is associated with a probability distribution that quantifies the likelihood of its states, conditioned on its parent nodes. This structure enables BNs to model joint probability distributions efficiently, facilitating reasoning and inference in uncertain environments[16].

Figure 1 illustrates a classic Asia BN comprising eight random variables: Whether the individual has traveled to Asia (A), has tuberculosis (B), has either tuberculosis or lung cancer (C), has a positive X-ray result (D), smokes (E), has lung cancer (F), has bronchitis (G), and has trouble breathing (H). As shown in the figure, difficulty breathing can result from tuberculosis, lung cancer, bronchitis, a combination of these conditions, or none of them. Recent travel to Asia increases the likelihood of tuberculosis. However, a single chest X-ray cannot differentiate between lung cancer and tuberculosis, nor can it determine the cause of difficulty breathing. It is well-established that smoking is a significant risk factor for both lung cancer and bronchitis. According to the conditional probability distribution, individuals who smoke have a 10% probability of developing lung cancer and a 60% probability of developing bronchitis. This indicates that the likelihood of smoking causing bronchitis is much higher than its likelihood of causing lung cancer. The probability distribution for the DAG in Figure 1 can be expressed as: P(A,B,C,D,E,F,G,H) = P(A)P(E)P(B│A)P(F│E)P(G│E)P(C│B,F)P(D│C)P(H|C,G).

Figure 1 A typical structure of a Bayesian network. It consists of a directed acyclic graph and the corresponding conditional probability tables. If node C is selected as the target node (yellow node), then the green nodes (B, F, D, H, G) form the Markov blanket of node C, where B and F are parent nodes, D and H are child nodes, and G is a spouse node.

The research on BN s primarily focuses on three aspects: Structure learning, parameter learning, and probabilistic inference. Each of these will be introduced below.

The methodologies of BN structure learning

BN structure learning focuses on constructing a DAG to represent the relationships between variables. This process involves identifying dependency and independence among variables based on data. The learning methods are categorized into DAG-based algorithms, ordering space-based algorithms, and methods for incomplete datasets. Figure 2 illustrates the knowledge context of BN structure learning in a tree-like structure, as well as some representative algorithms.

Figure 2 Classification of algorithms related to Bayesian network structure learning. DAG: Directed acyclic graph; PC: Peter and Clark; ACOG: Ancestral constrained order graph; BDeu: Bayesian Drichlet equivalent uniform; BIC: Bayesian information criterion; MDL: Minimum description length; GS: Greedy search; OBS: Ordering-based search; BiHS: Bidirectional heuristic search; ILP: Integer linear programming; MMHC: Max-Min Hill-Climbing; MMPC: Max-Min Parent and Children; DP: Dynamic programming; AWA*: Anytime Window A* algorithm; MCMC: Markov Chain Monte Carlo; SEM: Structural expectation-maximization.

The methodologies of BN parameter learning

BN parameter learning involves estimating the CPTs that define the relationships between nodes in the network[17]. This process can be categorized into two types: Maximum likelihood estimation (MLE) and Bayesian estimation. MLE is used when the complete data is available, directly calculating probabilities from observed frequencies. Bayesian estimation incorporates prior knowledge into the learning process, making it suitable for handling incomplete or sparse datasets. For incomplete data, the expectation-maximization algorithm is commonly employed to iteratively estimate missing values and refine parameter estimates. Parameter learning is critical for building accurate and reliable BNs, especially in applications like medical diagnosis, where accurate probability estimates directly impact decision-making. Table 1 provides a concise overview of six Bayesian parameter learning algorithms mentioned in the document[18-21].

Table 1 Six Bayesian network parameter learning algorithms.

Algorithms	For incomplete datasets	Basic principle	Advantages & disadvantages	Ref.
Maximum likelihood estimate	No	Estimates parameters by maximizing the likelihood function based on observed data	Fast convergence; no prior knowledge used, leading to slow convergence	[18]
Bayesian method	No	Uses a prior distribution (often Dirichlet) and updates it with observed data to obtain a posterior distribution	Incorporates prior knowledge; computationally intensive	[19]
Expectation-maximization	Yes	Estimates parameters by iteratively applying expectation (E) and maximization (M) steps to handle missing data	Effective with missing data; can converge to local optima	[20]
Robust bayesian estimate	Yes	Estimates parameters using probability intervals to represent the ranges of conditional probabilities without assumptions	Does not require assumptions about missing data; interval width indicates reliability of estimation	[12]
Monte-Carlo method	Yes	Uses random sampling (e.g., Gibbs sampling) to estimate the expectation of the joint probability distribution	Flexible and can handle complex models; computationally expensive and convergence can be slow	[21]

The methodologies of BN inference

Inference is a critical capability of BNs. It involves calculating the probabilities of unobserved variables given the observed evidence, making BNs powerful tools for prediction and decision support. For instance, in cancer diagnosis, if a BN includes nodes for patient symptoms, test results, and possible cancer types, it can estimate the likelihood of each cancer type given observed symptoms and test results. Table 2 summarizes the commonly used algorithms in the field of BN inference[22-25]. The choice of these inference algorithms typically depends on the complexity of the problem, the size of the network, and the availability of computational resources.

Table 2 Some methodologies of Bayesian network inference.

Algorithm	Network type	Complexity	Accuracy	Advantages	Ref.
Variable elimination	Single, multi-connected networks	Exponential in the number of variables in factorization	Exact	Simple, easy to use	[22]
Junction tree	Single, multi-connected networks	Exponential in the size of the largest clique	Exact	Fastest method, suitable for sparse networks	[22]
Differential method	Single, multi-connected networks	Proportional to the complexity of differentiation operations	Exact	Can solve multiple problems simultaneously	[23]
Stochastic sampling	Single, multi-connected networks	Inversely proportional to the probability of evidence variables	Approximate	Simple, widely applicable, and generally effective	[24]
Loopy belief propagation	Single, multi-connected networks	Exponential in the number of loops in the network	Approximate	Performs well when the algorithm converges	[25]

Tools for BN

Several software tools and algorithms facilitate the development and application of BN in medicine. These tools simplify the creation of BNs, making them accessible to researchers without extensive computational expertise, as shown in Table 3[26-32].

Table 3 Some popular Bayesian network software tools.

Tools	Language	Description	Links
Bnlearn[26]	R	Python package for causal discovery by learning the graphical structure of Bayesian networks	http://www.bnlearn.com/
BNT[27]	MATLAB	Bayes net toolbox for Matlab	https://github.com/bayesnet/bnt
GOBNILP	C	Learning Bayesian network structure with integer programming	https://www.cs.york.ac.uk/aig/sw/gobnilp/
Bnstruct	R	Bnstruct is an R package which learns Bayesian networks from data with missing values	https://cran.r-project.org/web/packages/bnstruct
Bmmalone	C++	This project implements a number of algorithms for learning Bayesian network structures using state space search techniques.	https://github.com/bmmalone/urlearning-cpp
Causal-Learner[28]	MATLAB	A toolbox for causal structure and Markov blanket learning	https://github.com/z-dragonl/Causal-Learner
CausalFS[29]	C/C++	An open-source package of causal feature selection and causal (Bayesian network) structure learning	https://github.com/kuiy/CausalFS
Weka[30]	Java	Weka contains a collection of visualization tools and algorithms for data analysis and predictive modeling, together with graphical user interfaces for easy access to these functions	https://git.cms.waikato.ac.nz/weka/weka
Bene	C	An exact Bayesian network structure learning software based on dynamic programming	https://github.com/tomisilander/bene
Causal-learn	Python	Causal discovery in Python. It also includes (conditional) independence tests and score functions	https://github.com/py-why/causal-learn
pyCausalFS	Python	An open-source package of causal feature selection and causal (Bayesian network) structure learning	https://github.com/kuiy/pyCausalFS
CausalExplorer[31]	MATLAB	A MATLAB library of computational causal discovery and variable selection algorithms	https://github.com/mensxmachina/CausalExplorer
Pgmpy	Python	Python library for learning (structure and parameter), inference (probabilistic and causal), and simulations in Bayesian networks	https://github.com/pgmpy/pgmpy
Tetrad	Java	It provides algorithms the capability to discover causal models, search for models of latent structure	https://github.com/cmu-phil/tetrad
Causal discovery toolbox	Python	The causal discovery toolbox is a package for causal inference in graphs	https://github.com/FenTechSolutions/CausalDiscoveryToolbox
DoWhy[32]	Python	DoWhy is a Python library for causal inference that supports explicit modeling and testing of causal assumptions	https://github.com/py-why/dowhy

APPLICATIONS OF BN IN GASTROINTESTINAL CANCERS

BN has been effectively applied to address various challenges in gastrointestinal cancers. Their abilities to integrate diverse datasets, model uncertainty, and uncover causal relationships make them invaluable tools for improving early diagnosis, risk prediction, treatment planning, and prognosis. This section provides a detailed analysis of their applications in specific gastrointestinal cancers, including esophageal, gastric, colorectal, liver, gallbladder, and pancreatic cancers.

Esophageal cancer

Esophageal cancer is a highly aggressive malignancy that is often diagnosed at advanced stages, highlighting the urgent need for effective tools to enable early detection and personalized management[33]. BNs have emerged as valuable tools in addressing these challenges, demonstrating significant potential in various areas of esophageal cancer research and clinical practice.

One notable study developed machine learning models, including BN, to predict the five-year survival of esophageal cancer patients[34]. By identifying key predictors, this approach contributed to personalized treatment strategies and improved clinical outcomes. Similarly, another study utilized BN to synthesize data from 114 studies, creating a personalized risk prediction model for adenocarcinoma in Barrett's esophagus. By integrating critical risk factors, the model achieved high predictive accuracy, paving the way for more tailored surveillance strategies and enhancing early intervention[35]. Additionally, a serum-based biomarker panel for the early detection of esophageal adenocarcinoma was developed using a BN-based rule-learning predictive model. Leveraging proteomics data, this approach demonstrated high accuracy and area under curve (AUC), showcasing its potential for noninvasive disease classification and early diagnosis[36]. The integration of BN models into clinical workflows may enhance early detection and risk stratification in esophageal cancer, potentially allowing for more timely interventions and tailored surveillance in high-risk individuals.

Overall, these studies underscore the versatility and effectiveness of BN in advancing esophageal cancer research. From survival prediction and risk assessment to treatment optimization and biomarker development, BN offers powerful tools to enhance early detection, refine surveillance strategies, and improve patient care outcomes.

Gastric cancer

Gastric cancer remains a leading cause of cancer-related mortality worldwide, with significant variability in incidence and outcomes across populations. The application of BN has demonstrated great utility in risk prediction, diagnosis, prognosis, and treatment planning for gastric cancer. By integrating epidemiological factors, patient clinical data, and molecular profiles, BN models help identify high-risk populations, enabling targeted screening and early detection strategies. For instance, BN models using patient data from the public Surveillance, Epidemiology and End Results database and hospital cohorts identified key predictors such as age, T-stage, tumor size, and tumor location for distant metastasis in early-stage gastric cancer[37]. Similarly, models based on lncRNA expression profiles effectively stratified patients into risk groups and provided robust prognostic predictions with high AUC values[37]. In terms of treatment planning and survival prediction, BN models have been instrumental in handling high-dimensional clinical and molecular data. A two-slice temporal BN improved prediction accuracy for survival outcomes[38], while Bayesian meta-analysis identified nivolumab as the optimal therapy for metastatic gastric cancer without peritoneal metastasis, balancing efficacy and safety[39]. Additionally, Bayesian approaches integrating gene expression data successfully revealed clinically relevant pathways linked to molecular subtypes and immunotherapy response[40,41]. BN applications highlight key prognostic and predictive factors, supporting more accurate metastasis prediction and individualized treatment strategies, which could improve patient outcomes and resource allocation in clinical settings.

Collectively, the studies summarized in Table 4 demonstrate the versatility of BNs in advancing gastric cancer research, from risk prediction and molecular subtype identification to personalized treatment strategies and procedure outcome prediction[42-47]. This integrative approach holds significant promise for improving clinical decision-making and patient outcomes in gastric cancer management.

Table 4 Summary of Bayesian network applications in gastric cancer research.

Data type	Bayesian network algorithm	Key findings	Ref.
Patient data from the public SEER database; patient data from a hospital cohort	Naïve Bayesian model	The Bayesian network model identified key risk factors, including age, T-stage, N-stage, tumor size, grade, and tumor location, contributing to the prediction of distant metastasis in stage T1 gastric cancer	[37]
LncRNA expression profiles from 375 STAD samples in the TCGA database	Bayesian Lasso-logistic regression	The Bayesian-based approach identified seven lncRNAs, effectively stratified STAD patients by risk, and demonstrated robust prognostic prediction accuracy with AUC values above 0.69 for 1-, 3-, and 5-year survival	[37]
Survival and censorship data from 760 gastric cancer patients	A two-slice temporal Bayesian network model	The Bayesian network improved prediction accuracy, reduced bias, and aligned with classical methods while handling high-dimensional data effectively	[38]
Data from seven randomized clinical trials involving 2655 metastatic gastric cancer patients	Bayesian fixed-effect network meta-analysis model	The Bayesian analysis identified nivolumab as the optimal choice for OS in mGC patients without peritoneal metastases, providing the best balance of efficacy and safety	[39]
Gene expression data from TCGA gastric cancer and metastatic gastric cancer immunotherapy clinical trial datasets	Bayesian semi-nonnegative matrix trifactorization method	The Bayesian method identified clinically relevant pathways associated with molecular subtypes and immunotherapy response, enabling patient stratification and prognosis prediction in independent validation datasets	[40]
LncRNA-miRNA-disease association data, including known associations related to gastric cancer	A Naïve Bayesian Classifier was integrated into a CFNBC	CFNBC demonstrated reliable prediction performance (AUC of 0.8576) and successfully identified potential lncRNA-disease associations for gastric cancer in case studies	[42]
Clinical data from 339 gastric cancer patients	BNN	The BNN outperformed the ANN in predicting survival of gastric cancer patients, with higher sensitivity, specificity, prediction accuracy, and AUCs	[43]
Data from 245 gastric endoscopic submucosal dissections	Naïve Bayesian model	The Bayesian model demonstrated good discriminative power in predicting ESD outcomes, with naïve Bayesian models presenting AUCs of approximately 80% in the derivation cohort and at least 74% in cross-validation for both outcomes	[44]
Data from the structural domain characteristics of the p42.3 protein molecule	Bayesian network model	The study identified the most likely acting pathway for p42.3 in gastric cancer as "S100A11" - RAGE - P38 - MAPK - Microtubule-associated protein - spindle protein - centromere protein - cell proliferation" through Bayesian probability optimizing calculation, which was subsequently validated by biological experiments	[45]
Genome-wide gene expression profiles	Categorical Bayesian networks	The BN approach outperformed benchmark methods and successfully identified disease-specific changes in gene regulation that differentiate cancer types, improving prediction	[46]
Gene expression profile data from gastric cancer patients	A Bayesian Network was constructed using 18 genes selected by multiple logistic regression	The constructed Bayesian Network was very similar to the network from GeneMANIA, indicating the effectiveness of the Bayesian approach in modeling the relationships among genes associated with gastric cancer subtypes	[47]

SEER: Surveillance, Epidemiology and End Results; STAD: Stomach adenocarcinoma; AUC: Area under curve; OS: Overall survival; CFNBC: Collaborative filtering model; BNN: Bayesian neural network; ANN: Artificial neural network; ESD: Endoscopic submucosal dissection.

Colorectal cancer

Colorectal cancer (CRC) is one of the most extensively studied gastrointestinal cancers in the context of BNs. The application of BN in CRC research spans over two decades, with early studies illustrating their utility in predicting nodal metastasis through tumor biomarkers[48]. For instance, a Bayesian neural network with automatic relevance determination identified tumor matrilysin as a key predictor of nodal metastasis, providing valuable insights into its potential causal role. This study highlighted the predictive power of Bayesian approaches in analyzing clinical-pathological data[48].

Over the years, BN models have significantly broadened their scope, playing a pivotal role in early detection and risk stratification of CRC[49]. These models integrate diverse data types, including stool-based biomarkers (e.g., gut microbiota profiles), genetic testing, and clinical information, to predict the likelihood of advanced adenomas or CRC during routine screenings. Moreover, BNs have been utilized to incorporate lifestyle factors such as diet, smoking, and physical activity, along with genetic predispositions, enabling the identification of modifiable risk factors and the stratification of individuals into distinct risk categories based on their susceptibility to CRC.

Beyond early detection and risk assessment, BN have become indispensable in the treatment and prognosis of CRC. These models are employed to predict chemotherapy response, recurrence risk, and long-term survival outcomes by integrating tumor-specific genomic, proteomic, and clinical data[50]. For example, Bayesian belief networks and Bayesian additive regression trees have shown superior performance in survival prediction and patient stratification[51,52]. Table 5 provides a comprehensive summary of BN applications in CRC research over the past two decades, showcasing the transformative potential of Bayesian methodologies in advancing personalized medicine and supporting evidence-based clinical decision-making[48,50,52-78]. The use of BN in CRC enables comprehensive risk modeling, integrating modifiable and genetic factors. These tools could guide personalized screening intervals and optimize treatment decisions, improving overall care efficiency.

Table 5 Summary of Bayesian network applications in colorectal cancer research.

Data type	Bayesian network algorithm	Key findings	Ref.
Observational data on CRC, including risk factors such as alcohol consumption, smoking, diabetes, and hypertension	Structure learning algorithms combined with expert knowledge to construct BN model	The BN model effectively segmented populations into risk subgroups and identified modifiable risk factors with significant predictive influence on CRC risk	[53]
Simulation models of CRC progression and natural history, including parameters for risk factors and disease progression	Bayesian calibration using Hamiltonian Monte Carlo-based algorithms integrated with ANN emulators	The Bayesian framework successfully calibrated CRC simulation models, accurately predicting outcomes within confidence intervals, and reduced computational complexity, enabling efficient uncertainty quantification and improved policy analysis for CRC	[54]
Genetic and expression data from 275 normal colon and 276 CRC samples in the SYSCOL cohort	Bayesian network model	BN revealed tumor-specific (transposable elements) TE-eQTLs that influence the expression of cancer driver genes, demonstrating TEs' role in activating oncogenic pathways and providing insights into tumor-specific regulatory mechanisms	[55]
Clinical data of 1253 CRC patients under 50 years of age from the Yonsei Cancer Center, encompassing 93 clinical features	Bayesian network-based synthesizing model	The BN-based model generated a synthetic population of 5005 individuals with no significant statistical differences from the original data. Training predictive models with synthetic data improved performance, especially for small datasets	[56]
Plasma concentrations of heavy metals (As, Cd, Cr, Hg, Pb) and tumor tissue NGS data from CRC patients	BKMR	BKMR analysis revealed that Pb, As, and Cd were significant contributors to increased mutation rates, particularly indels. Mutational signatures showed strong correlations with heavy metal exposure, and shifts in the mutational landscape were observed between high and low exposure groups	[57]
CRC-associated loci from genome-wide association studies (GWAS) and multi-omics datasets	iRIGS, a Bayesian approach	The iRIGS identified 105 high-confidence risk genes, including CEBPB, which promotes CRC cell proliferation through oncogenic pathways such as MAPK, PI3K-Akt, and Ras signaling	[58]
Epidemiological data related to gut microbiome and CRC risk	Multivariate Mendelian randomization analysis based on Bayesian model	Nine bacteria were identified with a robust causal relationship to CRC development, including Streptococcus thermophilus, Bacteroides ovatus, and others	[59]
Clinicopathologic, immune, microbial, and genomic variables from 815 stage II-III CRC patients	BART	The BART risk model identified seven stable survival predictors and successfully stratified patients into low, intermediate, and high-risk groups with statistically significant survival differences	[52]
CRC patients with poorly differentiated and moderately differentiated tumors, analyzed through fecal microbiota	RDP classifier Bayesian algorithm	The study identified distinct GM associated with poorly differentiated CRC, including high abundance of Bifidobacterium and other bacteria	[60]
Colon cancer (microsatellite stable/instable stage III) samples analyzed through multi-omics data (gene expression, DNA methylation, copy number variation)	IntOMICS, an integrative framework based on Bayesian networks	IntOMICS successfully integrated multi-omics data and biological prior knowledge to uncover regulatory networks, revealing deeper insights into genetic information flow and identifying potential predictive biomarkers for stage III colon cancer	[61]
Rectal cancer clinical data from 705 patients who underwent radical resection	Tree-augmented naïve Bayes algorithm	The BN model, incorporating factors like age, CEA, CA19-9, CA125, differentiation status, T stage, N stage, KRAS mutation, and postoperative chemotherapy, showed higher accuracy (AUC = 80.11%) in predicting 3-year OS compared to a nomogram (AUC = 74.23%)	[62]
Time series transcriptomic data from normal and tumor cells of colorectal tissue	DBNs	The DBN-based classifier achieved high classification accuracy, revealing significant differences in gene regulatory networks between normal and tumor cells in CRC, particularly in the neighborhoods of oncogenes and cancer tissue markers	[63]
Gene expression profiles of COAD tumor samples from TCGA and normal colon tissues from GTEx	Bayesian network model	The BN analysis identified 14 upregulated DEGs significantly correlated with tumor stages, and Cox regression highlighted tumor stage, STMN4, and FAM135B dysregulation as independent prognostic factors for COAD survival outcomes	[64]
Clinical data of colon cancer patients, including 18 prognostic biomarkers and three clinical features	Bayesian binary classifiers, including a Bayesian bimodal neural network and a single modal BNN classifier	The Bayesian bimodal neural network achieved the best results in terms of AUC (0.8083), macro F1-score (0.7300), and concordance index (0.7238), demonstrating superior robustness compared to non-Bayesian models and the Bayesian single modal classifier	[65]
Normal mucosa samples from 100 colon cancer patients and 50 healthy donors, including genetic variants, DNA methylation markers, and gene expression data	Bayesian network model	The BN analysis revealed that most combinations showed the canonical pathway where methylation markers cause gene expression variation (60.1%), with 33.9% showing non-causal relationships, and 6% indicating gene expression causes variation in methylation markers	[66]
Genetic data from 55105 CRC cases and 65079 controls, along with an independent cohort of 101987 individuals including 1699 CRC cases	LDpred, a Bayesian approach	The LDpred-derived polygenic risk score showed the highest discriminatory accuracy for CRC risk prediction, identifying 30% of individuals without a family history at similar risk to those with a family history, suggesting the potential for earlier screening	[67]
Fecal microbiome samples from 45 rectal cancer patients before preoperative CCRT	Bayesian network model	The BN analysis identified Duodenibacillus massiliensis as linked with an improved complete response rate after preoperative CCRT, suggesting its potential as a predictive biomarker	[68]
Gene expression data from primary colon cancer and CLM samples	Fast and FFBN	FFBN successfully constructed gene regulatory networks for colon cancer and colon to liver metastasis, revealing unique molecular mechanisms for CLM and shared similarities with primary liver and colon cancers	[69]
Gut microbiota data related to CRC	Bayesian networks combined with IDA (Intervention calculus when the DAG is absent)	Four species-Fusobacterium, Citrobacter, Microbacterium, and Slackia-were identified as having non-null lower bounds of causal effects on CRC, supporting the role of specific microbial communities in CRC progression	[70]
CRC metastasis-related transcription factors (RNA and protein levels)	Bayesian network model	The BN analysis identified LMO7 and ARL8A as potential clinical biomarkers for CRC metastasis	[71]
Gene expression data from 153 colon cancer samples and 19 normal control samples (from TCGA project)	BRPCA	The approach identified 7 molecular subtypes of colon cancer with 44 feature genes, offering a finer classification compared to previous studies	[72]
Protein-protein interaction network data for CRC	Dynamic Bayesian network	The study identified biomarkers with high accuracy and F1-scores, with Alpha-2-HS-glycoprotein identified as a dominant hub gene in CRC	[73]
Gene expression data from LS174T cell lines, normal and adenoma samples, and CRC-related samples	Naive Bayesian network	The BN model demonstrated accurate and reproducible prediction results for normal, adenoma, CRC, and related test samples, with high prediction accuracies	[74]
Gene expression data related to Wnt signaling pathway in human CRC	Static Bayesian network	The biologically inspired Bayesian models, which include epigenetic modifications, improved prediction accuracy for CRC, revealing a significant difference in the activation state of the β-catenin transcription complex between tumorous and normal samples	[75]
Registry data of patients with colon cancer from the Department of Defense Automated Central Tumor Registry	ml-BBNs	The ml-BBNs demonstrated high accuracy in predicting recurrence and mortality in colon cancer, with AUCs ranging from 0.85 to 0.90, and positive predictive values for recurrence and mortality between 78% and 84%; the model identified which high-risk patients benefit from adjuvant therapy, with the largest benefit for elderly patients with high T-stage tumors	[50]
Somatic mutation data from 906 stage II/III CRC from the VICTOR clinical trial	Bayesian network model	The BN analysis revealed significant associations between microsatellite instability, chromosomal instability, and specific mutations (TP53, KRAS, BRAF, PIK3CA, NRAS), and proposed a new molecular classification for CRC with improved prognostic capabilities, particularly for disease-free survival in certain groups	[76]
Population-based data from the SEER registry, including 146248 records of colon cancer patients	ml-BBN	The ml-BBN model accurately estimated OS with an AUC of 0.85, identifying significant prognostic factors such as age, race, tumor histology, and AJCC staging, and demonstrating improved survival predictions compared to existing models	[77]
Clinical data from 53 patients with colon carcinomatosis, including 31 clinical-pathological, treatment-related, and outcome variables	Step-wise ml-BBN	The BBN model identified three predictors of OS: Performance status, Peritoneal Cancer Index, and the ability to undergo CRS +/- HIPEC. The model achieved an AUC of 0.71, with positive and negative predictive values of 63.3% and 68.3%, respectively, and demonstrated strong classification for OS predictions	[51]
Clinical data from 278 CRC patients undergoing SLN mapping	A probabilistic Bayesian network model	The BN model predicted FN SLN mapping with an (AUC of 0.84-0.86, achieving positive and negative predictive values of 83% and 97%, respectively. The number of SLN (< 3) and tumor-replaced nodes independently predicted FN SLN	[78]
Gene expression data from cDNA arrays and clinical-pathological data of 494 CRC patients, focused on nodal metastasis prediction	A Bayesian neural network with automatic relevance determination	Tumor matrilysin was identified as a key predictor of nodal metastasis, with the Bayesian model achieving strong predictive performance, suggesting potential causality between matrilysin expression and nodal metastasis	[48]

CRC: Colorectal cancer; BN: Bayesian network; ANN: Artificial neural network; eQTLs: Expression quantitative trait loci; BKMR: Bayesian kernel machine regression; iRIGS: Integrative risk gene selector; BART: Bayesian additive regression trees; AUC: Area under curve; OS: Overall survival; CEA: Carcinoembryonic antigen; CA19-9: Carbohydrate antigen199; DBNs: Dynamic Bayesian networks; COAD: Colorectal adenocarcinoma; CCRT: Concurrent chemoradiation; CLM: Colon to liver metastasis; FFBN: Furious Bayesian Network; BRPCA: Bayesian robust principal component analysis; ml-BBNs: Machine-learned Bayesian Belief Networks; AJCC: American Joint Committee on Cancer; FN: False negative; SLN: Sentinel lymph node.

Liver cancer

Liver cancer, primarily hepatocellular carcinoma (HCC), presents unique challenges due to its association with underlying liver diseases like hepatitis and cirrhosis. BN has been utilized to model the progression from chronic liver disease to cancer by incorporating clinical, serological, and genetic data, offering insights into various aspects of diagnosis, prognosis, and treatment. By integrating diverse data types such as radiomics features, genetic variations, gene expression profiles, and clinical data, BN can model complex relationships and identify key factors influencing disease progression. For instance, a logistic sparsity-based feature selection model optimized using Bayesian optimization has been shown to significantly improve classification performance for HCC, especially under limited training data conditions[79]. Additionally, BNs are used to predict survival outcomes by incorporating clinical factors such as tumor size, liver function, and recurrence patterns. For example, in HCC patients after hepatectomy, a tree-augmented naïve Bayes algorithm identified portal vein tumor thrombosis as the most significant predictor of survival time, highlighting the model's potential in clinical decision-making[80]. These models also enable the discovery of significant biomarkers for early diagnosis, such as the identification of gene polymorphisms and miRNA-mRNA pairs that play crucial roles in HCC susceptibility and progression[81,82]. In diagnostic settings, BNs have been utilized to classify regions of the liver as malignant or benign based on functional computed tomography (CT) perfusion data, aiding in the differentiation of cancerous tissues from healthy ones[83]. BN models that incorporate imaging, clinical, and genomic data may support earlier diagnosis and personalized prognostic evaluations in HCC, aiding in treatment planning and surveillance for patients with chronic liver disease.

A summary of BN applications in liver cancer research is provided in Table 6[79-89], which highlights the versatility of BN in handling diverse data sources, from radiomics and genetic data to clinical records and functional imaging, underscoring their potential to improve diagnosis, prognosis, and treatment strategies in liver cancer. Overall, BNs offer a comprehensive framework for integrating and analyzing heterogeneous data in liver cancer research, facilitating more accurate predictions and personalized treatment strategies.

Table 6 Summary of Bayesian network applications in liver cancer research.

Data type	Bayesian network algorithm	Key findings	Ref.
Radiomics features	A logistic sparsity-based feature selection model optimized using Bayesian optimization	The Bayesian optimization-based feature selection model significantly improved classification performance for HCC and other focal liver lesions, especially under limited training data conditions	[79]
Simulated concentration time curves for DCE-MRI and in vivo patient data with hepatic tumor lesions	BNN	The BNN provided more accurate parameter estimates compared to NLLS fitting and effectively identified uncertainties, particularly under high noise levels and out-of-distribution data, improving robustness for clinical applications	[84]
Genetic variation data from 33 meta-analytic studies on 45 polymorphisms across 35 genes related to HCC	BFDP	Fourteen gene polymorphisms, including CCND1, CTLA4, EGF, IL6, IL12A, KIF1B, MDM2, MICA, miR-499, MTHFR, PNPLA3, STAT4, TM6SF2, and XPD genes, were identified as significant biomarkers for HCC susceptibility	[81]
Gene expression profiles of liver tissue samples from two microarray platforms analyzed for HCC	An empirical Bayesian method	Three genes were identified as specific biomarkers for HCC diagnosis, achieving an AUC of 0.931	[85]
Single-cell multiomics data, including RNA-seq, Reduced Representation Bisulfite Sequencing, and copy number variation estimates	Bayesian network models	Best-fitted BN models identified 295 genes and provided novel insights into the mechanistic relationships of human lymphocyte antigen class I genes in HCC	[86]
miRNA and mRNA expression data from 39 HCC patients and 25 liver cirrhosis patients	A flexible Bayesian two-step integrative method	The study identified 66 significant miRNA-mRNA pairs, including molecules previously recognized as potential biomarkers in liver cancer	[82]
Multi-omics data, including genome (mutation and copy number), transcriptome, proteome, and phosphoproteome from HCC samples	A Bayesian network mixture model	The study identified three main HCC subtypes with distinct molecular characteristics, some associated with survival independent of clinical stage. Cluster-specific networks revealed connections between genotypes and molecular phenotypes	[87]
Electronic medical records from 10060 primary liver cancer patients, including TCM symptoms, signs, tongue diagnosis, and pulse diagnosis information	Bayesian network model	The Bayesian network model achieved a classification accuracy of 85.84% for syndrome diagnosis in primary liver cancer, demonstrating its effectiveness in mining nonlinear relationships in clinical data and providing reliable support for TCM-based syndrome differentiation and treatment in liver cancer	[88]
Clinical data of HCC patients, including recurrence outcomes (early, late, or no recurrence)	Bayesian network-based model	The Bayesian network model effectively distinguished between early, late, and no recurrence, significantly outperforming benchmark techniques in accuracy, precision, recall, and F-measures. It addressed the challenge of insufficient early-stage information by integrating latent variables, offering robust and reliable predictions validated across datasets, with potential implications for improving HCC recurrence management in clinical practice	[89]
Dataset of 299 HCC patients after hepatectomy, including factors like preoperative AFP level, liver function grade, tumor size, and postoperative treatment	Tree-augmented naïve Bayes algorithm	The Bayesian network model identified PVTT as the most significant predictor of survival time for HCC patients after hepatectomy. The model also highlighted the preoperative AFP level and postoperative performance of TACE as independent survival factors	[80]
Functional CT perfusion data of hepatic regions, including measurements from malignant and benign liver tissues, acquired over 590 seconds using repeated scans	A Bayesian semiparametric model	The model facilitated the clustering of liver regions based on their CT profiles, which can be used to predict and classify regions as malignant or benign, aiding in the discrimination of cancerous tissue from healthy tissue in diagnostic settings	[83]

HCC: Hepatocellular carcinoma; DCE-MRI: Dynamic contrast-enhanced magnetic resonance imaging; BNN: Bayesian neural network; NLLS: Nonlinear least squares; BFDP: Bayesian False Discovery Probability; AUC: Area under curve; BN: Bayesian network; TCM: Traditional Chinese medicine; PVTT: Portal vein tumor thrombosis; TACE: Transcatheter arterial chemoembolization; AFP: Alpha-fetoprotein; CT: Computed tomography.

Gallbladder cancer

Gallbladder cancer, although rare, is an aggressive malignancy that is often diagnosed incidentally during procedures for gallstone disease. Early detection and accurate prognosis prediction remain critical for improving outcomes. Recent studies have demonstrated the BN applications in enhancing diagnostic precision, survival predictions, and decision-making support for gallbladder cancer management.

For early detection, BN models have been particularly instrumental in identifying neoplastic gallbladder polyps. Using preoperative ultrasound features, these models accurately identified polyps larger than 10 mm with neoplastic potential, surpassing current clinical guidelines with an accuracy of over 81% in both training and testing sets[15,90]. Such findings provide refined surgical criteria, aiding clinicians in determining the necessity of surgical interventions.

For prognosis prediction, BN models have been developed to identify key survival factors and support treatment decisions. One study utilizing clinical data from 362 patients with gallbladder adenocarcinoma employed a tree-augmented naïve Bayesian algorithm to classify survival outcomes. The results emphasized that R0 resection significantly improves survival, even in advanced stages such as T4 and N2, suggesting that surgery remains a viable option for these patients[91]. Similarly, another study using data from 366 patients constructed a BN model with BayesiaLab software, identifying surgical type and tumor-node-metastasis stages as the most significant prognostic factors for gallbladder cancer[92].

Furthermore, BN models have been applied to optimize lymph node (LN) assessment in gallbladder adenocarcinoma. A study analyzing data from 1268 patients revealed that harvesting a minimum of seven LNs, with an optimal range of 7 to 10, maximized survival outcomes for patients undergoing curative resection[93]. This finding underscores the importance of adequate lymphadenectomy in surgical management.

To further enhance survival prediction, BN models have outperformed traditional methods such as nomograms. By integrating imaging findings, such as gallbladder wall thickening, with patient risk factors like age, gender, and gallstone history, BN models have demonstrated superior accuracy in differentiating benign from malignant conditions and predicting survival following curative-intent resections[94]. In addition, BN-based survival models have provided decision support for advanced gallbladder carcinoma, showing that adjuvant chemoradiotherapy may significantly improve survival in node-positive patients[95]. BN-based predictions support surgical decision-making and prognosis estimation, offering clinicians a more objective basis for managing complex cases and potentially expanding curative treatment options for advanced-stage patients.

In summary, BNs have shown significant promise in the management of gallbladder cancer, offering robust tools for early detection, prognosis prediction, and treatment optimization. Their ability to integrate diverse clinical, imaging, and surgical data allows for improved accuracy over traditional methods, ultimately guiding clinicians in delivering personalized and timely interventions for better patient outcomes.

Cholangiocarcinoma

BN models have emerged as valuable tools for prognostic and predictive modeling in cholangiocarcinoma, offering insights into complex clinical decision-making scenarios. A study utilizing clinical data from 531 patients with intrahepatic cholangiocarcinoma (ICC) developed and validated a BN prediction model for microvascular invasion (MVI). The model, constructed using five preoperative risk factors-obstructive jaundice, prognostic nutritional index, carbohydrate antigen 19-9 (CA19-9), tumor size, and major vascular invasion-achieved AUC values of 78.92% and 83.01% in the training and testing sets, respectively, demonstrating its effectiveness in preoperative MVI prediction[96]. Similarly, another study leveraged clinical and pathological data from 516 ICC patients to construct BN models for predicting 1-year survival after curative resection. The naïve Bayesian model, based on seven independent prognostic factors, demonstrated the highest predictive performance with an AUC of 79.5%, outperforming nomogram-based models in survival prognostication[97]. These findings underscore the potential of BN models in enhancing personalized care and improving predictive accuracy in cholangiocarcinoma management. BN models help predict key outcomes like MVI and survival, offering noninvasive, data-driven tools to inform surgical planning and postoperative care, thus enhancing precision in clinical decision-making.

Pancreatic cancer

Pancreatic cancer is one of the deadliest malignancies, often diagnosed at advanced stages due to the lack of early symptoms. To address this challenge, multiple studies have employed BNs to improve diagnostic, prognostic, and treatment strategies for pancreatic cancer.

Using DNA methylation and transcriptome data from the TCGA database, researchers identified 14 specifically methylated genes that served as the foundation for a BN-based prognostic prediction model in pancreatic adenocarcinoma. This model achieved an impressive predictive performance (AUC = 0.937), showcasing its potential to refine subtype classification and guide personalized treatment strategies[98]. Similarly, a study using small RNA sequencing data from blood small extracellular vesicle miRNAs applied a BN model to analyze causal relationships. This revealed miR-95-3p as linked to pancreatic ductal adenocarcinoma (PDAC) and miR-26b-5p to chronic pancreatitis (CP), providing valuable insights into miRNA-mediated disease mechanisms and aiding differentiation between PDAC and CP[99].

In the realm of survival analysis, researchers developed a BN model using clinical data to predict survival outcomes for potentially resectable pancreatic cancer. The model achieved AUCs of 0.7 for pre-operative predictions and 0.8 for post-operative updates, offering clinicians valuable tools for tailored patient management[100]. Furthermore, another study utilized delta radiomic features (DRFs) extracted from longitudinal non-contrast CT images of pancreatic cancer patients to predict treatment response. A Bayesian-regularization-neural-network model achieved a cross-validated AUC of 0.94, demonstrating the utility of DRFs in early response prediction[101].

To enhance diagnostic accuracy, several BN-based models have been developed. A Bayesian combination model integrating a random forest classifier and a convolutional neural network used CT image data and demographic information to classify four common types of pancreatic cysts, achieving a classification accuracy of 83.6%[102]. Similarly, an automated differential diagnosis system for pancreatic cystic tumors utilized digital pathology data, distinguishing between benign serous cystadenoma and potentially malignant mucinous cystadenoma. Among the classifiers tested, the Bayesian model demonstrated superior performance based on morphological features, emphasizing its diagnostic value[103].

Innovative approaches have also integrated external knowledge into BN frameworks. A study combined PubMed knowledge with Electronic Health Records (EHR) to develop a weighted Bayesian Network Inference (BNI) model for pancreatic cancer prediction. By incorporating risk factor weights derived from PubMed abstracts, the weighted BNI model demonstrated superior accuracy compared to conventional BNI and other classifiers, underscoring its potential for clinical applications[104]. Another study applied a BN model to hospital admission data, including type of admission, procedure, primary diagnosis, and Charlson co-morbidity index, to predict the probability of in-hospital death. This analysis highlighted the role of co-morbidities and admission details in influencing survival outcomes, showcasing the BN model’s ability to evaluate multiple hypotheses and measure variable impact[105]. These models may facilitate early intervention and guide therapy selection in high-risk pancreatic cancer patients.

Collectively, these studies illustrate the versatility and potential of BN in improving the diagnosis, prognosis, and treatment of pancreatic cancer. By integrating diverse data types and leveraging advanced algorithms, BN-based approaches are paving the way for more precise and personalized healthcare solutions in pancreatic cancer management.

Other related studies

BN applications in other (or rare) gastrointestinal cancer research: A recent study applied BN methodology to develop a computational tool, PROMETheus, for preoperative risk stratification in gastrointestinal stromal tumors (GISTs). Using clinicopathological data from 160 real-world GIST cases, the BN model integrated key parameters such as tumor size, location, biopsy-derived mitotic count, and tumor response to therapy. The model exhibited excellent diagnostic performance, with posterior predictive checks confirming its accuracy. PROMETheus, an intuitive tool based on this BN model, provides dynamic predictions of mitotic count and risk assessment, enhancing preoperative decision-making for GIST patients and offering a foundation for personalized therapeutic strategies[106]. Moreover, study on malignant peritoneal mesothelioma, a rare gastrointestinal cancer, utilized clinicopathological data from 154 patients treated with cytoreductive surgery and hyperthermic intraperitoneal chemotherapy to establish a BN model. The model incorporated ten prognostic factors identified through survival analysis, with its structure refined based on clinical expertise and previous research. Demonstrating an accuracy of 72.7% and an AUC of 0.74, the BN model showed strong potential as a clinical decision support tool for predicting patient survival[107]. Similarly, another study on pseudomyxoma peritonei leveraged clinicopathological data from 453 patients undergoing similar treatments to establish a BN model. Incorporating seven independent prognostic factors, including gender, previous operation history, histological grading, lymphatic metastasis, peritoneal cancer index, completeness of cytoreduction, and splenectomy. Internal validation demonstrated the BN model's predictive accuracy of 70.3% and an AUC of 73.5%[108]. These findings underscore the versatility and efficacy of BN approaches in addressing the complexities of diverse gastrointestinal cancers.

BN applications in multi-cancer research for gastrointestinal cancers: BN models have been applied in multi-cancer research to uncover critical insights into gastrointestinal cancers. In liver and pancreatic cancers, BN models were used to integrate dose volume histograms and clinical factors, such as tumor location, patient age, and planning target volume size. This approach achieved an AUC of 83.56% and identified tumor location as the most critical factor in selecting between radiotherapy plans using TrueBeam or MRIdian[109]. In another study focusing on gastric and CRCs analyzed within a pan-cancer series, BN were employed to examine gene expression data and survival outcomes. The analysis highlighted key prognostic markers, such as TYMS and RGS1, and revealed gene interactions related to cell cycle, apoptosis, and metabolism[110]. These findings provided valuable insights into survival prediction and the molecular mechanisms underlying gastrointestinal cancers, showcasing the significant utility of BNs in multi-cancer research.

CHALLENGES IN BN APPLICATIONS

BN holds considerable promise in advancing gastrointestinal cancer research and clinical practice, yet their implementation faces several significant challenges. These challenges span issues related to data, computational methodologies, and clinical translation. A detailed analysis is presented below, incorporating both general challenges and those specific to gastrointestinal cancers.

Data-related challenges

Data-related challenges are prominent in cancer studies, particularly in gastrointestinal cancers which heterogeneity and missing data complicate model construction. For esophageal and gastric cancers, early-stage data are scarce due to late diagnoses, hindering the development of reliable early detection models[111]. Multi-omics integration. CRC, while benefiting from large-scale data from screening programs, faces challenges in generalization due to population variations like genetic diversity and dietary differences. Liver cancer is further complicated by associated comorbidities such as hepatitis and cirrhosis, which introduce additional variability. The rarity of gallbladder and pancreatic cancers limits the availability of high-quality datasets, increasing the risk of overfitting in models. Additionally, imbalanced data representation, where advanced-stage cases dominate, skew predictions and hinder early detection efforts, particularly for pancreatic and liver cancers. Integrating data from multiple centers also presents difficulties due to differences in data collection protocols and standards. Expanding early screening programs, creating dedicated biobanks, and leveraging natural language processing to extract structured data from electronic medical records can help enrich early-stage datasets. Standardizing data collection, promoting data sharing, and employing techniques like transfer learning and synthetic data generation can effectively address data scarcity, heterogeneity, and imbalance.

Computational and methodological challenges

BN faces significant computational and methodological challenges, particularly in handling large, complex datasets. Multi-omics integration in cancers like colorectal and gastric cancers, which generate high-dimensional data, requires substantial computational resources for training BN[87,112]. Furthermore, dynamic models used for cancers like liver cancer, which track progression or treatment response over time, are computationally intensive. Rare cancers like gallbladder and pancreatic cancers face the risk of overfitting due to limited data, as smaller datasets may fail to capture essential relationships. Balancing model complexity is crucial-simpler models may not capture necessary nuances, while more complex models risk overfitting[113]. Techniques like cross-validation and Bayesian regularization can help, but they may not fully address the limitations posed by small datasets. Dimensionality reduction, regularization, and scalable computing frameworks help manage high-dimensional data and prevent overfitting in complex or rare cancer models.

Clinical translation challenges

The clinical translation of BN faces challenges related to interpretability and acceptance among clinicians. While BN has an intuitive structure, their outputs, such as probabilistic risk scores or survival probabilities, may not align with traditional clinical decision-making, especially in cancers like esophageal and pancreatic cancer[114]. Clinicians often prefer simple, actionable outputs, and models lacking clear visualization or an understandable explanation may face resistance. Validation for real-world implementation is also crucial but challenging. Regional differences in patient characteristics and risk factors complicate external validation in cancers like esophageal and gastric cancer. Liver cancer’s dynamic models require longitudinal datasets, which are resource-intensive to obtain. For rare cancers, such as gallbladder and pancreatic cancers, the limited availability of validation cohorts reduces confidence in the robustness of the models. Enhancing model interpretability, aligning outputs with clinical workflows, and validating across diverse populations are key to improving clinical acceptance and real-world utility.

FUTURE DIRECTIONS

Addressing the challenges in applying BN to gastrointestinal cancers requires a forward-looking approach. Future advancements span algorithmic innovations, technological integration, personalized medicine, and collaborative efforts.

Advances in BN algorithms

BN-based methodologies are evolving to accommodate the complexities of cancer research. Dynamic BN is promising for modeling disease progression and treatment response over time[115]. For example, these models could track biomarker changes in liver or pancreatic cancer, providing real-time insights into disease dynamics. Additionally, developing scalable algorithms optimized for high-dimensional data is critical for reducing computational burdens, allowing for faster training and real-time inference. This is especially important for cancers with large multi-omics datasets, such as colorectal and gastric cancer. Developing scalable algorithms optimized for high-dimensional datasets will enable faster training and real-time inference, crucial for integrating extensive genomic, transcriptomic, and epigenetic data from cancers such as gastric and CRC.

Integration with emerging technologies

Emerging technologies are significantly enhancing the utility and scope of BN in cancer research. The integration of multi-omics data, including genomic, proteomic, and metabolomic information, offers a more comprehensive understanding of cancer biology[64], particularly for complex cancers like pancreatic and liver cancer. Moreover, artificial intelligence (AI) has emerged as techniques, such as deep learning, complement BN by identifying latent patterns and improving feature selection. For example, AI-powered preprocessing can refine inputs for Bayesian models in esophageal and gastric cancer studies. Furthermore, BN can be combined with data from wearable devices (e.g., continuous glucose monitors, activity trackers) and EHRs using real-time data fusion approaches to enable continuous risk monitoring and early alert systems in outpatient settings.

Personalized medicine and precision oncology

BN are well-suited to advancing personalized medicine and precision oncology. By incorporating individual patient data, these networks can identify the most effective treatment pathways, such as recommending targeted therapies for colorectal or gastric cancer patients based on their genetic profiles. Furthermore, dynamic Bayesian models can monitor treatment responses over time, enabling timely adjustments to therapeutic strategies. This capability is particularly valuable for cancers with aggressive progression, such as pancreatic cancer, where rapid adaptation of treatment plans can significantly impact patient outcomes. By advancing algorithmic capabilities, integrating with emerging technologies, and fostering collaborative ecosystems, BN can transform the diagnosis, treatment, and management of gastrointestinal cancers. These future directions provide a roadmap for overcoming current limitations and realizing the full potential of this promising technology.

CONCLUSION

BNs are powerful tools in gastrointestinal cancer research, excelling in integrating diverse data, identifying causal relationships, and managing uncertainty. They have shown significant potential in risk prediction, early diagnosis, treatment optimization, and outcome forecasting. However, challenges remain, such as data scarcity, particularly in early detection, computational complexity as network size increases, and barriers to clinical implementation. To address these challenges, future efforts should focus on advancing algorithms to handle dynamic and temporal data, integrating BNs with multi-omics and AI approaches, and promoting collaborative data sharing to improve data availability. Developing user-friendly tools and aligning BN models with clinical workflows will further support their real-world adoption. As precision oncology continues to evolve, BNs hold great promise in enabling personalized treatment strategies and dynamic monitoring of therapeutic responses, ultimately transforming gastrointestinal cancer care and advancing personalized medicine to improve patient outcomes.