Development and validation of an interpretable model based on ultrasound radiomics for predicting Ki-67 expression levels in breast cancer

Abstract

Background

Ki-67 is a critical proliferation marker in breast cancer, but its preoperative assessment is limited by the invasiveness and sampling bias of core needle biopsy. This study aimed to establish and validate non-invasive prediction models of Ki-67 status of breast cancer based on conventional ultrasound radiomics features, clinical features, or their combination.

Methods

Retrospective analysis was performed on 558 patients with breast cancer who underwent two-dimensional (2D) ultrasound and Ki-67 detection. Among them, 398 patients in the training set were from Zhejiang Cancer Hospital, and 160 patients in the external validation set were from Lishui Central Hospital. According to the 14% threshold, the patients were divided into Ki-67 low expression group and Ki-67 high expression group. Clinical parameters, conventional ultrasound characteristics, and 2D ultrasound images of the tumor’s maximum cross-section were collected. Radiomics features were extracted from the delineated regions of interest (ROIs) with the PyRadiomics package. We used univariate analysis, least absolute shrinkage and selection operator (LASSO) regression, and multivariate logistic regression to determine the independent predictors. Three models—clinical, radiomics, and a combined clinical-radiomics model—were developed. We constructed a nomogram based on the combined model. Model evaluation was undertaken via receiver operating characteristic (ROC) curve analysis [calculating area under the curve (AUC), accuracy, sensitivity, specificity, positive predictive value (PPV), negative predictive value (NPV), precision, recall, and F1 score], calibration curves, and decision curve analysis (DCA). In addition, SHapley Additive exPlanations (SHAP) were used to interpret the model.

Results

In the training (n=398) and external validation (n=160) sets, multivariate logistic regression identified age [odds ratio (OR) =0.971, P=0.026], maximum lesion diameter (OR =1.051, P<0.001), microcalcification (OR =1.548, P=0.109), and posterior echo (OR =0.358, P=0.001) as independent predictors of Ki‑67 expression in breast cancer. LASSO with 5‑fold cross‑validation selected three radiomics features (two texture, one shape). A clinical‑radiomics combined model achieved AUCs of 0.731 [95% confidence interval (CI): 0.670–0.792] and 0.709 (95% CI: 0.614–0.804) in the training and validation sets, with accuracies of 0.643 and 0.750 and F1 scores of 0.728 and 0.840, respectively. Calibration and decision curve analyses demonstrated good consistency and clinical net benefit. A visualized risk nomogram was constructed to estimate individual probabilities. SHAP analysis revealed that radiomics features (e.g., original_glcm_MaximumProbability) and clinical features (microcalcification and posterior echo) contributed most; positive microcalcification increased the likelihood of high Ki‑67 expression, whereas posterior echo attenuation decreased it.

Conclusions

Ultrasound-derived radiomics features provide incremental value for predicting Ki-67 expression in breast cancer. This comprehensive clinical-radiomics model demonstrates excellent diagnostic performance and has been interpreted using the SHAP method. It has the potential to serve as a non-invasive preoperative tool to complement core needle aspiration biopsy and play a complementary role in clinical decision-making.

Highlight box.

Key findings

• The combined clinical‑radiomics model achieved areas under the curve of 0.731 (training) and 0.709 (external validation) for predicting high Ki‑67 expression (≥14%) in breast cancer.

• SHapley Additive ExPlanations (SHAP) analysis identified radiomics features (especially original_glcm_MaximumProbability), microcalcifications, and posterior echo attenuation as the most influential predictors.

What is known and what is new?

• Ki‑67 is a key proliferation marker for breast cancer prognosis and treatment decisions, but its assessment relies on invasive biopsy with potential sampling bias.

• This study develops an interpretable, non‑invasive model integrating conventional ultrasound radiomics and clinical features to preoperatively estimate Ki‑67 expression, with external validation and SHAP‑based explanation.

What is the implication, and what should change now?

• The model can serve as a preoperative adjunct to core needle biopsy, aiding individualized treatment planning (e.g., neoadjuvant chemotherapy) and enabling repeat assessment without re‑biopsy.

• Prospective multi‑center studies and automated segmentation are needed to further validate and translate this approach into routine clinical practice.

Introduction

Breast cancer is the most common malignant tumor in women worldwide, with its high heterogeneity complicating treatment selection and prognosis assessment (1). Ki-67 is a nuclear antigen related to cell proliferation and is a critical biomarker for evaluating tumor proliferative activity and invasiveness in breast cancer (2). Elevated Ki-67 levels are associated with higher histological grade, increased proliferative capacity, and poorer clinical outcomes, guiding neoadjuvant chemotherapy, endocrine therapy, and recurrence risk prediction (3). Currently, Ki-67 assessment relies on immunohistochemical (IHC) analysis of biopsy or surgical specimens. Although this is the gold standard, this method is invasive, prone to sampling bias, non-repeatable for real-time monitoring, and may not capture spatial tumor heterogeneity (4). Thus, accurate, reproducible and non-invasive preoperative Ki-67 assessment is needed to support personalized precision medicine.

Advances in medical imaging, particularly radiomics, enable the non-invasive decoding of intratumoral phenotypic characteristics (5). Ultrasound radiomics, a subset of radiomics, can extract and analyze quantitative features from conventional ultrasound images with high throughput, and reveal associations between imaging data and underlying genomics, pathology, and clinical behavior (6). Preliminary studies suggest that ultrasound radiomics features can differentiate molecular subtypes, predict lymph node metastasis, and estimate Ki-67 expression (7,8). However, radiomics-only models may overemphasize morphological/textural characteristics while overlooking clinically relevant biological dimensions.

Preoperative clinical data offer complementary predictive value. Conventional ultrasound features (e.g., tumor size, shape, margin, posterior acoustic pattern, calcifications) are fundamental to diagnosis, with several correlating with tumor aggressiveness (9). Additionally, circulating serological biomarkers [e.g., cancer antigen 125 (CA125), cancer antigen 153 (CA153), systemic immune-inflammation index (SII)] reflect systemic tumor burden and biological activity, with growing prognostic recognition (10-12). Integrating these accessible clinical variables with deep radiomics features into a multimodal fusion model may provide a more comprehensive representation of tumor biology, mitigate single-source biases, and improve predictive performance.

Therefore, this study aimed to develop and validate a multimodal predictive model integrating preoperative ultrasound radiomics features with clinical variables for the non-invasive estimation of Ki-67 expression in breast cancer, serving as a decision-support tool for individualized treatment planning. We present this article in accordance with the TRIPOD reporting checklist (available at https://tcr.amegroups.com/article/view/10.21037/tcr-2026-1-0384/rc).

Methods

Patient cohort

Patients with breast masses who underwent ultrasound examination in Zhejiang Cancer Hospital and Lishui Central Hospital from January 2020 to December 2023 were retrospectively enrolled. The inclusion criteria were: (I) histopathologically confirmed breast cancer with a documented Ki-67 index; (II) ultrasonography was performed no more than one week before the biopsy or surgical procedure; and (III) no treatment for breast cancer was received either before undergoing ultrasound examination or before the biopsy/surgery. Exclusion criteria included: (I) history of other malignancies or severe comorbidities; or (II) inadequate ultrasound image quality. Figure 1 illustrates the patient selection flowchart. The final cohort consisted of 558 patients: a training set of 398 from Zhejiang Cancer Hospital and an external validation set of 160 from Lishui Central Hospital. This study was conducted in accordance with the Declaration of Helsinki and its subsequent amendments. The study was approved by the Ethics Committee of Zhejiang Cancer Hospital (No. IRB-2024-1272 [IIT]) and the Ethics Committee of Lishui Central Hospital, Zhejiang Province (No. 2024-402). For this retrospective analysis, individual informed consent has been waived.

Figure 1.

Flowchart of patient selection. ZCH, Zhejiang Cancer Hospital; ZP LCH, Lishui Central Hospital of Zhejiang Province.

Clinical characteristics

Baseline clinical data were obtained via review of the electronic medical records: (I) demographic characteristics, including age and body mass index (BMI); (II) clinical laboratory markers, including tumor markers [CA125, CA153, carcinoembryonic antigen (CEA), CA724], lipid profile [triglycerides, high-density lipoprotein cholesterol (HDL-C), low-density lipoprotein cholesterol (LDL-C)], the parameters of the liver function [alanine aminotransferase (ALT), aspartate aminotransferase (AST), total bilirubin (TBIL), direct bilirubin (DBIL), indirect bilirubin (IBIL)], inflammatory indices [SII, systemic immune response index (SIRI), pan-immune inflammation value (PIV), absolute eosinophil count], and hormonal markers (estradiol, progesterone, prolactin). Data quality was assessed: (I) missing data (CA724 8.2%, eosinophil count 5.1%, others <3%) were imputed using multiple imputation by chained equations (MICE). (II) Outliers (CEA: 10; SII: 9) were identified via box plots and the 3σ criterion and addressed by winsorization (replacement with 1st/99th percentile values).

Inflammatory indices were calculated as: SII = platelet count × neutrophil count/lymphocyte count; SIRI = (neutrophil count × monocyte count)/lymphocyte count; PIV = (platelet count × neutrophil count × monocyte count)/lymphocyte count.

Ki-67 expression was assessed via IHC per the St. Gallen International Expert Consensus; tumors with ≥14% positive nuclei were classified as high expression, <14% as low expression. The pathologists responsible for Ki-67 assessment were blinded to all clinical and radiomics data.

Ultrasound features

Ultrasound examinations at Zhejiang Cancer Hospital used Logiq E9, Canon Aplio 900, and Mindray Resona R9S systems. At Lishui Central Hospital, Logiq E9 and Hitachi HI VISION Preirus/ARIETTA 70 devices were used. All systems employed high-frequency linear array transducers (5–13 MHz). Patients were positioned supine with arms abducted. Multiplanar scanning covered all breast quadrants. Two experienced radiologists (13 and 20 years of experience), blinded to pathology, independently recorded ultrasound features per the 2017 Breast Imaging Reporting and Data System (BI-RADS) guidelines. Parameters included: maximum tumor diameter, composition (cystic/cystic-solid vs. solid), shape (regular vs. irregular), margin (smooth vs. unsmooth), orientation (parallel vs. non-parallel), microcalcifications, hyperechoic halo, and posterior acoustic features (no change/enhancement vs. attenuation). Discrepancies were resolved by consensus with a third senior radiologist.

Tumor segmentation, feature extraction and selection

Two radiologists (>5 years of breast imaging experience) manually segmented regions of interest (ROI) on gray scale ultrasound images (maximum diameter cross section), blinded to clinical/pathological data. Sonographer 1 delineated all ROIs using ITK-SNAP. Sonographer 2 independently segmented a random subset of 140 tumors (100 from Zhejiang Cancer Hospital, 40 from Lishui Central Hospital). Two weeks later, Sonographer 1 re-segmented the same subset. We assessed inter- and intraobserver reproducibility via intraclass correlation coefficients (ICCs) and retained features with ICC >0.75.

Prior to extraction, images were resampled to 1 mm × 1 mm and normalized via z-score transformation to mitigate inter-scanner intensity variations. Features were extracted using PyRadiomics. Feature selection involved: (I) univariate analysis (t-test or Mann-Whitney U test, P<0.05); (II) Spearman correlation analysis (r>0.90) to remove highly correlated features; (III) least absolute shrinkage and selection operator (LASSO) regression with fivefold cross-validation to select features with non-zero coefficients.

Model development, validation, and evaluation

To compare performance, three models—clinical, radiomics, and a combined model—were built using multivariable logistic regression. Their evaluation included receiver operating characteristic (ROC) curves (providing area under the curve (AUC), accuracy, sensitivity, specificity, positive predictive value (PPV), negative predictive value (NPV), precision, recall, and F1 score), calibration curves, and decision curve analysis (DCA). The best-performing model was used to generate a nomogram for clinical translation, while SHapley Additive exPlanations (SHAP) analysis offered insights into its decision-making process.

To enhance the reproducibility and interpretability of the final model, SHAP values were calculated using the LinearExplainer, which is specifically designed for linear models and provides exact, deterministic SHAP values. The expected value for the SHAP explanation was computed using the mean feature vector of the entire training set (n=398) as the reference background dataset.

Statistical analysis

Sample size adequacy was assessed using the events-per-variable (EPV) criterion, which recommends a minimum of 10–20 outcome events per predictor to minimize overfitting. In the training cohort (398 patients, 313 high Ki-67 events), the final model included seven predictors, yielding an EPV of 44.7, well above the recommended threshold, confirming sufficient statistical power.

To select radiomics features and mitigate overfitting, LASSO regression with five-fold cross-validation was applied. The optimal penalty parameter λ was determined by minimizing binomial deviance, and features with non-zero coefficients were retained for subsequent model development. The final combined model was then validated in the independent external cohort.

Continuous variables were tested for normality using the Kolmogorov–Smirnov test and are presented as mean ± standard deviation (analyzed by t-test) or median with interquartile range (IQR) (analyzed by Mann-Whitney U test), as appropriate. Categorical variables are expressed as frequencies and percentages and were compared using the Chi-squared test. All statistical analyses were performed using Python (version 3.9.19), with the “glmnet” package used for LASSO regression. A two-tailed P value <0.05 was considered statistically significant.

Results

Patient characteristics

A total of 558 patients were included and allocated to a training cohort (n=398; 313 high Ki-67 and 85 low Ki-67) and a validation cohort (n=160; 122 high Ki-67 and 38 low Ki-67). Median age was 53.0 years (IQR, 47.0–59.8 years); median nodule size was 22.0 mm (IQR, 15.0–29.0 mm). Table 1 compares baseline clinical and ultrasound characteristics between cohorts, showing no significant differences for most variables (P>0.05). Figure 2 (heatmap) illustrates feature distribution differences between high and low Ki-67 expression groups within the training cohort, with age, microcalcifications, maximum diameter, posterior echo, and radiomics features showing pronounced differences.

Table 1. Baseline features of the training and external validation cohorts.

Characteristic	Total patients (N=558)	Training cohort (N=398)	Validation cohort (N=160)	P value
Age (years)	53.00 [47.00, 59.75]	53.00 [46.00, 59.00]	54.00 [47.00, 61.25]	0.31
BMI (kg/m2)	23.53 [21.75, 25.78]	23.50 [21.77, 25.71]	23.79 [21.70, 26.02]	0.50
Ultrasound features
Lesion size (mm)	22.00 [15.00, 29.00]	22.00 [15.25, 29.00]	21.00 [14.00, 29.25]	0.31
Texture				>0.99
Cystic or solid	23 (4.12)	16 (4.02)	7 (4.38)
Reality	535 (95.88)	382 (95.98)	153 (95.62)
Shape				0.60
Regular	89 (15.95)	66 (16.58)	23 (14.37)
Irregular	469 (84.05)	332 (83.42)	137 (85.62)
Edge				0.93
Smooth	48 (8.60)	35 (8.79)	13 (8.12)
Not smooth	510 (91.40)	363 (91.21)	147 (91.88)
Orientation				0.06
Parallel	425 (76.16)	302 (75.88)	123 (76.88)
Nonparallel	133 (23.84)	96 (24.12)	37 (23.12)
Microcalcification				0.26
No	298 (53.41)	219 (55.03)	79 (49.38)
Yes	260 (46.59)	179 (44.97)	81 (50.62)
High echo halo				0.89
No	390 (69.89)	277 (69.60)	113 (70.62)
Yes	168 (30.11)	121 (30.40)	47 (29.38)
Posterior echo				0.19
No or enhancement	469 (84.05)	329 (82.66)	140 (87.50)
Decrease	89 (15.95)	69 (17.34)	20 (12.50)
Serum indicators
CA125 (U/mL)	13.00 [9.20, 19.15]	13.20 [9.20, 19.52]	12.40 [9.25, 18.45]	0.26
CA153 (U/mL)	8.10 [5.40, 12.88]	7.95 [5.32, 12.88]	8.45 [5.57, 12.72]	0.10
CEA (ng/mL)	1.29 [0.70, 2.28]	1.23 [0.62, 2.15]	1.60 [0.90, 2.42]	0.10
CA724 (U/mL)	1.75 [1.10, 4.04]	1.69 [1.16, 4.08]	1.90 [1.00, 3.80]	0.68
SII (×109/L)	524.00 [355.43, 810.10]	508.50 [355.82, 810.43]	548.45 [354.96, 805.34]	0.57
SIRI (×109/L)	0.74 [0.50, 1.15]	0.72 [0.47, 1.15]	0.76 [0.53, 1.17]	0.23
PIV (×109/L)	165.34 [101.34, 290.60]	161.84 [98.41, 286.40]	182.79 [125.46, 312.49]	0.055
EOS (×109/L)	0.10 [0.01, 0.10]	0.10 [0.00, 0.10]	0.08 [0.05, 0.14]	0.006
TG (mmol/L)	1.18 [0.82, 1.83]	1.14 [0.80, 1.77]	1.23 [0.86, 1.90]	0.09
HDL-C (mmol/L)	1.30 [1.11, 1.55]	1.31 [1.13, 1.54]	1.25 [1.03, 1.63]	0.35
LDL-C (mmol/L)	2.81 [2.26, 3.39]	2.79 [2.26, 3.37]	2.90 [2.26, 3.51]	0.59
ALT (U/L)	17.00 [13.00, 23.00]	17.00 [13.00, 23.00]	15.50 [12.00, 28.00]	0.49
AST (U/L)	19.00 [17.00, 24.00]	19.00 [17.00, 23.00]	19.00 [17.00, 26.00]	0.68
TBIL (μmol/L)	10.00 [7.60, 13.10]	9.65 [7.30, 12.40]	11.60 [8.40, 14.50]	<0.001
DBIL (μmol/L)	3.40 [2.50, 4.40]	3.00 [2.30, 4.00]	4.20 [3.30, 5.20]	<0.001
IBIL (μmol/L)	6.60 [4.95, 8.65]	6.40 [4.80, 8.50]	7.30 [5.10, 9.60]	0.007
Estradiol (pg/mL)	27.00 [11.80, 91.58]	28.00 [13.18, 84.00]	19.00 [10.00, 126.75]	0.11
Progesterone (ng/mL)	0.39 [0.21, 1.20]	0.37[ 0.21, 0.80]	0.42 [0.16, 1.59]	0.20
Prolactin (ng/mL)	9.09 [6.21, 15.03]	8.88 [6.10, 14.95]	9.64 [6.70, 15.90]	0.16
Testosterone (ng/mL)	0.28 [0.20, 0.38]	0.28 [0.19, 0.39]	0.29 [0.22, 0.37]	0.26
Pathological features
Ki-67				0.82
≥14%	435 (77.96)	313 (78.64)	122 (76.25)
<14%	123 (22.04)	85 (21.36)	38 (23.75)

Data are presented as median [interquartile range] or n (%). ALT, alanine aminotransferase; AST, aspartate aminotransferase; BMI, body mass index; CA125, carbohydrate antigen 125; CA153, carbohydrate antigen 153; CA724, carbohydrate antigen 724; CEA, carcinoembryonic antigen; DBIL, direct bilirubin; EOS, absolute eosinophil count; HDL-C, high-density lipoprotein cholesterol; IBIL, indirect bilirubin; LDL-C, low-density lipoprotein cholesterol; PIV, pan-immune inflammation value; SII, systemic immune inflammation index; SIRI, systemic immune response index; TBIL, total bilirubin; TG, triglyceride.

Figure 2.

The heatmap visualizes the distribution patterns of clinical, ultrasound, and radiomics features across Ki-67 expression groups (high vs. low) in the training set. ALT, alanine aminotransferase; AST, aspartate aminotransferase; BMI, body mass index; CA125, carbohydrate antigen 125; CA153, carbohydrate antigen 153; CA724, carbohydrate antigen 724; CEA, carcinoembryonic antigen; DBIL, direct bilirubin; EOS, absolute eosinophil count; HDL-C, high-density lipoprotein cholesterol; IBIL, indirect bilirubin; LDL-C, low-density lipoprotein cholesterol; PIV, pan-immune inflammation value; SII, systemic immune inflammation index; SIRI, systemic immune response index; TBIL, total bilirubin; TG, triglyceride.

Feature selection and prediction model establishment

Clinical feature selection: multivariate logistic regression established age, maximum lesion diameter, microcalcifications, and posterior echo as independent predictors of high Ki-67 expression, following their initial identification in univariate analysis (P<0.05; Table 2).

Table 2. Univariate and multivariate logistic regression analysis of risk factors (training cohort).

Characteristics	B	SE	OR (95% CI)	Z	P
Univariate
Age	−0.031	0.012	0.969 (0.946–0.992)	−2.576	0.01
Lesion size	0.054	0.014	1.055 (1.028–1.086)	3.826	<0.001
Microcalcification
No			1.0 (Reference)
Yes	0.575	0.255	1.777 (1.085–2.96)	2.253	0.02
Posterior echo
No or enhancement			1.0 (Reference)
Decrease	−0.935	0.288	0.393 (0.224–0.697)	−3.243	0.001
Multivariate
Clinical model
Age	−0.028	0.013	0.971 (0.947–0.996)	−2.22	0.026
Lesion size	0.05	0.014	1.051 (1.023–1.082)	3.503	<0.001
Microcalcification
No			1.0 (Reference)
Yes	0.437	0.272	1.548 (0.912–2.665)	1.604	0.10
Posterior echo
No or enhancement			1.0 (Reference)
Decrease	−1.027	0.305	0.358 (0.197–0.654)	−3.371	0.001
Radiomics feature model
original_glcm_MaximumProbability	4.265	1.487	71.16 (4.273–1,474)	2.868	0.004
original_glszm_SizeZoneNonUniformity	0.01	0.005	1.010 (1.001–1.021)	1.994	0.046
original_shape_Maximum2DDiameterColumn	0.003	0.001	1.002 (1.000–1.005)	2.278	0.02
Combined model
Intercept	0.729	0.847	2.074 (0.394–10.912)	0.861	0.38
Age	−0.029	0.013	0.971 (0.947–0.996)	−2.254	0.02
Lesion size	0.015	0.023	1.015 (0.971–1.061)	0.658	0.51
Microcalcification
No			1.0 (Reference)
Yes	0.469	0.278	1.599 (0.927–2.759)	1.687	0.09
Posterior echo
No or enhancement			1.0 (Reference)
Decrease	−0.984	0.310	0.374 (0.204–0.686)	−3.175	0.001
Radiomics feature
original_glcm_MaximumProbability	4.219	1.523	67.944 (3.432–1,345.214)	2.769	0.006
original_glszm_SizeZoneNonUniformity	0.008	0.005	1.008 (0.997–1.018)	1.462	0.14
original_shape_Maximum2DDiameterColumn	0.002	0.002	1.002 (0.999–1.005)	1.111	0.26

CI, confidence interval; OR, odds ratio; SE, standard error.

Radiomics feature selection: from 864 initially extracted features, 107 with ICC >0.75 and significant univariate differences (P<0.05) were selected. In the training set, the high Ki-67 group exhibited a significantly elevated Rad-score compared to the low Ki-67 group (P<0.0001). However, no significant between-group difference was found in the validation set (Figure 3A,3B). After Spearman correlation filtering and LASSO regression, three radiomics features were selected based on their non-zero coefficients: one texture feature and two shape features (Figure 4). Their predictive value was confirmed by multivariate logistic regression (Table 2).

Figure 3.

The distribution of radiomics scores (RadScore) for Ki-67 high- and low-expression groups in the training (A) and validation (B) datasets, with boxplots used to visualize intergroup differences.

Figure 4.

The radiomics feature selection process in the training cohort, employing the LASSO method. LASSO, least absolute shrinkage and selection operator.

Prediction model establishment: three models were built: clinical (age, diameter, microcalcifications, posterior echo), radiomics (three features), and combined. The combined model showed the best overall performance (Table 3, Figure 5A,5B), with validation set metrics as follows: AUC =0.709 (95% CI: 0.614–0.804); accuracy =0.750; F1 score =0.840; sensitivity =0.861; specificity =0.395. DeLong test results confirmed that these AUC differences were not statistically significant for either cohort (all P>0.05; Table 4).

Table 3. Comparative diagnostic performance of the models among training and external validation cohorts.

Model	AUC (95% CI)	Accuracy	Sensitivity	Specificity	PPV	NPV	Precision	Recall	F1 score
Training cohort
Clinical model	0.707 (0.645–0.770)	0.658	0.649	0.694	0.887	0.349	0.887	0.649	0.749
Radiomics model	0.689 (0.628–0.750)	0.626	0.610	0.682	0.876	0.322	0.876	0.610	0.719
Combined model	0.731 (0.67–0.792)	0.643	0.607	0.777	0.909	0.349	0.909	0.607	0.728
Validation cohort
Clinical model	0.683 (0.578–0.788)	0.65	0.656	0.632	0.851	0.364	0.851	0.656	0.741
Radiomics model	0.706 (0.613–0.798)	0.731	0.902	0.184	0.780	0.368	0.780	0.902	0.837
Combined model	0.709 (0.614–0.804)	0.75	0.861	0.395	0.820	0.469	0.820	0.861	0.840

AUC, area under the curve; CI, confidence interval; F1 score, comprehensive evaluation index; NPV, negative predicted value; PPV, positive predicted value.

Figure 5.

The ROC curves of the different models across both the training (A) and validation (B) cohorts, as well as the combined model nomogram (C). glcm: original_glcm_MaximumProbability; glszm: original_glszm_SizeZoneNonUniformity; shape: original_shape_Maximum2DDiameterColumn. AUC, area under the curve; CI, confidence interval; ROC, receiver operating characteristic.

Table 4. Results of DeLong’s test for pairwise model comparison across training and external validation sets.

Comparison	Training set (N=398)				Validation set (N=160)
	AUC difference	95% CI	P value		AUC difference	95% CI	P value
Clinical model vs. radiomics model	+0.018	−0.049 to 0.085	0.599		−0.022	−0.121 to 0.076	0.656
Clinical model vs. combined model	−0.024	−0.058 to 0.011	0.186		−0.026	−0.090 to 0.039	0.432
Radiomics model vs. combined model	−0.042	−0.058 to 0.002	0.061		−0.003	−0.060 to 0.054	0.906

AUC, area under the curve; CI, confidence interval.

A nomogram for the combined model integrated the seven predictors (Figure 5C). Calibration curves indicated good agreement (Figure 6A,6B). In both cohorts, the combined model was associated with the highest net clinical benefit over a wide range of threshold probabilities (0.00–0.70), based on DCA (Figure 6C,6D), indicating its superior clinical utility compared to the ‘treat-all’ or ‘treat-none’ strategies. Two optimal thresholds from the validation cohort were identified: 0.58 (specificity, 0.623; sensitivity, 0.785) for minimizing false positives in chemotherapy-sensitive patients, and 0.22 (sensitivity, 0.917; specificity, 0.316) for maximizing high Ki-67 detection in high-risk patients.

Figure 6.

The performance of the Ki-67 predictive model in breast cancer patients. Calibration plots (A,B) and decision curve analyses (C,D) are shown for the training and validation cohorts, respectively. The DCA plots assess the net clinical benefit across various threshold probabilities for each cohort. DCA, decision curve analysis.

SHAP interpretability analysis: SHAP analysis (Figure 7) indicated original_glcm_MaximumProbability contributed most (mean |SHAP| =0.32), followed by posterior echo (0.28) and microcalcifications (0.25). Age and original_shape_Maximum2DDiameterColumn had lower contributions (<0.15). The dependence plot (Figure 7B) showed microcalcifications, larger diameter, and higher original_glcm_MaximumProbability increased the prediction probability for high Ki-67, while posterior echo attenuation decreased it. A waterfall plot (Figure 7C) illustrated individual feature contributions for a sample case.

Figure 7.

A comprehensive SHAP summary for the logistic regression model: (A) a SHAP feature importance plot; (B) a SHAP dependence scatter plot: features are listed on the vertical axis (one per row), SHAP values on the horizontal axis, and feature magnitudes are color-coded (orange for high, purple for low); each point is an individual sample; (C) a SHAP waterfall plot illustrating the feature contributions to a single prediction instance, clearly showing features that push the prediction higher (positive) versus lower (negative). glcm: original_glcm_MaximumProbability; glszm: original_glszm_SizeZoneNonUniformity; shape: original_shape_Maximum2DdiameterColumn. SHAP, SHapley Additive exPlanations.

Based on the multivariable logistic regression analysis, the full specification of the combined model for predicting the probability of high Ki-67 expression (≥14%) is as follows: logit(P) =0.729 − 0.029 × Age + 0.015 × lesion size + 0.469 × microcalcification_Yes − 0.984 × posterior echo_Decrease + 4.219 × original_glcm_MaximumProbability + 0.008 × original_glszm_SizeZoneNonUniformity + 0.002 × original_shape_Maximum2DDiameterColumn, where P denotes the probability of Ki-67 high expression. Microcalcification_{\text{Yes}} and Posteriorecho_{\text{Decrease}} are binary variables coded as 1 for presence and 0 for absence. All continuous predictors (age, lesion size, and the three radiomics features) were entered into the model with their original values. The predicted probability for an individual patient can then be obtained using the logistic transformation: $P=\frac{1}{1+e^{-logit\left(P\right)}}$. This formula can be used to predict the Ki-67 expression status of individual patients, and has been visualized in the form of a nomogram (Figure 5C).

Case demonstration

Two representative cases from the validation cohort are presented.

Case 1: Ki-67 high expression (≥14%) (Figure 8A)

Figure 8.

Two representative ultrasound images and their corresponding ROI delineations of breast cancer patients from the external validation cohort are presented. (A) A 45-year-old female with a 28-mm solid, irregular, microcalcification-present lesion without posterior shadowing. Radiomics features were elevated. The combined model predicted a high Ki-67 probability (~0.90). Pathology confirmed Ki-67 index of 30% (invasive ductal carcinoma, Grade II). (B) A 60-year-old female with a 9-mm solid, irregular, microcalcification-absent lesion with posterior attenuation. Radiomics features were lower. The combined model predicted a low Ki-67 probability (~0.38). Pathology confirmed Ki-67 index of 10% (invasive ductal carcinoma, Grade I). ROI, region of interest.

Case 1 was a 45-year-old female with a 28-mm solid, irregular, microcalcification-present lesion without posterior shadowing. Radiomics features were elevated. The combined model predicted a high Ki-67 probability (~0.90). Pathology confirmed Ki-67 index of 30% (invasive ductal carcinoma, Grade II).

Case 2: Ki-67 low expression (<14%) (Figure 8B)

Case 2 was a 60-year-old female with a 9-mm solid, irregular, microcalcification-absent lesion with posterior attenuation. Radiomics features were lower. The combined model predicted a low Ki-67 probability (~0.38). Pathology confirmed Ki-67 index of 10% (invasive ductal carcinoma, Grade I).

Summary

The cases’ features aligned with characteristic patterns of their respective Ki-67 groups. The model’s predictions, using clinically informed thresholds, matched pathological outcomes, demonstrating practical utility.

Discussion

Accurate preoperative prediction of Ki-67 expression is clinically valuable for treatment planning and prognosis (13,14). While core needle biopsy provides tissue for IHC, it samples only a portion of the tumor and may be influenced by intratumoral heterogeneity or procedural artifacts (15-17). Non-invasive imaging like ultrasound offers a holistic, real-time assessment alternative. In this study, we developed and validated a multimodal model integrating ultrasound radiomics and clinical features to address this need. The combined model achieved an AUC of 0.731 (95% CI: 0.67–0.792) in the training cohort and 0.709 (95% CI: 0.614–0.804) in the external validation cohort, demonstrating consistent discriminative ability. This finding suggests that the integration of radiomics and clinical data provides a stable and generalizable tool for non-invasively estimating Ki-67 status.

Consistent with prior research (18-20), we found age, tumor diameter, microcalcifications, and posterior echo attenuation to be independent predictors. Microcalcifications may reflect increased cellular proliferation and necrosis, while posterior attenuation might indicate fibrous stromal proliferation in slower-growing tumors. Notably, serological markers (CEA, CA153, SII) showed no significant association with Ki-67 in our cohort, potentially due to sample size limitations in the low-expression group, lack of stage-specific stratification, or cohort characteristics (21-23). Future studies with larger, stratified cohorts are needed.

Radiomics provided additional quantitative insights. The selected features—original_glcm_MaximumProbability, original_glszm_SizeZoneNonUniformity, and original_shape_Maximum2DDiameterColumn—reflect tumor texture heterogeneity and morphology, aligning with biological aggression (24-26). Interestingly, high MaximumProbability, often linked to homogeneity and benignity, might here indicate large necrotic areas in aggressive tumors, highlighting context-dependent interpretation.

The combined model outperformed all others in the validation phase, yielding the highest comprehensive performance metrics: an AUC of 0.709 (95% CI: 0.614–0.804), an accuracy of 0.750, and an F1 score of 0.840. Although the AUC improvement over single-modality models was not statistically significant, likely due to feature redundancy (e.g., diameter vs. shape features) and the linear integration method, the combined model demonstrated superior calibration and net clinical benefit across decision thresholds. This underscores the practical advantage of multimodal integration, even with modest discriminative gain.

Regarding the choice of Ki-67 cutoff, the present study adopted the 14% threshold proposed by the 2011 St. Gallen International Expert Consensus, which aligns with the routine clinical practice at our institution. Nevertheless, the optimal cutoff for stratifying Ki-67 expression remains a subject of ongoing debate, with some studies advocating for a threshold of 20% or higher to better discriminate between luminal-like and more aggressive tumor phenotypes (27,28). To address this uncertainty and assess the robustness of our model to different cutoff definitions, we performed a sensitivity analysis by redefining Ki-67 status using a 20% threshold. Encouragingly, the combined model maintained stable discriminatory performance, achieving an AUC of 0.716 (95% CI: 0.662–0.770) in the training cohort and 0.730 (95% CI: 0.645–0.815) in the external validation cohort. These findings suggest that the predictive utility of our model is not critically dependent on the specific Ki-67 cutoff value within the clinically debated range, further supporting its generalizability and potential applicability across different clinical settings.

Our model’s AUC is moderate compared to some studies reporting higher values [e.g., 0.88 using automated breast volume scanning (ABVS) with peritumoral features] (29). This difference may stem from our use of conventional 2D grayscale ultrasound alone, excluding functional (e.g., elastography) or 3D features. However, our approach prioritizes generalizability across diverse ultrasound equipment and healthcare settings, enhancing its potential for broad clinical adoption, particularly in resource-limited contexts.

We acknowledge that there are limitations in this study. First, the sample size, though multi-center, remains modest, especially for the low-expression subgroup, affecting statistical power and generalizability. Second, reliance on a single 2D grayscale image of the tumor’s maximum cross-section may not fully capture the entire tumor’s volumetric heterogeneity, potentially introducing sampling bias. Future studies incorporating 3D ultrasound or whole-volume radiomics could provide a more holistic representation of the tumor phenotype. Third, although we performed image normalization (z-score) and a post-hoc ComBat harmonization analysis, the absence of prospective, pre-planned harmonization for radiomics features across different ultrasound vendors remains a limitation. Nevertheless, the ComBat analysis confirmed the robustness of our original model, while also suggesting that more advanced harmonization techniques could further improve generalizability in future multi-center studies. Fourth, manual ROI segmentation introduces subjectivity; automated methods should be explored. Finally, the model’s performance, while clinically useful, has room for improvement.

Conclusions

In conclusion, ultrasound radiomics features offer incremental predictive value for expression of Ki-67 in breast cancer. The integrated clinical-radiomics model demonstrates favorable and stable diagnostic performance, presenting a non-invasive preoperative adjunct to complement biopsy. Future work should focus on larger multi-center cohorts, incorporation of advanced imaging modalities, exploration of non-linear fusion techniques, and prospective validation to further enhance predictive accuracy and clinical utility.

Supplementary

The article’s supplementary files as

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. This study was conducted in accordance with the Declaration of Helsinki and its subsequent amendments. The study was approved by the Ethics Committee of Zhejiang Cancer Hospital (No. IRB-2024-1272 [IIT]) and the Ethics Committee of Lishui Central Hospital, Zhejiang Province (No. 2024-402). For this retrospective analysis, individual informed consent has been waived.

Data Sharing Statement

Available at https://tcr.amegroups.com/article/view/10.21037/tcr-2026-1-0384/dss

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DOI: 10.21037/tcr-2026-1-0384