Introduction

Hereditary multiple exostoses (HME) commonly occurs in individuals with a similar family history, with an incidence ranging from 1:50,000 to 1:100,000 [1,2,3] It is typically characterized by multiple osteochondromas in the metaphyses of long and flat bones [4,5,6]. Compared with solitary osteochondroma (a common bone tumor in children and adolescents), HME has an incidence approximately 1/6 that of the solitary form. Most patients present with more than six lesion sites and often have multifocal skeletal deformities [7, 8]. According to a study by Alvaro Rueda-de-Eusebio et al. [9]the prevalence of osteochondromas in the knee joint among HME patients ranges from 70 to 98%, and in the ankle joint from 25 to 54%.

Multiple studies have shown that genu valgum and ankle valgus are among the most common lower limb deformities caused by HME, with incidence rates of 8–33% and 45–73%, respectively [4, 10, 11]. These deformities often lead to lower limb length discrepancy, abnormal gait, and limited functional activity. Genu valgum typically arises from damage to the proximal tibia, occasionally involving damage to the distal femur or proximal fibula [4]. The clinical manifestations of HME are diverse, with the most common being exostosis. Others include, but are not limited to, pain, bone growth disorders, long bone curvature, and limb length discrepancies [1, 12]. In HME, Ankle valgus is often caused by fibular shortening and can severely lead to medial subluxation of the talus [13]increasing the risk of secondary osteoarthritis, which reaches a prevalence of 19% by age 42 [14]. Early surgical intervention on weight-bearing joints of the lower limbs is crucial to prevent deformity progression and preserve joint function [5].

Current HME research often focuses on genetic aspects, such as the EXT1 and EXT2 genes [15,16,17]which influence disease development. However, no study has investigated the relationship between blood biomarkers measured 3 months prior to lower limb deformity and the occurrence of genu valgum or ankle valgus in HME patients. During the literature review, we found that the average growth rate of the lower limbs in normal children aged 5–12 is 0.4 mm/week − 0.5 mm/week [18], and after 3 months, it can have a relatively significant impact on children’s lower limbs. Secondly, in a systematic review, during the correction of children’s lower limb deformities using flexible plates, the average correction rates of the lateral distal femoral angle (LDFA) and medial proximal tibial angle (MPTA) were 0.87° and 0.72° per month [19]respectively. These findings, combined with our daily clinical observations and considerations of diagnostic results, form the basis for our relevant research design. According to the research by Dénes B Horváthy et al. [20]it has been found that serum albumin and other substances have the function of promoting osteogenesis. Therefore, this retrospective study analyzed HME patients treated at our hospital between January 1, 2010, and October 31, 2024, aiming to collect blood test results from 3 months prior to admission and develop explainable prediction models and a nomogram for genu valgum and ankle valgus in HME patients based on multiple blood parameters. These tools aim to provide low-cost, noninvasive, early-stage, and user-friendly predictions to assist clinicians in making timely decisions.

Materials and methods

Patient cohort

This was a single-center retrospective cohort study. We enrolled patients (no history of undergoing surgery or having other progressive deformity diseases) diagnosed with HME at the First Affiliated Hospital of Guangxi Medical University between January 1, 2010, and October 31, 2023. The inclusion criteria were as follows:

• Diagnosis of HME (Diagnosed by an experienced pediatric orthopedic surgeon.) based on:

(a) Family history of HME;

(b) Clinical manifestations: Multiple bony protuberances on the extremities; upper limb shortening with or without radial dislocation; joint deformities in the lower limbs, often accompanied by abnormal gait;

(c) Imaging findings: X-ray, MRI and CT showing multiple osteochondroma-like imaging features in the extremities, including continuous changes between the lesion site and normal bone and characteristic cartilage caps.

•Diagnosis of genu valgum: A hip-knee-ankle angle (HKA, the angle between the mechanical axes of the femur and tibia) > 3° on standing full-length radiographs.

•Diagnosis of ankle valgus: A distal tibial articular surface angle > 15° relative to the ground, or > 10° combined with limited ankle mobility and significant pain.

Exclusion criteria included:

  1. 1.

    Age > 18 years;

  2. 2.

    Inability to obtain X-ray or CT imaging;

  3. 3.

    Diagnosis of solitary osteochondroma or metastatic tumors from other sites;

  4. 4.

    Recent use of anticoagulant or antiplatelet medications;

  5. 5.

    Concomitant immune or hematological disorders.

As this was a retrospective study, the ethics committee approved the waiver of informed consent in accordance with national laws and institutional guidelines (approval number: 2025-E0410). Patient identities were anonymized throughout the study.

Data collection and definitions

This study collected relevant results from patients’ outpatient follow-ups three months before they were admitted to the hospital for surgery (including but not limited to flexible plate-guided lower limb growth modulation surgery, simple tumor resection, upper limb osteotomy, orthopedic surgery, etc.), including clinical data and laboratory results, encompassing complete blood count, blood biochemistry, and coagulation function assessments. Baseline clinical data included sex, age, history of hepatitis, tuberculosis, favism, thalassemia, alcohol use, smoking, height, weight, and BMI. Specifically:

  • A history of hepatitis was defined as a prior diagnosis of hepatitis;

  • A history of tuberculosis was defined as a prior diagnosis of tuberculosis;

  • A history of favism was defined as a prior diagnosis of favism;

  • A history of thalassemia was defined as a prior diagnosis of thalassemia.

Additionally, the following laboratory data were collected at admission:

  • White blood cell count (WBC), red blood cell count (RBC), hemoglobin (Hb), platelet count (PLT), mean corpuscular hemoglobin concentration (MCHC), mean corpuscular hemoglobin (MCH), mean corpuscular volume (MCV), neutrophils (NEU), lymphocytes (LYM), monocytes (MONO), eosinophils (EOS), basophils (BAS), hematocrit (HCT), red cell distribution width (RDW-CV), platelet distribution width (PDW), plateletcrit (PCT), mean platelet volume (MPV);

  • Total bilirubin (TBIL), direct bilirubin (DBIL), albumin (ALB), globulin (GLB), glutamyl transpeptidase (GGT), aspartate aminotransferase (AST), alanine aminotransferase (ALT), alkaline phosphatase (ALP), serum prealbumin (PA), cholinesterase (CHE);

  • Blood urea nitrogen (BUN), serum creatinine (Scr), uric acid (UA), bicarbonate (HCO₃⁻), potassium (K), sodium (Na), calcium (Ca), magnesium (Mg), phosphorus (P);

  • Prothrombin time (PT), international normalized ratio (INR), thrombin time (TT), prothrombin time activity (PTA), activated partial thromboplastin time (APTT), fibrinogen (FIB).

Inflammatory factors analyzed in this study included:

  • Systemic immune-inflammation response index (SIRI) = (NEU × MONO)/LYM.

  • Systemic immune-inflammation index (SII) = PLT × NEU/LYM.

  • Platelet-lymphocyte ratio (PLR) = PLT/LYM.

  • Aspartate aminotransferase-neutrophil ratio (ANRI) = AST/NEU.

  • Gamma-glutamyl transpeptidase-platelet ratio (GPR) = GGT/PLT.

  • Neutrophil-lymphocyte ratio (NLR) = NEU/LYM.

  • Derived neutrophil-lymphocyte ratio (dNLR) = (WBC-NEU)/LYM.

  • Monocyte-lymphocyte ratio (MLR) = MONO/LYM.

  • Albumin-globulin ratio (AGR) = ALB/GLB.

Outcome

The primary outcome was the development of genu valgum or ankle valgus within 3 months in HME patients. The presence of genu valgum or ankle valgus was defined as a positive outcome, while their absence was defined as a negative outcome. Full-length lower limb imaging served as the gold standard for diagnosing genu valgum or ankle valgus. Diagnoses were confirmed by experienced radiologists through formal imaging reports.

Statistical analysis

First, the data were randomly divided into a training set and a validation set at a 7:3 ratio. Baseline data were compared to verify consistency between datasets. Samples in the training set were then grouped by the presence or absence of genu valgum or ankle valgus. Clinical and laboratory data were compared between groups using SPSS 27.0 (SPSS Inc., Chicago, IL).

  • Continuous data were assessed for normality using the Shapiro test. Normally distributed data were expressed as mean ± standard deviation and compared using independent one-way ANOVA. Non-normally distributed data were expressed as median (25th percentile, 75th percentile) and compared using the Kruskal-Wallis test.

  • Categorical data were described using frequency (percentage) and compared using the chi-square test or Fisher’s exact test. A two-sided p-value < 0.05 was considered statistically significant.

Independent variables were dichotomized at the mean (values < mean = group0; values ≥ mean = group1). LASSO regression was used to analyze screened differential factors. Risk factors were selected using 10-fold cross-validation at λ = lambda.min to balance model prediction accuracy. We used three methods—IQR-based filtering, z-score, and isolation forest—to explore the outliers among the sample of selected risk factors. Selected factors were then analyzed using five machine learning models: K-nearest neighbors (KNN), linear regression (LR), random forest (RF), support vector machine (SVM), and eXtreme Gradient Boosting (XGB). Model performance was evaluated using metrics including: area under the receiver operating characteristic curve (AUC), sensitivity, specificity, positive predictive value (PPV), and negative predictive value (NPV). In order to evaluate the optimal model, we used the 5-fold cross-validation method to test the model, and the results include Accuracy, Precision, Recall, and F1-score. To enhance model interpretability, the SHapley Additive exPlanations (SHAP) method was applied to interpret RF model results. Feature importance in predicting outcomes was measured using SHAP values, analyzed in Python with the SHAP 0.46.0 package.

Finally, multivariate logistic regression was performed using SPSS to identify independent risk factors. ROC curves were plotted and AUC was calculated using GraphPad Prism 9.5.0. A nomogram of independent predictors was constructed using R Studio (version 4.2.2) and JD_DCPM (V6.03, Jingding Medical Technology Co., Ltd.). Model performance was evaluated via ROC curves and AUC, calibration plots (mean error), and decision curve analysis (DCA) to assess clinical utility.

Results

Association between clinical factors and genu valgum in HME patients

A total of 155 patients were initially screened, with 15 excluded due to the above criteria, leaving 140 patients included in the retrospective study (flowchart in Fig. 1). Patients were grouped by the presence of genu valgum: Genu Valgum group (n = 64) and No Genu Valgum group (n = 76). Data were randomly divided into a training set and validation set at a 7:3 ratio. Baseline comparisons showed no significant differences in sex [40 females (40.82%) vs. 58 males (59.18%)], history of hepatitis, tuberculosis, hemophilia [1 case (1.02%)], thalassemia [1 case (1.02%)], smoking [1 case (1.02%)], or alcohol use, as well as age, height, weight, and BMI (all p > 0.05), indicating comparable baseline characteristics between groups (Table 1).

Fig. 1
figure 1

Flow chart of this study

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Table 1 Baseline data table for comparison of training group and validation group
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For genu valgum analysis in HME patients, training set samples were compared by genu valgum status. Continuous variables were dichotomized at the mean, revealing significant group differences in RBC, Hb, LYM, ALB, GLB, PA, dNLR, and MLR (p < 0.05) (Table 2).

Table 2 Data table for comparison of no genu valgum group and genu valgum group
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Feature selection, explainable model development, and importance comparison for genu valgum in HME patients

The above factors were input into the LASSO regression model for feature selection (Fig. 2). To optimize model accuracy, the λ value was set to lambda.min = 0.02977899, identifying ALB, GLB, PA, and dNLR as risk factors for genu valgum. Their corresponding lambda.min coefficients were − 2.173151, -1.497893, -2.453225, and 0.234625, respectively.We also employed three outlier detection methods to filter outliers in the samples (Supplementary materials 1 A- D). Considering the low incidence rate of the disease and the few outliers in the samples, to avoid bias, we will retain all samples to continue building the machine learning model.

Fig. 2
figure 2

Best match factor screening by lasso regression of genu valgum. A is the Lasso regression path diagram; B shows the plot of the best matching factors screened by the ten-fold cross validation method, and the best matching factors were selected using lambda.min as the criterion

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Performance comparisons of five machine learning models are shown in Table 3, with predictive performance visualized via ROC curves and histograms (Fig. 3). The random forest (RF) model demonstrated the best performance: in the training set, sensitivity was 0.977, accuracy 0.836, and C-index 0.963; in the validation set, sensitivity was 0.9, accuracy 0.895, and optimal ROC cutoff 0.913, outperforming other models.Using a 5-fold cross-validation to validate the RF model, the results are shown in Supplementary materials 2 A - C. The average accuracy of the RF model is 0. 8643, average precision is 0. 8702, average recall is 0. 8643, the average F1 score is 0. 8639, the overall accuracy of the model is relatively high, and the fluctuations across folds are small.

Table 3 Predictive performance comparison of machine learning algorithms in genu valgum
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Fig. 3
figure 3

ROC curve analysis and bar plots of machine learning algorithms. A ROC curve of machine learning of training group in genu valgum patients; B ROC curve of machine learning of validation group in genu valgum patients; C Bar plot of each model in the training group; D Bar plot of each model in the validation group

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Using SHAP analysis with the RF model, we evaluated factor importance and case-specific impacts. Table 4 shows mean SHAP values: PA (0.195), ALB (0.159), GLB (0.118), dNLR (0.043). Figure 4A displays SHAP values for all samples, with PA demonstrating a significant impact on improving the model confidence for genu valgum prediction in HME patients (Fig. 4B). Waterfall plots for randomly selected patients #5 (prediction probability = 0.872) and #2 (0.00783) aligned with clinical observations (Fig. 5).

Table 4 SHAP value of variables in random forest model
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Fig. 4
figure 4

A Bee plot of random forest model; B Bar plot of variable importance in random forest model

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Fig. 5
figure 5

SHAP waterfall plot showing feature contributions. A Waterfall plot of case 5 patient; B Waterfall plot of case 2 patient

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Nomogram construction and evaluation for genu valgum

Multivariate binary logistic regression identified PA (0.025 [0.002–0.137]), ALB (0.037 [0.003–0.203]), and GLB (0.083 [0.010–0.416]) as independent predictors (Table 5). Based on these results, a nomogram was constructed using R Studio and JD_DCPM software (Fig. 6).

Table 5 Multivariate binary logistic regression analysis results of Genu Valgum
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Fig. 6
figure 6

Nomogram of genu valgum in HME patients

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  • Training set validation:

    • ROC curve (Fig. 7A) showed a C-index of 0.963, indicating excellent predictive accuracy.

    • Calibration curve (Fig. 7B) showed a mean error of 0.011, reflecting high consistency between predicted and observed outcomes.

    • Decision curve analysis (DCA, Fig. 7D) demonstrated substantial clinical benefit across most patient subgroups.

Fig. 7
figure 7

Validation of variables of genu valgum in HME patients. A ROC curve of training group and validation group; B Calibration curve of training group; C Calibration curve of validation group; D DCA curve of training group

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  • Validation set validation:

    • ROC curve (Fig. 7A) had a C-index of 0.899.

    • Calibration curve (Fig. 7C) showed a mean error of 0.063.

    • DCA (Fig. 7E) confirmed clinical utility in real-world applications.

Overall, the nomogram exhibited robust predictive performance and minimal error in both training and validation sets, offering clear clinical benefits for most patients.

Association between clinical factors and ankle valgus in HME patients

A total of 140 patients were included, grouped by the presence of ankle valgus: Ankle Valgus group (n = 69) and No Ankle Valgus group (n = 71). Using the same training/validation set division as prior analyses, continuous variables were dichotomized at the mean. Significant group differences were observed in RBC, LYM, Hb, GLB, ALB, PA, UA, and SII (p < 0.05) (Table 6).

Table 6 Data table for comparison of no ankle valgus group and ankle valgus group
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Feature selection, explainable model development, and importance comparison for ankle valgus

Incorporating the above factors into LASSO regression (Fig. 8), λ was set to lambda.min = 0.2975143 to minimize model error. Selected risk factors for ankle valgus included RBC, Hb, LYM, GLB, PA, UA, and SII, with lambda.min coefficients: 0.9686683, -0.4275660, -0.1877094, -0.3126753, -1.2450450, -1.3153751, and 1.3090361.Our approach to outlier detection is similar to that described in genu valgum (Supplementary materials 1 E-I). To avoid bias, we will also retain all samples to continue building the machine learning model.

Fig. 8
figure 8

Best match factor screening by lasso regression of ankle valgus. A is the lasso regression path diagram; B shows the plot of the best matching factors screened by the ten-fold cross validation method, and the best matching factors were selected using lambda.min as the criterion

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Performance comparisons of five machine learning models using these risk factors are shown in Table 6, with ROC curves and histograms visualizing model performance (Fig. 9). The RF model demonstrated stable performance: in the training set, sensitivity was 1, accuracy 0.855, and C-index 0.947; in the validation set, sensitivity was 0.826, accuracy 0.688, and C-index 0.770, outperforming other models in predictive capability(Table 7). For this model, we also used a 5-fold cross-validation to validate the RF model. The results are shown in Supplementary materials 2 D-F, with the RF model achieving an average accuracy of 0. 8071, the average precision is 0. 8188, average recall is 0. 8071, the average F1 score is 0. 8061, the overall accuracy of the model is relatively high, and the fluctuations across folds are small.

Fig. 9
figure 9

ROC curve analysis and bar plots of machine learning algorithms. A ROC curve of machine learning of training group in ankle valgus patients; B ROC curve of machine learning of validation group in ankle valgus patients; C Bar plot of each model in the training group; D Bar plot of each model in the validation group

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Table 7 Predictive performance comparison of machine learning algorithms in ankle valgus
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SHAP analysis based on the RF model evaluated factor importance and case-specific impacts. Table 8 shows mean SHAP values: RBC (0.061), LYM (0.047), Hb (0.038), GLB (0.105), PA (0.081), UA (0.080), SII (0.024). Figure 10A displays SHAP values for all samples, with PA demonstrating a significant impact on improving the model confidence for ankle valgus prediction in HME patients (Fig. 10B). We randomly selected patient #6 and #10 for force plot analysis (Fig. 11), with prediction probabilities of 0.823 and 0.179, respectively, consistent with collected information.

Table 8 SHAP value of variables in random forest model
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Fig. 10
figure 10

A Bee plot of random forest model; B Bar plot of variable importance in random forest model

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Fig. 11
figure 11

SHAP force plot showing feature contributions. A Force plot of case 6 patient; B Force plot of case 10 patient

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Nomogram construction and evaluation for ankle valgus

To further optimize the model, significant factors were included in multivariate binary logistic regression analysis, identifying GLB (0.183 [0.053–0.571]), PA (0.162 [0.035–0.631]), UA (7.156 [1.841–34.03]) as independent predictors (Table 9).

Table 9 Multivariate binary logistic regression analysis results of ankle valgus
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Based on multivariate analysis results (GLB, PA, UA), a nomogram model was constructed using R Studio and JD_DCPM software (Fig. 12). The training set ROC curve (Fig. 13A) showed a C-index of 0.865, indicating good predictive efficacy. The training set calibration curve (Fig. 13B) showed a mean error of 0.054, and the training set DCA (Fig. 13D) demonstrated good clinical benefit for most patients. Validation using the validation set data showed a C-index of 0.823 on the ROC curve (Fig. 13A), a mean error of 0.052 on the calibration curve (Fig. 13C), and a DCA (Fig. 13E) indicating good clinical benefit for most patients. The nomogram exhibited good predictive efficacy with small errors in both training and validation sets, benefiting most clinical patients.

Fig. 12
figure 12

Nomogram of ankle valgus in HME patients

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Fig. 13
figure 13

Validation of variables of ankle valgus in HME patients. A ROC curve of training group and validation group; BCalibration curve of training group; C Calibration curve of validation group; D DCA curve of training group; E DCA curve of validation group

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Discussion

Given that HME is a hereditary disease, current research on HME primarily focuses on mutations in the EXT gene family [21, 22]. However, no studies have investigated the association between common blood biomarkers and lower limb deformities in this population. In our clinical practice, we observed that patients with poor nutrition are more likely to develop lower limb deformities. A study by J Alvear et al. [23]found that early postnatal malnutrition leads to growth retardation, with children from low-socioeconomic backgrounds experiencing shorter stature than those from high-socioeconomic groups. Aurore Bonnet-Lebrun et al. reported that changes in blood phosphorus levels can cause abnormal mineralization of bone and dental tissues, contributing to lower limb deformities in children with rickets.

This study investigated risk factors forgenu valgum and ankle valgus in HME patients. In the RF model, PA emerged as a important factor in both analyses. PA, also known as transthyretin, is a thyroid hormone transport protein synthesized in the liver and partially degraded by the kidneys, with thyroid hormone transport being one of its primary functions [24]. PA is highly sensitive to acute changes in protein balance and promptly reflects nutritional status [25, 26]and numerous studies have confirmed its utility as a single parameter for assessing protein-energy malnutrition [27, 28].According to the research by Han et al. [29]PA is related to the levels of calcium and phosphorus in tissues, and these levels are associated with skeletal development. Based on our observations in daily clinical practice, we hypothesize that there is some correlation in lower limb deformities in HME patients, which was validated by this retrospective analysis. Additionally, ALB was identified as an independent predictor of genu valgum, while GLB was a common independent predictor for both genu valgum and ankle valgus. Previous studies have shown that low ALB levels impact hip fracture prognosis [30]and since HME-related deformities involve abnormal bone growth. In accordance with the research of Zhang et al. [31]low ALB levels stand as an independent predictor for the emergence of low bone mass in children. In addition to the aforementioned nutritional indicators, our study has also demonstrated that UA as an independent predictor can predict the occurrence of ankle valgus. According to the research by Luis Pereira-da-Silva [32]UA can also serve as one of the indicators to assist in the diagnosis of metabolic bone disease. Our regression analysis confirmed these hypotheses, with nutritional indicators validated in randomly selected individuals.

This study demonstrates that blood biomarkers measured 3 months prior to admission are associated with the risk of genu valgum and ankle valgus in HME patients. Forgenu valgum, PA, ALB, GLB, and dNLR were prioritized in factor importance analysis, with a nomogram built on PA, ALB, and GLB. The above factors are all protective factors. For ankle valgus, PA, UA, GLB, RBC, Hb, LYM, and SII were evaluated, with a nomogram based on GLB, PA, and UA. In this nomogram, GLB and PA are protective factors, while UA is a pathogenic factor. We selected the data of patient No. 17 from the overall sample to further demonstrate the application of the corresponding nomogram. The relevant indicators are as follows: ALB: 41.2, GLB: 22.3, PA: 178.3, UA: 158. For the patient, the predicted score of the genu valgum model is approximately 189, indicating a probability of over 90% for the occurrence of genu valgum; the predicted score of the ankle valgus model is about 104, meaning the patient has a probability of more than 40% but less than 50% of developing ankle valgus. In the final observation, the patient only developed genu valgum, which is quite consistent with our expectations.These findings provide reliable diagnostic and prognostic clues for early intervention, potentially improving outcomes and reducing surgical risks.

Strengths of this study include:

  1. 1.

    A retrospective design with model development in a training set and validation in a separate dataset, ensuring reliability and clinical applicability.

  2. 2.

    Use of routine preoperative blood tests (collected up to 3 months prior to admission) for early prediction, maximizing patient accessibility.

Limitations include:

  1. 1.

    Lack of long-term follow-up and longitudinal cohort study to assess disease incidence. This may underestimate the dynamic effects of risk factors.

  2. 2.

    Potential for expanded multi-center data collection to enhance generalizability.

  3. 3.

    This study only used routine admission blood test results for research, which has good generalizability, but still lacks further research on nutritional indicators and physical examinations.

Conclusion

In conclusion, this study identifies prealbumin (PA), albumin (ALB), and globulin (GLB) as independent predictors of genu valgum, while GLB, PA, and uric acid (UA) are key independent predictors of ankle valgus in patients with HME, with PA demonstrating the highest importance across both deformities. The developed nomograms, based on these nutritional and biochemical markers, offer a reliable, noninvasive, and early-stage tool for clinicians to predict the risk of lower limb deformities in HME patients. By leveraging routine blood test data collected up to 3 months prior to admission, these models enable timely clinical intervention, potentially improving outcomes through early prevention and reducing the need for advanced surgical interventions. While further multi-center studies with long-term follow-up are warranted, the findings highlight the critical role of nutritional status in HME-related deformities and provide a practical framework for risk assessment in clinical practice.