Results

Cohort demographics and clinical predictors

The study analyzed 312 patients across two centers, comprising 174 (55.8%) PNI-positive and 138 (44.2%) PNI-negative cases. Demographic and clinical characteristics showed no statistically significant differences between the training, internal validation, and external testing cohorts (p > 0.05), ensuring balanced randomization (Table 1). In univariate analysis, tumor longitudinal diameter, MRI nodal stage, and histologic differentiation showed potential predictive value. However, in the multivariate logistic regression restricted to clinical variables, only tumor length (OR: 1.062; 95% CI: 1.014–1.112; p = 0.032) retained statistical significance as an independent predictor. Consequently, tumor length was the sole clinical variable integrated into the final Combined Model (Table 2).

Feature name | Train | Val | Test | p-value
Age (mean ± SD, years) | 64.76 ± 10.17 | 65.51 ± 7.96 | 62.32 ± 10.37 | 0.736
Tumor length (mean ± SD, cm) | 4.19 ± 1.41 | 4.31 ± 1.51 | 4.17 ± 1.56 | 0.742
Gender |  |  |  | 0.627
Female | 63 (36.63) | 24 (32.43) | 31 (46.97) | 
Male | 109 (63.37) | 50 (67.57) | 35 (53.03) | 
Tumor location |  |  |  | 0.793
Low | 67 (38.95) | 28 (37.84) | 32 (48.48) | 
Middle | 89 (51.74) | 37 (50.00) | 28 (42.42) | 
High | 16 (9.30) | 9 (12.16) | 6 (9.09) | 
mrT_stage |  |  |  | 0.066
2 | 43 (25.00) | 22 (29.73) | 23 (34.85) | 
3 | 119 (69.19) | 42 (56.76) | 31 (46.97) | 
4 | 10 (5.81) | 10 (13.51) | 12 (18.18) | 
mrN_stage |  |  |  | 0.725
0 | 33 (19.19) | 13 (17.57) | 6 (9.09) | 
1 | 56 (32.56) | 28 (37.84) | 27 (40.91) | 
2 | 83 (48.26) | 33 (44.59) | 33 (50.00) | 
mrMRF |  |  |  | 0.88
Negative | 108 (62.79) | 45 (60.81) | 50 (75.76) | 
Positive | 64 (37.21) | 29 (39.19) | 16 (24.24) | 
mrEMVI |  |  |  | 0.845
Negative | 110 (63.95) | 49 (66.22) | 41 (62.12) | 
Positive | 62 (36.05) | 25 (33.78) | 25 (37.88) | 
Differentiation |  |  |  | 0.512
Well | 27 (15.70) | 9 (12.16) | 7 (10.61) | 
Moderately | 131 (76.16) | 56 (75.68) | 54 (81.82) | 
Poorly | 14 (8.14) | 9 (12.16) | 5 (7.58) | 
CEA |  |  |  | 0.322
Normal (< 5 ng/mL) | 104 (60.47) | 39 (52.70) | 44 (66.67) | 
Elevated (≥ 5 ng/mL) | 68 (39.53) | 35 (47.30) | 22 (33.33) | 
CA19_9 |  |  |  | 0.433
Normal (< 37 U/mL) | 150 (87.21) | 61 (82.43) | 64 (96.97) | 
Elevated (≥ 37 U/mL) | 22 (12.79) | 13 (17.57) | 2 (3.03) | 

Feature name | OR_UNI | 95% CI_UNI | p_UNI | OR_MULTI | 95% CI_MULTI | p_MULTI
Gender | 0.873 | 0.7660–0.9950 | 0.088 |  |  | 
mrEMVI | 0.973 | 0.8530–1.1110 | 0.733 |  |  | 
Age | 0.998 | 0.9920–1.0040 | 0.624 |  |  | 
mrMRF | 1.022 | 0.8970–1.1650 | 0.782 |  |  | 
CEA | 1.045 | 0.9190–1.1900 | 0.574 |  |  | 
Tumor length | 1.085 | 1.0380–1.1330 | < 0.05 | 1.062 | 1.0140–1.1120 | 0.032
Tumor localization | 1.099 | 0.9940–1.2140 | 0.122 |  |  | 
mrT_stage | 1.115 | 0.9880–1.2590 | 0.139 |  |  | 
mrN_stage | 1.149 | 1.0610–1.2460 | < 0.05 | 1.09 | 1.0020–1.1860 | 0.093
CA19_9 | 1.207 | 1.0000–1.4580 | 0.1 |  |  | 
Differentiation | 1.213 | 1.0660–1.3800 | < 0.05 | 1.164 | 1.0240–1.3230 | 0.051

Deep learning architecture selection and feature visualization

For the 2.5D deep learning component, three architectures were benchmarked (Table 3). ResNet101 demonstrated the optimal balance between learning capacity and generalization. In the internal validation cohort, it achieved an AUC of 0.705 (95% CI: 0.658–0.751), with a sensitivity of 0.539 and specificity of 0.766 (Fig. 3b). Importantly, this performance remained robust in the external testing cohort (AUC = 0.708; 95% CI: 0.660–0.755; accuracy = 0.682), confirming its stability (Fig. 3c). Conversely, DenseNet201 showed high training metrics (Fig. 3a) but poor validation performance (AUC = 0.660), suggesting overfitting. Based on these results, ResNet101 was selected as the backbone. To interpret the model’s focus, gradient-weighted class activation mapping (Grad-CAM) was employed, providing qualitative interpretability that suggested the model’s attention was focused on the tumor-neural interface (Supplementary Fig. 5).

Fig. 3: ROC curves illustrating the slice-level predictive performance of different architectures in the training (a), internal validation (b), and external testing group (c)

Model name | Accuracy | AUC | 95% CI | Sensitivity | Specificity | PPV | NPV | Cohort
resnet101 | 0.761 | 0.841 | 0.8191–0.8625 | 0.820 | 0.697 | 0.744 | 0.783 | train
resnet101 | 0.616 | 0.705 | 0.6581–0.7512 | 0.539 | 0.766 | 0.819 | 0.459 | val
resnet101 | 0.682 | 0.708 | 0.6605–0.7545 | 0.611 | 0.767 | 0.759 | 0.622 | test
vgg19 | 0.648 | 0.701 | 0.6717–0.7300 | 0.690 | 0.602 | 0.651 | 0.645 | train
vgg19 | 0.633 | 0.599 | 0.5464–0.6511 | 0.738 | 0.429 | 0.717 | 0.455 | val
vgg19 | 0.595 | 0.603 | 0.5508–0.6543 | 0.655 | 0.524 | 0.623 | 0.558 | test
densenet201 | 0.820 | 0.907 | 0.8906–0.9226 | 0.791 | 0.850 | 0.850 | 0.792 | train
densenet201 | 0.618 | 0.660 | 0.6109–0.7099 | 0.589 | 0.674 | 0.780 | 0.456 | val
densenet201 | 0.652 | 0.684 | 0.6362–0.7325 | 0.563 | 0.757 | 0.736 | 0.591 | test

MIL fusion and radiomics signature construction

Regarding the fusion of multi-instance learning (MIL) features, the ExtraTrees classifier outperformed SVM, Random Forest, and LightGBM. In the validation phase, ExtraTrees achieved the highest AUC of 0.863 (95% CI: 0.783–0.943), with an accuracy of 0.770 and sensitivity of 0.857, significantly surpassing the Random Forest (AUC = 0.821) and SVM (AUC = 0.787) models (Fig. 4 and Table 4). Simultaneously, radiomic analysis identified the “Peri2mm” model (tumor + 2 mm margin) as the most effective signature among the tested expansions (1–5 mm). The Peri2mm model yielded an AUC of 0.798 in validation, offering a superior sensitivity-specificity balance compared to the intratumoral-only model (AUC = 0.744) (Supplementary 2A).

Fig. 4: ROC curve analysis of subgroup-specific models in 2.5D multi-instance learning (MIL) features across the training (a), internal validation (b), and external testing cohort (c). AUC, area under the curve; CI, confidence interval

Model name | Accuracy | AUC | 95% CI | Sensitivity | Specificity | PPV | NPV | Cohort
SVM | 0.919 | 0.988 | 0.975–1.000 | 0.978 | 0.855 | 0.879 | 0.973 | train
SVM | 0.770 | 0.787 | 0.672–0.901 | 0.918 | 0.480 | 0.776 | 0.750 | val
SVM | 0.697 | 0.758 | 0.642–0.874 | 0.722 | 0.667 | 0.722 | 0.667 | test
RandomForest | 0.959 | 0.986 | 0.973–0.999 | 0.989 | 0.928 | 0.936 | 0.987 | train
RandomForest | 0.770 | 0.821 | 0.722–0.920 | 0.857 | 0.600 | 0.808 | 0.682 | val
RandomForest | 0.712 | 0.764 | 0.653–0.876 | 0.722 | 0.700 | 0.743 | 0.677 | test
ExtraTrees | 0.959 | 0.987 | 0.976–0.998 | 0.989 | 0.928 | 0.936 | 0.987 | train
ExtraTrees | 0.770 | 0.863 | 0.783–0.943 | 0.857 | 0.600 | 0.808 | 0.682 | val
ExtraTrees | 0.727 | 0.812 | 0.713–0.912 | 0.750 | 0.700 | 0.750 | 0.700 | test
LightGBM | 0.936 | 0.972 | 0.949–0.995 | 0.989 | 0.880 | 0.898 | 0.986 | train
LightGBM | 0.757 | 0.793 | 0.687–0.900 | 0.857 | 0.560 | 0.792 | 0.667 | val
LightGBM | 0.697 | 0.753 | 0.640–0.865 | 0.722 | 0.667 | 0.722 | 0.667 | test

Performance of the combined model

The final Combined Model, integrating the MIL signature, intratumoral/Peri2mm radiomics, and tumor length, demonstrated exceptional discriminative ability across all datasets. In the training set, it achieved near-perfect stratification (AUC = 0.993; 95% CI: 0.987–1.000). Crucially, this advantage translated to the internal validation cohort, where the Combined Model attained an AUC of 0.912 (95% CI: 0.850–0.974), an accuracy of 0.811, and a specificity of 0.920 (Fig. 5b). In the independent external testing cohort, the model maintained high performance with an AUC of 0.868 (95% CI: 0.783–0.952), achieving higher AUC values compared to the standalone MIL (AUC = 0.812) and radiomics sub-models, although the difference between the Combined Model and the MIL model did not reach statistical significance (Fig. 5c). Detailed performance metrics are provided in Table 5.

Fig. 5: AUCs of ROC curves for different signatures across the training (a), internal validation (b), and external testing cohort (c)

Signature | Accuracy | AUC | 95% CI | Sensitivity | Specificity | PPV | NPV | Cohort
Clinical | 0.680 | 0.730 | 0.6557–0.8043 | 0.944 | 0.398 | 0.627 | 0.868 | train
Intra | 0.738 | 0.822 | 0.7612–0.8831 | 0.663 | 0.819 | 0.797 | 0.694 | train
Peri1mm | 0.826 | 0.881 | 0.8302–0.9321 | 0.854 | 0.795 | 0.817 | 0.835 | train
Peri2mm | 0.767 | 0.837 | 0.7778–0.8954 | 0.742 | 0.795 | 0.795 | 0.742 | train
Peri3mm | 0.802 | 0.883 | 0.8343–0.9310 | 0.798 | 0.807 | 0.816 | 0.788 | train
Peri4mm | 0.779 | 0.860 | 0.8064–0.9143 | 0.674 | 0.892 | 0.870 | 0.718 | train
Peri5mm | 0.785 | 0.856 | 0.7999–0.9114 | 0.798 | 0.771 | 0.789 | 0.780 | train
Ensemble | 0.936 | 0.989 | 0.9788–0.9984 | 0.933 | 0.940 | 0.943 | 0.929 | train
MIL | 0.860 | 0.987 | 0.9759–0.9981 | 0.742 | 0.988 | 0.985 | 0.781 | train
Combined | 0.953 | 0.993 | 0.9866–1.0000 | 0.944 | 0.964 | 0.966 | 0.941 | train
Clinical | 0.757 | 0.715 | 0.5860–0.8442 | 0.918 | 0.440 | 0.763 | 0.733 | val
Intra | 0.716 | 0.744 | 0.6209–0.8681 | 0.653 | 0.840 | 0.889 | 0.553 | val
Peri1mm | 0.770 | 0.765 | 0.6460–0.8838 | 0.918 | 0.480 | 0.776 | 0.750 | val
Peri2mm | 0.770 | 0.798 | 0.6821–0.9138 | 0.776 | 0.760 | 0.864 | 0.633 | val
Peri3mm | 0.770 | 0.740 | 0.6054–0.8737 | 0.837 | 0.640 | 0.820 | 0.667 | val
Peri4mm | 0.770 | 0.742 | 0.6162–0.8678 | 0.898 | 0.520 | 0.786 | 0.722 | val
Peri5mm | 0.662 | 0.751 | 0.6371–0.8650 | 0.592 | 0.800 | 0.853 | 0.500 | val
Ensemble | 0.770 | 0.832 | 0.7302–0.9335 | 0.755 | 0.800 | 0.881 | 0.625 | val
MIL | 0.689 | 0.863 | 0.7832–0.9433 | 0.531 | 1.000 | 1.000 | 0.521 | val
Combined | 0.811 | 0.912 | 0.8499–0.9737 | 0.755 | 0.920 | 0.949 | 0.657 | val
Clinical | 0.636 | 0.704 | 0.5760–0.8314 | 0.611 | 0.667 | 0.687 | 0.588 | test
Intra | 0.682 | 0.668 | 0.5316–0.8036 | 0.611 | 0.767 | 0.759 | 0.622 | test
Peri1mm | 0.667 | 0.717 | 0.5906–0.8437 | 0.556 | 0.800 | 0.769 | 0.600 | test
Peri2mm | 0.667 | 0.720 | 0.5972–0.8435 | 0.389 | 1.000 | 1.000 | 0.577 | test
Peri3mm | 0.682 | 0.710 | 0.5852–0.8352 | 0.694 | 0.667 | 0.714 | 0.645 | test
Peri4mm | 0.682 | 0.693 | 0.5632–0.8220 | 0.528 | 0.867 | 0.826 | 0.605 | test
Peri5mm | 0.606 | 0.635 | 0.4996–0.7699 | 0.333 | 0.933 | 0.857 | 0.538 | test
Ensemble | 0.818 | 0.808 | 0.6932–0.9235 | 0.694 | 0.967 | 0.962 | 0.725 | test
MIL | 0.727 | 0.812 | 0.7127–0.9123 | 0.750 | 0.700 | 0.750 | 0.700 | test
Combined | 0.788 | 0.868 | 0.7834–0.9518 | 0.722 | 0.867 | 0.867 | 0.722 | test

Validation and clinical utility

Calibration curves for the Combined Model showed high concordance between predicted probabilities and observed PNI status (Fig. 6). Decision curve analysis (DCA) demonstrated that the Combined Model provided a higher net benefit than treat-all or treat-none strategies across a wide range of threshold probabilities (Supplementary Fig. 6). DeLong tests confirmed statistically significant performance gains for the Combined Model. In the internal validation cohort, the Combined Model significantly outperformed the Clinical model (p = 0.005), the Intratumoral radiomics model (p = 0.003), and the Peri2mm radiomics model (p = 0.022). Similarly, in the external testing cohort, the Combined Model maintained significant superiority over the Clinical (p = 0.005), Intratumoral (p = 0.003), and Peri2mm (p = 0.011) models (Supplementary Fig. 7). A nomogram visually delineated the contributory weights of tumor length, intratumoral (Intra) features, peritumoral (Peri2mm) radiomics, and multi-instance learning (MIL) components in predicting pathological PNI status (Supplementary Fig. 8).

Fig. 6: The calibration curves of all models in the training (a), internal validation (b), and external testing cohorts (c)