This retrospective study, approved by our Institutional Review Board (IRB) with waived written consent, identified 433 consecutive female patients who were diagnosed with invasive BC and had available preoperative mammography at our institution between February 2019 and June 2023. This study has been approved by the Ethics Committee of S&T Program of Hebei (20377783D), Medical Science Research Project of Hebei (20221342), and Medical Science Research Project of Hebei (20230863)). All patients included in the study met the following inclusion criteria: (1) underwent DBT examination within one month prior to surgery; (2) were pathologically diagnosed with invasive breast carcinoma; (3) had no documented history of any other malignancy; and (4) did not undergo a biopsy or receive treatment for the breast tumor before the DBT examination. Patients were excluded from the study if they met any of the following exclusion criteria: (1) insufficient clinicopathological data or suboptimal image quality; (2) pathological diagnosis of non-invasive breast carcinoma, or concurrent presence of other malignancies; (3) multiple BC lesions or distant metastases; (4) tumors on DBT images that did not appear as masses but presented in other forms, such as pure calcification, asymmetry, or architectural distortion. The 433 cases included 111 patients with subtype A BC, 100 patients with subtype B BC, 107 patients with HER2-positive BC, and 112 patients with basal-like BC. These cases were used to screen for regions of interest (ROI) and extract image-omics features ( Figure 1A ).

In this study, the patients were scanned using GE Senographe Essential digital mammography (GE Healthineers) fullfield digital mammography systems. The typical imaging parameters were established within the ranges of 27–32 kV and 28–68 mAs. Additionally, both craniocaudal and mediolateral oblique images were successfully obtained for every patient. This imaging technique facilitated the acquisition of both a standard digital mammogram and a tomosynthesis scan under the same breast compression (23, 24). With a single low-dose exposure, the X-ray tube was rotated through an angular range of 12.5 degrees, completing a total of nine rotations. Advanced computerized imaging algorithms were then employed to reconstruct projections from each viewing angle, enabling three-dimensional visualization of breast tissue.

Two experienced radiologists, each with more than 5 years of professional expertise, performed an impartial evaluation of DBT images, which were anonymized. The three-dimensional ROI that encompassed the tumor on synthetic mammography was manually segmented (as shown in Figures 2 , 3 ) by a resident radiologist with five years of experience (referred to as reader 1) using the “3D Slicer” software (https://www.slicer.org/). Subsequently, the delineated ROIs were meticulously examined and verified by a breast radiologist who possessed a decade of subspecialty experience (referred to as reader 2). In cases where there were discrepancies regarding the ROI, they were resolved through consensus-based discussions. This assessment was conducted in a blinded manner, meaning that the radiologists were not provided access to the associated histopathological information to ensure an unbiased judgment. In instances where discrepancies arose between the two radiologists, a third radiologist with more than 10 years of experience was consulted to resolve the discrepancies.

Surgical resection of BC specimens was performed, followed by validation of diagnoses through histopathological examination. IHC analyses were conducted to assess the expression levels of estrogen receptor (ER), progesterone receptor (PR), human epidermal growth factor receptor 2 (HER-2), and the Ki-67 antigen (25, 26). The absence of positive staining in 1% or fewer carcinoma nuclei indicated a negative status for both ER and PR, as per references (26, 27). According to the IHC scoring system, HER-2 expression was categorized into four levels: 0, 1+, 2+, or 3 +. Confirmation of a negative HER-2 status can be achieved through two methods: obtaining an IHC score of either 0 or 1+, or achieving an IHC score of 2+ alongside a negative result from fluorescence in situ hybridization (FISH) testing. Conversely, a positive HER-2 status can be confirmed with either a score of 3+ or a score of 2+ combined with a positive FISH test result (27, 28). Furthermore, if a patient presented with an IHC score of 2+ but lacked FISH results, the recorded status for HER-2 was classified as suspicious positive. A Ki-67 proliferation index below 14% was categorized as a low level of proliferation, while a value equal to or exceeding 14% was regarded as a high level of proliferation (28). The IHC antibodies used in this study were as follows: ER (Roche, Clone Number SP1), PR (Roche, Clone number IE2), HER2 (Roche, Clone number 4B5), and KI-67 (Maxin, Clone number MX006).

The ROI on the cranio-caudal (CC) and mediolateral oblique (MLO) views of DBT images was manually delineated, following the contours of the tumor’s maximum diameter area. The lesion segmentation task was conducted by two radiologists, referred to as Radiologist 1 and Radiologist 2, who possessed 10 and 7 years of experience in BC diagnosis, respectively. They employed 3D Slicer (version 4.11; available at http://www.slicer.org) to outline all ROIs while remaining unaware of the histopathological data during this process. Figure 1B presents a diagrammatic representation illustrating the segmentation of the ROI. Prior to commencing feature extraction, the images underwent resampling and grayscale discretization for normalization purposes, adhering to recommendations established in prior research studies (28, 29). Radiomic features were extracted from both CC and MLO images encompassing each patient’s ROI.

Radiomic feature extraction was performed using Python (version 3.7) of the PyRadiomics package (version 3.0.1, http://pyradiomics.readthedocs.io), according to the original, wavelet, gauss Laplace (LoG), index, square, square root, logarithm and gradient image retrieval. These image omics features were statistically processed by Z-score and Kruskal-Wallis rank sum test to screen out candidate features (p < 0.05).

For the sake of screening features for predicting BC, the dataset was randomly split into training and validation subsets at a 7:3 ratio. The radiomics features were normalized via Z-score standardization (28). To precisely identify the most effective set of predictive features, the study utilized least absolute shrinkage and selection operator (LASSO) regression, implementing five-fold cross-validation. The One-vs-Rest (OvR) strategy was utilized for predicting the sample subtypes via building a binary classifier. Based on the training set, the LASSO regression model was then constructed by the R package ‘glmnet’ (Ver. 4.1-6) to select LASSO features with the parameters of ‘famil’=‘binomial’ and ‘type.measure’=‘class’. The results of multivariate classification were determined by taking the category with the highest probability (HER2-positive) through 10-fold cross-validation. And the LASSO features were ascertained when the error rate of model was lowest. Moreover, the receiver operating characteristic (ROC) curves were plotted in training and testing set to evaluate the performance of the model in predicting the subtypes of BC (area under of ROC curves (AUCs) > 0.70).

In order to assess the correlations between LASSO features and BC subtypes, Dunn’s test was exploited to determine whether there were significant discrepancies in LASSO features between luminal A-subtype, luminal B-subtype, HER2-positive BC and basal-like BC. The violin plots were created via the R package ‘ggstatsplot’ (Ver. 0.12.0) to exhibit the outcomes.

To screen the optimal classifier for further predicting BC subtypes using image-omics LASSO features, 8 machine learning (ML) models in the R package ‘caret’ (Ver. 6.0-94) were constructed. In the training set, Regularized Logistic Regression (regLogistic), support vector machine (SVM), Random Forest (RF), k-nearest neighbors (KNN), eXtreme Gradient Boosting (xgboost), Gradient Boosting Machine (GBM), Naive Bayes and Neural Network (NNET) models were constructed to predict the categories of samples, and the diagnostic efficacy of each model was calculated separately with the 5-fold cross-validation. The predictive performances of the 8 models were evaluated with ROC curve and confusion matrix in training and testing sets, and AUCs of 8 models in the training and testing sets were compared. Simultaneously, accuracy, sensitivity, specificity, recall, precision and F1 score of each model were estimated to filter the classifier with the best performance. Eventually, the optimal classifier was used to rank the importance of each LASSO feature. Ulteriorly, univariate (p < 0.05) and multivariate Cox regression analyses (p < 0.05) were proceeded through the R package ‘rms’ (Ver. 6.5-0) to acquire crucial features for nomogram modeling. The relationships between crucial features and BC were predicted in the light of the odds ratio (OR) of the patients in the nomogram model. Additionally, calibration curve and Decision Curve Analysis (DCA) were adopted to evaluate the predictive power of nomogram model.

Bioinformatics analyses were conducted using R software (Version 6.0-94). Significant differences among three or more groups were assessed by the Kruskal-Wallis rank sum test, followed by Dunn’s test for pairwise comparisons between multiple groups. A p-value or adjusted p-value (p.adj) of less than 0.05 was considered statistically significant.

A total of 7 types of features, encompassing 306 first-order features, 14 shape features, and 1,241 texture features (glcm, gldm, glrlm, glszm and ngtdm) emerged from the original, wavelet, LoG, exponential, square, squareRoot, logarithm, gradient images ( Table 1 , Figure 4A ). In sum of 1,175 candidate features were obtained after Z-score standardization and Kruskal-Wallis rank sum test for 7 types ( Figure 4B ). In order to screen features that were strongly associated with BC, a LASSO regression model was built in the training set, producing 14 LASSO features when the minimum Lambda value was 0.0481 ( Figures 4C, D ). The AUCs of the training and testing sets were 0.723 and 0.727, respectively ( Figures 4E, F ). The correlation analysis between LASSO features and BC subtypes revealed significant differences among the 14 LASSO features across different subtype comparisons. Specifically, between luminal B and HER2-positive subtypes, the following nine features showed significant differences: gradient glszm SmallAreaLowGrayLevelEmphasis, log sigma 1–0 mm 3D glcm Idmn, logarithm ngtdm Busyness, squareroot glcm Imc1, wavelet HHH firstorder RobustMeanAbsoluteDeviat, wavelet LHH ngtdm Busyness, wavelet LLH firstorder Entropy, wavelet LLL glcm Idm and wavelet LLL glszm SizeZoneNonUniformityNormalized. Additionally, between luminal A and luminal B subtypes, eight features exhibited significant differences: gradient glszm SmallAreaLowGrayLevelEmphasis, squareroot glcm Imc1, wavelet LHH firstorder Entropy, wavelet LHH ngtdm Busyness, wavelet LLH firstorder Entropy, wavelet LLH firstorder InterquartileRangewavelet LLL glcm Idm and wavelet LLL glszm SizeZoneNonUniformityNormalized ( Figure 5 ).

In sum of 8 ML models were constructed in the training set to select the best classifier to accurately predict the BC subtypes. Among 8 ML models, RF possessed the highest AUC value and accuracy in training set ( Figures 6A, B ), As presented in training and testing sets, the RF model retained the highest AUC values for the four BC subtypes, as did the Macro average AUC and Micro average AUC values, demonstrating the excellent predictive capacity of RF ( Figure 6C ). In addition, the abilities of 8 ML models were assessed using confusion matrix, highlighting RF had the highest accuracy, sensitivity, recall and F1 score in 8 ML models ( Table 2 , Figure 6D ). The line graph illustrating the AUC discrepancies of 8 ML models between training and testing sets emphasized the highest AUCs of RF in both sets ( Figure 6E ). In conclusion, RF was the optimal classifier predicting image-omics LASSO features of BC. As a consequence,14 LASSO features were sorted by Random Forest model according to their importance. Among these, logarithm ngtdm Busyness and original shape Surface Volume Ratio contributed the most to the model due to their higher importance values ( Figure 6F ).

To identify BC features for nomogram modeling, univariate Cox regression analysis was performed, followed by multivariate Cox analysis. Ten LASSO-selected features (p < 0.05) from the univariate analysis were subsequently incorporated into the multivariate model ( Table 3 , Figure 7A ), yielding 5 crucial features, namely logarithm glrlm RunLengthNonUniformityNormalized, logarithm ngtdm Busyness, original sape SurfaceVolumeRatio, wavelet LLH firstorder InterquartileRange and wavelet LLL glcm Idm ( Table 4 , Figure 7B ). A nomogram model embracing 5 crucial features was developed immediately; the OR values of BC patients increased with the elevated total points ( Figure 7C ). Importantly, the validity and universality of the nomogram model were certified via calibration curve and DCA curve. The calibration curve manifested that the slope of the nomogram model almost achieved to 1. In addition, the c-index of 0.732 after model correction was close to the c-index of 0.759 ( Figure 7D ). Further DCA demonstrated that the nomogram model outweighed any single crucial feature by providing a superior net benefit ( Figure 7E ).