The present study included a retrospective cohort of patients who underwent surgery for RCC between January 2019 and February 2022, and a prospective cohort of patients enrolled between March 2022 and November 2023. All patients were treated at the Affiliated Hospital of Hebei University (Baoding, China). Eventually, 137 patients were enrolled after strict screening with inclusion and exclusion criteria, including 124 cases of ccRCC, 7 cases of chRCC, 4 cases of pRCC, 1 case of collecting duct RCC and 1 case of sarcomatoid RCC.

The following inclusion criteria were applied: i) Having complete clinical data; ii) having preoperative four-phase CT scan images (including plain scan phase, arterial phase, venous phase and excretion phase) from the Affiliated Hospital of Hebei University with high image quality and no artifacts; iii) being diagnosed for the first time and not having undergone any form of treatment such as radiotherapy, chemotherapy, immunotherapy and surgical treatment prior to the CT scan; and iv) being scanned by the same CT scanning equipment with the same scanning parameters.

The following exclusion criteria were applied: i) Not having CT plain scan + enhancement scans in the Affiliated Hospital of Hebei University before surgery or not having pathologic examination results; ii) having unclear CT scan images and poorly displayed lesions; iii) have a tumor that has developed metastases; and iv) have missing or incomplete clinical data.

The initially screened CT images were manually outlined for the region of interest (ROI) of the tumor by two experienced urologists using the labelme tool (version 4.5.6; github.com/wkentaro/labelme) to form the volume of interest of the whole tumor. The outline was based on the maximum diameter of the tumor and extended outward by 1–2 mm. To ensure annotation consistency and minimize inter-observer variability, both urologists independently annotated 50 randomly selected CT images (25 from high-grade and 25 from low-grade patients). The intraclass correlation coefficient (ICC) was calculated to assess inter-observer agreement for the annotated ROI volumes. An ICC value >0.75 indicated good agreement, and any discrepancies were resolved by consensus discussion with a third senior radiologist. After outlining, the images were saved as a json file, on which the tumor region was cropped according to the annotations in the file, and they were uniformly resized to 224×224 pixels (Figs. 1 and 2).

The enrolled 137 patients were divided into a model construction group of 110 cases (26 cases of high grade and 84 cases of low grade) and a clinical validation group of 27 cases (9 cases of high grade and 18 cases of low grade). Patients in the model construction group underwent model construction, training and optimization, while those in the clinical validation group underwent clinical validation of model efficacy. The model construction group was further subdivided into the training group of 87 cases (20 cases of high grade and 67 cases of low grade) and the test group of 23 cases (6 cases of high grade and 17 cases of low grade). CT images were categorized and stored by phase and grade, with 3,533 images in the arterial phase, 3,656 images in the venous phase, 3,278 images in the excretion phase, 2,619 images in the planar phase and 13,086 images in the combined four phases in the training group, whereas there were 944 images in the arterial phase, 975 images in the venous phase, 931 images in the excretion phase, 793 images in the planar phase and 3,643 images in the combined four phases in the test group. In response to the small number of high-grade patients, high-grade CT images in the training group were augmented by brightness enhancement, random flip and 20° random rotation, and the test group was augmented by brightness enhancement. After augmentation, the training group had 5,372 images in the arterial phase, 5,558 images in the venous phase, 5,090 images in the excretion phase, 3,999 images in the plain scan phase and 20,019 images in the combined four phases; the test group had 1,187 images in the arterial phase, 1,234 images in the venous phase, 1,167 images in the excretory phase, 1,005 images in the plain phase and 4,593 images in the combined four phases. The specific augmentation methods (brightness enhancement, random flip and 20° random rotation) were chosen to simulate real-world image variations while preserving pathological integrity, thereby improving model generalizability without introducing unrealistic artifacts (16).

The CT data of each phase of the training group were input into the Mobilenetv3-large network(PyTorch 1.10, github.com/tensorflow/models/tree/master/research/slim/nets/mobilenet;) for network training, and the plain scan phase model, arterial phase model, venous phase model, excretion phase model and combined four-phase model were constructed. Adaptive moment estimation (Adam) and cross-entropy loss function were used for all network training. The final hyperparameters of the trained models in the present study were learning rate=0.0001, batch size=16 and number of optimizations=100. To determine these hyperparameters, a sensitivity analysis was performed using the training set with 5-fold cross-validation. Specifically, learning rates of {0.1, 0.01, 0.001, 0.0001, 0.00001}, batch sizes of {8, 16, 32, 64} and epochs of {50, 100, 150, 200} were evaluated. A learning rate of 0.0001 provided the most stable convergence without oscillation, while higher rates (≥0.001) led to loss divergence. Batch size 16 achieved the best balance between gradient stability and generalization, as smaller batches (8) caused noisy gradients and overfitting (training accuracy >0.95 but validation accuracy <0.72), and larger batches (32, 64) resulted in poor convergence. Regarding epoch count, validation performance plateaued after ~80 epochs, and early stopping at 100 epochs prevented overfitting while preserving optimal weights. These hyperparameter choices were particularly critical due to the relatively small sample size, especially for the high-grade group.

All models were created using the Python 3.7 (python.org/downloads/release/python-370/)programming language and subsequently compiled and trained using Pytorch 1.10 (pytorch.org/get-started/previous-versions/) and Cuda 11.2(developer.nvidia.com/cuda-11-2-0-download-archive). Desktop workstations with RTX 3060 GPUs were used for these models and Jupyter software (version 6.4.5, jupyter.org) was used for the integrated development environment (IDE) tool. Mobilenetv3-large was selected as the primary model due to its proven efficiency in medical image analysis, balancing high accuracy with low computational cost compared with heavier architectures such as ResNet (pytorch.org/vision/stable/models/resnet.html) and VGG (pytorch.org/vision/stable/models/vgg.html).

To justify the selection of MobileNetV3-Large as the primary model, the present study trained and tested two widely used deep learning architectures, ResNet50 (available at http://pytorch.org/vision/stable/models/resnet.html) and VGG16 (available at http://pytorch.org/vision/stable/models/vgg.html), on the same venous-phase CT dataset. Both models were trained under identical conditions to ensure fair comparison: learning rate=0.0001, batch size=16, and number of epochs=100, using the same adaptive moment estimation (Adam) optimizer and cross-entropy loss function as used for the MobileNetV3-Large model. The same training, test, and validation set splits were applied. The performance of ResNet50 and VGG16 was evaluated using the same metrics (accuracy, AUC, precision, sensitivity, specificity, and F1-score). Computational efficiency was compared based on the number of trainable parameters and inference time per image (averaged over the test set using an RTX 3060 GPU).

Following the initial construction and training of the models for each phase, their performance was tested using data from the test group. The CT data of each phase of the test group were input into the constructed models of each phase, thus outputting their respective accuracy, precision, sensitivity, specificity, F1-score and area under the curve (AUC) value in terms of prediction. The optimal model was selected based on the evaluation output. Eventually, the optimal model was screened based on the evaluation output.

Prediction accuracy is the ratio of correctly predicted observations to the total observations. It measures the overall correctness of a model and is calculated as the sum of true positives (TP) and true negatives (TN) divided by the total number of observations. Precision, also known as the positive predictive value, is the ratio of true positives to the total number of predicted positives (TP + FP). It indicates the proportion of positive identifications that were actually correct. Sensitivity, also known as the true positive rate, is the ratio of true positives to the possible positives (TP + FN). It measures how well a model identifies actual positive instances. Specificity, also known as the true negative rate, is the ratio of true negatives to the possible negatives (TN + FP). It measures how well a model avoids false positives. The F1-Score is the harmonic mean of precision and recall (sensitivity). It is a single metric that balances both false positives and false negatives. It is particularly useful when the class distribution is imbalanced. AUC, specifically referring to the area under the receiver operating characteristic (ROC) curve, measures the ability of a classifier to distinguish between classes. AUC is the probability that a classifier will rank a random positive instance higher than a random negative instance. An AUC of 1 indicates perfect classification, while an AUC of 0.5 suggests no discriminative ability. Each of these metrics provides a different perspective on the performance of a classification model, and they are often used in conjunction to provide a comprehensive assessment.

To validate the clinical application and predictive performance of the optimal model, the corresponding CT data of 27 patients in the validation group were input into the optimal model and the diagnostic results of their Ki-67 high and low grades were the output. To begin with, three corresponding CT images of patients in the verification group were randomly selected, which were subsequently pre-processed by labeling and cropping and imported into the optimal model, and finally their outputs were compared with their actual postoperative pathology results. Consistent results indicate a correct diagnosis, otherwise an incorrect diagnosis was assigned. If each patient had ≥2 correctly diagnosed CT images, its Ki-67 expression was considered to be correctly predicted, in which case the accuracy of prediction and other corresponding results was calculated.

All data were statistically analyzed using the SPSS 26.0 software (IBM Corp.). Measurement data are expressed as mean ± standard deviation, and the high-grade and low-grade groups were compared using an independent two-sample Student's t-test after normality verification using a Shapiro-Wilk test. Categorical variables (sex, tumor size, AJCC stage, hypertension, diabetes mellitus and pathological type) are presented as frequences and percentages and group differences were assessed using a Pearson's χ² test. For 2×2 contingency tables where any expected cell count was <5, a Fisher's exact test was applied instead. The confusion matrix plots and ROC curves of the optimal model were constructed using Python 3.7. In the process of clinical verification, the accuracy, sensitivity and specificity of the optimal model to predict the verification group were calculated, and the consistency between the prediction results of the model and the actual pathological results was evaluated using the k-value. A k-value ≤0.2 indicates weak consistency, a value between 0.21–0.40 indicates weak consistency, a value between 0.41–0.60 indicates moderate consistency, a value between 0.61–0.80 indicates notable consistency and a value between 0.81–0.99 indicates optimal consistency. The 95% confidence intervals were then calculated, and the efficacy of the optimal model for clinical application was assessed combined with all the results obtained.

Existing studies (17–19) defined Ki-67 ≥10% as high grade and Ki-67 <10% as low grade. There were 35 cases in the high-grade group, including 28 male and 7 women, aged 28–75 years old, with a mean age of 58.00±8.94 years; 14 cases were on the left side and 21 cases were on the right side, and the maximum diameter of the tumors ranged from 1.8–13.0 cm, with a mean maximum diameter of 5.11±2.57 cm; ii) there were 102 cases in the low-grade group, including 57 men and 45 women, aged 30–76 years old, with a mean age of 57.46±10.84 years; 46 cases were on the left side and 56 cases were on the right side, and the maximum diameter of the tumors ranged from 1.0–12.5 cm, with a mean maximum diameter of 4.35±2.39 cm. Regarding tumor stage based on the AJCC 8th edition (20), in the high-grade group, 11 cases were stage I, 9 were stage II, 10 were stage III and 5 were stage IV; in the low-grade group, 58 cases were stage I, 22 were stage II, 15 were stage III and 7 were stage IV. Common comorbidities included hypertension (31 cases in high- vs. 58 in low-grade) and diabetes mellitus (12 cases in high-grade vs. 33 in low-grade). Sex distribution differed significantly (P=0.011), with a higher proportion of males in the high-(28/35, 80.0%) compared with the low-grade group (57/102, 55.9%). Tumor stage also showed a significant difference (P=0.018), as the high-grade group had a greater proportion of advanced-stage disease (stage III/IV: 15/35, 42.9%) relative to the low-grade group (22/102, 21.6%). In addition, the prevalence of hypertension was significantly higher in the high-grade group (31/35, 88.6%) than in the low-grade group (58/102, 56.9%) (P=0.001). The details of the clinical data are shown in Table I.

Following the establishment and training of the predictive models for each of the four phases and the combined four-phase, the CT images of the relevant test groups were used to test the prediction performance of each model. The prediction performance of each model in the prediction of both low- and high-grade groups was tested separately, which was mainly evaluated by the indexes of prediction accuracy, precision, sensitivity, specificity, F1-score and AUC value. The results are shown in Table II. To quantitatively evaluate the impact of data augmentation, the venous phase Mobilenetv3-large model was additionally trained and tested without augmentation using the same training and test sets. Before augmentation, the model achieved an average accuracy of 0.742, sensitivity of 0.708 and F1-score of 0.721 for the high-grade group. After augmentation (brightness enhancement, random flip and 20° random rotation), these metrics improved to 0.784, 0.764 and 0.770, respectively, with the most notable improvement observed in sensitivity for the high-grade group (from 0.683 to 0.744). This indicates that augmentation effectively alleviated the data imbalance issue and enhanced model robustness. To exclude the influencing factors of high-grade and low-grade and thus improve evaluation of the prediction performance among models, the prediction accuracy, precision, sensitivity, F1-score and AUC value of both low- and high-grade groups were compared in each model by summing them up and taking the arithmetic mean. The results are shown in Table III.

The prediction performance of the models was compared in terms of average prediction performance, as shown in Table III. The average prediction accuracy, sensitivity, precision, F1-score and AUC value for the plain scan phase model of Mobilenetv3-large were 0.701, 0.702, 0.694, 0.694 and 0.755, respectively; the aforementioned metrics for the arterial phase model of Mobilenetv3-large were 0.767, 0.761, 0.825, 0.754 and 0.894, respectively. For the venous phase model of Mobilenetv3-large, the average prediction accuracy, sensitivity, precision, F1-score and AUC value metrics were 0.784, 0.764, 0.789, 0.770 and 0.823, respectively; and for the excretion phase model of Mobilenetv3-large, these metrics were 0.730, 0.726, 0.730, 0.726 and 0.775, respectively. The aforementioned indicators for the combined four-phase model of Mobilenetv3-large were 0.774, 0.764, 0.802, 0.763 and 0.877, respectively.

To systematically select the optimal model, the following predefined criteria were established based on the clinical context of class imbalance (high-grade:low-grade ≈1:3): i) Primary priority was given to average accuracy, sensitivity for high-grade and F1-score, as these metrics directly reflect the model's ability to correctly identify the minority high-grade class; and ii) secondary priority was given to AUC and precision, which assess overall discriminative ability and positive predictive value, respectively. Performance differences between models were evaluated by directly comparing these metrics, with a difference of ≥0.02 considered practically significant based on the scale of the validation cohort. As shown in Table III, the venous phase model achieved the highest average accuracy (0.784), highest average sensitivity (0.764) and highest average F1-score (0.770) among all five models. Additionally, its average precision (0.789) and AUC (0.823) were ranked second and third, respectively, but remained within 0.02 of the top-performing models (arterial phase, precision 0.825; AUC 0.894). Given that sensitivity for the high-grade group is clinically paramount for avoiding missed aggressive tumors, and considering its superior robustness across multiple metrics, the venous phase model was selected as the optimal model for subsequent clinical validation. The confusion matrix (Fig. 3A) showed that the model correctly classified 15/17 low- and 4/6 high-grade patients, yielding a sensitivity of 0.667 and a specificity of 0.882 for the high-grade group. The ROC curve (Fig. 3B) demonstrated an AUC of 0.823 (95% CI: 0.751–0.895), indicating good predictive performance.

The optimal model, the venous phase model of Mobilenetv3-large, was used for the prediction of Ki-67 expression in the validation group of 27 patients (18 low- and 9 high-grade). Three CT images of each patient in the venous phase were randomly selected and input into the venous phase model, and two or more correctly predicted CT images were determined to be correctly predicted. The results show that the model predicted in the validation group with an accuracy of 0.814, a sensitivity of 0.889 and a specificity of 0.667 for predicting the low-grade, and a sensitivity of 0.667 and a specificity of 0.889 for predicting the high-grade. The prediction results are shown in detail in Table IV. The k-value of the consistency test between the predicted and actual pathologic diagnosis of Ki-67 expression of the venous phase model of Mobilenetv3-large was 0.57 (P=0.003), indicating a moderate consistency between the prediction results of the optimal model and the actual pathological diagnosis of the patient, with 95% confidence intervals of 0.24 and 0.90.

To justify the selection of Mobilenetv3-large, two other widely used DL architectures, ResNet50 and VGG16, were additionally trained and tested on the same venous-phase CT dataset under identical training conditions. As shown in Table V, Mobilenetv3-large achieved superior performance with an average accuracy of 0.784 and AUC of 0.823, compared with ResNet50 (accuracy, 0.761; AUC, 0.805) and VGG16 (accuracy, 0.743; AUC, 0.791). Furthermore, Mobilenetv3-large had ~4.0 million parameters, markedly fewer than ResNet50 (25.6 million) and VGG16 (138 million), resulting in faster inference time (12 vs. 28 vs. 45 msec/image). These results demonstrate that Mobilenetv3-large offers an optimal trade-off between predictive performance and computational efficiency for this task.