Development and validation of a robust logistic regression model for predicting osteoporosis in older people

Osteoporosis (OP) represents a significant public health challenge in the aging population, often leading to debilitating fractures. Early identification of high-risk individuals through routine clinical data is vital for preventive care. This study aimed to develop and validate a robust machine learning-based framework to predict OP in older people using comprehensive physical examination indicators.

We analyzed a retrospective single-center cohort of 852 participants (age ≧ 60 years) from a physical examination center. The cohort was randomly partitioned into a training set (n = 598) and an internal validation set (n = 254) at a 7:3 ratio. Nineteen potential predictors, including demographics (Age, Sex, BMI), lifestyle habits, comorbidities, and biochemical markers (e.g., SUA, Hb, LDL), were evaluated. After feature selection via LASSO regression, five algorithms-Logistic Regression (LR), Random Forest (RF), Decision Tree (DT), Support Vector Machine (SVM), and XGBoost-were constructed. Hyperparameter tuning was performed only within the training set using 5-fold cross-validation and grid search, and the internal validation set was kept separate for final performance assessment. Model performance was evaluated using the Area Under the Curve (AUC), calibration curves, and Decision Curve Analysis (DCA). Restricted cubic spline (RCS) analysis was further employed to evaluate dose-response associations between selected variables and osteoporosis risk.

The prevalence of OP in the study population was 28.87% (246/852). LASSO regression identified 12 optimal features for model development. While ensemble methods (RF and XGBoost) exhibited high discriminative power, they showed signs of potential overfitting with perfect training set performance. In contrast, the LR model demonstrated superior robustness and stability, achieving an AUC of 0.809 in the training set and 0.782 in the internal validation set. In the validation cohort, the LR model maintained balanced performance with a sensitivity of 0.767 and a specificity of 0.702. Calibration curves indicated agreement between predicted and observed risks, and DCA suggested clinical net benefit across a broad range of threshold probabilities. SHAP (SHapley Additive exPlanations) analysis indicated that Sex, Age, and BMI were the most influential predictors. Lower levels of serum creatinine (Scr), serum uric acid (SUA), and fasting plasma glucose (FPG) were also associated with higher predicted osteoporosis risk. Multivariable-adjusted RCS analysis suggested an upward trend between HDL-C and OP risk, particularly in the female subgroup (OR = 3.35, 95% CI: 0.86-13.04; p = 0.081), but this finding did not reach conventional statistical significance and should be interpreted cautiously.

Compared with complex ensemble algorithms, the LR model provides a stable and interpretable approach for identifying older people who may warrant DXA assessment or closer bone-health evaluation. Because this study used a retrospective single-center cohort and internal validation only, external multi-center validation is required before routine clinical deployment.