Dual-center development and external validation of machine learning models integrating PSA-derived and peripheral inflammatory markers for prostate cancer diagnosis

Introduction

Prostate cancer (PCa) is one of the most frequently diagnosed malignancies among men worldwide (1). Prostate-specific antigen (PSA) remains a widely used screening biomarker, but it is not cancer-specific. The PSA gray zone is commonly defined as a serum PSA concentration of 4–10 ng/mL; within this interval, benign prostatic hyperplasia (BPH), inflammation, and PCa can produce overlapping PSA values, making biopsy selection particularly uncertain (2). Improving risk stratification in this group could reduce unnecessary biopsies while limiting missed clinically relevant disease.

Systemic tumor-related inflammation may alter circulating leukocyte profiles. Neutrophils can support inflammatory signaling and tumor progression, reduced lymphocyte counts may reflect weakened antitumor immune surveillance, and circulating monocytes may reflect recruitment of cells capable of differentiating into tumor-associated macrophages. Ratios such as the neutrophil-to-lymphocyte ratio (NLR) and monocyte-to-lymphocyte ratio (MLR) therefore integrate pro-inflammatory and immune components, although their standalone diagnostic performance is variable and they are susceptible to nonmalignant conditions and medications (3,4).

Existing PCa prediction studies frequently rely on imaging, radiomics, or specialized biomarker panels, whereas fewer studies have directly compared conventional and machine-learning approaches based only on low-cost PSA-derived and routine blood-cell variables across institutions. Logistic regression provides a transparent linear benchmark; a decision tree offers traceable threshold-based rules; and XGBoost can model nonlinear effects and higher-order interactions while using regularization to limit overfitting (5-8). Comparing these complementary approaches may clarify whether additional complexity produces clinically meaningful gains.

The primary objective of this study was to develop and evaluate logistic regression, decision tree, and XGBoost models that integrate PSA-derived variables with peripheral blood inflammatory markers for distinguishing PCa from BPH. Secondary objectives were to compare the models on a common internal-validation set, evaluate transportability in an independent institutional cohort, and examine performance in the PSA gray-zone subgroup. We present this article in accordance with the TRIPOD reporting checklist (available at https://tau.amegroups.com/article/view/10.21037/tau-2026-0678/rc).

Methods

Study population

This retrospective study consecutively screened patients according to the prespecified inclusion and exclusion criteria and enrolled 317 eligible patients who underwent prostate histopathological examination at Hainan General Hospital between January 2019 and December 2024. All participants were newly diagnosed and treatment-naïve at enrollment. Based on the final pathological diagnosis, 166 patients had BPH and 151 had PCa. The development cohort was divided by outcome-stratified random sampling into a training set (80%) and an internal-validation set (20%). Previously established random seeds were fixed before the present rerun to reproduce the original data partitions and model results.

External validation used an independent cohort of 60 consecutively screened patients treated at The First Affiliated Hospital of Hainan Medical University between January 2023 and December 2024, including 30 patients with BPH and 30 with PCa. This cohort originated from a different institution and was selected using the same eligibility criteria, predictor definitions, outcome definition, and specimen-testing schedule as the development cohort.

The inclusion criteria were: (I) a first diagnosis of PCa or BPH confirmed by prostate histopathology; (II) availability of total PSA (tPSA), free PSA (fPSA), and routine blood-cell results from the first blood draw after admission and before biopsy, surgery, or any anticancer treatment; and (III) complete pathological outcome data. The exclusion criteria were: (I) active infection or inflammatory disease at admission, including clinically documented urinary tract infection or acute prostatitis; (II) autoimmune, immunodeficiency, or hematologic disease likely to alter leukocyte-derived indices; (III) another concurrent malignancy; (IV) any chemotherapy, radiotherapy, endocrine therapy, immunotherapy, or prostate surgery before blood collection; (V) use before sampling of systemic glucocorticoids, immunosuppressants, or other drugs known to markedly affect circulating leukocyte counts; (VI) missing key predictor or outcome data; and (VII) recent urinary catheterization, prostate manipulation or biopsy, antibiotic use, or anti-inflammatory medication use. The study was conducted in accordance with the Declaration of Helsinki and its subsequent amendments. The study was approved by Ethics Committee of Hainan General Hospital (Hainan Affiliated Hospital of Hainan Medical University) (No. EC- YLY-2026-287-01) and Ethics Committee of The First Affiliated Hospital of Hainan Medical University (No.) [if no ethical approval number, kindly ignore the content in parentheses]. Written informed consent was obtained from the patients for participation in this study.

Data collection

Venous blood results were obtained from the first blood draw after admission, before pathological diagnosis and before any biopsy-related intervention, surgery, or anticancer treatment. Recorded variables included total PSA (tPSA), free PSA (fPSA), white blood cell count (WBC), neutrophil count (NeuC), neutrophil percentage (NeuP), lymphocyte count (LymC), lymphocyte percentage (LymP), monocyte count (MonC), and monocyte percentage (MonP). Derived variables were calculated as follows: f/t PSA = fPSA/tPSA; NLR = NeuC/LymC; and MLR = MonC/LymC. The earliest eligible measurements were used when more than one result was available.

The reference outcome was the final histopathological diagnosis of PCa or BPH recorded after clinically indicated examination of prostate tissue at each participating center.

PSA and routine blood-cell results obtained during routine clinical care were extracted from the laboratory information systems of the two participating centers; details regarding analyzers, reagents, and assay principles were not consistently available in the retrospective dataset. These technical details are therefore not reported to avoid unsupported specificity; possible interlaboratory measurement heterogeneity is acknowledged as a study limitation.

Statistical analysis

The distribution of continuous variables was assessed using the Shapiro-Wilk test. Normally distributed variables were presented as mean (standard deviation) and compared using the independent-samples t-test. Non-normally distributed variables were presented as median [interquartile range (IQR)] and compared using the Mann-Whitney U test. Categorical variables were presented as number (percentage) and compared using the Chi-squared test or Fisher’s exact test as appropriate. Patients with missing pathological outcomes were excluded. In accordance with the analysis code, missing numeric predictor values, if present, were median-imputed before model fitting; for the common-split comparison, imputation values were estimated from the training set and then applied to the internal-validation set.

Receiver operating characteristic (ROC) analyses were performed to evaluate the diagnostic performance of single indicators, and the area under the curve (AUC) values were calculated. Three multivariable approaches were then examined for complementary reasons: logistic regression served as the conventional linear and interpretable benchmark, with stepwise selection based on the Akaike information criterion; the decision tree used recursive binary splitting to produce explicit clinical thresholds; and XGBoost used regularized gradient boosting to capture nonlinear effects and interactions. Model interpretability was summarized using the decision-tree splitting rules and XGBoost gain-based feature importance. Logistic-regression coefficients were interpreted cautiously because several raw and derived predictors were correlated.

For each model-specific reproducibility analysis, outcome-stratified random sampling allocated 80% of the development cohort to model fitting and 20% to internal validation. In the same-split comparison analysis, all individual indicators and all of the three models were evaluated in the internal-validation subset generated by the fixed overall decision-tree split. Within these training data, the 10-fold cross-validation procedure implemented in part was used to estimate the cross-validated error of the decision tree, whereas 10-fold XGBoost cross-validation was used to select the number of boosting iterations. Neither cross-validation procedure replaced the final performance evaluation in the held-out 20% internal-validation subset. Model performance was primarily assessed based on the AUC and its 95% confidence interval (CI). AUCs calculated from the same patients were compared using the paired DeLong test, and the resulting P values were adjusted for multiple comparisons using the Benjamini–Hochberg method. A two-sided P value <0.05 was considered statistically significant. All analyses were performed in R software (version 2025.09.1) with relevant packages (e.g., xgboost, pROC, caret, data. table, ggplot2, rpart, rpart.plot, readxl, openxlsx, Matrix, dplyr, purrr, writexl, openxlsx, tidyverse, broom, car, Resource Selection, showtext, sysfonts).

Results

Descriptive analysis of the overall cohort

Clinical and laboratory characteristics were compared between the BPH and PCa groups to identify candidate predictors for diagnostic modeling. The overall cohort comprised 317 patients, including 166 patients with BPH and 151 patients with PCa. Given the marked skewness of PSA distributions, comparisons were performed using medians and IQRs, and tPSA values were log10-transformed for boxplot visualization.

The PCa group demonstrated significantly higher tPSA, fPSA, NLR, and MLR levels, and a significantly lower f/t PSA ratio and LymC than the BPH group (all P<0.05). Age, WBC, MonC, and NeuC did not differ significantly between the groups. These findings suggested that PSA-related variables and selected inflammatory indicators were associated with PCa and could serve as potential predictors for subsequent diagnostic model development (Table 1 and Figure S1).

The external-validation cohort included 30 patients with BPH and 30 with PCa, with complete data for all 12 available laboratory predictors. The PCa group had higher tPSA and fPSA and a lower f/t PSA ratio (all P=0.01), whereas leukocyte variables, NLR, and MLR did not differ significantly (all P=0.58). PSA-related differences were directionally consistent with the development cohort, but inflammatory-marker differences were not reproduced. Age was unavailable (Table 2).

Comparison of diagnostic performance between individual indicators and multivariable models in the overall cohort

Diagnostic performance of individual markers in the overall cohort

ROC analysis was performed to assess the discriminative ability of each single indicator. Among the single indicators, tPSA showed the best diagnostic performance, with an AUC of 0.801 [95% confidence interval (CI): 0.751–0.851], a sensitivity of 0.775, a specificity of 0.711, and a Youden index of 0.486. Notably, f/t PSA ratio (AUC =0.771) and fPSA (AUC =0.703) showed moderate discriminative ability, with fPSA demonstrating relatively high specificity (0.843). NLR had an AUC of 0.624 with relatively high sensitivity (0.775), whereas MLR showed lower diagnostic accuracy (AUC =0.582). The AUC values of NeuP, LymP, MonP, and WBC were all below 0.62 (Table 3 and Figure S2).

Logistic regression model based on the overall cohort

Given the limited diagnostic performance of single indicators, combined models were developed to determine whether the integration of multiple indicators could improve PCa diagnosis. The logistic regression model achieved an AUC of 0.847 (95% CI: 0.799–0.896) in the training set and 0.777 (95% CI: 0.660–0.894) in the test set (Figure 1), indicating improved performance compared with the single‑indicator models but reduced performance in the test set. Variable-importance analysis based on absolute values of regression coefficients identified MonC, LymC, MLR, f/t PSA ratio, and NeuC as the top contributing variables (Figure S3). Given that PSA-related variables and blood cell-derived indices may exhibit correlations within the regression model, absolute coefficient values were interpreted as measures of model contribution rather than independent causal effects. The complete logistic regression model specification is shown in Table S1.

Figure 1 ROC curve of the logistic regression model based on the overall data. AUC, area under the curve; CI, confidence interval; ROC, receiver operating characteristic.

Decision tree model based on the overall cohort

To establish a clinically interpretable stratification rule, a decision tree model was developed. The root-node split in the model was based on tPSA at a threshold of 11 ng/mL. Patients with tPSA <11 ng/mL were more likely to be classified as having BPH, whereas those with tPSA ≥11 ng/mL were more likely to be classified as having PCa. In the low-tPSA branch, patients were further stratified by tPSA, NLR, and f/t PSA ratio, while in the high-tPSA branch, patients were further stratified by tPSA, MLR, f/t PSA ratio, and LymC. Patients with tPSA ≥31 ng/mL or those with tPSA ≥11 ng/mL combined with a MLR ≥0.29 had a higher predicted probability of PCa (Figure 2). The decision tree model achieved AUC values of 0.903 (95% CI: 0.866–0.940), 0.867 (95% CI: 0.780–0.954), and 0.724 (95% CI: 0.593–0.856) in the training, internal validation, and external validation sets, respectively (Figure 3, Figures S4,S5 and Table S2).

Figure 2 Decision tree model based on the overall data. In the figure, “negative” and “positive” denote model predictions of benign prostatic hyperplasia and prostate cancer, respectively; The two values in each node represent the predicted probabilities of benign prostatic hyperplasia and prostate cancer, respectively, within that node. The percentage indicates the proportion of samples assigned to each node relative to the total sample size. f/t PSA ratio, free-to-total prostate-specific antigen ratio; LymC, lymphocyte count; MLR, monocyte-to-lymphocyte ratio; NLR, neutrophil-to-lymphocyte ratio; tPSA, total prostate-specific antigen.

Figure 3 ROC curve of the decision tree model for the overall data. AUC, area under the curve; CI, confidence interval; ROC, receiver operating characteristic.

XGBoost model based on the overall cohort

The XGBoost model showed strong discriminative performance, achieving an AUC of 0.930 in the training set (Figure 4), 0.933 in the internal validation set, and 0.781 in the external validation set (Figures S6,S7). Feature-importance analysis identified tPSA, f/t PSA ratio, fPSA, NLR, and MLR as the five most important variables in the model (Figure 5). The XGBoost parameter settings are presented in Table S3.

Figure 4 ROC curve of the eXtreme Gradient Boosting (XGBoost) model for the overall data (training set). AUC, area under the curve; CI, confidence interval; ROC, receiver operating characteristic.

Figure 5 Feature importance of the eXtreme Gradient Boosting (XGBoost) model for the overall data. f/t PSA ratio, free to total prostate-specific antigen ratio; fPSA, free prostate-specific antigen; LymC, lymphocyte count; LymP, lymphocyte percentage; MLR, monocyte to lymphocyte ratio; MonC, monocyte count; MonP, monocyte percentage; NeuC, neutrophil count; NeuP, neutrophil percentage; NLR, neutrophil to lymphocyte ratio; tPSA, total prostate-specific antigen; WBC, white blood cell count.

Model comparison in the overall cohort

For a paired comparison on identical participants, all markers and multivariable models were refitted or evaluated using the same fixed training/internal-validation split defined by the overall decision-tree analysis. In this common internal-validation subset, the decision tree had the highest AUC (0.867), followed by f/t PSA ratio (0.865), XGBoost (0.851), logistic regression model (0.811), tPSA (0.792), and NLR (0.703). These comparison-set AUCs differed from the model-specific AUCs reported above because the latter came from each model’s previously fixed reproducibility split. After multiple-comparison correction, no significant differences in AUC were observed among the three multivariable models, indicating comparable discriminative performance within the validation set. Compared with NLR alone, the decision tree model achieved a significantly higher AUC after correction (adjusted P=0.03) (Table 4).

Analysis and comparison of diagnostic performance in the PSA gray-zone subgroup

Given the reduced discriminative performance of tPSA in the PSA gray zone (4–10 ng/mL), a gray-zone subgroup was derived from the overall cohort. The subgroup comprised 116 patients, including 46 patients with PCa and 70 patients with BPH.

Univariate analysis in the gray-zone subgroup

In the gray-zone subgroup, tPSA showed a reduced AUC of 0.625, with a sensitivity of 0.595 and a specificity of 0.656. fPSA had an AUC of 0.627 and the highest specificity (0.844). In contrast, f/t PSA ratio achieved the highest AUC among the single indicators in this subgroup (0.683). NLR (AUC =0.584) and MLR (AUC =0.492) showed reduced diagnostic performance, although NLR and WBC had relatively high sensitivity (0.865). The AUC values of NeuP, LymP, MonP, and WBC were all below 0.60 (Table 5 and Figure S8).

Logistic regression model in the gray-zone subgroup

Given the reduced performance of single indicators in the gray-zone subgroup, combined models were further evaluated. The logistic regression model achieved an AUC of 0.796 (95% CI: 0.690–0.902) in the training set and 0.584 (95% CI: 0.376–0.792) in the test set (Figure 6). The lower AUC in the test set may reflect the limited sample size. Variable-importance analysis showed relatively high absolute regression coefficients for MonC and f/t PSA ratio, followed by NeuC, WBC, LymC, and MLR. Notably, tPSA was not among the top 10 variables (Figure S9). The logistic regression model parameters for the gray-zone subgroup are presented in Table S4.

Figure 6 ROC curve of the logistic regression model in the gray zone. AUC, area under the curve; CI, confidence interval; ROC, receiver operating characteristic.

Decision tree model in the gray-zone subgroup

To improve diagnostic accuracy among patients in the PSA gray zone, a decision tree model was constructed. f/t PSA ratio served as the primary splitting variable, with a root-node threshold of approximately 0.10. The model further incorporated LymP, NLR, MonC, and tPSA for subsequent risk stratification (Figure 7). The decision tree achieved an AUC of 0.832 (95% CI: 0.733–0.932) in the training set and 0.768 (95% CI: 0.524–1.000) in the validation set (Figure S10). The decision tree parameters for the gray-zone subgroup are presented in Table S5.

Figure 7 Decision tree model in the gray zone. In the figure, “negative” and “positive” denote model predictions of benign prostatic hyperplasia and prostate cancer, respectively. The two values in each node represent the predicted probabilities of benign prostatic hyperplasia and prostate cancer, respectively, within that node. The percentage indicates the proportion of samples assigned to each node relative to the total sample size. f/t PSA ratio, free-to-total prostate-specific antigen ratio; LymP, lymphocyte percentage; MonC, monocyte count; NLR, neutrophil-to-lymphocyte ratio; tPSA, total prostate-specific antigen.

XGBoost model in the gray-zone subgroup

The gray-zone XGBoost model achieved an AUC of 0.806 (95% CI: 0.712–0.900) in the training set (Figure 8) and 0.869 in the internal validation set (Figure S11). Feature-importance analysis showed that the five most important variables were f/t PSA ratio, tPSA, NLR, WBC, and fPSA (Figure 9). The gray-zone XGBoost hyperparameters are presented in Table S6.

Figure 8 ROC curve of the eXtreme Gradient Boosting (XGBoost) model in the gray zone. AUC, area under the curve; CI, confidence interval; ROC, receiver operating characteristic.

Figure 9 Feature importance of each indicator in the gray zone. f/t PSA ratio, free to total prostate-specific antigen ratio; fPSA, free prostate-specific antigen; LymC, lymphocyte count; LymP, lymphocyte percentage; MLR, monocyte to lymphocyte ratio; MonC, monocyte count; MonP, monocyte percentage; NeuC, neutrophil count; NeuP, neutrophil percentage; NLR, neutrophil to lymphocyte ratio; tPSA, total prostate-specific antigen; WBC, white blood cell count.

Comparison of models in the PSA gray-zone subgroup

The DeLong test performed on the same validation set revealed no statistically significant differences in AUC among the gray-zone models or between these models and the main single-factor indicators. Given the limited sample size of the gray-zone subgroup and the potential instability of performance estimates from a single training-validation split, bootstrap resampling was additionally applied for optimism correction.

The decision tree model achieved an apparent AUC of 0.916, with a mean optimism of 0.159 and an optimism-corrected AUC of 0.757. The optimism-corrected AUC values of the XGBoost and logistic regression models were 0.649 and 0.609, respectively (Table 6).

Discussion

PSA-related variables and peripheral inflammatory markers provided complementary diagnostic information for PCa; however, the magnitude and stability of discrimination varied across modeling approaches. In the overall cohort, tPSA remained the best-performing single marker (AUC =0.801), whereas f/t PSA ratio and fPSA also showed moderate diagnostic value. After multivariable modeling, the logistic regression model achieved an AUC of 0.847 in the training set and an AUC of 0.777 in the test set, while the decision tree and XGBoost models showed higher apparent or internal discrimination, with external validation AUC values of 0.724 and 0.781, respectively. However, DeLong testing based on the same internal validation set revealed no statistically significant differences among the three multivariable models after multiple-comparison correction. These findings suggest that the observed improvement over conventional modeling approaches should be interpreted as mainly numerical rather than definitively superior in this dataset.

The variable-importance profiles and splitting patterns provide insights into differences in model performance. In the overall cohort decision tree, tPSA remained the root splitting variable at a threshold of 11 ng/mL, which is consistent with the established role of PSA in initial PCa risk stratification. However, subsequent splits involving NLR, MLR, f/t PSA ratio, and LymC indicate that inflammatory and immune-cell-related parameters may help refine classification after PSA-based stratification. Neutrophil- and monocyte-dominant indices reflect systemic innate inflammatory activity, whereas lymphocyte-related measures partly reflect host immune competence; because these indices can also be altered by benign prostatic or systemic inflammation, their role is more plausibly complementary than disease-specific (9,10). In the PSA gray-zone subgroup, the diagnostic contribution of individual variables shifted: f/t PSA ratio became the first splitting variable in the decision tree, and f/t PSA ratio, tPSA, NLR, WBC, and fPSA ranked the highest in the gray-zone XGBoost model. These findings suggest that when tPSA levels fall within the 4–10 ng/mL range, its standalone discriminatory value declines, whereas f/t PSA ratio and selected inflammatory markers may provide complementary information. This shift is clinically plausible because tPSA values overlap substantially between BPH and PCa within the 4–10 ng/mL range, whereas the f/t PSA ratio adds information beyond tPSA alone and has shown better discrimination in this setting. Previous studies have similarly reported that NLR may have diagnostic value for PCa with limited standalone performance, and that monocyte- and lymphocyte-related indices are more appropriate as adjunctive rather than independent diagnostic tools (9,10).

The gray-zone analysis carries particular clinical relevance because biopsy decisions are most uncertain in this range. In this subgroup, tPSA showed limited discriminative ability (AUC =0.625), whereas f/t PSA ratio achieved a higher AUC (0.683) and served as the primary splitting variable in the decision tree model. Although the gray-zone XGBoost model achieved a numerically high validation AUC (AUC =0.869), the CI was wide and reached 1.000. This pattern is compatible with sampling variability and potential overfitting in a small validation subset rather than conclusive superiority (8). These findings are consistent with previous reports suggesting that machine learning approaches may improve discrimination in gray-zone or equivocal-risk settings (11,12); however, they also show that performance estimates in small subgroups can fluctuate. Compared with radiomics- or video-based models, the current models use routinely available PSA and blood cell-derived parameters, which may facilitate clinical implementation; however, their stability requires further verification. The observation that f/t PSA ratio outperformed tPSA in the gray zone is also consistent with previous reviews (13).

These results suggest that model selection should not be based solely on the highest point estimate of AUC. In the overall validation set, the decision tree model had the highest AUC, whereas XGBoost had the highest numerical AUC in the gray-zone validation set. However, DeLong testing revealed no statistically significant differences among the multivariable models, and the gray-zone estimates were unstable. Therefore, the practical value of each model should be considered together with interpretability and clinical workflow requirements. XGBoost can capture nonlinear interactions, potentially achieving strong discriminative performance; however, its ensemble structure limits direct clinical interpretation. In contrast, the decision tree provides explicit decision thresholds, such as tPSA =11 ng/mL in the overall cohort and f/t PSA ratio ~0.10 in the gray-zone subgroup, enabling clinicians to trace the classification pathway for individual patients.

From a clinical application perspective, the decision tree may thus be the most suitable auxiliary decision model in this study. Its threshold-based structure can support outpatient triage, risk communication, and biopsy-related decision-making, particularly when the objective is not only to estimate risk probability but also to provide an explanation for patient classification as high or low risk. The bootstrap optimism-correction results further support this cautious interpretation: in the PSA gray-zone subgroup, the decision tree retained the highest optimism-corrected AUC (0.757), whereas XGBoost and the logistic regression model showed lower corrected AUC values (0.649 and 0.609, respectively). These findings suggest that, despite the potential for overfitting in the small gray-zone subgroup, the decision tree may provide a more favorable balance among discrimination, stability, and interpretability.

Several limitations should be acknowledged. First, the retrospective single-center development design and small external cohort limit generalizability. The lower external-validation AUCs may reflect differences in case mix and unmeasured interlaboratory variation, but the small sample precluded definitive assessment. Unavailable age data and incomplete laboratory and pathology metadata further limited cross-center comparison and harmonization. Second, the sample size of the PSA gray-zone subgroup was small, and the wide CIs observed in the validation results indicate uncertainty; thus, larger prospective multicentre studies are needed. Third, BPH-related histological inflammation, unrecorded subclinical infection, or recent anti-inflammatory treatment may influence PSA levels and blood cell-derived indices, introducing potential bias (14,15). Fourth, some predictors and derived ratios were biologically or mathematically correlated; thus, regression coefficients and odds ratios should be interpreted cautiously and considered primarily as measures of model contribution rather than independent causal effects. Fifth, imaging and volume-related variables, such as Prostate Imaging-Reporting and Data System (PI-RADS) score, prostate volume, and free prostate-specific antigen density (FPSAD) were not included in the models, although these factors may improve diagnosis in the gray zone (16). Future studies should incorporate these variables and evaluate calibration, decision-curve analysis, and prospective clinical utility.

Conclusions

Overall, this study suggests that the integration of PSA-related indicators with peripheral blood inflammatory markers may improve PCa risk stratification, particularly in patients in the PSA gray zone. No statistically significant superiority of any multivariable model was demonstrated after correction; however, the findings indicate that the decision tree provides a favorable balance of discrimination, optimism-corrected stability, and clinical interpretability. It provides directly traceable thresholds, but prospective multicenter validation, calibration assessment, and decision-curve analysis are required before these models can be considered for clinical implementation.

Acknowledgments

None.

Footnote

Reporting Checklist: The authors have completed the TRIPOD reporting checklist. Available at https://tau.amegroups.com/article/view/10.21037/tau-2026-0678/rc

Data Sharing Statement: Available at https://tau.amegroups.com/article/view/10.21037/tau-2026-0678/dss

Peer Review File: Available at https://tau.amegroups.com/article/view/10.21037/tau-2026-0678/prf

Funding: This work was supported by the Hainan Provincial Natural Science Foundation of China (General Program) (No. 823MS135).

Conflicts of Interest: All authors have completed the ICMJE uniform disclosure form (available at https://tau.amegroups.com/article/view/10.21037/tau-2026-0678/coif). G.L. reports funding from the Hainan Provincial Natural Science Foundation of China (General Program) (No. 823MS135). The other authors have no conflicts of interest to declare.

Ethical Statement: The authors are accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved. The study was conducted in accordance with the Declaration of Helsinki and its subsequent amendments. The study was approved by Ethics Committee of Hainan General Hospital (Hainan Affiliated Hospital of Hainan Medical University) (No. EC- YLY-2026-287-01) and Ethics Committee of The First Affiliated Hospital of Hainan Medical University (No.) [if no ethical approval number, kindly ignore the content in parentheses]. Written informed consent was obtained from the patients for participation in this study.

Open Access Statement: This is an Open Access article distributed in accordance with the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International License (CC BY-NC-ND 4.0), which permits the non-commercial replication and distribution of the article with the strict proviso that no changes or edits are made and the original work is properly cited (including links to both the formal publication through the relevant DOI and the license). See: https://creativecommons.org/licenses/by-nc-nd/4.0/.

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(English Language Editor: L. Huleatt)