Prediction model for recurrent laryngeal nerve injury in microwave ablation of thyroid nodules

Abstract

Objective

This study aims to develop an explainable machine learning (ML) framework integrating clinical, imaging, and procedural features for predicting recurrent laryngeal nerve (RLN) injury risk during microwave ablation (MWA) of thyroid nodules.

Methods

A retrospective study is conducted using data from 254 patients who underwent thyroid nodule MWA. Recursive feature elimination (RFE) with 5 × fivefold cross-validation selected 12 optimal features across four ML models: logistic regression (LR), decision tree (DT), random forest (RF), and support vector machine (SVM). Model performance is evaluated via AUC, accuracy, sensitivity, specificity, Brier score, and decision curve analysis (DCA). SHapley Additive exPlanations (SHAP) provides interpretability by quantifying feature contributions.

Results

The RandomForest model achieved the highest discriminative performance (AUC = 0.9755 ± 0.0242, accuracy = 0.9729 ± 0.0155) and calibration (Brier score = 0.038). Key predictors included nodule volume, ablation time, and proximity to the tracheoesophageal groove. SHAP analysis revealed model-specific interactions: nodule orientation (SVM) and post-ablation dimensions (RF) significantly influenced risk. DCA confirmed clinical utility, with RF providing the highest net benefit across thresholds (0.2–0.6). Laboratory markers and echogenicity demonstrated cross-model consistency, underscoring their biological relevance.

Conclusion

This study establishes the first interpretable ML framework for RLN injury prediction in thyroid nodule MWA, highlighting the superiority of ensemble learning and clinical-imaging integration. Future validation in diverse cohorts and real-time integration into ablation systems may enhance procedural safety.

Introduction

In recent years, the clinical detection rate of thyroid nodules has risen significantly due to the widespread application of ultrasound technology, making them one of the most common endocrine disorders. Although most nodules are benign, the incidence of malignant transformation has shown an upward trend, with epidemiological data highlighting a pronounced prevalence of malignancy among female patients [1–3]. While traditional thyroidectomy remains the gold standard for treatment, its invasive nature and associated complications (e.g., hypoparathyroidism, recurrent laryngeal nerve injury) have driven demand for minimally invasive alternatives. In this context, thermal ablation has emerged as a pivotal option for thyroid nodule management, owing to its procedural efficiency, rapid recovery, and low invasiveness [2–4]. For benign nodules, multiple international guidelines endorse thermal ablation as a reliable modality for reducing lesion volume and alleviating symptoms [5–7]. Similarly, recent studies support the feasibility of thermal ablation as a surgical alternative for select low-risk papillary thyroid microcarcinomas (PTMCs), demonstrating comparable long-term outcomes to conventional surgery [8–10].

However, the widespread adoption of thermal ablation has raised concerns regarding its safety profile. Recurrent laryngeal nerve (RLN) injury, a major postoperative complication, can lead to voice hoarseness, dyspnea, and other functional impairments, with reported incidence rates ranging from 0 to 6.3% [11], significantly impacting patients’ quality of life. Previous studies have attempted to identify RLN injury risk factors—such as anatomical proximity to the tracheoesophageal groove [12–14], nodule volume, and Zuckerkandl tubercle [15] location—through statistical analyses [16–18]. Nevertheless, conventional approaches suffer from critical limitations: (1) linear regression models fail to capture complex nonlinear relationships and feature interactions; (2) single-center retrospective studies with limited sample sizes restrict generalizability; and (3) static models cannot dynamically integrate multimodal data (e.g., ultrasound imaging features, real-time ablation parameters), hindering personalized risk assessment.

Notably, ablation strategies fundamentally differ between benign and malignant nodules: malignant lesions require extended ablation zones to ensure tumor eradication, whereas benign lesions prioritize precision to minimize collateral damage [19]. Evidence indicates that RLN injury risks are markedly higher in malignant nodules compared to benign ones [20], suggesting distinct injury mechanisms across risk strata. Consequently, risk stratification based on ultrasound characteristics and tailored analysis of RLN injury factors are essential for optimizing preoperative planning [21].

This study aims to develop and validate an explainable Machine Learning (ML) model for accurate predication of the risk of RLN. This study uses the SHapley Additive exPlanations (SHAP) method to clarify the feature importance and explain the prediction results of the model to determine the practical significance of the model for predicting RLN.

Results

Patient information

Detailed patient demographics and clinical characteristics relevant to this research are thoroughly outlined in Table 2.

Table 2.

Demographic characteristics and clinical characteristics among RLN patients

Characteristic	Overall, N = 254	L0, N = 200	L1, N = 54	P-value
Age	47.00 (35.00, 56.50)	48.00 (34.00, 57.00)	47.00 (39.00, 54.00)	0.864
NS-v	9.10 (5.00, 28.95)	9.10 (5.00, 31.30)	9.05 (4.75, 25.25)	0.445
NS-t	8.00 (4.65, 21.90)	8.00 (4.60, 23.00)	7.40 (4.70, 16.95)	0.032
NS-ap	7.80 (4.85, 16.50)	7.30 (4.90, 18.20)	8.40 (4.72, 13.20)	0.090
NV	254.80 (54.46,5374.96)	254.80 (52.00,6882.68)	256.22 (57.30,3074.78)	0.155
DAC	1.00 (0.00, 1.00)	1.00 (0.00, 1.00)	0.00 (0.00, 1.00)	< 0.001
AP	25.00 (20.00, 30.00)	25.00 (20.00, 30.00)	22.50 (20.00, 30.00)	0.025
AT	123.00 (66.50, 183.50)	124.00 (66.00, 192.00)	118.00 (71.00, 171.25)	0.931
PNS-v	17.90 (13.20, 26.00)	17.90 (13.00, 27.00)	18.10 (14.20, 23.70)	0.883
PNS-t	15.90 (13.00, 21.45)	15.50 (13.00, 23.00)	15.95 (13.20, 18.82)	0.840
PNS-ap	12.30 (10.00, 15.95)	12.30 (10.00, 16.50)	12.65 (10.12, 14.97)	0.613
Gender Male Female	57 (22.0%) 202 (78.0%)	38 (20.5%) 147 (79.5%)	19 (25.7%) 55 (74.3%)	0.462
NP
Left	125 (48.3%)	86 (46.5%)	39 (52.7%)
Right	126 (48.6%)	92 (49.7%)	34 (45.9%)
Isthmus	8 (3.1%)	7 (3.8%)	1 (1.4%)	0.451
AR
> 1	73 (28.2%)	49 (26.5%)	24 (32.4%)
< 1	185 (71.4%)	135 (73.0%)	50 (67.6%)	< 0.001
NO
Entire	22 (8.5%)	13 (7.0%)	9 (12.2%)
Upper	37 (14.3%)	24 (13.0%)	13 (17.6%)
Middle	135 (52.1%)	97 (52.4%)	38 (51.4%)
Lower	65 (25.1%)	51 (27.6%)	14 (18.9%)	0.260
ZN
No	207 (79.9%)	155 (83.8%)	52 (70.3%)
Yes	52 (20.1%)	30 (16.2%)	22 (29.7%)	0.023
DNT
> 2 mm	144 (55.6%)	114 (61.6%)	30 (40.5%)
< 2 mm	115 (44.4%)	71 (38.4%)	44 (59.5%)	0.003
EP
Very low	14 (5.4%)	4 (2.2%)	10 (13.5%)
Low	124 (47.9%)	92 (49.7%)	32 (43.2%)
Iso	13 (5.0%)	11 (5.9%)	2 (2.7%)
High	1 (0.4%)	1 (0.5%)	0 (0.0%)
Mixed	103 (39.8%)	76 (41.1%)	27 (36.5%)
Anechoic	4 (1.5%)	1 (0.5%)	3 (4.1%)	< 0.001
IEP
Yes	98 (37.8%)	69 (37.3%)	29 (39.2%)
No	161 (62.2%)	116 (62.7%)	45 (60.8%)	0.887
ET
Cystic-solid	78 (30.1%)	62 (33.5%)	16 (21.6%)	0.083
Solid	181 (69.9%)	123 (66.5%)	58 (78.4%)
DPC
< 2 mm	44 (17.0%)	32 (17.3%)	12 (16.2%)
> 2 mm	155 (59.8%)	103 (55.7%)	52 (70.3%)
Beyond capsule	60 (23.2%)	50 (27.0%)	10 (13.5%)	0.048
CA
No	202 (78.0%)	150 (81.1%)	52 (70.3%)
> 2 mm	23 (8.9%)	15 (8.1%)	8 (10.8%)
< 2 mm	33 (12.7%)	20 (10.8%)	13 (17.6%)	0.021
HR
No	140 (54.1%)	106 (57.3%)	34 (45.9%)
Low	107 (41.3%)	75 (40.5%)	32 (43.2%)
Middle	2 (0.8%)	0 (0.0%)	2 (2.7%)
High	10 (3.9%)	4 (2.2%)	6 (8.1%)	< 0.001
BD
No	253 (97.7%)	182 (98.4%)	71 (95.9%)
Yes	5 (1.9%)	3 (1.6%)	2 (2.7%)	0.932
LE
No	42 (16.2%)	0 (0.0%)	42 (56.8%)
LE1	166 (64.1%)	162 (87.6%)	4 (5.4%)
LE2	21 (8.1%)	21 (11.4%)	0 (0.0%)	< 0.001

NS-v nodule size (vertical diameter), NS-t nodule size (transverse diameter), NS-ap nodule size (anterior–posterior diameter), NV Nodule volume, DAC Distance from the anterior capsule, AP Ablation power, AT Ablation time, PNS-v Post-ablation nodule size (vertical diameter), PNS-t Post-ablation nodule size (transverse diameter), PNS-ap Post-ablation nodule size (anterior–posterior diameter), NP Node position, AR Aspect ratio, NO Nodule orientation, ZN Whether the nodule is located on the Z-nodule, DNT Distance between the nodule and the tracheoesophageal groove, EP Echo pattern, IEP Internal echo pattern, ET Echo type, DPC Distance from the posterior capsule, CA Calcification, HR High Risk, BD Bridge, LE Laboratory Examination

Feature selection results

The recursive feature elimination (RFE) method was applied to refine the initial set of 25 features, retaining 12 optimal features for each machine learning model to enhance predictive performance and stability. The results of feature selection consistency and model performance across the four algorithms are summarized as follows.

For the logistic regression (LR) model, features demonstrating 100% selection consistency across all cross-validation iterations included the aspect ratio, nodule location on the Z-nodule, distance from the tracheoesophageal groove, echogenicity, and presence of laboratory tests. Additional features, such as ablation time, nodule size (left–right diameter), nodule volume, nodule orientation, and calcification, were retained in 80% of iterations.

For the decision tree (DT) model, high-consistency features (100% retention) comprised nodule size (anterior–posterior diameter), nodule volume, nodule orientation, distance from the posterior capsule, presence of Hashimoto’s thyroiditis, and laboratory test results. Echogenicity was retained in 80% of iterations.

For the random forest (RF) model, features consistently selected (100% retention) included age, ablation time, post-ablation nodule dimensions (superior-inferior, left–right, and anterior–posterior diameters), original nodule size, nodule volume, and laboratory test results. Distance from the anterior capsule was retained in 80% of iterations.

In the support vector machine (SVM) model, a supervised learning algorithm that constructs an optimal hyperplane in a high-dimensional feature space to maximize the margin between classes (using a radial basis function kernel in this study to handle nonlinear relationships) demonstrated 100% retention of features including ablation time, nodule volume, nodule location on the Zuckerkandl’s tubercle, distance from the tracheoesophageal groove, echogenicity, and laboratory test results. Nodule size (left–right diameter) and calcification were retained in 80% of iterations.

Across all models, nodule volume, echogenicity, and laboratory test results demonstrated the highest selection consistency, underscoring their critical role in predicting recurrent laryngeal nerve injury risk. Other features, such as ablation time, nodule dimensions (across radial planes), distance from the tracheoesophageal groove, and Z-nodule location, exhibited strong retention rates in multiple models. These findings confirm that RFE effectively identified key clinical and imaging biomarkers associated with nerve injury, establishing a robust foundation for subsequent model refinement and clinical application.

Evaluation performance

The predictive performance of the developed models was rigorously evaluated using a comprehensive suite of metrics, including discrimination, calibration, and clinical utility, on the independent test set (Fig. 1).

Fig. 1.

Models structure

Discriminative ability

The area under the receiver operating characteristic curve (AUC) demonstrated robust model performance across all algorithms. The random forest (RF) model achieved the highest AUC of 0.9855 ± 0.0242, followed by the decision tree (DT, AUC = 0.9406 ± 0.0437), logistic regression (LR, AUC = 0.9022 ± 0.0371), and support vector machine (SVM, AUC = 0.8993 ± 0.0481). Accuracy (ACC) mirrored this trend, with RF attaining the highest value (0.9729 ± 0.0155), while SVM showed relatively lower performance (ACC = 0.8766 ± 0.0393). Sensitivity and specificity analyses revealed trade-offs inherent to model design: DT exhibited the highest sensitivity (0.9190 ± 0.0776), whereas RF achieved near-perfect specificity (0.9892 ± 0.0132). The ROC curves are shown in Fig. 2A, B and other evaluation results are shown in Fig. 3.

Fig. 2.

Performance of machine learning models

Fig. 3.

Forest figure for ML model performance

Calibration analysis

Calibration curves and Brier scores were employed to assess the agreement between predicted probabilities and observed outcomes. RF demonstrated superior calibration (Brier score = 0.038), closely followed by DT (0.034). In contrast, SVM displayed suboptimal calibration (Brier score = 0.096), indicating a tendency toward overconfident predictions. The logistic regression model exhibited moderate calibration (Brier score = 0.085), with its curve deviating from the ideal diagonal at higher probability thresholds. The calibration curves are shown in Fig. 2C, D.

Clinical utility via decision curve analysis (DCA)

All models outperformed the "treat none" and "treat all" strategies within clinically relevant threshold ranges (0.2–0.6). RF consistently provided the highest net benefit, particularly at thresholds > 0.3, followed by DT and LR. SVM showed diminished utility at thresholds > 0.5 due to its lower sensitivity. The decision curves are shown in Fig. 2E, F.

Additional performance metrics

The F1-score, harmonizing precision and recall, further confirmed RF’s dominance (F1 = 0.9324 ± 0.0597), while SVM’s performance lagged (F1 = 0.5962 ± 0.1072). Negative predictive value (NPV) exceeded 0.96 for all models, reflecting strong rule-out capability. Parallel coordinate plots of metrics (AUC, ACC, F1, Brier) highlighted RF’s balanced superiority across evaluation domains, with minimal performance variance between cross-validation folds. The addition performance matrics are shown in Fig. 2G, H.

Model explanation

The SHapley Additive exPlanations (SHAP) framework was applied to quantify feature importance and interpret model predictions across all algorithms. Figure 4 integrates the SHAP summary plots for the decision tree (DT), logistic regression (LR), random forest (RF), and support vector machine (SVM) models, revealing both shared and model-specific feature contributions to recurrent laryngeal nerve injury risk prediction.

Fig. 4.

SHAP value for interpretability value visualization

Decision tree (Fig. 4A)

The SHAP summary plot identified nodule volume (NV), distance from the posterior capsule (DPC), and ablation time (AT) as the most influential features, with absolute SHAP values ranging from − 0.6 to 0.6. Features such as nodule size in the transverse plane (NS-t) and echogenicity (EP) exhibited bidirectional effects, where higher values either increased or decreased risk depending on contextual interactions.

Logistic regression (Fig. 4B)

Linear relationships dominated feature impacts, with laboratory test results (LE) and nodule location on the Z-nodule (ZN) showing the strongest positive associations (SHAP range: − 8 to + 6). Calcification (CA) and distance from the tracheoesophageal groove (DNT) demonstrated significant negative contributions, suppressing predicted injury risk.

Random forest (Fig. 4C)

Nonlinear interactions were evident, with age and post-ablation nodule dimensions (PNS-v, PNS-ap) ranking highest (SHAP range: − 0.2 to + 0.6). Notably, nodule volume (NV) and ablation time (AT) maintained consistent directional effects across trees, reinforcing their biological plausibility.

Support vector machine (Fig. 4D)

The radial basis function (RBF) kernel amplified the importance of complex interactions, particularly for nodule orientation (NO) and Hashimoto’s thyroiditis (HR) (SHAP range: − 2 to + 4). Echoic patterns (EP) and calcification (CA) exhibited divergent impacts compared to other models, highlighting kernel-specific sensitivity.

Discussion

This study presents the first machine learning (ML)-based framework for predicting recurrent laryngeal nerve (RLN) injury during microwave ablation (MWA) of thyroid nodules, addressing a critical gap in optimizing procedural safety for this minimally invasive technique. By integrating clinical, imaging, and procedural features, our model demonstrates robust predictive performance and interpretability, offering a clinically actionable tool to mitigate RLN injury risks.

This study represents the first application of machine learning (ML) algorithms to predict recurrent laryngeal nerve (RLN) injury during microwave ablation (MWA) of thyroid nodules, addressing a critical gap in enhancing the safety of this minimally invasive technique. In contrast to prior studies, which often relied on single-center datasets or conventional statistical approaches, our research leverages data and integrates advanced ML models to capture complex, nonlinear relationships among clinical, imaging, and procedural characteristics. This approach transcends the limitations of traditional logistic regression, enabling a more comprehensive exploration of potential risk factors and offering novel insights for clinical decision-making.

Methodologically, we employed recursive feature elimination (RFE) to systematically select the most predictive features for RLN injury, ensuring robustness through multiple rounds of cross-validation. This rigorous process enhanced the generalizability of the model by identifying features such as nodule volume, ablation time, and proximity to the tracheoesophageal groove, which align closely with established clinical and anatomical risk factors, thereby reinforcing the biological plausibility of our findings. The random forest model, in particular, exhibited superior predictive performance due to its ability to effectively manage high-dimensional data and intricate feature interactions. The scientific rigor of our approach is further evidenced by the systematic validation framework, which ensured model stability and reliability across diverse data subsets, establishing a solid foundation for clinical translation.

A key strength of this study lies in the interpretability of the model, achieved through the application of SHapley Additive exPlanations (SHAP). This method provided both local and global explanations of model predictions, mitigating the “black-box” challenge commonly associated with ML. SHAP analysis elucidated the specific contributions of individual features, such as nodule orientation and echogenicity, to the risk of RLN injury, offering actionable guidance for preoperative risk assessment and intraoperative decision-making. For instance, nodules located near critical anatomical structures may prompt clinicians to adopt more cautious ablation parameters or implement enhanced neuromonitoring. This seamless integration of data-driven insights with clinical applicability underscores the unique contribution of our research, paving the way for the development of more precise, personalized treatment strategies in thyroid nodule ablation.

The clinical utility of our model is twofold. Features such as nodule orientation and echogenicity, identified via SHapley Additive exPlanations (SHAP), provide actionable insights for preprocedural planning. For instance, nodules located on the Z-nodule or adjacent to the tracheoesophageal groove may necessitate adjusted ablation parameters or real-time neuromonitoring.

Despite its strengths, this study has limitations. First, its retrospective design may introduce selection bias, though rigorous cross-validation mitigates overfitting concerns. Second, the model was trained on single-center data, and external validation in diverse populations is warranted. Third, while we included key imaging features, emerging biomarkers such as elastography or radiomic signatures were not evaluated due to data availability. Future studies should explore integrating multimodal data (e.g., intraoperative ultrasound thermography) to refine prediction accuracy. Lastly, prospective trials are needed to validate whether model-guided interventions reduce RLN injury incidence in real-world settings.

By combining interpretable ML algorithms with clinically accessible features, this study advances personalized risk assessment for thyroid nodule MWA. The random forest (RF)-based model, with its high discriminative performance and transparent decision pathways, represents a significant step toward safer ablation practices. Future work should focus on real-time integration of predictive analytics into ablation systems and validation to ensure global applicability.

Conclusion

This study successfully developed and validated an explainable machine learning model to predict recurrent laryngeal nerve (RLN) injury during microwave ablation (MWA) of thyroid nodules. By integrating clinical, anatomical, and procedural features, the random forest (RF) model demonstrated exceptional discriminative performance and calibration, outperforming conventional statistical approaches.

Methods

Study cohorts

This retrospective study was approved by the Ethics Committee of Beijing Friendship Hospital, Capital Medical University. As it was a retrospective study with patient privacy protected, informed consent was waived. Medical records of all patients who underwent microwave ablation in the Ultrasound Department of Beijing Friendship Hospital from September 2022 to August 2024 were reviewed. Cases with recurrent laryngeal nerve (RLN) injury during ablation, as documented in surgical records (all cases recovered within 3–6 months), were included. All nodules were classified according to the American College of Radiology Thyroid Imaging Reporting and Data System (TI-RADS). Nodules were divided into high-risk and low-risk groups using TI-RADS 4a as the cutoff (TI-RADS 4a was included in the high-risk group). For each group, ablation cases without RLN injury were matched based on age, sex, and operator, with the following criteria: (1) age difference not exceeding 2 years; (2) consistent sex ratio; and (3) operators being senior physicians with ≥ 3 years of ablation experience. The inclusion criteria were as follows: (1) single lesion ablated in a single session; (2) preoperative ultrasound examination performed; (3) high-risk nodules without evidence of extrathyroidal invasion, lymph node metastasis, or distant metastasis; and (4) underwent microwave ablation therapy and signed written informed consent for treatment. The exclusion criteria were as follows: (1) incomplete clinical or follow-up data; (2) presence of other malignant tumors; (3) poor ultrasound image quality or artifacts; and (4) received radiofrequency ablation treatment or lacked written informed consent.

Clinical feature and data processing

Based on the patients' surgical records and stored images, a total of 23 parameters across five major categories are collected as model features and are shown in Table 1. Demographic characteristics and clinical characteristics among RLN patients are shown in Table 2.

Table 1.

Collected model features

Parameter category	Specific indicators
Basic information parameters (2)	Gender Age
Nodule pathology and morphology parameters (9)	Nodule benignity/malignancy Superior-inferior diameter Left–right diameter Anterior–posterior diameter Aspect ratio (> 1, ≤ 1) Nodule volume: V = abcπ/6 (a: transverse diameter; b: longitudinal diameter; c: anterior–posterior diameter) Overall echogenicity (very low, low, high, mixed) Cystic-solid nature (solid, cystic-solid) Calcification (none, macrocalcification, microcalcification)
Nodule anatomical location parameters (6)	Left–right location (left lobe, right lobe, isthmus), Superior-inferior location (upper pole, middle, lower pole), Distance to anterior thyroid capsule, Distance to posterior thyroid capsule (≤ 2 mm, > 2 mm), Located on Zuckerkandl’s tubercle, Distance to tracheoesophageal groove (TEG) (≤ 2 mm, > 2 mm)
Ablation parameters (5)	Ablation power Ablation time Post-ablation superior-inferior diameter Post-ablation left–right diameter Post-ablation anterior–posterior diameter
Laboratory examination (1)	Laboratory examination

Variable selection

This study employs the Recursive Feature Elimination (RFE) method for variable selection to enhance the predictive performance and improve the stability of the models. RFE, a mainstream feature selection technique in machine learning, iteratively removes less important features to ultimately identify the optimal feature subset, thereby achieving optimal model performance. Throughout the RFE process, we utilized 5 repetitions of fivefold cross-validation to evaluate model performance, ensuring the robustness of the variable selection procedure and the generalizability of the models.

Model development and validation

Four machine learning models—Logistic Regression (LR), Decision Tree (DT), Random Forest (RF), and Support Vector Machine (SVM)—were developed to predict the risk of recurrent laryngeal nerve injury during microwave ablation of thyroid nodules. Logistic regression, a linear probabilistic model, employs a sigmoid activation function to map linear combinations of features to binary outcome probabilities, offering high interpretability through coefficients that directly quantify feature associations with risk. Decision tree uses recursive partitioning based on feature thresholds to split data into homogeneous subsets, generating intuitive, tree-structured decision rules that mimic clinical reasoning but may suffer from overfitting to noise. Random forest, an ensemble learning framework, mitigates this limitation by constructing multiple uncorrelated decision trees via bootstrap sampling and random feature selection, aggregating predictions through majority voting to enhance robustness and reduce variance. Support vector machine, a margin-maximizing model, transforms input features into a high-dimensional space via kernel functions (radial basis function in this study) to identify optimal hyperplanes that separate high-risk and low-risk cases, excelling at capturing nonlinear relationships in complex datasets. To optimize model performance, hyperparameter tuning was conducted for each algorithm: for LR, regularization strength (C) was adjusted; for DT, maximum depth and minimum samples per leaf were optimized; for RF, the number of trees and maximum features were tuned; and for SVM, kernel coefficient (γ) and regularization parameter (C) were calibrated—all via 5 repetitions of fivefold cross-validation to ensure generalizability. The model structure is illustrated in Fig. 1.

Model performance comparison

The reliability of the models is evaluated using several commonly used metrics, including the area under the receiver operating characteristic (ROC) curve (AUC), sensitivity, specificity, positive predictive value (PPV), negative predictive value (NPV), accuracy, F1-score, and Brier score. Decision Curve Analysis (DCA) was further applied to assess the net benefit of the models across varying threshold probabilities.

This study is conducted using data from 254 patients who underwent thyroid nodule MWA. To ensure robust evaluation, the dataset was randomly stratified into a training set (80%, n = 203) for model development and a held-out test set (20%, n = 51) to assess generalizability. All feature selection and hyperparameter tuning were performed exclusively on the training set using 5 × fivefold cross-validation, preventing data leakage. The performance of these evaluation metrics was systematically compared between the training and test sets.

Model explanation

To interpret the predictive logic of the four machine learning models (logistic regression, decision tree, random forest, support vector machine) and clarify their risk assessment mechanisms for RLN injury, we employed the SHapley Additive exPlanations (SHAP) framework. Rooted in cooperative game theory, SHAP quantifies each feature’s contribution to predictions by calculating "Shapley values"—a metric that distributes the total prediction difference (from the baseline average) among individual features, ensuring fair and consistent attribution of influence across all features. This property enables both global interpretability (identifying universally impactful features) and local interpretability (explaining single-case predictions), addressing the "black-box" limitation of complex models.

In this study, SHAP was applied as follows: for each model, we computed SHAP values for all features across the test set. Summary plots visualized the overall importance of features (ranked by mean absolute SHAP values) and their directional effects (positive values indicating increased injury risk, negative values indicating decreased risk). For tree-based models (decision tree, random forest), we further analyzed nonlinear relationships (e.g., how nodule volume interacts with ablation time to affect risk) via SHAP dependency plots. For representative cases, force plots illustrated how top features collectively drove specific risk predictions. This approach revealed both shared key predictors (e.g., distance to tracheoesophageal groove) and model-specific feature interactions, making the models’ decision logic clinically transparent.

Statistical analysis

Statistical analysis was performed using SPSS version 26.0. For normally distributed data, results are expressed as mean ± standard deviation (SD). For nonnormally distributed data, the median and interquartile range (IQR, 25th to 75th percentiles) were used. For continuous variables, normality was assessed using the Shapiro–Wilk test, a statistical method specifically designed to test the null hypothesis that a sample comes from a normally distributed population. The test works by comparing the observed data quantiles with the expected quantiles of a normal distribution, generating a W statistic (ranging from 0 to 1, where values closer to 1 indicate stronger conformity to normality) and a corresponding p-value. In this study, the Shapiro–Wilk test was applied to all continuous variables (e.g., nodule volume, ablation time, distances to anatomical structures) to guide data presentation: if the p-value from the test was > 0.05, the variable was considered normally distributed, and results are expressed as mean ± standard deviation (SD); if p ≤ 0.05 (indicating nonnormal distribution), data were presented as median and interquartile range (IQR, 25th to 75th percentiles). Differences in medians of continuous variables with nonnormal distributions were evaluated using the two-sided Mann–Whitney U test, while differences in means of normally distributed data were assessed using the two-sided Student’s t-test. Categorical data were analyzed using the chi-square test or Fisher’s exact test, as appropriate. Binary logistic regression was employed to identify risk factors associated with recurrent laryngeal nerve (RLN) injury.

Author contributions

Zhixiang Wang and Yawen Wang contributed equally as co-first authors. Zhixiang Wang and Yawen Wang conceived the study design, collected clinical data, and participated in model development and validation. Yiran Wang performed statistical analysis, developed machine learning algorithms, and optimized feature selection. Mingyang Hu and Sunfan Pu contributed to data curation, preprocessing, and clinical interpretation of imaging features. Yanjia Gou assisted in model validation, performance evaluation, and visualization of results. Dong Liu, as the corresponding author, supervised the entire research process, provided critical revisions to the manuscript, and ensured methodological rigor. All authors reviewed and approved the final manuscript.

Funding

This study was funded by Beijing Friendship Hospital; Capital Medical University: YYZZ202453.

Data availability

No datasets were generated or analysed during the current study.

Declarations

Ethics approval and consent to participate

This retrospective study was approved by the Ethics Committee of Beijing Friendship Hospital, Capital Medical University (Approval No. 2022-P2-035-02).

This study was approved by our institutional review board. Informed consent was waived due to the retrospective and anonymous nature of our study.

This study complies with the Declaration of Helsinki. All data were anonymized prior to analysis under ethical committee supervision.

Consent for publication

Before the submission of the manuscript, the authors have obtained consent to publish from all individuals who participated in this study. This includes consent for the publication of anonymized data and any other potentially identifiable information included in the manuscript. The authors understand that the responsibility for ensuring this consent lies with them, and they have taken all necessary steps to safeguard the privacy and rights of the participants. They have also ensured that all participants have been informed about the nature of the publication and the potential use of the data in the public domain.

The requirement for informed consent was waived by the Ethics Committee due to the retrospective nature of the study and the use of fully de-identified patient data.

Competing interests

The authors declare no competing interests.