Interpretable machine learning analysis of multidimensional biomarkers associated with osteoporosis in postmenopausal women with metabolic syndrome

Osteoporosis (OP) and metabolic syndrome (MetS) are both highly prevalent in postmenopausal women and share complex pathophysiological links. However, existing studies on the association between MetS and bone health have reported inconsistent findings, particularly in Asian populations, reflecting substantial inter-individual variability that is not fully captured by conventional approaches. There remains a lack of tools that integrate multidimensional biomarkers for comprehensive and precise risk assessment in this context. This study aimed to identify metabolic characteristics associated with osteoporosis and to develop an interpretable machine learning model based on multidimensional biomarkers for discriminating osteoporosis status in postmenopausal women with metabolic syndrome. This retrospective cross-sectional study initially screened 2675 postmenopausal women with MetS from three tertiary hospitals. After applying exclusion criteria, 984 participants were enrolled. After excluding patients with prior anti-osteoporosis medication use, 820 participants remained eligible for propensity score matching. Among these, 444 had OP and 376 did not, with OP status determined based on bone mineral density (BMD) measurements. Propensity score matching on clinical covariates yielded 290 well-matched pairs (580 participants) for final analysis. General patient data and laboratory biochemical indicators were collected, and 12 composite indices were calculated. LASSO regression was used for feature selection, and propensity score matching was employed to balance baseline differences between the groups. Multivariate logistic regression, RCS analysis, and correlation analysis were used to explore the relationships between biomarkers and OP. Ten machine learning algorithms were utilized to construct Machine Learning models, and the optimal model was interpreted using the SHAP method. Finally, a score chart was constructed based on the key variables. After excluding patients with prior anti-osteoporosis medication use, 820 participants were eligible. Propensity score matching on clinical covariates (age, BMI, menopausal age, surgery history, antihypertensive, antidiabetic, lipid-lowering medications, and other chronic diseases) yielded 290 well-matched pairs (580 participants). LASSO regression retained Na + , Cl − , and 25(OH)D as key biomarkers. Multivariable logistic regression showed that Cl − was positively associated with osteoporosis (OR = 1.218, 95% CI: 1.128–1.315, P < 0.001), whereas Na + (OR = 0.838, 95% CI: 0.765–0.919, P < 0.001) and 25(OH)D (OR = 0.943, 95% CI: 0.932–0.954, P < 0.001) were protective. Restricted cubic spline analysis revealed a linear inverse association between Cl − and bone mineral density, and a non-linear positive association for 25(OH)D. Among the ten machine learning models, XGBoost achieved a test-set AUC of 0.806 and demonstrated the highest sensitivity and F1 score, and was therefore selected as the reference model for SHAP-based interpretation. SHAP analysis ranked 25(OH)D, Cl − , Na + , age, and BMI as the most influential features in the XGBoost model. A separate logistic score chart was constructed using the three LASSO-selected variables (Cl − , Na + and 25(OH)D) and showed good internal calibration. Serum Na + , Cl − , and 25(OH)D are multidimensional biomarkers independently associated with osteoporosis in postmenopausal women with MetS. The XGBoost-based interpretable model and the derived score chart provide a potentially useful tool for individualized risk stratification using routine laboratory tests. However, these findings are hypothesis-generating, and the clinical utility of the score chart requires prospective validation before implementation.