Development and validation of prediction models for biochemical hypocalcemia after parathyroidectomy in primary hyperparathyroidism

Postoperative biochemical hypocalcemia is a common complication after parathyroidectomy for primary hyperparathyroidism (PHPT). This study aimed to develop and internally validate preoperative prediction models and to determine whether machine-learning methods improve prediction over conventional logistic regression (LR).

This single-center retrospective study included 453 patients with PHPT who underwent parathyroidectomy between January 2017 and December 2025. Nine preoperative predictors were prespecified. Eight primary models, including LR and seven machine-learning algorithms, were evaluated using repeated nested stratified cross-validation. A spline-augmented LR model was examined in sensitivity analysis. Performance was assessed using area under the curve (AUC), Brier score, calibration, and decision-curve analysis.

Postoperative biochemical hypocalcemia occurred in 89 patients (19.7%). LR showed the most favorable overall performance, with a mean AUC of 0.814 [standard deviation (SD), 0.004] and Brier score of 0.115 (SD, 0.001). Extreme gradient boosting (XGBoost) achieved the highest AUC among machine-learning models (0.796; SD, 0.009). Based on averaged repeated out-of-fold predictions, AUCs were 0.817 [95% confidence interval (CI): 0.767-0.863] for LR and 0.808 (95% CI: 0.754-0.856) for XGBoost, with no evidence of superior discrimination by XGBoost. The spline sensitivity analysis did not improve performance. LR showed acceptable calibration, and both LR and XGBoost demonstrated positive net benefit across the evaluated threshold range.

More complex machine-learning algorithms did not demonstrate a clear predictive advantage over conventional LR. LR provided stable discrimination, low overall prediction error and acceptable calibration and was retained as the primary model. External validation and prospective assessment of clinical impact are required before routine clinical implementation.