Abstract

Introduction

Thyroid cancer is a common malignant tumor of the endocrine system, with its global incidence continuing to rise [1-4]. Papillary thyroid carcinoma (PTC) is the most common pathological type. Patients with cervical lymph node metastasis have a higher risk of recurrence and distant metastasis, leading to a poorer prognosis [5-10]. Relevant guidelines recommend that PTC patients assessed preoperatively with lymph node metastasis should undergo surgical treatment [11]. Cervical lymph node dissection is a critical step in surgery, and the extent of dissection needs to balance complete tumor removal with postoperative quality of life. For lateral cervical lymph nodes, current guidelines recommend therapeutic dissection only when preoperative imaging suggests metastasis [3, 12]. However, existing imaging modalities have limitations in assessing lymph node metastasis [13, 14]. Therefore, accurately predicting lateral cervical lymph node metastasis is of great significance for formulating individualized surgical strategies. Current preoperative assessment primarily relies on ultrasound, CT, etc., but their sensitivity and specificity are limited [2, 15-18]. Preoperative lymph node biopsy is the standard method for evaluating LLNM [3]. However, ultrasound-guided fine-needle aspiration (FNA) has limitations in accuracy and carries the potential for sampling error [3, 19]. Constructing prediction models by combining clinicopathological features has become an important approach to improving preoperative assessment accuracy. This study aims to develop an individualized prediction model for lateral cervical lymph node metastasis using routine clinical indicators and to validate its performance through various statistical methods and machine learning algorithms, thereby providing a tool for clinical decision-making.

Methods

Clinical Study and DesignStudy Design

This study included patients with PTC who were admitted to the First Affiliated Hospital of Anhui Medical University from March 2021 to September 2025 and to the Hefei Cancer Hospital of the Chinese Academy of Sciences from March 2019 to September 2025. All surgeries were performed by surgeons from the same treatment team, and postoperative pathological examination confirmed the diagnosis of PTC. Patients who underwent concurrent central and lateral neck lymph node dissection during surgery were selected. Inclusion criteria were: ① preoperative conventional ultrasound examination; ② no history of thyroid surgery. Exclusion criteria were: ① history of head and neck radiotherapy; ② concurrent other head and neck malignancies; ③ incomplete clinical, pathological, or ultrasound data (see Figure 1). The study protocol was approved by the Ethics Committees of The First Affiliated Hospital of Anhui Medical University and Hefei Cancer Hospital of Chinese Academy of Sciences.

Data Collection

Data were retrieved from inpatient medical records. Based on guidelines and previous studies [20-23], 14 variables were selected as candidate predictors: age, sex, maximum tumor diameter, central compartment lymph node metastasis (assessed based on preoperative imaging and intraoperative frozen section pathology), number of metastatic central lymph nodes, number of tumor foci, capsular invasion, calcification, aspect ratio, punctate-strip blood flow signal, nodule margin, nodule location, preoperative TSH, and preoperative Parathyroid Hormone (PTH). Additionally, the three-dimensional measurements (long, intermediate, and short axes) of all tumor foci were collected.

Statistical Analysis

SPSS software (version 26.0) was used for statistical analysis. Categorical data are presented as n (%), and comparisons between groups were performed using the χ² test. Variables with a P value < 0.1 in univariate analysis were included in a subsequent multivariate logistic regression analysis to identify independent predictors. The predictive performance of individual factors and combined indicators was evaluated using Receiver Operating Characteristic (ROC) curves. A P value < 0.05 was considered statistically significant.

Further modeling was conducted using R software (version 4.5.1). The analysis was performed in two stages. Stage 1: Development and internal validation of the logistic regression model using the full dataset. A prediction model and a corresponding nomogram were constructed based on the independent predictors. Model performance was evaluated in terms of: ① Discrimination ability (Receiver Operating Characteristic [ROC] curve and Area Under the Curve, AUC); ② Calibration (calibration curve and Hosmer-Lemeshow test); ③ Clinical utility (Decision Curve Analysis and Clinical Impact Curve). Internal validation was performed using the bootstrap method with 1000 resamples. Stage 2: Comparative analysis using a training-test set split (70%/30%). The data were split into training and validation sets in a 7:3 ratio. Applied machine learning algorithms included: Decision Tree, Random Forest, XGBoost, Support Vector Machine, K-Nearest Neighbors, LightGBM, and Naïve Bayes. These algorithms were selected to represent a diverse range of machine learning paradigms, thereby enabling a comprehensive comparison with the traditional logistic regression model. Specifically, Decision Tree provides an intuitive, rule-based approach for risk classification; Random Forest and XGBoost (extreme gradient boosting) are ensemble methods that handle non-linear relationships and feature interactions effectively, with XGBoost known for its robust performance in structured data; LightGBM (light gradient boosting machine) offers high efficiency and accuracy in gradient boosting frameworks; Support Vector Machine (SVM) is suitable for high-dimensional feature spaces through kernel transformation; K-Nearest Neighbors (KNN) serves as a non-parametric, instance-based learning method; and Naïve Bayes provides a probabilistic approach based on conditional independence assumptions. Collectively, this set of algorithms covers key categories—including tree-based models, ensemble methods, kernel-based methods, distance-based methods, and probabilistic classifiers—allowing for a rigorous evaluation of model performance across different analytical frameworks. Models were comprehensively assessed using the Area Under the ROC Curve, calibration curves, and decision curves. The SHAP (SHapley Additive exPlanations) method was used to interpret the model decision mechanisms.

Using an ellipsoid geometric model, we calculated three refined metrics beyond the "maximum tumor diameter" for each patient: total volume sum of all tumor foci (V = (π/6)abc), total surface area sum (S ≈ π(((ab)^p + (ac)^p + (bc)^p)/3)^1/p, p = 1.6075), and sphericity of the largest tumor focus (Ψ = 3a/(a+b+c)) (see Figure 1).

The ellipsoid model was selected because it is the most commonly used geometric approximation for thyroid nodules in clinical ultrasound practice. In this setting, tumors are typically measured along three orthogonal axes (long, intermediate, and short). In our study population, the majority of tumor foci exhibited a shape consistent with the ellipsoid assumption (i.e., well-defined, roughly ovoid contours), as confirmed by preoperative ultrasound imaging. While more sophisticated three-dimensional reconstruction techniques exist, the ellipsoid model offers a practical and reproducible method for routine clinical application.

Results

Development of a Prediction Model Based on Logistic Regression

Univariate and Multivariate Analysis. Among the 241 patients, significant differences (P < 0.1) were found between the metastasis and non-metastasis groups regarding the following variables: age, sex, maximum tumor diameter (> 1 cm), central compartment lymph node metastasis, number of metastatic central lymph nodes, ill-defined nodule margin, aspect ratio (> 1), nodule location, preoperative TSH, and preoperative PTH. These variables were included in a multivariate logistic regression analysis. The results identified the following as independent risk factors for predicting lateral lymph node metastasis (LLNM): maximum tumor diameter, central compartment lymph node metastasis status, nodule location, and preoperative TSH level (see Table 1, Table 2, and Table 3).

Development and Predictive Performance of Model. Using the full dataset (241 patients), ROC curves were plotted for each independent predictor to evaluate their individual predictive value (see Figure 2). The prediction model was converted into a nomogram for direct clinical application (see Figure 3). The model exhibited good discriminatory ability with an AUC of 0.832. Internal validation using the bootstrap method (1000 repetitions) showed a high consistency between predicted and actual probabilities on the calibration curve (mean absolute deviation [MAD] = 0.023). The Hosmer-Lemeshow test yielded a P-value of 0.137, suggesting good model calibration. Decision curve analysis demonstrated that within the threshold probability range of 0.1 to 0.5, the net benefit of applying this model was higher than both the "intervention for all" and "intervention for none" strategies, indicating its potential clinical utility.

Construction and Comparison

To compare the performance of different modeling approaches, a training-test set split strategy (70%/30%) was employed. Based on the preliminary analysis, four predictive variables were included: central compartment lymph node metastasis status, maximum tumor diameter, nodule location, and preoperative TSH. All models were developed on the training set (70% of the data) and evaluated on the validation set (30% of the data). Multivariate logistic regression was used as the primary method to construct the prediction model. For supplementary comparison, seven machine learning algorithms were also applied, resulting in a total of eight prediction models. The confusion matrices for each model in the validation set are shown in Figure 4. The LightGBM model achieved the highest F1 score (0.56), indicating the best balance between sensitivity and specificity. However, the logistic regression model outperformed all other models in terms of discriminative ability (highest AUC), calibration (lowest Brier score [a measure of calibration accuracy], 0.124), and clinical utility (broadest range of net benefit on the decision curve analysis), suggesting it holds the greatest potential for broad clinical applicability (see Figure 5).

Threshold Optimization. Systematic optimization of classification thresholds revealed that the default threshold (0.5) was not optimal. Logistic Regression achieved its best F1 score (0.917) at a threshold of 0.6, making it suitable for scenarios emphasizing specificity. LightGBM reached its optimal F1 score (0.889) at a threshold of 0.3, rendering it more appropriate for screening contexts requiring high sensitivity (see Table 4). After threshold optimization, Logistic Regression, with the highest AUC and the optimal F1 score, emerged as the prediction model with the best overall performance (see Figure 6).

Comprehensive Evaluation and Discussion of Algorithmic Models. Based on the comprehensive performance evaluation, the Logistic Regression model demonstrated the best performance in terms of predictive accuracy and clinical utility. This model exhibited the highest discriminative ability (AUC = 0.859), the most accurate predicted probabilities (Brier score = 0.124), and its calibration curve aligned most closely with the ideal diagonal line. Within the clinical decision threshold range of 0.05 to 0.75, this model could provide the greatest net benefit (0.579). It ranked first across all three core evaluation dimensions: the ROC curve, calibration curve, and decision curve analysis. Its performance improved significantly after optimizing the classification threshold to 0.6. This model was thus identified as the optimal prediction model in this study.

Model Interpretability Analysis Based on SHAP. Model interpretability analysis was conducted using the SHAP (SHapley Additive exPlanations) method. In the Logistic Regression model, the order of variable importance was as follows: Central Compartment Metastasis > Nodule Location > Maximum Tumor Diameter > Preoperative TSH (see Figure 7). In the LightGBM model, the order of feature importance was: Central Compartment Metastasis > Maximum Tumor Diameter > Nodule Location > Preoperative TSH (see Figure 8). The SHAP summary plot illustrates the contribution of each feature's value to the model's predictive output, visually explaining the process of transforming feature inputs into predicted probabilities.

Exploration of Multivariate Prediction Models Using Alternatives to Maximum Tumor Diameter

Consistent with the comparative analysis described above, the training-test set split strategy (70%/30%) was used in this section as well. The variable "maximum tumor diameter" in the original model was sequentially replaced with the total tumor volume, total tumor surface area, and sphericity, following the same modeling process. The results showed that the AUCs for models based on total tumor volume, total tumor surface area, and sphericity were 0.835, 0.839, and 0.816, respectively. Notably, the AUCs for models using total tumor volume and total surface area were 0.835 and 0.839, respectively, which were slightly higher compared to that of the original model (AUC = 0.832) (see Table 5).

ROC curves and nomograms were plotted for each alternative indicator (see Figure 9 and Figure 10). The optimal cut-off value of total tumor surface area for predicting LLNM was 4.6295 cm², yielding a sensitivity of 49.7% and a specificity of 82.3%, with an AUC of 0.689 (95% CI: 0.616–0.762). Patients with a total tumor surface area exceeding this threshold should be alerted to a higher risk of LLNM.

Maximum tumor diameter, total tumor volume, total tumor surface area, and sphericity provide complementary multidimensional information: maximum diameter serves as the classic one-dimensional indicator of linear growth; total tumor volume quantifies the overall tumor burden, which may be more directly related to metastatic potential; total tumor surface area characterizes the contact interface between the tumor and its microenvironment (blood vessels, lymphatic vessels) and is theoretically more closely associated with invasion and metastasis; sphericity reflects the morphological irregularity of the dominant tumor focus, potentially indicating more aggressive growth. Although these metrics are computationally related, they individually characterize the tumor's size, burden, interface, and shape features, holding independent biological significance. We regard them as a set of geometric candidate predictors to verify their incremental predictive value relative to maximum diameter indicators.

A baseline model was constructed based on maximum tumor diameter, central compartment metastasis, nodule location, and preoperative TSH, with each three-dimensional parameter subsequently added for comparison. The results revealed that the AUC of all combined models did not exceed that of the "Predicted probability (surface area sum)" model (AUC = 0.839) (Figure 11, Table 6). This model incorporated only the core three-dimensional parameter. This model achieved the highest sensitivity (87.7%) and accuracy (84.0%) while maintaining stable specificity (74.2%), and its AUC was also superior to that of the baseline model (0.839 vs. 0.832). The performance of other models containing three-dimensional parameters was comparable but did not surpass it, suggesting that three-dimensional parameters—especially surface area sum—already possess promising independent predictive potential.

To further validate the incremental predictive value of three-dimensional geometric parameters, this study adopted a training-test set split strategy (70%/30%) to redevelop and systematically compare 11 prediction models. It should be noted that while the specific numerical results obtained from this validation approach differ from those derived from the Stage 1 full-dataset analysis, the core conclusions remain consistent, reflecting the generalization performance of the models in an independent test set.

In the test set, the model with the highest AUC was the "Basic + Volume" model (AUC = 0.8475, 95% CI: 0.7521–0.9428). Although its point estimate of AUC was marginally higher than that of the basic model (AUC = 0.8455), the difference was not statistically significant (Delong test, adjusted P = 1.000) (Table 7). This finding suggests that adding total tumor volume to the maximum diameter may provide modest complementary information in quantifying tumor burden, thereby achieving favorable discriminative performance within this dataset.

From a clinical perspective, the lack of statistical significance indicates that the basic model—which relies on the more readily available maximum tumor diameter—achieves predictive performance comparable to the more complex model incorporating total tumor volume. However, the slightly higher AUC of the "Basic + Volume" model suggests that total tumor volume may capture additional information related to overall tumor burden in multifocal cases, which could be clinically valuable when preoperative assessment aims to maximize predictive accuracy. Thus, model selection can be tailored to clinical priorities: the basic model offers simplicity and ease of use, making it a more practical alternative for general application, while the "Basic + Volume" model may be considered when a marginally higher discriminative performance is desired, particularly in patients with multifocal disease. By incorporating only four routine variables, the basic model achieves nearly equivalent discriminative efficacy (AUC difference: 0.002) while substantially enhancing generalizability and operational feasibility.

Discussion

Surgery is the primary treatment for papillary thyroid carcinoma (PTC). Accurate preoperative assessment of lateral cervical lymph node metastasis (LLNM) status is crucial for determining the extent of lymph node dissection, which directly impacts surgical complications (such as recurrent laryngeal nerve injury [24], hypoparathyroidism [25], chylous leakage [26], etc.) and patients' quality of life.

This study collected data from PTC patients across two centers. Based on three indicators—maximum tumor diameter, central compartment lymph node metastasis status, and nodule location—an individualized prediction model for LLNM was developed. The model demonstrated good predictive performance (AUC = 0.832) and calibration. Decision curve analysis confirmed its clinical utility.

To further enhance and compare performance, this study constructed multiple models, including multivariate logistic regression and seven machine learning algorithms. A comprehensive comparison revealed that after threshold optimization, the Logistic Regression model performed optimally at a threshold of 0.6, making it suitable for decision-making scenarios emphasizing specificity. The LightGBM model performed best at a threshold of 0.3, rendering it more appropriate for high-sensitivity screening. Considering all evaluation metrics, Logistic Regression was identified as the optimal prediction model.

Furthermore, this study innovatively introduced three-dimensional morphological parameters. For multifocal PTC, the total tumor volume and total tumor surface area were calculated. Models based on total tumor surface area (AUC = 0.839) or total tumor volume (AUC = 0.835) showed slightly higher predictive performance than the model based on maximum diameter (AUC = 0.832). When the total tumor surface area exceeds 4.6295 cm², a high risk of LLNM should be strongly suspected. This finding validates the hypothesis that three-dimensional morphological parameters possess complementary discriminatory power, providing a new basis for clinical assessment.

Maximum tumor diameter reflects only unidimensional linear growth and does not accurately quantify total tumor burden or the true spatial configuration of multifocal lesions. Total tumor volume directly represents the overall tumor cell load, and its association with metastatic potential may be stronger than that of maximum diameter alone in multifocal PTC. Total surface area more closely approximates the interface between the tumor and surrounding lymphatic and vascular pathways. A larger surface area may provide greater opportunity for tumor cells to breach the basement membrane and invade the vasculature, thus serving as a more direct indicator of invasive potential. Sphericity, as a morphological descriptor, offers a novel perspective for evaluating tumor growth patterns, with irregular morphology often suggesting enhanced proliferative activity and aggressive behavior.

Although the inclusion of three-dimensional parameters did not significantly improve the AUC of the basic model, both the "Surface area substitution" and "Volume substitution" models demonstrated predictive performance comparable to that of the basic model, with no statistically significant differences. These findings indicate that the predictive information embedded in three-dimensional parameters—particularly total surface area—largely encompasses that conveyed by unidimensional maximum diameter, conferring independent and equivalent discriminative capacity. Accordingly, total surface area derived from 3D imaging reconstruction holds promise as a preoperative predictive biomarker. It is at least equivalent to, and potentially provides more information than, maximum tumor diameter. It may facilitate risk assessment and guide individualized surgical decision-making, underscoring its clear potential for clinical translation.

In summary, this study advances the exploration from "unidimensional metrics" to the refinement of "three-dimensional geometric characterization." The results demonstrate that three-dimensional geometric parameters—especially total surface area—more comprehensively elucidate metastatic risk across dimensions such as tumor burden, interfacial effects, and growth morphology. These findings establish them as valuable complementary predictors of lateral cervical lymph node metastasis in PTC. Future research should validate their robustness in prospective, multicenter cohorts and investigate their integrated application with radiomic features and molecular markers.

Analysis of Predictive Factors

This study confirms that the maximum tumor diameter is an independent predictive factor for LLNM, consistent with previous research [27-30]. Larger tumor diameters are typically associated with greater invasiveness and a higher risk of metastasis. Central compartment lymph node metastasis was also confirmed as a robust predictive indicator [31, 32]. As the primary lymphatic drainage site, its status effectively reflects the tumor's metastatic propensity. However, in some cases, patients may exhibit skip metastasis: negative central lymph nodes with positive lateral lymph nodes [33, 34], which can be easily missed during preoperative evaluation and surgery [35]. The influence of tumor location on metastasis risk may be related to anatomical differences in lymphatic drainage [27, 36, 37]. The results of this study indicate that when the total tumor surface area exceeds 4.6295 cm², patients face a significantly increased risk of LLNM. This threshold can serve as an effective early-warning indicator.

Model Comparison and Strengths

Compared to previous studies, the strengths of our model include: ① It integrates multiple independent predictive factors to provide individualized risk assessment; ② Visualization through a nomogram facilitates direct clinical application; ③ Comprehensive validation of model performance using various statistical methods; and ④ Systematic comparison of multiple machine learning algorithms, revealing their respective application potentials.

Clinical Significance and Application

The prediction model and nomogram tool developed herein can assist clinicians in more accurately assessing the risk of lateral cervical lymph node metastasis preoperatively, thereby facilitating the formulation of individualized surgical plans. For patients identified as high-risk by the model, therapeutic or prophylactic lateral neck dissection may be considered. For low-risk patients, overtreatment can be potentially avoided.

Study Limitations and Future Directions

This study is a dual-center investigation with a limited sample size; therefore, its conclusions require further validation through multicenter, prospective studies with larger cohorts. Future research could integrate multi-dimensional information such as radiomics and circulating tumor markers [29, 38-40] to enhance predictive accuracy. Despite these limitations, this study successfully developed and validated a prediction model based on readily available clinical indicators. It demonstrates good predictive performance and clinical utility, providing a valuable reference for individualized preoperative lymph node assessment in PTC patients.

Conclusion

In this study, an effective clinical prediction model for assessing lateral lymph node metastasis risk was successfully developed using readily available clinical indicators, demonstrating good predictive performance and clinical utility. This model, based on four routine variables (maximum tumor diameter, central lymph node metastasis, nodule location, and preoperative TSH), is well-suited for widespread application across various clinical settings—from primary hospitals where advanced imaging resources may be limited to tertiary referral centers seeking rapid, standardized risk stratification. The incorporation of three-dimensional morphological parameters—particularly total tumor surface area and total tumor volume—shows promising potential for enhancing risk assessment in multifocal papillary thyroid carcinoma. However, these findings require further validation in prospective, multicenter cohorts before clinical implementation. Additionally, the relatively complex measurement procedures and the need for automated tools currently limit the widespread applicability of three-dimensional parameters. Future efforts should focus on developing efficient, automated measurement tools to facilitate clinical translation.

Abbreviations

AUC: Area Under the Curve; CI: Confidence Interval; CT: Computed Tomography; FNA: Fine-Needle Aspiration; KNN: K-Nearest Neighbors; LightGBM: Light Gradient Boosting Machine; LLNM: Lateral Lymph Node Metastasis; MAD: Mean Absolute Deviation; PTC: Papillary Thyroid Carcinoma; PTH: Parathyroid Hormone; ROC: Receiver Operating Characteristic; SHAP: SHapley Additive exPlanations; SVM: Support Vector Machine; TSH: Thyroid-Stimulating Hormone; XGBoost: Extreme Gradient Boosting.

Declarations

Acknowledgements

Not applicable.

Author Contributions

The manuscript was conceived by all authors. Shu Wang, Yanqiang Zhang and Kaile Wu designed the article; Shu Wang drafted the manuscript which was subsequently edited by Ziyue Fu, Chuanlu Shen, Siyu Jia, Shugang Zhao and Kaile Wu. All authors reviewed the manuscript.

Funding information

Not applicable.

Ethics Approval and Consent to Participate

This study was conducted in accordance with the principles of the Declaration of Helsinki. With approval from the Ethics Committees of The First Affiliated Hospital of Anhui Medical University (Approval No. PJ 2024-12-91) and Hefei Cancer Hospital of Chinese Academy of Sciences (Approval No. PJ-KY2025-008), the need for informed consent was waived due to the non-interventional, retrospective study design.

Consent for Publication

Not applicable.

Competing Interests

The authors declare no competing interests.

Data availability

The datasets obtained and/or analyzed during the current study are available from the corresponding author on reasonable request.

References