Predicting ki-67 expression in breast cancer via transformer and multiple instance learning on DCE-MRI

Abstract

Background

Accurate assessment of Ki-67 expression levels in breast cancer is crucial for determining prognosis and making informed treatment decisions. Current immunohistochemical methods relying on needle biopsy introduce sampling errors due to tumor spatial heterogeneity, making the development of non-invasive, precise preoperative prediction methods of significant clinical importance. This study aims to explore and compare advanced deep learning models based on dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) for noninvasive assessment of Ki-67 expression.

Methods

This retrospective study analyzed preoperative DCE-MRI data from 308 patients with histologically confirmed breast cancer. Adjacent slices centered on the tumor’s most significant cross-section were obtained to create a 2.5-dimensional (2·5D) dataset. We innovatively developed two deep learning models using the same dataset (1): a Multi-Instance Learning (MIL) model that combines slice-level predictive features with Predictive Likelihood Histogram (PLH) and Bag-of-Words (BoW) techniques (2); a Transformer-based fusion model that directly captures global contextual relationships between slices via self-attention mechanisms. The predictive performance of both models was systematically compared with traditional radiomics and clinical models.

Results

On an independent test set, the Transformer fusion model demonstrated optimal predictive performance with an area under the curve (AUC) of 0.875, achieving accuracy, sensitivity, and specificity of 0.839, 0.848, and 0.833, respectively. The MIL model ranked second (AUC = 0.825), with both models significantly outperforming traditional radiomics models (AUC = 0.698) and clinical models (AUC = 0.648).

Conclusions

Deep learning models based on 2·5D DCE-MRI, especially Transformer models that achieve global feature fusion through self-attention mechanisms, can effectively and non-invasively predict Ki-67 expression status in breast cancer, surpassing traditional methods. This model shows potential as a reliable tool to help clinicians accurately assess tumor proliferation activity before surgery.

Background

Breast cancer is the most common malignant tumor in women, with its incidence continuing to rise. Despite advances in multimodal integrated approaches, it remains one of the leading causes of cancer-related mortality [1]. As a key immunohistochemical marker, the cell proliferation antigen Ki-67 not only assesses tumor proliferation activity and predicts prognosis [2–4], but is also widely used as an essential reference for evaluating sensitivity to cytotoxic chemotherapy, reflecting tumor malignancy and treatment response [5]. Currently, Ki-67 assessment primarily relies on immunohistochemical analysis following needle biopsy. However, these results often fail to represent the tumor’s overall status due to tumor spatial heterogeneity and sampling limitations [6]. Therefore, developing non-invasive, accurate preoperative methods for predicting Ki-67 expression holds significant clinical importance.

Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) provides multi-phase hemodynamic information and has become a vital tool for breast cancer assessment. In image-based deep learning models, while 3-dimensional (3D) convolutional neural networks can fully utilize whole-tumor spatial information, they face challenges of massive parameters and high computational costs, limiting their practical application in clinical settings. Traditional 2-dimensional (2D) models, while efficient, analyze only a single slice, inevitably overlooking the tumor’s three-dimensional morphology and contextual information [7]. Addressing the challenges of high-dimensionality and heterogeneity in 3-dimensional imaging data, 2.5-dimensional (2.5D) deep learning strategies integrate multiple adjacent slices of the target region. This approach preserves spatial information while reducing computational burden, providing a stable and efficient input foundation for subsequent advanced deep learning models [8–10].

Building upon this foundation, Transformer fusion and Multi-Instance Learning (MIL) demonstrate significant potential in medical applications [11]. Transformer Fusion models global dependencies in image sequences composed of multiple consecutive slices through self-attention mechanisms; MIL treats the entire tumor region as a “package,” dividing it into multiple local images as “instances” on 2.5D slices. It aggregates local features via weakly supervised learning to automatically identify key regions, particularly suited for spatial heterogeneity in Ki-67 expression. Both approaches enhance tumor information analysis capabilities from global semantic association and local feature aggregation perspectives, respectively.

Although Transformers and MIL have demonstrated potential in medical applications, no systematic comparison exists for Ki-67 prediction based on DCE-MRI. Therefore, this study will construct Transformer-based fusion and MIL models using the same dataset, comparing their performance against traditional radiomics and clinical models to provide reliable model selection criteria for non-invasive Ki-67 assessment in breast cancer.

Methods

Study samples

This retrospective study adheres to the medical research guidelines of the Declaration of Helsinki and has been approved by the Institutional Review Boards of two hospitals (2025092305、KY2023111730). Written informed consent was not required for this retrospective study. Cases were collected from January 2022 to August 2025 at Hospitals A and B, involving patients with breast cancer confirmed by needle biopsy or surgical pathology. Inclusion criteria were: (1) Pathologically confirmed female breast cancer patients with complete clinical and imaging data. (2) Underwent routine preoperative breast magnetic resonance imaging (MRI). (3) Clear assessment of Ki-67 expression levels. Exclusion criteria were: (1) Poor or incomplete image quality. (2) History of other tumors. (3) Prior interventions (e.g., biopsy, chemotherapy) before DCE-MRI. Detailed inclusion/exclusion criteria and participant enrollment process are illustrated in Fig. 1. Ultimately, 208 cases from Hospital A and 100 from Hospital B were enrolled, totaling 308 cases. The study divided the samples into a training and validation cohort at a 7:3 ratio. We continued randomization until no statistically significant differences existed between samples in the training and validation cohorts, with all feature p-values exceeding 0.05.

Fig. 1.

Flowchart of study population with inclusion and exclusion criteria

Definition of Ki-67

Ki-67 expression was assessed in all breast cancer surgical or biopsy specimens included in this study. Ki-67 positive expression was localized to the cell nucleus, with positive cells exhibiting pale yellow to brownish-yellow staining. The proportion of nuclei stained positively in hotspot areas was used as the Ki-67 expression score. The Ki-67 index was defined as the percentage of Ki-67-positive cells in 10 high-power fields. <30% was classified as low expression, while a percentage ≥ 30% was classified as high expression [12].

Clinical characteristics

The clinical characteristics of breast cancer patients in our cohort included age, menopausal status, BMI, lymph node metastasis status, PR, ER, HER-2, and preoperative serum tumor marker levels covering CEA, CA12-5, CA15-3, and CA19-9. MRI morphological features of breast lesions were assessed, including: multifocal or multicentric lesions, peritumoral edema, high T2-weighted imaging signal within the tumor, mass morphology, mass margins, internal enhancement patterns, and time-signal intensity curves. All MRI images were reviewed independently by two primary diagnostic radiologists. In cases of disagreement, a third senior radiologist was consulted for review, with a unified opinion reached through consensus. Participating physicians remained unaware of the patients’ final pathological diagnoses throughout the evaluation process to ensure assessment independence and objectivity.

Image acquisition and Preprocessing

Images of breast cancer patients from Hospitals A and B were acquired using GE Discovery 3.0T MRI and SIEMENS skyra 3.0T MRI, respectively. The scanning sequences included: T1-weighted imaging, fat-suppressed T2-weighted imaging, diffusion-weighted imaging, and dynamic contrast-enhanced scanning. Following plain scanning, gadopentetate dimegumate contrast agent was administered via the elbow vein using a high-pressure syringe at a dose of 0.2 ml/kg and an injection flow rate of 2.0–3.0 ml/s, starting before the second dynamic contrast-enhanced phase. Continuous scanning commenced 30 seconds after contrast agent injection, with each scan lasting 60–66 seconds. Subsequently, 20–30 mmol of saline was injected at the same flow rate. The scanning parameters for both hospitals are shown in Table 1.

Table 1.

MRI scanning parameters

Variables	Sequence	Slice-thickness (mm)	Slice-gap (mm)	TR* (ms)	TE * (ms)
GE Discovery 3.0T MRI	T1WI *	4.0	1.0	573	13.5
	T2WI-FS *	4.0	1.0	4350	82.9
	DWI *	4.0	1.0	2552	70.5
SIEMENS skyra 3.0T MRI	T1WI *	1.6	1.0	600	2.46
	T2WI-FS *	3.5	1.0	3800	70.0
	DWI *	5.0	1.0	7500	70.0

DWI, diffusion-weighted imaging; MRI, magnetic resonance imaging; T1WI, T1-weighted imaging; T2WI-FS, T2-weighted imaging with fat suppression; TE, time to echo; TR, time of repetition

All DCE-MRI images were exported from Picture Archiving and Communication System in DICOM format. To minimize the impact of variations in machine types and scanning parameters, all images underwent the following preprocessing steps: resampling using linear interpolation, voxel spacing standardized to 1 mm × 1 mm × 1 mm, followed by N4 bias field correction to eliminate intensity fluctuations caused by magnetic field inhomogeneities, thereby enhancing image quality and accuracy. Two experienced radiologists manually delineated regions of interest (ROI) on the DCE-MRI images using ITK-SNAP software (version 3.8.0, http://www.itksnap.org) without patient clinical or pathological information access. To assess feature reproducibility, imaging data from 30 randomly selected patients were evaluated using the intra-class correlation coefficient (ICC). In addition, the Dice similarity coefficient was calculated to quantify the consistency of the input regions of interest for the deep learning models.

2.5D deep learning

We constructed models based on the 2.5D MIL proposed by Cen et al. [13] and Zhu et al. [14] and developed a Transformer-integrated model. The latter performs context-aware feature fusion, aiming to characterize better the spatial heterogeneity of tumors associated with high Ki-67 expression by capturing long-range dependencies between image patches. This approach enables comparison of different models’ predictive performance for Ki-67 expression levels in breast cancer. The specific implementation steps and operations are as follows（Fig. 2）.

Fig. 2.

Depicts the comprehensive workflow of the deep learning and radiomic models

Slice Data Acquisition: To balance three-dimensional spatial context information with computational efficiency, DCE-MRI images were selected at intervals of ±1, ±3, ±5, ±7, and ±9 centered on the tumor’s maximum cross-sectional plane. Using the patient ID as the fundamental unit, this approach constructed a 2.5D composite dataset comprising 11 slices per patient, ensuring that slices from the same patient were not distributed across different subsets. The “OKT_crop_max_roi” tool provided by the OnekeyAI platform was used for uniform image cropping to maintain consistency in the regions of interest.

Data Normalization: Standardizing image data is a critical step in deep learning, aimed at eliminating intensity variations caused by different scanning devices or protocols, thereby enhancing model training stability and convergence speed. This study employs the minimum-maximum scaling method to normalize image grayscale values within the range [−1,1]. Additionally, all cropped subregion images are resampled to a uniform size of 224 × 224 pixels using the nearest-neighbor interpolation algorithm, meeting the input requirements of the predefined deep learning model.

Data Augmentation: Z-score normalization was applied to standardize the intensity distribution across RGB channels in training and validation set images. The processed images were then fed into the model as input. During model training, data augmentation strategies were implemented on the training set, specifically including random cropping, horizontal flipping, and vertical flipping. It is crucial to emphasize that validation set images undergo no augmentation transformations. Otherwise, this would compromise the objective evaluation of the model’s predictive performance on data retaining the original distribution, thereby failing to reflect the model’s generalization capability accurately.

Slice-level model training: The preserved 2.5D dataset was utilized for subsequent deep learning model training. Three classic network architectures—ResNet50, VGG11, and DenseNet121—were selected. Each patient’s slices were treated as an independent data unit for training and validation. The predictive performance of various deep learning architectures was comprehensively compared and evaluated to identify the optimal feature processor, laying the foundation for subsequent patient-level analysis.

MIL Model

Early fusion of MIL initial features

First, each slice is predicted using the optimal slice-level model, yielding a probability value (Sliceprob) and classification label (Slicepred) for each slice. Subsequently, two MIL strategies are employed for early feature fusion: the first is the Predictive Likelihood Histogram (PLH), which divides different predicted values into several bins and counts the frequency of occurrence of Sliceprob and Slicepred within each bin. After min-max normalization, fixed-length feature vectors with uniform scale are obtained, named histogram probability features (Histoprob) and histogram prediction features (Histopred). These emphasize describing the distribution patterns of the model’s predictions across all slices at a macro level. The second approach employs a Bag-of-Words (BoW) model. It constructs two independent “dictionaries” based on each slice’s predicted probability (Sliceprob) and binary classification label (Slicepred), respectively. Statistically analyzing the occurrence frequency of each case slice. Through Term Frequency-Inverse Document Frequency processing, it highlights key BoW probability features (BoWprob) and BoW prediction features (BoWpred). This approach preserves the model’s original confidence information while reflecting the spatial distribution of different category slices.

Finally, each case’s PLH is integrated with BoW data into a high-quality, full-dimensional MIL feature for subsequent feature selection and model building. The training formula is:

Featurefusion = Histoprob + Histopred + BoWprob + BoWpred

MIL feature optimization and signature construction

We optimized the MIL features obtained from the initial fusion to suppress model overfitting and enhance its generalization capability. First, all features underwent Z-score normalization. Dimension reduction was then performed based on the significance of t-tests/Mann-Whitney U tests, Pearson correlation coefficients, and the regularization paths from Lasso regression models to select statistically significant features. During model construction, we employed three established machine learning models—Naive Bayes, Logistic Regression (LR), and Multilayer Perceptron (MLP)—to build predictive models for the reduced-dimensional MIL features. To address data class imbalance, we utilized the Synthetic Minority Oversampling Technique, synthesizing minority class samples to achieve data equilibrium. The model demonstrating optimal performance was selected as the final MIL signature.

Transformer fusion Model

Compared to MIL methods, Transformer fusion first selects the best-performing slice-level model to extract deep features from each patient’s slices. These features are normalized and fed into the Transformer fusion model. A pre-trained Multi-Transformer encoder is the core fusion module, which adaptively learns correlation weights between different slice features through a multi-head self-attention mechanism. The model training employs the AdamW optimizer with a cosine decay coefficient to adjust the learning rate dynamically. The initial learning rate is set to 0.01, with training repeated over 200 epochs using a batch size 64. GPU acceleration is utilized to expedite the training process. Finally, a hyperparameter tuning method is applied to validate model stability. After repeated training, model performance is evaluated on an independent test set.

Radiomics

Traditional radiomics models utilize the open-source software PyRadiomics on the Python 3.7 platform to extract features. Feature stability screening and redundancy removal are performed based on intra-group correlation coefficients and Spearman correlation analysis. Subsequently, the Minimum Redundancy Maximum Relevance and Least Absolute Shrinkage and Selection Operator regression methods were combined to select the most predictive features. The radiomics features were modeled using the same machine learning algorithms as the MIL model, with the highest-performing model designated the radiomics model.

Clinical feature Model

The Shapiro-Wilk test was first applied to assess variable normality in clinical-imaging data analysis. Subsequently, based on data types, t-tests, Mann–Whitney U tests, or chi-square tests were selected for univariate and multivariate analyses to screen for statistically significant indicators (significance level set at p < 0.05). Subsequently, three machine learning frameworks—LR, Naive Bayes, and Support Vector Machines—were employed for training and modeling. The model demonstrating the highest predictive efficacy was ultimately selected as the clinical feature model.

Results

In this study, we selected appropriate statistical inference methods for different data types based on the results of the Shapiro-Wilk test. Data meeting the assumption of normality were analyzed using t-tests. In contrast, data failing this assumption were processed with Mann-Whitney U tests to ensure the accuracy of parametric and nonparametric statistical inferences, respectively. For categorical variables, chi-square tests were employed to assess associations. This method is highly versatile and demonstrates exemplary performance in discerning relationships between categorical variables, meeting the data processing requirements of the current study. Each model was comprehensively evaluated using multiple metrics, including AUC, accuracy, sensitivity, specificity, and positive and negative predictive values. All data analysis was performed on the OnekeyAI platform (version 3.5.28) using Python 3.7.12.

Patient baseline characteristics and data preprocessing

This study included 308 breast cancer patients, categorized into high-expression and low-expression groups based on Ki-67 levels. No significant differences were observed between groups in clinical characteristics (age, tumor number, hormone receptor status, etc.) (all p > 0.05). Indicating good comparability between groups. This allows subsequent model performance differences to be more accurately attributed to the modeling approach rather than baseline biases in the patient population. All patients’ DCE-MRI images underwent a 2.5D data acquisition workflow, generating a comprehensive dataset of 11 slices per patient. These images were then normalized and enhanced before being input into the model.

2.5D deep learning

In slice-level model training, the ResNet50, VGG11, and DenseNet121 architectures demonstrated stable predictive capabilities on the validation set. Among these, ResNet50 performed most notably in distinguishing Ki-67 high/low expression slices, achieving an AUC of 0.716, sensitivity = 0.694, and specificity = 0.727, significantly outperforming other models (Table 2). Consequently, we selected ResNet50 (with the final fully connected classification layer removed, retaining only up to the ‘avgpool’ layer) as the fixed feature extractor. This converts each MRI slice from every patient into a 2048-dimensional deep feature vector.

Table 2.

Comparison of slice-level prediction performance across different deep learning approaches

Model	AUC *(95%CI *)	Accuracy	Sensitivity	Specific	Dataset
ResNet50	0.712（0.642–0.782）	0.693	0.730	0.654	Train
ResNet50	0.716（0.611–0.821	0.710	0.694	0.727	Test
VGG11 *	0.696（0.626–0.766）	0.665	0.685	0.644	Train
VGG11 *	0.661（0.547–0.775	0.677	0.837	0.500	Test
DenseNet121	0.719（0.650–0.788）	0.702	0.739	0.663	Train
DenseNet121	0.635（0.521–0.749	0.602	0.408	0.818	Test

AUC: Area under the curve; CI: Confidence interval; VGG11: Visual Geometry Group 11

MIL Model

Based on slice-level predictions from ResNet50, 22 MIL features per patient were extracted through PLH and BoW strategy fusion. After Z-score normalization and Lasso regression screening, nine significant features (p < 0.05) were retained for constructing the MIL signature. We compared three machine learning algorithms to identify the optimal patient-level classifier: Naive Bayes, LR, and MLP. Results indicate Naive Bayes achieved optimal performance (Table 3), with an AUC of 0.825 (95% CI: 0.7381–0.9122), accuracy, sensitivity, and specificity of 0.796, 0.848, and 0.745, respectively. The MIL model demonstrated good discriminatory ability for Ki-67 expression on the test set, but its performance was inferior to the subsequent Transformer-based ensemble model (Table 4).

Table 3.

Performance comparison of different deep learning models in MIL method evaluation

Model	AUC *(95%CI *)	Accuracy	Sensitivity	Specific	Dataset
LR *	0.852（0.800–0.904）	0.819	0.798	0.842	Train
LR *	0.807（0.715–0.899）	0.796	0.870	0.723	Test
Naive Bayes	0.852（0.801–0.904）	0.814	0.781	0.851	Train
Naive Bayes	0.825（0.738–0.912）	0.796	0.848	0.745	Test
MLP *	0.861（0.813–0.910）	0.809	0.816	0.802	Train
MLP *	0.814（0.725–0.903）	0.785	0.870	0.702	Test

AUC: Area under the curve; CI: Confidence interval; LR: Logistic Regression; MLP: Multilayer Perceptron

Table 4.

Predictive performance of four models

Signature	AUC *	95% CI *	Accuracy	Sensitivity	Specificity	Dataset
Transformer	0.913	0.8726 - 0.9537	0.865	0.851	0.881	Train
Transformer	0.875	0.8212 - 0.9282	0.839	0.848	0.830	test
MIL *	0.852	0.8006 - 0.9041	0.814	0.781	0.851	Train
MIL *	0.825	0.7639 - 0.8864	0.796	0.848	0.745	test
Radiomics	0.764	0.6999 - 0.8273	0.712	0.632	0.802	Train
Radiomics	0.698	0.6214 - 0.7745	0.699	0.761	0.638	test
Clinic	0.758	0.6940 - 0.8227	0.726	0.772	0.673	Train
Clinic	0.648	0.5682 - 0.7269	0.645	0.630	0.660	test

AUC: Area under the curve; CI: Confidence interval; MIL: Multiple-Instance Learning

Transformer fusion Model

The Transformer model directly modeled inter-slice dependencies through self-attention mechanisms, achieving optimal predictive performance on the test set with an AUC of 0.875 (95% CI: 0.8212–0.9282), along with accuracy, sensitivity, and specificity of 0.839, 0.848, and 0.83, respectively (Table 4). Compared with the MIL model, the Transformer demonstrated significantly higher AUC (DeLong test, p = 0.135), indicating its superior global context capture capability is more suitable for assessing proliferative activity in heterogeneous tumors.

Radiomics and clinical models

The traditional radiomics model identified seven key features via mRMR-LASSO screening. Its optimal classifier, Naive Bayes, achieved an AUC of 0.698, accuracy = 0.699, sensitivity = 0.761, and specificity = 0.638. This performance surpassed the clinical model (p < 0.05) but fell below the MIL and Transformer models. In both training and validation datasets, univariate analysis revealed significant differences in CA125, HER-2, tumor margin status, and lymph node metastasis status (p < 0.05). Multivariate regression analysis further narrowed these features, with only HER-2 retaining independent statistical significance (p < 0.05). Among the three prediction models developed based on HER-2, SVM demonstrated the best performance (AUC = 0.648, accuracy = 0.645, sensitivity = 0.63, specificity = 0.66) and was designated as the clinical feature model, despite exhibiting the lowest overall performance among all models (Table 4).

Model visualization analysis

This study employs Grad-CAM for visualization analysis to enhance the transparency of the model’s decision-making mechanism and gain deeper insight into its judgment basis. As shown in Fig. 3, this method generates heatmaps that visually highlight the key image regions contributing most significantly to the network’s classification results [15, 16]. High-attention regions were predominantly located in the tumor parenchyma, with partial coverage of the tumor margin and internal necrotic areas. This distribution pattern suggests that the Transformer model integrates information from different spatial locations through its self-attention mechanism, rather than relying solely on locally optimal regions.

Fig. 3.

A, B displays the visualization results for two cases

From left to right: the original DCE-MRI image, the Grad-CAM heatmap, and the fusion image. The red-marked regions indicate key areas with higher weight and strong correlation with breast cancer KI-67 expression. Refer to the color bar provided on the right side of the figure for interpretation.

Bootstrap resampling analysis

To assess the stability of model performance, Bootstrap resampling (1,000 iterations) was performed on the independent test set. The mean AUC, standard deviation, and 95% confidence intervals were calculated for each model. Additionally, the dispersion and symmetry of the AUC distributions were analyzed to evaluate model stability when trained on varying data. These comparisons provide insight into the robustness of each model under fluctuations in training data composition.

Bootstrap analysis demonstrated that the Transformer model achieved the highest mean AUC (0.875, 95% CI: 0.794–0.945), the smallest standard deviation (0.039), and the narrowest confidence interval (0.151), indicating its superior performance, stability, and precision among all models evaluated. The MIL model followed with a mean AUC of 0.824 (95% CI: 0.731–0.904; Std = 0.044). Partial overlap was observed between the confidence intervals of the Transformer and MIL models (0.794–0.904), suggesting that the difference between them did not reach statistical significance. In contrast, the confidence intervals of the radiomics model (0.698, 95% CI: 0.583–0.801) and the clinical model (0.533, 95% CI: 0.436–0.631) showed no overlap with those of the deep learning models, confirming the marked superiority of deep learning approaches (Table 5). The AUC distributions for all models were approximately symmetric, with no evidence of extreme outliers (Fig. 4).

Table 5.

Bootstrap resampling results for the four models

Model	Mean AUC	Std	95% CI	CI Lower	CI Upper
Transformer	0.875	0.039	[0.794–0.945]	0.793	0.944
MIL	0.824	0.044	[0.731–0.904]	0.731	0.903
Radiomics	0.698	0.056	[0.583–0.801]	0.582	0.801
Clinic	0.533	0.050	[0.436–0.631]	0.436	0.630

AUC: Area under the curve; Std:Standard Deviation; CI: Confidence interval; MIL:Multiple-Instance Learning

Fig. 4.

Bootsrap ROC curves

Discussion

This study systematically evaluated and compared the efficacy of Transformer fusion, MIL, traditional radiomics, and clinical models based on 2.5D deep learning strategies for preoperative non-invasive prediction of Ki-67 expression status in breast cancer (Fig. 5). Our findings indicate that deep learning models based on DCE-MRI can effectively predict Ki-67 status, with significantly superior performance to traditional radiomics and clinical models. Among these, the Transformer-based fusion model demonstrated the highest predictive capability (AUC = 0.875), slightly outperforming the MIL model (AUC = 0.825). This provides a novel and effective solution for addressing the challenges in Ki-67 assessment caused by tumor heterogeneity.

Fig. 5.

A: ROC curves of different models in cohort training set. B: ROC curves of different models in cohort testing set. C: Delong test results of model performance comparisons in cohort training set. D: Delong test results of model performance comparisons in cohort testing set. E: DCA of different models in cohort training set. F: DCA of different models in cohort testing set. Performance comparison results of different models (transformer, MIL, radiomics, Clinic). A,B: ROC curves for training and testing datasets, showing AUC and 95% CI of each model on the training set.C, D: Delong test heatmaps for training and testing datasets, comparing the statistical significance of AUC differences between models. E, F: decision analysis curves for the training set (E) and test set (F), evaluating the practical value of predictive models in clinical decision-making.AUC: area under the curve; ROC: receiver operating characteristic; 95% CI: 95% confidence interval; DCA: decision curve analysis

2.5D deep learning: balancing computational efficiency and information richness

The 2.5D deep learning strategy adopted in this study is a crucial foundation for achieving superior performance. Compared to 2D models that solely utilize the tumor’s maximum layer, the 2.5D approach significantly enriches the spatial contextual information available to the model by incorporating adjacent slices, without incurring the high computational costs associated with 3D models. Comparative studies by Zhang et al. [8]across various tasks confirm that 2.5D approaches exhibit substantially lower parameter counts and computational overhead than 3D CNNs while outperforming 2D models. This aligns with our observation: deep learning models trained on 2.5D data consistently demonstrate superior performance to traditional methods. This approach skillfully balances model complexity and feature expressiveness, avoiding the heavy computational burden of 3D models while providing richer, spatially contextual information inputs for subsequent advanced feature fusion. It offers new insights for achieving high-performance prediction under clinically feasible conditions.

MIL model: an effective strategy for addressing tumor spatial heterogeneity

MIL inherently aligns with the clinical practice of Ki-67 immunohistochemical assessment. When evaluating the Ki-67 index, pathologists typically scan entire tissue sections and integrate results from multiple fields of view—particularly high-expression “hot spots”—to derive an overall judgment [17]. This process acknowledges the intrinsic spatial heterogeneity of Ki-67 expression within tumors [18, 19]. This study treats multiple DCE-MRI slices from each patient as a “batch,” integrating slice-level prediction results via PLH and BoW methods. This approach quantifies the distribution pattern of a deep learning model’s predictive confidence across individual slices. PLH reflects the overall distribution pattern of model prediction probabilities, while BoW focuses on capturing the spatial frequency of slices with discriminative labels. This approach enables the model to adaptively focus on key slices or regions potentially harboring high Ki-67 expression without relying on complex computations across the entire tumor volume data. Our results (MIL AUC = 0.825) confirm that MIL effectively integrates information from multiple sections, robustly addressing challenges posed by tumor heterogeneity. This aligns with Zhu et al.‘s [14] findings, which demonstrated that the MIL framework can extract heterogeneity features correlated with tumor malignancy from DCE-MRI, achieving strong predictive performance.

Transformer fusion model: performance advantages based on global context modeling

Although the MIL model achieved favorable predictive performance (AUC = 0.825), the Transformer fusion model demonstrated superior overall predictive efficacy in this study, with a test set AUC of 0.875. At the optimal decision threshold, it maintained high accuracy (0.839), sensitivity (0.848), and specificity (0.833). This balanced high performance indicates that the Transformer model not only possesses strong overall discriminative ability but also exhibits more robust decision boundaries, enabling more consistent and accurate assessment of tumor proliferative activity. Unlike MIL, which primarily relies on post-hoc statistical aggregation of instance-level predictions, the Transformer directly computes mutual relationship weights between all slice feature vectors at the feature level. High Ki-67 expression is not only reflected in localized rapid cell proliferation but may also correlate with macroscopic features such as vascular distribution throughout the tumor and the spatial conformation of metabolically active regions [20]. Grad-CAM visualizations provided intuitive evidence for understanding the performance advantages of the Transformer model. The attention distribution shown in Fig. 3 illustrates that the model not only identifies locally discriminative features but also establishes feature associations between these regions and other tumor subregions. Consequently, it evaluates the importance of individual slices similarly to MIL while also comprehending the intrinsic correlations and collaborative patterns among different tumor regions represented by distinct slices, thereby constructing a holistic tumor representation that integrates global spatial semantics.Notably, this attention distribution pattern aligns closely with clinical pathological assessment practice. When evaluating Ki-67 status, pathologists do not rely solely on a single “hot spot” but rather integrate observations from multiple representative regions to derive an overall score. The Transformer model simulates this cognitive process through its self-attention mechanism, which may explain its superior predictive efficacy.

Our findings are consistent with the emerging trend in tumor analysis of leveraging Transformer architectures to capture long-range dependencies. For instance, Kumar et al. developed an advanced framework integrating Transformers with attention mechanisms for histopathological image analysis in renal cell carcinoma, achieving high precision in reflecting tumor malignancy [21]. Our study extends this approach to Ki-67 prediction in breast cancer and confirms its slight superiority over MIL methods. This suggests that for tasks requiring holistic evaluation of tumor biological characteristics, model architectures capable of end-to-end global context fusion hold greater potential.

Limitations of traditional models: constraints from feature expressiveness and indirect biomarker relationships

The predictive efficacy of traditional radiomics models (AUC = 0.698) and clinical models (AUC = 0.648) is significantly lower than that of deep learning models. This gap reflects inherent limitations in both conventional approaches. The radiomics model relies on artificially designed features that may fail to adequately capture the deep, nonlinear biological characteristics associated with Ki-67 expression.

The clinical model in this study demonstrated the lowest performance, fundamentally because the metrics it relies on (e.g., HER-2 status, tumor markers) are not direct measures of Ki-67 proliferation activity but indirect, correlated biological representations. While these clinical-pathological indicators correlate with overall tumor behavior, they exhibit complex, non-one-to-one mapping relationships with cellular proliferation rates. For instance, HER-2 positivity drives specific signaling pathways associated with and relatively independent from cell cycle progression, as represented by Ki-67. Consequently, limited clinical parameters alone struggle to construct particular and sensitive predictive models for Ki-67 expression status, resulting in suboptimal predictive capabilities.

Bootstrap resampling analysis: a comprehensive evaluation of model performance

Bootstrap analysis provided a comprehensive assessment of model stability and performance. The Transformer model not only achieved the highest mean AUC (0.875) but also outperformed the other models across all metrics in terms of stability (standard deviation: 0.039) and estimation precision (confidence interval width: 0.151). These findings indicate that the Transformer model was the least sensitive to variations in test set composition and exhibited the most robust performance, suggesting its greatest potential for clinical translation among the four models evaluated. Furthermore, a substantial performance gap was observed between deep learning models and traditional approaches. The 95% confidence intervals of both the Transformer and MIL models showed no overlap with those of the radiomics or clinical models, confirming the significant advantage of deep learning methods in predicting Ki-67 expression status. This conclusion remained consistent regardless of data partitioning, demonstrating strong generalizability. Finally, the comparative relationship between the Transformer and MIL models warrants further investigation. Although the Transformer model outperformed MIL across all evaluated metrics, partial overlap was observed between their confidence intervals (0.794–0.904), suggesting that the observed difference did not reach statistical significance. Future studies with larger sample sizes or optimized model architectures are needed to determine whether the Transformer model can achieve substantial superiority over the MIL approach.

Limitations

This study still has limitations. At the data level, it currently relies solely on a single contrast-enhanced phase of DCE-MRI, failing to fully exploit hemodynamic information from multi-phase dynamic curves or integrate multi-sequence features such as diffusion-weighted imaging. This restricts the model’s ability to capture tumor biological characteristics comprehensively. Future work could develop a combined model integrating multi-sequence and multi-phase data to more fully characterize tumor heterogeneity. Regarding model architecture, while both MIL and Transformer models demonstrate strong predictive capabilities, their synergistic advantages—MIL’s modeling of regional heterogeneity and Transformers’ capture of long-range contextual dependencies—remain underutilized due to their lack of organic integration. MIL-Transformer hybrid architectures have shown great promise in pathological image analysis [22, 23]. Its core approach of explicitly modeling complex inter-instance correlations through self-attention mechanisms equally applies to multi-slice sequence data like MRI. Therefore, exploring end-to-end MIL-Transformer fusion models tailored for MRI holds promise for further enhancing predictive performance while pioneering more generalizable approaches for preoperative non-invasive assessment. Regarding model dimensionality, this study adopted a 2.5D architecture, which offers a favorable trade-off between computational efficiency and predictive performance. Although a direct comparison with full 3D convolutional neural networks was not conducted, emerging evidence suggests that on moderate-sized datasets, 2.5D approaches can achieve performance comparable to or even exceeding that of 3D methods [24, 25]. Systematic comparisons between these two dimensional approaches will be pursued in future investigations.

Conclusion

In summary, this study successfully constructed and compared a Transformer-based fusion model and an MIL model utilizing breast DCE-MRI for preoperative prediction of Ki-67 expression status. Results demonstrate that both deep learning models effectively overcome tumor heterogeneity, significantly outperforming traditional methods. Specifically, the Transformer model demonstrated optimal predictive efficacy due to its robust global context awareness, offering a more suitable deep learning solution for this task. This study confirms the feasibility of non-invasively decoding key molecular information from routine medical images using advanced AI technologies, providing a powerful auxiliary tool for precision diagnosis and treatment decisions in breast cancer.

Abbreviations

DCE-MRI

Dynamic Contrast-Enhanced Magnetic Resonance Imaging

MRI

Magnetic Resonance Imaging

MIL

Multi-Instance Learning

2.5D

2.5-Dimensional

2D

2-Dimensional

3D

3-Dimensional

PLH

Predictive Likelihood Histogram

BoW

Bag-of-Words

AUC

Area Under the Curve

ROI

Regions of Interest

LR

Logistic Regression

MLP

Multilayer Perceptron

Author contributions

The individual contributions of the authors to this study are specified as follows: YC and ML jointly conceived and designed the study. ML was responsible for the construction of the algorithm model, while YC drafted the initial manuscript. YW, as the corresponding author, oversaw the conception and supervision of the entire research project, and performed the final review and approval of the manuscript. YO and CZ provided crucial software and technical support for the model implementation. NH, XZ, and JY were responsible for the collection and annotation of clinical data. QW and DT participated in the processing and analysis of the data. All authors have read and approved the final manuscript.

Funding

Not applicable.

Data availability

No datasets were generated or analysed during the current study.

Declarations

Ethics approval and consent to participate

This study is a retrospective investigation that has obtained approval from the Ethics Committees of Youjiang Medical University for Nationalities (Approval No. 2,025,092,305) and Baise People’s Hospital (Approval No. KY2023111730), in accordance with the ethical principles of the Declaration of Helsinki. The requirement for individual informed consent has been waived by the ethics committees.

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.