Clinical characteristics

Among the 121 patients, 51 patients were diagnosed with benign VCFs, with 67 vertebral bodies (27 males, 24 females, age 70.6 ± 8.9 years, range 50–92 years), and 70 patients were diagnosed with malignant VCFs, with 77 vertebral bodies (40 males, 30 females, age 60.6 ± 13.4 years, range 13–81 years). The difference between benign and malignant VCFs was statistically significant in age (p < 0.05), but not in sex (p > 0.05).

All cases were confirmed by histopathology or clinical follow-up examination. Of the 67 benign VCFs, 6 were surgically confirmed and 61 were confirmed by clinical follow-up; among them, 39 cases had a history of malignant tumors. Of the 77 malignant VCFs, 31 were confirmed by puncture or surgery, and 46 were confirmed by comprehensive imaging diagnosis and follow-up. Among them, 64 cases were metastatic solid tumors (28 lung cancers, 7 breast cancers, 6 prostatic cancers, 5 thyroid cancers, 4 colorectal cancers, 4 hepatocellular carcinomas, 2 gastric cancers, 2 renal cancers, 2 esophageal cancers, cervical cancer, ovarian cancer, pancreatic cancer, and synovial sarcoma), 6 cases were multiple myeloma, 5 cases were lymphoma, and 2 cases were Langerhans cell histiocytosis.

Radiomics feature selection, establishment and performance of the radiomics model

Twenty-six features, consisting of 9 PET features (6 first-order features and 3 texture features) and 17 CT features (3 first-order features, 13 texture features and 1 shape feature) were selected to construct the radiomics model after LASSO regression and tenfold cross-validation (Fig. 3). The details of the selected features are shown in Fig. 4. The formula of the radiomics signature score (rad-score) for each patient is shown in Table 1.

Fig. 3

LASSO regression and tenfold cross-validation were used to select the radiomics features. a LASSO coefficient profiles of the radiomic features. b Optimal feature selection of CV. LASSO least absolute shrinkage and selection operator. CV cross-validation. MSE mean square error

Fig. 4

Histogram of the coefficients of the selected features

Table 1 Formular of radiomics signature score (rad-score)

The AUC of the radiomics model for predicting the probability of malignancy of the VCFs was 0.986 (95% confidence interval [CI], 0.9714–1.0000) for the training group and 0.962 (95% CI, 0.9137–1.0000) for the test group (Fig. 5). The accuracy, sensitivity, specificity, PPV, and NPV were 0.940, 0.887, 1.000, 1.000, and 0.887 in the training group and 0.932, 0.917, 0.950, 0.957, and 0.905 in the test group, respectively (Table 2).

Fig. 5

AUCs of the prediction models. a The training group. b The test group. AUC area under the curve

Table 2 Performance of the prediction modelsEstablishment and performance of the clinical model and clinical–radiomics model

The selection of features for establishing the clinical model was based on a p value < 0.05 in the training and test groups. SUVmax, SUVpeak, SULmax, SULpeak, age, osteolytic destruction, fracture line and involvement of the appendices/posterior vertebrae met the conditions and were used to build clinical model (Table 3).

Table 3 Clinical variables of benign and malignant VCFs in the training and test groups

The AUC of the clinical model for predicting the probability of malignancy of the VCFs was 0.884 (95% CI, 0.8153–0.9518) for the training group and 0.858(95% CI, 0.7437–0.9729) for the test group (Fig. 5). The accuracy, sensitivity, specificity, PPV, and NPV were 0.850, 0.830, 0.872, 0.880, and 0.820 in the training group and 0.841, 0.875, 0.800, 0.840, and 0.842 in the test group, respectively (Table 2).

The AUC of the clinical–radiomics model for predicting the probability of malignancy of the VCFs was 0.987 (95% CI, 0.9716–1.0000) for the training group and 0.948 (95% CI, 0.8787–1.0000) for the test group (Fig. 5). The accuracy, sensitivity, specificity, PPV, and NPV were 0.950, 0.906, 1.000, 1.000, and 0.904 in the training group and 0.932, 0.958, 0.900, 0.920, and 0.947 in the test group, respectively (Table 2).

Performance of the prediction models and nomogram construction

The clinical model, radiomics model and clinical–radiomics model all showed good calibration. The p values of the Hosmer–Lemeshow test for the three models were 0.664, 0.787, and 0.422 in the training group and 0.241, 0.237, and 0.051 in the test group, respectively. The Delong test was used to compare the AUCs of the three models. In both the training and test groups, the radiomics model and clinical–radiomics model were significantly different from the clinical model (p < 0.05), but there was no significant difference between the radiomics model and clinical–radiomics model (p > 0.05). The DCA demonstrated that the radiomics model and clinical–radiomics model could provide higher overall net benefit than the clinical model (Fig. 6). A nomogram based on the rad-score and clinical risk factors was developed (Fig. 7).

Fig. 6

DCA of the prediction model. a The training group. b The test group. DCA decision curve analysis

Fig. 7

Nomogram to predict the malignancy of VCFs