We conducted a retrospective study of consecutive patients with AF who underwent RFCA at two tertiary centers. The cohort from Tongji Hospital (January 2020-December 2022) was used as the training set, while the cohort from the Second Hospital of Lanzhou University (June 2020-June 2023) served as the external validation set.

Inclusion criteria were as follows: (i) a diagnosis of AF according to the 2020 European Society of Cardiology (ESC) guidelines; (ii) eligibility for RFCA based on standard clinical indications; and (iii) a minimum follow-up duration of 6 months. Exclusion criteria were as follows: (i) severe pulmonary disease, hepatic or renal insufficiency, coagulation disorders, or advanced heart failure that precluded ablation; (ii) missing key baseline or outcome data; (iii) significant bradyarrhythmias (e.g., sick sinus syndrome or third-degree atrioventricular block); (iv) left atrial appendage or mural thrombus detected by transesophageal echocardiography; and (v) valvular AF.

Baseline clinical, laboratory, imaging, and electrophysiological data were extracted from electronic medical records. Data collection was performed by trained investigators and verified for accuracy.

AF was classified as paroxysmal if episodes terminated spontaneously or with intervention within 7 days. Non-paroxysmal AF included persistent AF (lasting > 7 days) and long-standing persistent AF (lasting > 12 months in patients undergoing a rhythm control strategy)^[14].

Antiarrhythmic drugs, except for amiodarone, were discontinued at least five half-lives before ablation. All patients received guideline-directed anticoagulation prior to the procedure. Transesophageal echocardiography was performed before ablation to exclude left atrial thrombus. After ablation, patients with non-paroxysmal AF routinely received short-term antiarrhythmic therapy (amiodarone or propafenone) during the blanking period, whereas in patients with paroxysmal AF, therapy was prescribed at the discretion of the treating physician.

The study was conducted in accordance with the Declaration of Helsinki and approved by the ethics committees of Tongji Hospital (TJ-IRB202404056) and the Second Hospital of Lanzhou University (2024A-1246). Given the retrospective study design, the requirement for informed consent was waived by the institutional review boards. This study was designed and reported in accordance with the TRIPOD guidelines for multivariable prediction models to enhance transparency and reproducibility^[15]. A total of 459 eligible patients were included. The participant selection process is shown in Figure 1.

All procedures were performed using a three-dimensional electroanatomical mapping system. In patients with paroxysmal AF, circumferential pulmonary vein isolation (CPVI) was performed as the cornerstone of the ablation strategy. In patients with non-paroxysmal AF, additional linear ablation was performed after CPVI at the operator’s discretion, based on institutional protocols and substrate characteristics. These additional lesions included a left atrial roof line, posterior inferior wall lines (“roof and floor” lines), mitral isthmus line, and/or cavotricuspid isthmus line, as clinically indicated.

If AF persisted after completion of the planned ablation strategy, synchronized direct current cardioversion (150 or 200 J) was performed to restore sinus rhythm. Cardioversion was systematically applied to all patients who remained in AF at the end of the procedure, rather than being performed selectively.

Intraprocedural anticoagulation was maintained with intravenous heparin to achieve an activated clotting time (ACT) of 250-350 seconds. After ablation, all patients underwent continuous electrocardiographic monitoring for at least 24 h.

Candidate variables were pre-specified based on prior literature, clinical relevance, and availability in routine practice^[16]. A comprehensive set of demographic, clinical, laboratory, and procedural variables was collected to identify potential predictors of AF recurrence.

Demographic variables included age, sex, smoking status, and alcohol consumption. Clinical and echocardiographic variables included body mass index (BMI), blood pressure (systolic and diastolic), resting heart rate, left atrial diameter, and left ventricular ejection fraction (LVEF). Laboratory variables included hemoglobin, C-reactive protein (CRP), serum creatinine, N-terminal pro-B-type natriuretic peptide (NT-proBNP), thyroid hormones (TSH, FT4, and FT3), and glycated hemoglobin (HbA1c).

AF-related variables included AF duration, AF type (paroxysmal vs. non-paroxysmal), intraoperative cardioversion, and early AF recurrence. Comorbidities included heart failure, hypertension, diabetes mellitus, ischemic stroke or transient ischemic attack, and coronary artery disease. Perioperative medications included ACEIs, ARBs, ARNIs, β-blockers, anticoagulants, statins, and sodium-glucose cotransporter-2 inhibitors (SGLT2i). Procedural characteristics included total ablation duration.

Supplementary Figure 1 shows the proportion of missing values for each variable. Variables with more than 30% missing data were excluded. The remaining missing values were handled using the imputation methods described below.

Patients were followed at 1, 3, 6, 12, and 18 months after catheter ablation through outpatient visits or structured telephone interviews using a standardized questionnaire. Follow-up was completed in December 2024, and duration was calculated in months. At each visit, postoperative symptoms were assessed, and a standard 12-lead electrocardiogram (ECG) was obtained or reviewed. Additional 24-h Holter monitoring was performed when clinically indicated. A blanking period of 3 months after ablation was applied. AF recurrence was defined as any documented episode of atrial tachyarrhythmia, including AF, atrial flutter, or atrial tachycardia, lasting ≥ 30 s.

Early recurrence was defined as any atrial tachyarrhythmia occurring within the first 3 months after ablation, whereas late recurrence was defined as events occurring thereafter^[17]. During the blanking period, short-term antiarrhythmic therapy was permitted in accordance with standard practice. Early recurrence was treated as a potential prognostic indicator rather than procedural failure. All study endpoints were adjudicated by a blinded, independent Clinical Events Committee.

A nomogram was developed based on the final multivariable model to provide individualized estimates of AF recurrence risk^[18-20]. In the training cohort, candidate variables were initially screened using the least absolute shrinkage and selection operator (LASSO) regression and the Boruta algorithm for dimensionality reduction. Variables identified by these methods, together with clinically relevant factors, were then entered into a multivariable Cox proportional hazards model. Backward stepwise selection was applied, guided by the Akaike Information Criterion (AIC), which emphasizes overall model fit rather than individual P values. Hazard ratios (HRs) with 95% confidence intervals (CIs) were estimated, and the proportional hazards assumption was assessed before finalizing the model.

Based on the final Cox model, a nomogram was developed to estimate the probability of AF recurrence at 6, 12, and 18 months. Model performance was assessed using Harrell’s C-index and time-dependent area under the receiver operating characteristic curve (AUC). Calibration was evaluated by comparing predicted and observed recurrence rates using calibration plots. Decision curve analysis (DCA) was performed to assess the potential clinical benefit across a range of decision thresholds^[21,22]. Internal validation was conducted in the training cohort, and external validation was performed in the independent validation cohort.

Continuous variables were tested for normality using the Shapiro-Wilk test. Normally distributed variables were summarized as mean ± standard deviation (SD) and compared using the Student’s t-test, whereas non-normally distributed variables were presented as median (interquartile range, IQR) and compared using the Mann-Whitney U test. Categorical variables were expressed as counts and percentages and compared using the chi-square test or Fisher’s exact test, as appropriate.

Variables with less than 30% missing data were imputed using the MissForest method, whereas variables with more than 30% missing data were excluded from further analysis^[23]. Missing data were assumed to be missing at random. Imputation performance was evaluated using the normalized root mean square error (NRMSE) for continuous variables and the proportion of falsely classified entries (PFC) for categorical variables. The overall proportion of missing data is presented in Supplementary Figure 1.

Multivariable modeling was performed using R software (version 4.4.2). The proportional hazards assumption for the Cox model was assessed prior to model fitting. Model performance metrics, including the C-index and time-dependent AUC, were estimated with corresponding 95% confidence intervals. Internal validation was conducted using bootstrap resampling to reduce optimism bias. To minimize the risk of overfitting, variable selection was guided by a combination of data-driven methods and clinical relevance. A two-sided P value < 0.05 was considered statistically significant.

A total of 459 eligible patients with AF were included, comprising 256 in the training cohort and 203 in the external validation cohort. In the training cohort, 157 patients (61.3%) were male and 99 (38.7%) were female, with a median age of 64 years [Table 1]. Compared with patients without recurrence, those with late AF recurrence had a larger left atrial diameter (4.54 ± 0.78 cm vs. 4.24 ± 0.67 cm) and a longer AF duration [24.0 (11.5-51.0) months vs. 12.0 (3.0-36.0) months]. Patients with recurrence also showed mildly elevated liver enzymes, including higher alanine aminotransferase (ALT) [22.0 (17.0-34.25) vs. 19.5 (15.0-26.0) U/L] and aspartate aminotransferase (AST) levels [23.0 (19.0-29.0) vs. 21.0 (18.0-25.0) U/L]. Serum creatinine levels were also higher [79.5 (72.0-94.0) vs. 77.0 (66.8-89.0) µmol/L], along with a greater prevalence of renal insufficiency (17.9% vs. 6.5%). In terms of procedural and clinical characteristics, intraoperative ECV was more frequently performed in the recurrence group (48.2% vs. 27.5%). Early recurrence during the blanking period was also more common in these patients (32.1% vs. 5.0%).

No significant differences were observed in other demographic, clinical, or echocardiographic characteristics between the training and validation cohorts. A detailed summary of baseline characteristics for both cohorts is provided in Supplementary Table 1.

Candidate predictors were screened in the training cohort using two complementary feature selection methods: LASSO regression and the Boruta random forest algorithm.

The LASSO model was optimized using 10-fold cross-validation, yielding an optimal λ of 0.0537 that minimized the partial likelihood deviance^[24]. Five variables with non-zero coefficients were identified, including intraoperative ECV, early recurrence, ACEI/ARB/ARNI therapy, left atrial diameter, and serum creatinine [Supplementary Figure 2].

In parallel, the Boruta algorithm identified early recurrence, AF duration, left atrial diameter, and serum creatinine as important predictors [Figure 2C and D]. These findings were largely consistent with the variables selected by the LASSO model.

Variables identified by either method were entered into a multivariable Cox proportional hazards model with backward stepwise selection [Table 2]. In the final model, six variables were retained: early recurrence (HR = 7.616, 95%CI: 4.124-14.062), left atrial diameter (HR = 1.684, 95%CI: 1.074-2.642), intraoperative ECV (HR = 1.423, 95%CI: 0.800-2.531), serum creatinine (HR = 1.018, 95%CI: 1.007-1.029), ACEI/ARB/ARNI therapy (HR = 0.426, 95%CI: 0.238-0.760), and AF duration (HR = 1.003, 95%CI: 0.999-1.006). Early recurrence was the strongest predictor of late AF recurrence, while ACEI/ARB/ARNI therapy was associated with a reduced risk.

Based on the final multivariable Cox model, a nomogram was developed to estimate the probability of AF recurrence at 6, 12, and 18 months in the training cohort [Figure 3]. In the nomogram, early recurrence contributed the highest number of points, followed by left atrial diameter, ACEI/ARB/ARNI therapy, intraoperative ECV, serum creatinine, and AF duration.

Variance inflation factors (VIFs) for all predictors were close to 1, indicating minimal multicollinearity [Supplementary Table 2]. The proportional hazards assumption was assessed for each predictor and for the global model, with no significant violations detected (all P > 0.05) [Supplementary Figure 3]. These findings support the appropriateness of the Cox proportional hazards model for this analysis.

Model performance was evaluated in terms of discrimination, calibration, and clinical usefulness^[25]. The C-index was 0.776 (95%CI: 0.705-0.847) in the training cohort and 0.779 (95%CI: 0.699-0.859) in the validation cohort, indicating good discriminative ability and consistent performance across cohorts.

Internal validation was performed using nonparametric bootstrap resampling with 500 iterations to estimate optimism. In the training cohort, the apparent C-index was 0.776, with an estimated optimism of 0.007 and a standard error of 0.035. The bias-corrected C-index remained highly consistent with the apparent estimate. These results indicate minimal optimism and support the stability and robustness of the model.

Time-dependent AUCs at 6, 12, and 18 months were 0.869 (95%CI: 0.765-0.972), 0.810 (95%CI: 0.709-0.911), and 0.776 (95%CI: 0.662-0.890), respectively, in the training cohort. In the external validation cohort, the corresponding AUCs were 0.831 (95%CI: 0.689-0.973), 0.848 (95%CI: 0.743-0.953), and 0.789 (95%CI: 0.664-0.913) [Figure 4A and B]. These results indicate good and consistent discriminative performance across different time points and between cohorts.

Calibration plots showed good agreement between predicted and observed recurrence probabilities at all evaluated time points [Figure 4C and D]. The calibration slope was 1.00 (95%CI: 0.75-1.25) in the training cohort and 0.99 (95%CI: 0.70-1.27) in the validation cohort, indicating no evidence of model overfitting. Calibration-in-the-large at 6, 12, and 18 months showed intercepts of 0.37 (95%CI: -0.09 to 0.84), 0.45 (95%CI: 0.10-0.81), and -0.20 (95%CI: -0.56 to 0.16), respectively, in the training cohort. In the validation cohort, the corresponding values were 0.36 (95%CI: -0.16 to 0.89), 0.41 (95%CI: 0.00-0.81), and -0.32 (95%CI: -0.73 to 0.10). Overall, calibration-in-the-large was close to zero, although a mild underestimation of risk was observed at 12 months in the training cohort. The calibration slope remained close to 1.0, and similar patterns were observed in the validation cohort, indicating good calibration and preserved model structure.

DCA demonstrated that the nomogram provided meaningful clinical benefit across a range of decision thresholds [Figure 5].

To further assess the incremental predictive value of early recurrence, a sensitivity analysis was performed by reconstructing the model without this variable. The reduced model showed a lower C-index of 0.683 (95%CI: 0.605-0.761), compared with 0.776 (95%CI: 0.705-0.847) for the full model. Time-dependent C-index and AUC analyses for both models are presented in Supplementary Figure 4, further confirming the additional discriminative contribution of early recurrence.

For comparative evaluation, the nomogram was assessed against the CAAP-AF and APPLE scores. As shown in Table 3, the nomogram demonstrated higher area under the receiver operating characteristic curve (AUROC) values and improved classification performance. Net reclassification improvement (NRI) and integrated discrimination improvement (IDI) analyses further confirmed the incremental predictive value of the nomogram over CAAP-AF (continuous NRI = 0.724; IDI = 0.159) and APPLE (continuous NRI = 0.623; IDI = 0.139) (all P < 0.05). Consistent findings were observed in decision curve analysis [Figure 6], indicating superior clinical utility of the nomogram.

In addition, individualized 18-month recurrence-free probabilities were estimated based on three key predictors identified in the model: early AF recurrence, intra-procedural cardioversion, and left atrial diameter above the cohort median (4.3 cm). The corresponding stratified estimates are presented in Supplementary Table 3.

Based on nomogram-derived risk scores, patients were stratified into high- and low-risk groups using the median value as the cutoff. Kaplan-Meier analysis showed a clear and consistent separation in recurrence-free survival between the two groups in both the training and validation cohorts. Patients in the high-risk group had significantly worse outcomes than those in the low-risk group. The hazard ratios for recurrence-free survival were 0.22 (95%CI: 0.11-0.43) in the training cohort and 0.17 (95%CI: 0.07-0.40) in the validation cohort (log-rank P < 0.001 for both; Figure 7).

In this two-center retrospective study, we developed and externally validated a nomogram to estimate the risk of late AF recurrence following RFCA. The model demonstrated good discrimination and consistent performance in an independent validation cohort. By integrating clinical and procedural factors into an individualized risk prediction framework, the nomogram may aid post-ablation risk stratification and follow-up planning. Further prospective studies are warranted to confirm its generalizability in broader clinical settings.