Advanced Numerical Modelling and Statistical Analysis of Predictive Risk Factors for Early Post-Total Thyroidectomy Hypocalcemia: A Retrospective Cohort Study

Abstract

Early transient hypocalcemia is the most frequent and clinically challenging complication following total thyroidectomy. A mathematical logistic model was formulated and implemented, with numerical optimisation via Maximum Likelihood Estimation (MLE), solved with the Newton-Raphson algorithm, to identify predictive risk factors and estimate adjusted odds ratios (aOR). A retrospective analysis of clinical and surgical data from 290 patients who underwent total thyroidectomy at Tobruk Medical Centre was performed. Gradient vectors and Hessian matrices were constructed, and model goodness-of-fit was validated using the Hosmer-Lemeshow test alongside ROC-AUC evaluation. The overall incidence of early postoperative hypocalcemia was 12.8% (n = 37). Multivariable numerical logistic regression demonstrated that intraoperative parathyroid gland injury was the sole independent predictor significantly associated with hypocalcemia (aOR = 3.68, 95% CI: 1.65–8.21, p = 0.001). Secondary factors (surgical drain aOR = 1.88, lymph node dissection aOR = 1.85) lost statistical significance after multivariable adjustment. The proposed numerical model delivers a preliminary clinical risk prediction model that allows surgeons to evaluate risk intraoperatively and consider prophylactic oral calcium and active vitamin D therapy.