Rectal cancer is the eighth most common malignancy worldwide with a high mortality rate, resulting in about 340,000 deaths every year (1), and has become one of the major public health problems threatening human health. Despite the involvement of chemoradiotherapy and immunotherapy, the prognosis of rectal cancer has not improved significantly, and radical resection is still the primary treatment for rectal cancer at present (2). Prediction of the prognosis of rectal cancer is very important to the management of patients. The greatest significance of a more accurate prediction of survival is that it can effectively avoid excessive treatment and waste of medical resources, and at the same time provide a scientific basis for medical staff and patients to make medical decisions, such as whether to accept postoperative chemotherapy. In addition, it helps patients plan for the rest of their life and makes the best use of time to achieve some aspirations and make life more fulfilling. A series of methods based on clinical data have been applied to the analysis of prognostic factors for patients with rectal cancer. However, these studies only evaluate the separate impacts of individual parameters, such as age, surgical type, and body mass index (BMI) (3–5). In recent years, some prognostic studies based on multivariate survival analysis have become popular. Fan et al. screened out 8 independent prognostic clinicopathological factors (age, sex, preoperative CEA, perineural invasion, tumor deposits, tumor grade, T stage, and N stage) for non-metastatic rectal cancer, and constructed a prognostic prediction nomogram with the concordance index (C-index) of 0.71 (6). Liu et al. screened out 5 independent prognostic pathological factors (yp T stage, yp N stage, tumor location, differentiation status, and postoperative chemotherapy) and constructed a nomogram with a C-index of 0.72 through multivariate analysis of the prognosis of patients with rectal cancer who received neoadjuvant therapy (7). Nevertheless, these studies ignored the cause-and-effect relationships between these prognostic factors. The interaction between these factors and their mutual influences is not yet clear, so an effective modeling method is needed to analyze and represent the relationships among these factors.

A Bayesian network (BN) is a directed acyclic graph used to represent the causal relationship between random events and is a tool to apply probability and statistics to data analysis and inference in complex systems (8), and has become a popular method of machine learning. Based on Bayes' theorem, BN can effectively perform most data mining tasks, such as prediction, attribution, and classification (9), and has been applied in prognostic prediction, treatment decision-making, and other fields. For instance, Bradley et al. constructed a BN model for prognostic prediction of patients with pancreatic ductal adenocarcinoma using inflammatory markers, tumor factors, tumor markers, patient factors, response to neoadjuvant treatment, tumor pathology, and postoperative chemoradiotherapy, and its area under the curve (AUC) reached 80% (10). Nandra et al. constructed a 1-year survival prediction BN model of patients with bone sarcoma based on five variables (age, tumor size, tumor grade, metastasis, and pathologic fracture) with an AUC of 76.7%, and the conditional relationship among these variables was also found (11). Cong L et al. confirmed that patients with advanced gallbladder adenocarcinoma can obtain a better prognosis by R0 resection through the BN model, which would be helpful for clinical decision-making of gallbladder adenocarcinoma treatment (12). However, up to date, BN has not been used to predict the prognosis of rectal cancer.

Given this situation, the present study aimed to explore the prognostic factors based on the clinical parameters of rectal cancer patients, construct a prognostic prediction model using BN, and compare the prediction efficacy of BN with a nomogram.

Rectal cancer is one of the most concerned cancer types in the world with high morbidity and mortality (1). Surgical resection remains the primary treatment for rectal cancer (15). The establishment of a prognostic prediction model for postoperative patients will help medical workers and patients to evaluate the prognostic status and to make decisions on examination and treatment programs. A nomogram has been widely used for cancer prediction, which plays a role in personalized prediction for patients with rectal cancer (6, 7). However, it ignores the interaction of prognostic factors and their joint effect on cancer prognosis. Thus, a new modeling method is required to compensate for this deficiency. With the rapid development of machine learning algorithms, researchers propose that they can be used to supplement traditional statistical methods in the field of medical research. The BN model is a common and effective method in the field of machine learning, which can mine unknown information from observed data, and plays an important role in clinical decision-making, prognostic research, and other fields (12, 16). However, BN has not been used to predict the prognosis of rectal cancer so far. In this study, we constructed a BN model for prognostic prediction of rectal cancer based on the clinicopathological characteristics of patients using the Bayesian network for the first time and demonstrated that the BN model performed better than the nomogram.

In recent years, there have been some studies focusing on the prognosis prediction of patients with rectal cancer. Zhao et al. established a nomogram for the prognosis prediction of metastatic rectal cancer by using the patients' data from the U.S. National Cancer Database (17). Song et al. studied the prognostic factors of patients with locally advanced rectal cancer receiving neoadjuvant chemoradiotherapy and established a nomogram for prognostic prediction (18). In addition, another study explored the prognostic predictive role of pathologic features in locally advanced rectal cancer using a nomogram (7). Liu et al. established a prognostic prediction nomogram for middle-aged and older patients with rectal cancer using data from Surveillance, Epidemiology, and End Results database (19). So far, the prognostic prediction models for patients with rectal cancer were almost based on nomograms, which neglected the relationships among prognostic factors and their mutual influences.

Nowadays, using machine learning tools, such as BN, to build prognostic prediction models is becoming more and more widespread (10, 13, 20). Based on the combination of graph theory and probability theory, BN can reduce the complexity of reasoning (21). It is noteworthy that the BN model has been used to predict the prognosis of some kinds of malignant tumors, such as gallbladder cancer (9), pancreatic ductal adenocarcinoma (10), lung cancer (16), and bone sarcomas (11). So far as we know, although Fielding et al. have used Bayesian theory to predict the prognosis of patients with colon cancer (22), BN has not been used to predict the prognosis of patients with rectal cancer. The BN model could not only predict the prognosis but also identify the correlation between prognostic factors. The connection arrow between variables in the BN model represents the conditional probability from the parent node to the child node, which means, given the state of the parent node, the probability of certain events occurring in the child node would be affected (23). In this study, our BN model found the following conditional dependencies between variables: the state of the T stage would affect the probability of tumor size and macropathology type. Similarly, the state of vascular invasion would affect the probability of preoperative serum CA19-9, N stage, and differentiation status. These influences between variables form a joint probability distribution and make it possible to use the BN model to predict the personalized prognosis even if a few variables are missing, although the efficacy of prediction may be reduced (24). Such findings would also provide a reference direction for further study of the underlying pathological or pathophysiological mechanisms of the associations between variables. These capabilities are what nomograms do not have.

From the perspective of variable types, a nomogram is based on independent prognostic factors, while BN does not require independent variables, but integrates the association and joint effect of prognostic variables. These differences might make the prediction power and accuracy of the BN model better than that of the nomogram. In addition, Wu et al. found that the BN model performed better than the nomogram in prognosis prediction of gallbladder cancer (9), which was similar to our findings. To construct the BN model, continuous variables need to be converted into categorical variables, while the independent variables of the nomogram can be continuous, which makes the data processing more complicated before the BN model construction. In general, BN is easier to operate than the nomogram and more convenient for clinicians because it eliminates the process of analyzing independent prognostic factors and only requires BayesiaLab software.

During the follow-up, all patients were followed for more than 36 months except those who died within 36 months. This allows the study to predict whether patients will survive beyond 36 months after resection of rectal cancer with a sufficient follow-up period. Since the BN model can only predict categorical variables, patients' survival time needs to be dichotomized. To predict the probability of survival over 1-, 3-, or 5-year, it would be necessary to dichotomize the survival time of patients correspondingly and construct the corresponding BN prediction models accordingly (25), while a nomogram would only need to construct a model for one time to predict the survival probability of patients with different survival periods, which is a disadvantage of BN over nomogram. Since BN can only analyze survival time but not survival status in the process of modeling, premature loss to follow-up may affect machine learning, which is also a disadvantage compared with the nomogram and may affect the prediction efficiency of the model.

There are some limitations to the present study. First, this study was a single-center retrospective study. Second, although the follow-up time of patients in our study was up to 74 months, most patients were followed up for <5 years, thus it would not be possible to construct a prognostic model of 5-year OS. Third, some risk factors reported in other studies that may affect the prognosis of rectal cancer, such as perineural invasion (26), microsatellite stability status (27), and other gene mutation status (28, 29), were not included in this study due to lack of relevant testing or data availability. In the future, we may carry out multi-center studies with more cases, longer follow-ups, and more parameters, to construct a more accurate BN model for prognostic prediction of patients with rectal cancer.

In conclusion, this study analyzed clinicopathological factors influencing the prognosis of patients with rectal cancer after radical resection, constructed a 3-year OS prediction BN model for the first time, and investigated the underlying cause-and-effect relationships among variables. We also demonstrated that the BN model performed better than the nomogram. The BN model constructed in this study can be used for a personalized evaluation of the prognosis of patients with rectal cancer and provide clinicians with an accurate prognostic evaluation tool.

The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.

The studies involving human participants were reviewed and approved by the Medical Ethics Committee of Xijing Hospital. Xijing hospital, Fourth Military Medical University, Xi'an, China. The patients/participants provided their written informed consent to participate in this study.

RL, FF, and JZ designed the study. RD, GZ, HW, GR, and XD collected the data. RL, CZ, KD, HD, and ZX analyzed the data. RL, CZ, ZC, and LD visualized the data. RL drafted the manuscript. FF and JZ revised the manuscript. All authors have read and approved the final manuscript. All authors contributed to the article and approved the submitted version.

This study was supported by the National Natural Science Foundation of China (Grant No. 82072655).

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

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