The clinical and pathological characteristics of patients in the training, internal test and external validation cohorts are summarized in Table 1.

Among all candidate algorithms, the five best-performing base learners were gradient boosting, support vector machine (SVM), logistic regression, k-nearest neighbors (KNN) and decision tree. Figure 3 depicts the micro-averaged ROC curves of these models, and the corresponding quantitative results are summarized in Table 2. At the single-model level, all classifiers already achieved high discriminative performance, with AUCs ranging from 0.927 to 0.952; logistic regression yielded the highest AUC of 0.952 (95% CI, 0.934–0.970). On top of this strong baseline, the ensemble strategies further improved overall performance: the stacking ensemble achieved an AUC of 0.962 (95% CI, 0.936–0.983), and the voting ensemble achieved an AUC of 0.956 (95% CI, 0.930–0.978), both outperforming any individual base learner. Stacking also showed slightly higher accuracy (0.86 vs. 0.84) and macro-averaged F1 score (0.69 vs. 0.67) compared with voting. Macro-averaged PPV (0.86–0.87) and macro-averaged NPV (both 0.94), together with specificities approaching 1.000, indicated good negative-class recognition and overall stability for both ensembles. When high-risk PCa (Pos2) was treated as the positive class, SVM as a single model achieved the highest sensitivity (0.88), whereas the stacking and voting ensembles exhibited lower sensitivity for Pos2 (0.25 at the default decision threshold), reflecting a more conservative decision profile that prioritizes reduction of false positives.

External validation in the independent cohort showed that all models maintained good discrimination, with AUCs ranging from 0.884 to 0.928. The stacking and voting ensembles again performed slightly better than most single models, with AUCs of 0.928 (95% CI, 0.897–0.954) and 0.927 (95% CI, 0.895–0.955), respectively, compared with, for example, decision tree (AUC = 0.925), logistic regression (AUC = 0.913) and SVM (AUC = 0.921). In the external cohort, voting showed a modest advantage in terms of overall accuracy (0.75) and specificity (0.99), whereas stacking provided a more balanced trade-off between sensitivity and specificity, and between PPV and NPV, across clinically relevant decision thresholds (Table 2; Figure 3).

Taken together, the ensemble learning strategies enhanced the overall discriminative ability and robustness of PCa risk stratification beyond what was achievable with individual models alone. Among them, stacking appears more suitable when the primary objective is to maximize predictive performance and net clinical benefit, whereas voting—characterized by a simpler structure and consistently high specificity and NPV—offers an attractive and operationally straightforward option for clinical implementation.

To systematically quantify the incremental diagnostic value conferred by UL, we evaluated both calibration and clinical decision-analytic performance before and after incorporating UL into the models. Calibration was assessed using the multiclass Brier score and stratified calibration plots to examine the agreement between predicted probabilities and observed risks, and to compare the extent of calibration improvement after adding UL. Clinical utility was evaluated using decision curve analysis (DCA), which estimates the net benefit across a range of threshold probabilities (PT). We further computed ΔNB and ΔTP/ΔFP per 100 patients to visually illustrate the impact of UL on key clinical decisions (e.g., whether to perform biopsy or escalate management).

As shown in Figures 4a–f, incorporation of UL led to a consistent improvement in calibration performance in both the internal and external cohorts. In the internal dataset, the multiclass Brier score decreased after adding UL (e.g. from 0.216 to 0.210 for stacking, from 0.257 to 0.247 for voting, and from 0.256 to 0.242 for gradient boosting), indicating better agreement between predicted probabilities and observed risks. Stratified calibration curves further demonstrated that the with UL models (solid lines) were generally closer to the 45° identity line than their without UL counterparts (dashed lines), suggesting a reduction in over- or underestimation, particularly in the high-risk probability range.

Decision curve analysis (DCA) provided complementary evidence at the clinical decision level. Within clinically relevant threshold probability ranges (PT ≈ 0.05–0.30), the with UL curves for all models lay above both the without UL curves and the “treat-all”/”treat-none” strategies. Among them, the stacking and voting ensembles yielded the highest net benefit, with peak ΔNB values of approximately 0.03–0.04 in the internal cohort, corresponding to an increase of about 2–4 correctly identified high-risk patients per 100 individuals (ΔTP ≈ 2–4/100 patients), without a substantial increase in false positives. In the external validation cohort, the absolute magnitude of ΔNB was somewhat smaller (on the order of 0.01–0.02) and more variable, but the overall pattern remained consistent, with UL models providing higher net benefit across a broad range of decision thresholds.

Taken together, these findings indicate that incorporating UL improves probability calibration and net clinical benefit for PCa risk stratification, while not materially increasing the risk of false positives. The incremental gain is stable across different PSA ranges and is particularly pronounced for ensemble models such as stacking and voting, supporting the role of UL as an independent, quantifiable biomarker with added diagnostic value in PCa risk prediction.

To investigate whether the incremental value of UL varies across different levels of tumor burden, we performed a pre-specified subgroup analysis stratified by baseline PSA. In the internal test set (Figures 5a, c, e), all models maintained high discriminative ability within the PSA 4–10 and 10–20 ng/mL strata, with micro-averaged AUCs clustering around 0.93. Upon incorporation of UL, none of the models showed performance deterioration in any subgroup; instead, the ROC curves shifted slightly towards the upper left. In the PSA 4–10 ng/mL subgroup, the absolute micro-AUC gains attributable to UL were modest but directionally consistent across model families—tree-based, linear and ensemble learners—with ΔAUC values largely confined to a narrow range of 0.002–0.005, suggesting a small yet robust incremental signal at low-to-intermediate PSA levels. In the PSA 10–20 ng/mL subgroup, the magnitude of AUC improvement was further attenuated, and ΔAUC varied slightly across algorithms, but changes remained predominantly small and positive with no evidence of systematic degradation. For the PSA >20 ng/mL subgroup, baseline micro-AUCs ranged from approximately 0.82 to 0.89; after adding UL, most models (particularly SVM, KNN and the Voting/Stacking ensembles) exhibited AUC increases of about 0.01–0.02, whereas Gradient Boosting and Logistic Regression were essentially unchanged, indicating that the contribution of UL in the high-PSA setting is more uncertain but, overall, unlikely to behave as pure noise.

Findings in the external validation cohort were broadly concordant with those of the internal cohort, albeit with greater variability (Figures 5b, d, f). Among patients with PSA 4–10 ng/mL, micro-AUCs for all models were consistently slightly higher after incorporating UL than for their respective baselines, with ΔAUC pointing in the same (favorable) direction, supporting the reproducibility of UL-related gains in the low-PSA range in an independent dataset. In the PSA 10–20 ng/mL subgroup, AUC differences largely fluctuated around zero, with only minor positive or negative deviations in individual models, indicating that the overall benefit approaches a marginal effect. In the PSA >20 ng/mL subgroup, where sample size was smaller and class imbalance more pronounced, ΔAUC values across algorithms included small positive shifts as well as values close to zero or slightly negative, and the ROC curves were visibly stepwise, underscoring limited estimation precision and an exploratory rather than definitive nature of the evidence in this range.

Taken together, UL did not compromise the discriminative performance of any model across PSA strata and provided a small but consistent incremental discriminative benefit within the PSA 4–20 ng/mL interval, with the clearest and most reproducible gains observed in the PSA 4–10 ng/mL low-to-intermediate PSA population. For patients with PSA >20 ng/mL, the direction of UL’s effect appears broadly non-negative in the current data, but given sample size constraints and unstable ROC estimation, conclusions in this high-PSA subgroup should be interpreted cautiously and confirmed in larger, multi-center cohorts.

SHAP analyses were conducted using the TreeExplainer, which is optimized for tree-based models, applied to the gradient boosting classifier. The internal training cohort was used as the background reference distribution. SHAP values were computed in a one-vs-rest framework for the high-risk class (class 2), such that positive values indicate increased predicted probability of high-risk PCa and negative values indicate a down-weighting effect. This formulation facilitates direct interpretation of feature contributions to clinically significant disease risk.

Using the internal test set, we computed SHAP values for the gradient boosting model including urinary leukocytes (UL), focusing on predictions for high-risk prostate cancer (class 2), in order to dissect the contribution of individual features to the model output. Global feature importance ranked by mean absolute SHAP value showed that nonlinearly transformed PSA-related indices and MRI-derived features (e.g. BMI:Sine, PHID:Tanh, PHID:Sigmoid, PHI, and PSAD:Tangent) were the principal drivers of high-risk predictions. In contrast, urinary leukocytes contributed more modestly, ranking in the lower tier of all features but exhibiting a small yet consistent impact (Figure 6b). This pattern is consistent with the intended role of UL as an inflammation-related contextual marker designed to complement, rather than replace, conventional quantitative risk indicators.

Univariate SHAP analysis for UL (Figure 6a) further clarified the directionality of its effect. Among UL-positive patients (UL = 1), SHAP values for the high-risk class were predominantly mildly negative, indicating that the model systematically down-weights the predicted probability of high-risk prostate cancer when urinary leukocytes are elevated. In contrast, UL-negative patients (UL = 0) exhibited SHAP values clustered around zero, with a subset showing slightly positive contributions. This finding suggests that, in the presence of abnormal PSA or MRI findings, the absence of urinary inflammatory signals is more compatible with a high-risk phenotype. Importantly, this behavior supports the interpretation of UL as a contextual inflammation marker rather than a direct indicator of tumor aggressiveness.

To illustrate this mechanism at the individual level, we examined a representative high-risk case (sample #14) and plotted paired SHAP waterfall diagrams for models trained without and with UL (Figure 6c). In the baseline model without UL, the predicted probability for class 2 was approximately 0.11. In the model including UL, although this patient was UL-negative and the direct SHAP contribution of UL itself remained close to zero, the overall feature attribution pattern became more sharply aligned with a high-risk profile. Specifically, the positive contributions of established PSA- and MRI-related features, such as p2PSA:Log, PSAD:Tangent, p2PSA, PHID:Sigmoid, and PIRADS:Square, were more coherently expressed, resulting in an increased predicted probability for class 2 of approximately 0.59. This observation indicates that UL does not increase risk by exerting a large direct effect on individual predictions; rather, its inclusion during model training improves the contextual separation between inflammation-related and non-inflammation-related PSA elevations, allowing canonical high-risk features to express their effects more consistently.

Taken together, the SHAP analyses demonstrate that although urinary leukocytes contribute only modestly in terms of global feature importance, their effect is directionally consistent, clinically interpretable, and mechanistically coherent. By delineating the boundary between inflammatory and non-inflammatory causes of PSA elevation, UL refines probability calibration and reduces misattribution of benign PSA increases to aggressive malignancy. Accordingly, UL should be regarded as an inflammation-related contextual modifier within the risk prediction framework, rather than as an independent tumor biomarker for high-risk prostate cancer.