We retrospectively reviewed 468 patients who were diagnosed with CM and underwent cardiac surgery in three tertiary comprehensive hospitals between January 2010 and January 2022. The following inclusion criteria were adopted: (i) patients diagnosed with CM by echocardiography before surgery; (ii) patients with postoperative pathological reports confirmed as CM; and (iii) patients with single CM or presenting for the first time with CM. The exclusion criteria were as follows: (i) patients with valvular heart disease, congenital heart disease, deep venous thrombosis, history of infective endocarditis, cardiac thrombosis, other tumors, migraine, unstable carotid artery plaques, or patients taking oral contraceptives; (ii) patients with missing clinical data. When a patient was admitted more than twice, only the data from the first admission were used in this study. The study was performed in accordance with the Declaration of Helsinki and approved by the Institutional Ethics Committee of Beijing Anzhen Hospital (2023013X). Written informed consent was obtained from all participants.

Demographic and clinical data were collected from electronic medical records, including age, sex, medical history, clinical symptoms, echocardiography, and laboratory tests (i.e., routine blood examination and coagulation function). Patients with IS were diagnosed based on medical history, clinical examination, and brain imaging results before cardiac surgery, and their diagnoses were confirmed by two attending neurologists. The collected variables during admission: including clinical, imaging, and laboratory data, were used in the statistical analysis and BN modeling.

With regard to echocardiographic data, CM with high-mobility refers to highly mobile phenomena of myxoma mass on transesophageal echocardiography as described elsewhere (1, 24). Additionally, we chose 30 mm as the threshold of the size of CM, because two previous studies reported that tumor diameter less than 30 mm were more commonly seen in patients with CM complicated by brain infarct (25).

After hospital discharge, follow-ups were performed by experienced investigators via face-to-face interviews or phone calls. The main outcomes included complications and mortality, which were monitored for periods lasting 1 month to 10 years.

The data extraction process from the medical records was standardized, and the investigators familiarized themselves with it before starting the data retrieval for this study. Data entry followed the double entry method. If discrepancies take place during the review process, medical records were consulted and the data were corrected.

Before building the predictive model, we reviewed the previous literature to preprocess the predictive variables. First, it was noted that CM-IS mainly affects middle-aged women (20, 26). For our analysis, sex and age were defined as the definite risk factors. Second, in addition to the traditional cerebrovascular risk factors [such as smoking (27, 28), hypertension (29), diabetes (30), and hyperlipidemia (31)], we also added “tumor characteristics” as risk factors involving tumor length, width, mobility, surface and stalk (11, 32). Furthermore, previous studies have demonstrated the clinical manifestations of CM, including cardiac, constitutional, and systemic embolic symptoms (4, 33). Elevated platelet counts have also been reported in CM-IS (12). Based on the above-mentioned findings, a total of 17 variables were identified, including sex, age, hypertension, diabetes, hyperlipidemia, tumor type, tumor size, tumor location, cardiac symptoms, constitutional symptoms, systemic embolic symptoms, and platelet count.

According to the biostatistics literature, data will lose their measure of confidence if their missing value ratio is >30%. These missing attributes normally result from time conflicts and test failures. In our study, some variables were removed from the dataset if they had more than six missing attributes. Finally, approximately six variables were used as the primary dataset.

A BN consists of a directed acyclic graph whose nodes represent random variables and links express dependencies between nodes (34). The node indicated by an arrow is called the child node, and the other node is called the parent node of the child node. Each node corresponds to a conditional probability distribution table (CPT), which represents the conditional probability of the child node under the condition that the parent node is known and quantifies the probability dependence between variables. The BN is a representation of the joint probability distributions of random variables X = [X₁, …, X_n]; thus, a probability expression can be obtained:P(X1,…,Xn)=P(X1)P(X2|X1)…P(Xn|X1,X2,…Xn−1)=∏1nP(Xi|π(Xi)Where π(X_i) represents the collection of the parents of Xi; π(X_i) ⊆ X₁ …, X_i-1.

The purpose of BN structure learning is to find the network that best matches a given dataset. Tabu Search (TS) is currently the most used search method for structure learning as it is able to overcome issues related to the local optimal searching process and can search for the global optimal solution. For the network structure G and the training dataset D, parameter learning modifies the parameters of the prior distribution and obtains the parameter of the posterior distribution, which determines the BN of the conditional probability of each node to p-value (D | θ, G). Maximum likelihood estimation is one of the main types of estimation for a complete dataset, and this method simply involves an attempt to find the parameter that maximizes the likelihood function. In this study, we constructed a BN model to predict CM-IS occurrence. 17 random variables were extracted from the patient data. We initially filtered the nodes using logistic regression to avoid including too many nodes and adding excessive complexity to the network structure. We established an optimal model based on the tabu search algorithm and maximum-likelihood estimation.

Continuous variables are presented as mean ± standard deviation or median [interquartile range (IQR)]. Categorical variables are expressed as percentages. Normally distributed data were analyzed using Student's t-test, and non-normally distributed data were analyzed using the Mann–Whitney U test. Categorical variables were analyzed using the chi-square test. Binary logistic regression analysis was used to screen for possible variables associated with CM-IS and evaluate their associated risk intensities. Variables with p-value < 0.05 were entered into the multivariable logistic regression analysis to identify the risk factors.

The BN model of the IS-related risk factors in patients with CM was conducted using the tabu search algorithm (35), and the conditional probability of each node was calculated using the maximum likelihood estimation method (36). The probability of each node of the network and the interrelationship between IS and related factors were qualitatively and quantitatively analyzed (37). Before establishing the BN model, all the IS-related factors were quantified and coded (Supplementary Table S1). The performance of the BN model was evaluated through discrimination and calibration. The discriminative ability of the model was reflected by the area under the receiver operating characteristic curve (AUC). Calibration was performed using the Hosmer–Lemeshow test and calibration plots. Furthermore, the Delong test was used to test the statistical significance of the difference between the AUC values. The BN model for predicting the probability of CM-IS was constructed using the bnlearn package in R 4.2.1 (https://www.rstudio.com/). In addition, the network topology was drawn using Netica 32.0 (Norsys Software Corp., Vancouver, BC, Canada). The AUC was used to evaluate the prediction efficiency of the model, which was completed using R studio software (https://www.rstudio.com/).

Among 468 consecutive patients with CM, 52 were excluded due to the presence of other concomitant diseases or missing data. Finally, 416 patients were enrolled in this study, including 61 with IS and 355 without IS (Figure 1). Baseline characteristics were also compared between the CM-IS (61 patients) and non-IS CM (355 patients) groups. The mean age of the participants included in this study was 53.81 years, and 62.0% of them were women. Compared with non-IS CM group (n = 355), patients with CM-IS more frequently had hypertension (42.6% vs. 28.2%, p-value = 0.023), hyperlipidemia (19.7% vs. 7.0%, p-value = 0.001), clinical manifestations of cardiac symptoms (65.5% vs. 58.9%, p-value < 0.001), and systemic embolic symptoms (9.8% vs. 1.1%, p-value < 0.001). Approximately 42 (68.6%) patients with CM-IS had tumors with high mobility (p-value = 0.03). The additional patient characteristics are presented in Table 1.

Regarding the outcomes of patients with CM after surgical excision, two patients had a stroke recurrence (two CM-IS cases) and three patients died (one CM-IS case, two non-IS CM cases). Causes of death were acute exacerbation of chronic heart failure (n = 1), acute myocardial infarction (n = 1), and severe lung infection (n = 1).

The variables included in this study were the basic characteristics and well-known risk factors. The results of the univariate logistic regression analysis are listed in Table 2. Of the 17 variables, six were associated with CM-IS according to the univariate logistic regression: hyperlipidemia [odds ratio (OR), 1.426; 95% confidence interval (CI), 1.187–1.970; p-value = 0.042], hypertension (OR, 1.537; 95% CI, 1.291–1.990; p-value = 0.046), cardiac symptoms (OR, 2.772; 95% CI, 2.515–5.071; p-value = 0.001), systemic embolic symptoms (OR, 1.172; 95% CI, 1.045–1.662; p-value < 0.010), platelet count (OR, 1.005; 95% CI, 1.001–1.008; p-value = 0.006), and tumors with high mobility (OR, 2.493; 95% CI, 1.661–5.643; p-value = 0.013).

In our research, six independent variables were included in the multivariate analysis. As the sample size should be at least 10 times the independent variable when developing a prediction model for dichotomous outcomes, the number of samples in each group should be at least 60. The number of cases of CM-IS and non-IS CM were 61 and 355, respectively. Thus, the sample size of this study was sufficient to develop a predictive model. Therefore, six significant variables were retained in the final multivariate logistic regression model after performing backward stepwise variable selection. In the multivariable analysis, hyperlipidemia (OR, 1.172; 95% CI, 0.940–5.019; p-value = 0.69), hypertension (OR, 1.937; 95% CI, 1.044–3.595; p-value = 0.36), cardiac symptoms (OR, 2.363; 95% CI, 1.198–0.667; p-value = 0.001), systemic embolic symptoms (OR, 1.324; 95% CI, 0.683–20.495; p-value = 0.015), platelet count (OR, 1.006; 95% CI, 1.001–1.008; p-value = 0.008), and tumors with high mobility (OR, 2.579; 95% CI, 1.292–5.148; p-value = 0.017) were independently associated with CM-IS (Table 2).

The structure learning of the BN was mainly constructed using the tabu search algorithm. The CM-IS model contained seven nodes and 10 directed edges, with nodes representing hypertension, hyperlipidemia, cardiac symptoms, systemic embolic symptoms, platelet counts, and tumor mobility, respectively. As shown in Figure 2, hypertension, hyperlipidemia, cardiac symptoms, systemic embolic symptoms, platelet counts, and tumor with high mobility were directly associated with CM-IS, and tumor with high mobility was indirectly linked to CM-IS through cardiac symptoms and systemic embolic symptoms. Hypertension may also be indirectly associated with CM-IS via cardiac and systemic embolic symptoms.

After determining the BN structure, the maximum likelihood estimation method was used to estimate the conditional probabilities of each node in the network. The prior probabilities of each node in the network are shown in Figure 2. According to the conditional probability distribution (Table 3), when CM was combined with systemic embolic symptoms and abnormal platelet counts, the probability of CM-IS was 0.50. In patients with high platelet counts complicated by cardiac symptoms and with co-occurring systemic embolic symptom disturbance, the probability of IS increased to 1.00, suggesting that great attention should be paid to prevent the occurrence of CM-IS when the above two phenomena occur.

Table 4 shows that the BN model for predicting CM-IS achieved higher scores on AUC and sensitivity, but lower scores on accuracies and specificity, than the logistic regression model. The AUC of the BN model was 0.706 (95% CI, 0.639–0.773), and its accuracies, sensitivity, and specificity were 85.82%, 99.44%, and 6.557%, respectively. The logistic regression predictive model achieved an AUC of 0.697 (95% CI, 0.629–0.766), accuracies of 86.06%, sensitivity of 98.87%, and specificity of 11.48% (Figure 3).

Notably, the Delong test revealed that there were no statistical differences in the AUC values between the BN model and the logistic regression model (p-value = 0.683). In addition, the calibration plots showed that the predicted probabilities of IS agreed well with the actual observations (Figure 4), and the Hosmer–Lemeshow test also demonstrated good calibration for the BN model (p-value = 1.000, χ² = 0.033, degrees of freedom = 8) and for the logistic regression model (p-value = 0.992, χ² = 1.536, degrees of freedom = 8).