The patients who underwent valvular surgery were identified from the Chinese Cardiac Surgery Registry (CCSR) database from January 2016 to December 2018. The CCSR database prospectively collected in-hospital and 30-day outcomes data on valvular surgery patients from 94 hospitals nationwide [18]. Patients were included in the study if they underwent valvular surgery procedures or valve surgery combined with coronary artery bypass graft surgery (CABG). Patients with missing information on perioperative complications and those who have not undergone cardiopulmonary bypass (CPB) were excluded from this study.

We selected 12 perioperative complications, prolonged intensive care unit (ICU) stays (defined as exceeding the 75th percentile for ICU length of stay [19]), prolonged mechanical ventilation (defined as more than 24 h by the Society of Thoracic Surgeons [STS] guidelines [20]), increased chest tube drainage (defined as exceeding the 75th percentile for chest tube drainage), postoperative AF, postoperative myocardial infarction (postoperative myocardial infarction [MI], defined as new-onset pathologic Q-wave or left bundle branch block on the 12-lead electrocardiogram [21]), sternal wound infections, pericardial tamponade, reoperation, secondary tracheal intubation, stroke (defined as an acute episode of focal or global neurologic dysfunction caused by brain, spinal cord, or retinal vascular injury as a result of hemorrhage or infarction in which the neurologic dysfunction lasts for more than 24 h), postoperative renal failure (RF), multiple organ dysfunction syndrome (MODS). Among the 12 outcomes, 6 outcomes were found in the Society of Thoracic Surgeons database, including prolonged mechanical ventilation, postoperative AF, sternal wound infections, reoperation, stroke, postoperative RF [22]. In addition, prolonged ICU stays, increased chest tube drainage, postoperative MI, and pericardial tamponade have been demonstrated to be associated with increased perioperative morbidity and mortality after cardiac surgery [23-26]. Secondary tracheal intubation is a common but critical issue in the management of patients requiring mechanical ventilation in the ICU [27], which may further worsen the overall prognosis of patients. MODS is also the major cause of mortality after heart valve surgery [28]. Therefore, the types of complications we included are representative and reasonable. Death was defined as death occurring during the hospitalization and after discharge from the hospital but before the end of the 30th postoperative day.

We calculated the proportion of common complications of valvular surgery. The number of deaths and the mortality rate for patients with each complication were also calculated to reflect the severity of different complications. The rate of co-occurring complications was defined as the percentage of patients that developed each complication and who also had other complications. The phi coefficient (phi) quantified the degree of concordance between any two complications. We used the rate of co-occurring complications and the phi to identify the co-occurrence relationships between complications. In addition, we compared the perioperative characteristics between patients with and without perioperative complications using the χ² test. R software (version 4.2.3; R Foundation for Statistical Computing) was used for statistical analyses.

To investigate further interactions among perioperative complications, we applied a Bayesian network to patients with at least one complication. A Bayesian network is a graphical representation of a joint probability distribution. Learning a Bayesian network implies two tasks: (1) structure learning: identifying the topology of the Bayesian network and (2) parametric learning: estimating numerical parameters (conditional probabilities) given a network topology [29].

During the structure learning stage, we constructed a directed acyclic graph (DAG) to describe the dependencies between these nodes. The nodes from which an arrow pointed were referred to as the “parent” nodes and the nodes pointed to by an arrow were referred to as “child” nodes. The state of the “parent” nodes affects their “child” nodes [30]. Taking into account the forbidden directions of the arcs (from death to other complications), we adopted the hill-climbing algorithm based on a score search to create a Bayesian network [31]. In addition, we used bootstrap resampling (1000 replicates, each with a resultant candidate network structure) to obtain a stable network structure. The arcs with strength probability >0.75 and direction probabilities ≥0.5 were considered finally.

Parameter values were obtained by using the maximum likelihood algorithm in the parameter learning phase [32]. The parameters are used to describe the probability distribution for each node, based on which we calculated the probability of a complication predicted using the Bayesian network. When one or more complications occurred, the probability of the occurrence of any complication was predicted, which we used to quantify the association between complications.

All analyses were performed using R software, including the UpSet, bnlearn, and gRain packages.

The CCSR database was generated in 2013, including 87 large cardiac centers across the country with routine data submission, strict data audits, and instant feedback. These sites are the leading cardiac centers in local regions and have many features that are common among large cardiac care centers in China. The study was conducted in accordance with the Declaration of Helsinki and approved by the Institutional Review Board of Fuwai Hospital (protocol code 2021‐1477; date of approval is August 11, 2021). Informed consent was obtained from all subjects involved in the study. Data were collected and analyzed using a pseudonymous form. The participants did not receive any form of financial compensation for participating in this trial.

Based on inclusion and exclusion criteria, 37,285 patients were included in the analysis. Table 1 shows that we compared the perioperative characteristics of patients with at least one complication with those without. Nearly all assessed perioperative characteristics showed significant differences between groups (P<.05). Compared with patients who did not develop perioperative complications, patients with at least one complication were more likely to be male and aged 65 years and older (2724/18,700, 14.6% vs 4686/18,585, 25.2%), have more comorbidities, and have longer CPB time (7539/18,700, 40.3% vs 11,102/18,585, 59.7%) and aortic cross-clamp (ACC) time (7701/18,700, 41.2% vs 10,702/18,585, 57.6%).

In total, 18,585 patients developed at least one complication. Table 2 shows the frequency and mortality for each complication. Prolonged ICU stays, prolonged mechanical ventilation, and increased chest tube drainage were the 3 most common complications, occurring in nearly half of patients, while patients with these complications had the lowest mortality rate, accounting for 4.8% (n=448), 4.9% (n=460), and 6.8% (n=579), respectively. Our results showed that sternal wound infections and stroke were least common in valvular disease patients undergoing cardiopulmonary bypass (0.5%), but were associated with higher mortality (20.2% [n=19] and 35.9% [n=33], respectively). The mortality rate for patients with different complications varied widely. Except for MODS, postoperative RF was the more common complication with the highest mortality rate (n=223, 49.2%).

The UpSet plot in Figure 1 describes the co-occurrence of 12 complications in the dataset, with the rate of co-occurrence on the left side. More than 40% of the participants who experienced complications had 2 or more complications. Nearly 90% of patients who died had 2 or more complications. The rate of co-occurrence of nearly all complications was more than 60%. Especially for some serious complications, such as stroke, postoperative RF, sternal wound infections, and MODS, tended to occur in clusters. The rate of co-occurrence of these complications exceeded 90%. Similarly, the correlation analysis showed the strong associations between postoperative RF, sternal wound infections, and MODS (see Figure 2). The strongest correlation was between postoperative RF and MODS (phi=0.41). Although some complications with lower mortality were milder, such as prolonged ICU stays, prolonged mechanical ventilation, and increased chest tube drainage, the rate of co-occurrence of these complications was also higher (63.5%, 73.2%, and 49.7%, respectively). These complications appeared to be the underlying factors for subsequent complications.

Figure 3 shows the Bayesian network modeling the relationships among complications in patients who developed complications. Each node in the figure represents a complication, and the arrows represent direct relationships among complications. There were 13 nodes and 34 directed arcs in the Bayesian network. All the arcs had a strength >0.85 and 30/34 arcs (88.2%) had a direction probability >0.70 (Multimedia Appendix 1). We identified complex relationships between multiple complications. In addition, by calculating the Markov blanket, we identified the critical complications of the network, namely secondary tracheal intubation, stroke, reoperation, and postoperative RF. Prolonged ICU stays, prolonged mechanical ventilation, and increased chest tube drainage appeared to be the starting points for these critical complications. By affecting the occurrence of postoperative RF, stroke, secondary tracheal intubation, and reoperation, prolonged ICU stays, prolonged mechanical ventilation, and increased chest tube drainage led indirectly to death, forming the path from primary complications to critical complications, ultimately leading to death. Postoperative AF, postoperative MI, sternal wound infections, and pericardial tamponade had no direct arc connected with death. In addition, there were more positively correlated arcs between serious complications than other complications, such as the strong relationships between the complications that could be connected to death and MODS, reflecting the cascading effect between complications.

The parameters (probability) of the Bayesian network were learned from the dataset containing 13 variables and 37,285 patients. When providing additional information regarding patients’ complications, the probability of each complication occurring in the network can be automatically updated. Therefore, we calculated the probability of the occurrence of other complications and death, given the occurrence of 1 complication (see Table 3). The probability of death of more than 40% was the complications consisting of secondary tracheal intubation, stroke, postoperative RF, and MODS. Except for stroke, there is a close relationship between secondary tracheal intubation, postoperative RF, and MODS. When any one of these complications occurred, the calculated probability of the other complication is around 20% or more. In addition, we found that postoperative MI, sternal wound infections, and stroke were less likely to occur secondary to other complications. Given the occurrence of other complications, the probability of postoperative MI, sternal wound infections, and stroke was all below 10%. The occurrence of these complications appeared to be mainly associated with the preoperative or intraoperative factors. We also calculated the probability of death when assuming that more than 1 complication co-occurred (see Table 4). When one complication eventually caused MODS, the mortality rate exceeded 90%.

In this study, we constructed, for the first time, a new Bayesian network-based model of 12 perioperative complications and death from 37,285 VHD patients undergoing valve surgery in the CCSR. According to the network model, we demonstrated possible associations and visualized development paths between perioperative complications and quantified the pathways of complication occurrence and progression. Therefore, we identified critical pathways for the development of complications associated with valve surgery, which help to explore ways to halt the cascade of complications in patients undergoing the valve surgery in our future work. Different from previous studies, our finding provides an intuitive perspective that emphasizes the overall correlation for improving the prevention strategies of perioperative complications of VHD.

The complication network describes the dependencies between perioperative complications after valve surgery. The complication in the network may represent a point of intervention. The associations among complications provide the basis for the measures that will prevent or interrupt the occurrence of more serious complications. Our network analysis showed that increased chest tube drainage might contribute to the development of postoperative AF and postoperative RF, and prolonged mechanical ventilation increases the risk of acute kidney injury. The work is consistent with evidence for the role of higher drainage volume on the emergence of postoperative acute kidney injury and postoperative AF [33,34]. Kimura et al [35] also demonstrated that in pediatric cardiac patients, cardiac surgery-associated acute kidney injury was associated with prolonged mechanical ventilation. While discovering the logical relationship between complications, we found stroke appears to be less related to other serious complications. Although previous studies have concluded that patients with postoperative AF have an increased risk of stroke, Rasmussen et al [36] demonstrated that there was no difference in the adjusted risk of postoperative stroke in postoperative AF versus non‐postoperative AF patients, which agreed with our results. The distinct trajectory for stroke suggests that postoperative factors may not be directly associated with the occurrence of stroke. For the prevention of stroke, it may be more appropriate to intervene in preoperative or intraoperative factors. In addition, we found that the association between serious complications was stronger. When secondary tracheal intubation, postoperative RF, and MODS occurred, the probability of any other of these complications occurring was higher. Therefore, when rescuing a certain organ, joint prevention and intervention measures must be formulated to protect the functions of other organs and minimize the compounding effects of multiple complications [37].

We also explored the synergistic effect of multiple complications on mortality. An increase in the number of multiple complications shows a positive cumulative effect, suggesting the importance of special measures for serious complications such as real-time monitoring. In addition, we calculated mortality in the presence of multiple complications. Therefore, the network could be used to inform real-time risk prediction models that alert surgical teams to the changing risks of associated events for individual patients. For example, patients with postoperative RF or stroke may require careful selection of secondary tracheal intubation to avoid progression to more serious consequences. Our analysis suggests that for patients with valvular disease undergoing surgery, the prediction and prevention of complications may meaningfully extend into the postoperative period. Strategies based on the postoperative events could significantly improve our predictive capabilities and thus initiate strategies to reduce secondary complications.

In the past, it has been witnessed that some studies have applied network models to explore the complex relationships underlying a wide range of perioperative complications [16,38]. These studies initially found the relationship between perioperative complications. However, complication networks in the above studies are defined pairwise associations between diseases, which might miss important synergistic relationships in data. The uncertainties, including the progress of complications in individual patients, hospital work-flow management, and other factors, render an overall understanding hard to achieve. Now, our attempt provides a starting point to implement network theory to dissect the mechanistic basis of complex perioperative complications of cardiac surgery, from which to generate new discoveries traditional approaches fail to identify.

Our study had several limitations. First, the complications we included are not comprehensive. In the future, we will include more perioperative complications, such as paravalvular leakage and blood transfusion, to reveal the development process of perioperative complications. In addition, we will also include the information of postdischarge complications to improve completeness of research of complications. Second, our data lacks the ability to sequence complication, which prevents further confirmation of the causality. In the follow-up, we will collect the cohort recording the time of complication occurrence and further explore the associations of perioperative complication development using dynamic Bayesian networks. Third, high collinearity between variables will affect Bayesian network performance, including inaccurate parameter estimation, increased model complexity, unreliable inference results, and difficulty in structure learning. We evaluated the multicollinearity between variables, and the results showed that the Pearson correlation coefficients between all variables were below 0.6 (Multimedia Appendix 1). The highest Pearson correlation coefficient was 0.55, between MODS and mortality. In addition, we performed eigenvalue analysis and calculated the condition number (5.660998, with a condition number greater than 30 indicating severe multicollinearity). The results indicate that the variables are linearly independent, and multicollinearity is minimal. In any case, the role of the network model is predicated on a tremendous advance in profiling the complex complication relationship. The model may also find more promising applications in analyzing the comprehensive impact of preoperative impact on multiple complications and the design of more personalized prevention of perioperative complications.

In conclusion, we have created a Bayesian network that elucidates the underlying relationships and evolving progress of complications in valve surgery, and we have quantified the associations between 12 complications, which provides a basis for the development of targeted preventive measures to prevent further deterioration in patients undergoing valve surgery.