Development of a nomogram for predicting severe post-parathyroidectomy hypocalcemia in patients with secondary hyperparathyroidism: a retrospective cohort study

Introduction

Background

Secondary hyperparathyroidism (sHPT) is one of the most significant complications in patients with chronic kidney disease (CKD) and poses a challenge to both nephrologists and endocrinologists (1). Approximately 30–50% of patients with end-stage renal disease (ESRD) in the United States and 500,000 people globally develop sHPT (1-3). The pathophysiology of hyperparathyroidism (HPT) involves an interplay between phosphate retention, vitamin D deficiency, fibroblast growth factor 23 elevation, and persistent parathyroid hormone (PTH) stimulation, which leads to hyperplasia of the parathyroid gland, severe mineral bone disorders, and increased cardiovascular mortality (4,5) (Figure 1).

Figure 1 Pathophysiology of severe post-parathyroidectomy hypocalcemia. PTH, parathyroid hormone.

Treatment of sHPT requires substantial resources and is managed both medically and surgically. Medical management includes the use of calcimimetics, vitamin D analogues, and phosphate binders. When medical management fails, surgical management with total parathyroidectomy and autotransplantation is the only definitive treatment for sHPT (6). Although this procedure controls mineral metabolism, large-scale studies have shown that 25–50% of patients develop profound and prolonged hypocalcaemia (7,8). There is considerable variation among institutions and treatment protocols (3,9).

Rationale and knowledge gap

In the literature, post-parathyroidectomy has been artificially categorized into two types: (I) hungry bone syndrome and (II) hypoparathyroidism-induced hypocalcemia. However, new evidence suggests that this distinction is problematic (10,11). First, most patients likely experience hypoparathyroidism due to both mechanisms simultaneously, namely: (I) gland removal and (II) accelerated skeletal mineral uptake due to sudden loss of PTH-mediated bone formation suppression (12,13). Second, the mechanistic contribution of each entity varies between individuals and may change throughout the disease process, making mechanistic attribution impractical in clinical practice (14).

Clinically, it is more important to identify patients who are most at risk of severe, prolonged hypocalcemia requiring intensive management resources than to identify mechanistic distinctions. Regardless of the mechanism, the result is the same: a 4–7-day increase in median hospitalization, up to 25% requiring intensive care, an additional healthcare cost between $6,000 to $15,000 per case, and patient morbidity including symptomatic hypocalcemia, cardiac arrhythmias, and potential neurological complications (15-17).

Previous research has identified several risk factors for severe post-parathyroidectomy hypocalcaemia (SPPH), notably elevated preoperative alkaline phosphatase (ALP) levels. Multiple independent studies have demonstrated odds ratios ranging from 1.007 to 4.11 per unit increase in ALP (18-20). This is biologically plausible because the bone-specific isoform of ALP reflects osteoblastic activity and bone formation potential. Regardless of the specific mechanistic pathway involved, patients with elevated ALP levels likely have primed skeletal systems capable of rapid mineral uptake following PTH withdrawal.

Other risk factors identified in the literature include younger age (reflecting a higher bone turnover), elevated preoperative PTH levels (indicating a more severe hyperparathyroid state), longer dialysis duration (suggesting more advanced bone disease), and various biochemical parameters reflecting mineral metabolism dysregulation (21-23). Despite previous research, most other prediction models have significant limitations, including small sample sizes, single-centre designs, lack of external validation, heterogeneous outcome definitions, and limited clinical utility assessments (24,25).

There is a lack of validated tools for individual patient risk assessment in post-parathyroidectomy management; hence, current approaches rely primarily on institutional protocols and clinical experience. The absence of a validated prediction model creates an unpleasant dichotomy of either universal, resource-intensive monitoring which is potentially unnecessary for low-risk patients, or reactive management which is potentially inadequate for high-risk patients.

There is a need for a robust and validated SPPH prediction model. First, it would optimise resource utilization by allowing risk stratification and identifying patients who would benefit from intensive interventions. Second, it would allow for preoperative patient counselling and informed consent regarding the expected recovery course and potential complications. Third, it would allow practitioners to administer the appropriate level of care, including consideration for intensive care unit monitoring in the highest-risk patients. Finally, the model could be a building block for future studies aimed at preventing SPPH through targeted prophylactic strategies (26,27).

Objective

Our objective was to develop and internally validate a risk prediction model for SPPH in patients with sHPT who underwent total parathyroidectomy. By creating a nomogram, our goal was to provide physicians with an easy-to-use tool for estimating an individual patient’s SPPH risk before surgery. This would enable stratified patient management; for example, high-risk patients could receive prophylactic calcium and vitamin D and enhanced monitoring, whereas low-risk patients might avoid unnecessary interventions. Ultimately, our objective was to improve clinical decision making and patient outcomes through early risk assessment, achieving both model development and internal validation in our cohort. We present this article in accordance with the TRIPOD reporting checklist (available at https://gs.amegroups.com/article/view/10.21037/gs-2026-0243/rc).

Methods

Study design and setting

We retrospectively reviewed the charts of patients with sHPT who underwent total parathyroidectomy with auto transplantation between 2019 and 2024 at two tertiary care institutions. This study was conducted in accordance with the Declaration of Helsinki and its subsequent amendments. Ethics approval was exempt from the Institutional Review Board of University of Manitoba as the data used was aggregated and anonymized (No. HS 22334 H/B 2018-436). Given the retrospective nature of this study, the requirement for written informed consent was waived.

Standardized perioperative management protocol

All patients received identical perioperative management according to our institutional protocol, which was created through multidisciplinary consensus and was based on current best practices to ensure treatment consistency and enable model generalizability within similar care settings (28,29). A key strength of our study is the use of this standardized approach for model interpretation. The standardized approach included three parts: (I) immediate postoperative management; (II) extended postoperative management; and (III) discharge criteria and long-term follow-up.

Within 24 hours of surgery, immediate postoperative management included prophylactic intravenous calcium supplementation. Calcium supplementation consisted of (I) 10–20 mmol of calcium gluconate diluted in 500 mL normal saline, administered as continuous infusion over 8–12 hours; (II) 2–3 grams of oral calcium carbonate was resumed every 6 hours as soon as oral intake was tolerated; and (III) 0.5–1.0 micrograms of calcitriol every 8 hours. During this critical period, serum calcium levels were performed every 4–6 hours.

During the extended postoperative management 24–72 hours post-surgery, serum calcium was monitored every 6 h for the first 48 h, and then every 12 h until stable. For serum calcium levels of <2.0 mmol/L, 10–20 mmol boluses of intravenous calcium gluconate were administered. If there was persistent hypocalcemia <1.8 mmol/L despite bolus therapy, calcium infusion protocols were escalated. Magnesium levels were monitored daily, as hypomagnesaemia can exacerbate hypocalcaemia and reduce responsiveness to calcium supplementation (30). For magnesium levels <0.7 mmol/L, patients received 4–8 mmol of magnesium daily.

Patients were considered for discharge when they could maintain serum calcium levels >2.0 mmol/L for 24 h on oral supplementation alone, without intravenous calcium. Medications upon discharge included 2–4 grams of calcium carbonate daily in divided doses and 1–2 micrograms of calcitriol daily, with specific dosing individualized based on calcium levels and clinical response. All patients were followed up with weekly calcium monitoring for one month. During the second month, the patient underwent biweekly calcium monitoring. Subsequent monitoring was performed to determine calcium stability and symptom resolution.

Primary outcome: severe post-parathyroidectomy hypocalcemia (SPPH)

Combining the clinical consensus among our multidisciplinary team and a comprehensive literature review, SPPH was defined by the clinical severity and healthcare resource impact of postoperative hypocalcaemia, regardless of the underlying pathophysiological mechanism (31,32). This approach allows for patient-centred outcomes in our prediction model and aligns with the recent methodological recommendations (33).

SPPH was defined as the occurrence of any one of the following criteria within 30 days of surgery:

• Severe hypocalcemia: two consecutive readings of serum calcium <1.9 mmol/L obtained ≥6 hours apart. This represents a high risk symptomatic complication;
• Intravenous calcium supplementation: if required beyond postoperative day 3, this indicates that the patient has an inadequate response to standard oral supplementation protocols;
• Symptomatic hypocalcemia: tetany, seizures, cardiac arrhythmias, laryngospasm, or other manifestations requiring urgent medical management;
• Hospital length of stay: staying for ≥7 days attributable primarily to hypocalcemia management (reflecting failure to achieve calcium stability on calcium supplementation);
• Unplanned readmission: admitted for hypocalcaemia-related complications or inadequate outpatient calcium control within 30 days.

This multifactorial definition avoids the uncertainty of differentiating between mechanistic causes, while capturing the multidimensional impacts of severe hypocalcaemia. The 30-day time-frame is critical as it captures the most severe short-term complications while excluding long-term complications, such as autograft function or chronic hypoparathyroidism (34,35).

Patient selection

We implemented inclusion and exclusion criteria based on best practices for prediction model studies to ensure a clinically homogeneous population for model development and to address concerns of surgical heterogeneity (36,37).

Inclusion criteria:

• Age: patients with CKD and sHPT who met criteria for surgical intervention and were ≥18 years old;
• Systematic pathological review: histopathological confirmation of complete removal of all four parathyroid glands;
• Biochemical confirmation: postoperative PTH <15 pmol/L within 24 hours of surgery, indicating effective parathyroid tissue removal;
• Successful autotransplantation: surgical report indicating 30–50 mg of viable parathyroid tissue successfully implanted in the non-dominant forearm;
• Complete preoperative and postoperative biochemical data available for all candidate predictor variables;
• Strict adherence to standardized perioperative calcium management protocol;
• Minimum 12-month clinical follow-up with documented outcomes assessment.

Exclusion criteria:

• Disease: primary or tertiary hyperparathyroidism. We specifically excluded tertiary hyperparathyroidism, defined as autonomous parathyroid function with calcium-independent PTH elevation following kidney transplantation or prolonged sHPT, as these patients have a fundamentally different pathophysiological trajectory. In sHPT, parathyroid hyperplasia remains responsive to calcium feedback, and the mineral derangements differ from the autonomous hypercalcemic state of tertiary disease. This distinction is clinically important because the risk of post-parathyroidectomy hypocalcemia may differ depending on whether the hyperparathyroid state is stimulus-driven (secondary) or autonomous (tertiary). Tertiary HPT patients were identified and excluded based on: (I) persistent hypercalcemia (serum calcium >2.62 mmol/L) despite adequate renal replacement therapy; (II) inappropriately normal or elevated PTH in the setting of hypercalcemia; and (III) prior kidney transplantation with recurrent hyperparathyroidism.
• Procedure: subtotal parathyroidectomy or parathyroidectomy without autotransplantation.
• Residual parathyroid tissue or unsuccessful procedure: postoperative PTH >15 pmol/L at 24 hours.
• Concurrent procedures: thyroid surgery or other procedures affecting calcium metabolism.
• Patient history affecting surgical approach: previous neck surgery, radiation therapy, or anatomical abnormalities.
• Confounding factors: parathyroid carcinoma, multiple myeloma, bone metastases, or other active malignancies known to affect calcium metabolism.
• Protocol deviations: significant departures from standardized perioperative management that could affect outcome assessment.
• Insufficient follow-up data: <12 months or loss to follow-up preventing outcome determination.
• Pregnancy or lactation at time of surgery.
• Severe comorbidities: severe heart failure, active infection, or other comorbidities precluding standard perioperative management.

These stringent criteria minimize confounding variables and enhance model reliability, as they ensure a homogeneous population who underwent successful total parathyroidectomy with standardized perioperative care (38).

Standardized techniques performed by an experienced endocrine surgeon were used for total parathyroidectomy with autotransplantation. A cervical approach was used to identify and resect all four parathyroid glands. A 30–50 mg parathyroid tissue from the most normal-appearing parathyroid gland was minced into 1–2 mm pieces and autotransplanted in the patient’s non-dominant arm.

Data collection

Two independent reviewers collected the data from the electronic medical records. The collected data included demographics, comorbidities, dialysis type, medications, surgical and pathological details, and postoperative outcomes. Data on calcium, phosphate, ALP, PTH, 25-hydroxyvitamin D, and other biochemical parameters were collected at 12, 6, 3, and 1 month before surgery and at 1, 3, 6, and 12 months after surgery.

Statistical analysis

Descriptive analysis

Continuous variables were expressed as means with 95% confidence intervals (CIs) or medians with interquartile ranges, depending on the distribution. Categorical variables were presented as frequencies and percentages. Comparisons between groups were performed using Student’s t-test or Mann-Whitney U test for continuous variables and Chi-squared or Fisher’s exact test for categorical variables.

Sample size calculation and power analysis

The sample size was determined using the events per variable (EPV) criteria (39). The traditional 10 EPV rule has been refined to include model complexity, expected effect sizes, and desired performance characteristics (40,41). EPV values between 10 and 20 (with preferred values greater than 20) are recommended for robust model performance and reduced overfitting risk (42).

Our final model included four variables with 113 SPPH events, yielding 28.25 EPV (113 SPPH events ÷ 4 predictor variables =28.25 EPV), which exceeds recommended thresholds and supports robust model development with minimal overfitting risk and stable coefficient estimation (39,43). Post-hoc power analysis confirmed >90% power to detect clinically meaningful associations [odds ratio (OR) ≥1.5] for our primary predictors at α=0.05.

Variable selection

The least absolute shrinkage and selection operator (LASSO) regression is recognized as the optimal method for high-dimensional prediction problems with potential multicollinearity (44,45). Hence, LASSO was used for our variable selection model as this approach offers better handling of correlated predictors, reduced overfitting, and improved generalizability than traditional approaches (46).

Initially, 47 candidate variables were considered based on clinical knowledge, a literature review, and biological plausibility. These included:

• Demographic variables: age, gender, body mass index, race/ethnicity;
• Comorbidities: diabetes, hypertension, cardiovascular disease, dialysis;
• Medications: calcimimetic use, vitamin D analog therapy, phosphate binder types;
• Biochemical parameters at 12, 6, 3, and 1 month preoperatively: PTH, calcium, phosphate, ALP, 25-hydroxyvitamin D, albumin, magnesium;
• Surgical characteristics: operative time, total parathyroid weight, surgeon experience;
• Pathological features: gland size, histological characteristics.

A full enumeration of all candidate variables with their univariable odds ratios, P values, and LASSO selection status is provided in Table S1.

The optimal regularization parameter (λ) was determined using LASSO regression with 10-fold cross-validation. This method minimizes prediction error while maintaining the parsimony of the model. The λ value that minimised cross-validated deviance was selected by evaluating the models across the entire regularization path, from the null model (λ→∞) to the full model (λ=0) (47).

Two criteria were used to determine the optimal λ: (I) the value that minimised the cross-validation error was λ.min; and (II) the largest λ within one standard error of the minimum was λ.1se which represents a more parsimonious model with comparable performance (48). To enhance the generalizability of the model and reduce the risk of overfitting, we selected λ.1se which is consistent with current best practices (49).

Model development and validation framework

Primary model development

Following LASSO variable selection, we developed a final prediction model using multivariate logistic regression with maximum likelihood estimation. Model coefficients were estimated with 95% confidence intervals using profile likelihood methods for enhanced accuracy compared to Wald-based intervals (50).

The final model is expressed as follows:

Logist(P(SPPH))=β0+β1(Age)+β2(Phosphate1-month)+β3(ALP1-month)+β4(PTH3-month)[1]

where P(SPPH) represents the probability of developing SPPH.

Internal validation

We employed bootstrap resampling with 200 iterations for internal validation, representing the gold standard approach for assessing optimism in the prediction model performance (51,52). For each bootstrap sample, we repeated the entire modelling process, including variable selection and coefficient estimation, ensuring an honest assessment of model performance (53).

Bootstrap validation provided optimism-corrected estimates for the key performance metrics:

• Discrimination (c-statistic): apparent performance minus optimism;
• Calibration slope: assessment of agreement between predicted and observed probabilities;
• Calibration-in-the-large: overall calibration across the prediction range.

Performance assessment framework

Model performance was evaluated using multiple complementary metrics following TRIPOD (Transparent Reporting of a multivariable prediction model for Individual Prognosis or Diagnosis) guidelines (54):

• Discrimination: assessed using the c-statistic (area under the ROC curve), with values >0.7 considered acceptable, >0.8 good, and >0.9 excellent for clinical prediction models (55).
• Calibration: evaluated using multiple approaches.
  • Calibration plots comparing observed versus predicted probabilities across deciles.
  • Hosmer-Lemeshow goodness-of-fit test (P>0.05 indicating good calibration).
  • Calibration slope (ideal value =1.0, indicating perfect calibration).
  • Calibration-in-the-large (ideal value =0.0, indicating no systematic over- or under-prediction).
• Clinical utility: assessed using decision curve analysis (DCA) to quantify the net benefit of using the prediction model compared to treating all patients or no patients across different threshold probabilities (56,57).

Nomogram development

The final model was translated into a nomogram by using standard methods. Points were assigned to each predictor variable in proportion to their regression coefficients, and a total-point scale was created to estimate individual patient probabilities. The nomogram was designed to be user friendly for clinical applications.

Risk stratification

Based on the predicted probabilities, we developed a risk stratification system by identifying the optimal cut-off points that maximized clinical utility while maintaining reasonable group sizes. Patients were classified into low-, intermediate-, and high-risk groups with specific management recommendations for each category.

All analyses were performed using Stata version 19.0 (StataCorp, College Station, TX, USA). The complete analytical code is available upon request to ensure reproducibility of the results. Missing data were handled using a complete case analysis. Among the 227 patients with known SPPH status, 157 (69.2%) had complete data for all four model predictors; the primary source of missingness was ALP at 1 month preoperatively (56/227, 24.7% missing). We addressed potential bias from complete-case analysis through a sensitivity analysis using multiple imputation (see Table S2).

Results

Patient characteristics

Of the 251 patients in the original database, 234 met initial screening criteria. Seven patients were subsequently excluded due to missing outcome data (SPPH status not determinable), yielding an analytic cohort of 227 patients. Of these, 157 patients had complete data for all four model predictors and constituted the primary analysis sample (Figure 2). In total, 113 of 227 (49.8%) patients developed SPPH. Of the 227 patients, 128 (56.4 %) were male.

Figure 2 STROBE flow diagram of patient selection. Of 251 patients identified from the parathyroidectomy database, 17 were excluded during initial screening (ineligible procedures, duplicate records, or non-sHPT indications), yielding a clean dataset of 234 patients. Seven patients with missing SPPH outcome data were excluded, producing an analytic cohort of 227 [SPPH: 113 (49.8%); no SPPH: 114 (50.2%)] used for descriptive analyses (Table 1). A further 70 patients were excluded due to missing values in one or more model predictors [ALP: n=56 (24.7%); phosphate: n=13; PTH 3-month preoperative: n=21; some patients missing multiple variables], yielding a complete-case analytic cohort of 157 patients [SPPH: 83 (52.9%); no SPPH: 74 (47.1%)] used for multivariable model development and internal validation. Diagram prepared in accordance with the STROBE statement for observational studies. ALP, alkaline phosphatase; sHPT, secondary hyperparathyroidism; SPPH, severe post-parathyroidectomy hypocalcaemia.

The mean age of the sample was 52.7 years (95% CI: 50.8–54.7). Younger patients (48.9 vs. 56.5 years, P<0.001) were significantly more likely to develop SPPH, potentially because of their more active bone metabolism and greater capacity for rapid mineral uptake post-parathyroidectomy. Patients categorized as having SPPH also had higher preoperative PTH levels at all times, most significantly at three months preoperatively (159.1 vs. 123.1 pmol/L, P<0.001). This suggests that serially elevated PTH levels at several preoperative time points are more predictive than a single measurement. ALP, a marker of osteoblastic activity, one month before surgery was significantly higher in patients with SPPH (387 vs. 298 U/L, P=0.003). Elevated ALP levels may indicate rapid mineral uptake by the SPPH. Patients with SPPH also had higher preoperative phosphate levels (2.2 vs. 1.9 mmol/L, P=0.045).

Both groups had similar operating times, surgical characteristics, and total parathyroid weight removed (1,139 vs. 1,256 mg, P=0.61). Postoperatively, patients with SPPH had an increased length of hospital stay (median 7 vs. 3 days, P<0.001), greater number of ICU admissions (24.8% vs. 2.6%, P<0.001), and increased 30-day readmission rates (17.7% vs. 4.4%, P=0.001) than those without SPPH (Table 1).

Variable selection and model development results

• LASSO variable selection process: the LASSO regularization path identified the optimal variable selection at λ=0.0847 (λ.1se), which selected four variables from the initial pool of 47 candidates. The cross-validation error was minimised at this regularization level with a mean cross-validated deviance of 1.234 (SE =0.089). The selected variables demonstrated biological plausibility and clinical relevance, thus supporting the validity of the data-driven selection process.
• Final prediction model: the four variables incorporated into the final multivariable logistic regression model demonstrated the following associations with SPPH (Figure 3):
  

  Figure 3 Risk factors for severe post-parathyroidectomy hypocalcemia—forest plot. Forest plot of adjusted odds ratios from the multivariable logistic regression model (N=157). Diamond markers represent point estimates; horizontal lines indicate 95% confidence intervals on a logarithmic scale. The vertical dashed line at OR =1.0 represents the null effect. Sage green diamonds indicate a protective association (OR <1) and coral diamonds indicate increased risk (OR ≥1); directional labels are annotated below the plot area. The right-hand columns display the odds ratio with 95% CI and the corresponding two-sided P value, positioned outside the confidence-interval whiskers to avoid overlap. Odds ratios are scaled per clinically meaningful increments: age per year, phosphate per 1 mmol/L, ALP per 100 U/L, and preoperative parathyroid hormone at 3 months per 10 pmol/L. Model fitted on complete cases with all four predictors available. ALP, alkaline phosphatase; CI, confidence interval; OR, odds ratio; PTH, parathyroid hormone.
• Age (per year increase): OR 0.87 (95% CI: 0.76–0.99, P=0.03)
  • Protective effect reflecting age-related decreases in bone turnover and osteoblastic activity;
  • Clinically significant association with each decade of age reducing odds by approximately 25%.
• Phosphate at 1 month preoperatively (per mmol/L increase): OR 1.29 (95% CI: 0.96–1.71, P=0.09)
  • Borderline significant association reflecting mineral metabolism dysregulation;
  • Higher phosphate levels indicating more severe sHPT.
• ALP at 1 month preoperatively (per 100 U/L increase): OR 4.11 (95% CI: 1.89–8.92, P<0.001)
  • Strongest predictor in the model with highly significant association;
  • Reflects heightened osteoblastic activity and bone formation potential;
  • Each 100 U/L increase associated with 4-fold increase in SPPH odds.
• PTH at 3 months preoperatively (per 10 pmol/L increase): OR 0.87 (95% CI: 0.68–1.13, P=0.30)
  • Unexpected protective trend, possibly reflecting PTH resistance in severely elevated cases;
  • Non-significant association suggesting complex relationship with hypocalcemia risk.
• Model performance metrics: the final model demonstrated robust performance across multiple evaluation criteria.
• Discrimination performance:
  • Apparent c-statistic: 0.751 (95% CI: 0.674–0.828);
  • Optimism-corrected c-statistic: 0.739;
  • Bootstrap optimism: 0.012 (indicating minimal overfitting).
• Calibration performance:
  • Hosmer-Lemeshow test: χ²(8) =5.91, P=0.66 (indicating good calibration);
  • Apparent calibration slope: 1.000;
  • Calibration-in-the-large: 0.000.
• Clinical utility assessment: decision curve analysis demonstrated positive net benefit across threshold probabilities from 0.1 to 0.8, indicating clinical utility across a wide range of decision-making scenarios. The model provided superior net benefit compared to treating all patients or no patients across this range, with maximum net benefit at threshold probability of 0.4 (corresponding to intermediate-risk classification).

Model performance and validation

The model demonstrated good discrimination with a c-statistic of 0.751 (95% CI: 0.674–0.828) in the original dataset and 0.739 (95% CI: 0.678–0.806) after optimism correction (Figure 4, Table S3).

Figure 4 ROC curve for optimism-adjusted model. ROC curve for the prediction model (N=157). The solid teal curve plots sensitivity against 1 − specificity across all classification thresholds. The shaded area under the curve corresponds to the apparent AUC. The apparent AUC and the optimism-corrected AUC (derived from 200 bootstrap resamples) are annotated on the plot. The dashed diagonal represents a non-discriminating classifier (AUC =0.5). Per TRIPOD guidelines, the optimism-corrected AUC is a summary scalar and does not produce a separate plottable curve; recalibrating the linear predictor preserves rank ordering and thus the ROC curve shape. AUC, area under the ROC curve; ROC, receiver operating characteristic.

Calibration analysis revealed good agreement between the predicted and observed probabilities across the full range of risk estimates. The calibration plot showed that the predicted probabilities closely matched the observed frequencies, with most points falling near the line of perfect calibration. The Hosmer-Lemeshow test was non-significant [χ²(8) =5.91, P=0.66], confirming good calibration. The optimism-corrected (bootstrap) calibration slope was 0.89 (95% CI: 0.76–1.02), close to the ideal value of 1.0, consistent with minimal to modest overfitting (Figure 5).

Figure 5 Calibration analysis: model comparison. (A) Calibration plot for the apparent model. (B) Calibration plot after optimism adjustment (200 bootstrap resamples). In both panels, the x-axis represents model-predicted probabilities and the y-axis represents observed proportions of SPPH within deciles of predicted risk. Circles with error bars show observed proportions with 95% confidence intervals; the dashed line represents perfect calibration (intercept =0, slope =1); the colored LOWESS smoother traces the empirical calibration trend. Hosmer-Lemeshow goodness-of-fit: χ²(8) =5.91, P=0.66. Apparent calibration slope =1.000; CITL ≈0.000. N=157 complete cases across 10 risk deciles. CI, confidence interval; CITL, calibration-in-the-large; HL, Hosmer-Lemeshow; SPPH, severe post-parathyroidectomy hypocalcemia.

Decision curve analysis demonstrated substantial clinical utility across threshold probabilities ranging from 0.1 to 0.8. The model showed a positive net benefit compared to both “treat all” and “treat none” strategies, with the greatest benefit observed at intermediate threshold probabilities (0.3–0.6) where clinical decision-making is most challenging. This analysis confirmed that the model could meaningfully inform clinical decisions regarding risk stratification and management intensity (Figures 6,7).

Figure 6 Predicted probability distributions by SPPH status. Kernel density distributions of predicted probabilities by SPPH status (N=157). All four distributions are overlaid on a single plot for direct comparison. Solid lines represent apparent model predictions; dashed lines represent optimism-adjusted predictions. Teal curves represent patients without SPPH (n=74); coral curves represent patients with SPPH (n=83). Greater separation between curves indicates better model discrimination. Epanechnikov kernel density estimation used. Predictions derived from the four-variable logistic regression model (age, phosphate, ALP, PTH 3-month preoperative). ALP, alkaline phosphatase; PTH, parathyroid hormone; SPPH, severe post-parathyroidectomy hypocalcaemia.

Figure 7 Decision curve analysis: model comparison. DCA for clinical utility assessment (N=157). (A) Apparent model. (B) Optimism-adjusted model. The y-axis shows standardized net benefit and the x-axis shows threshold probability, defined as the minimum predicted risk at which treatment (e.g., intensive calcium monitoring) would be initiated. The solid teal curve represents the nomogram-based strategy; the long-dashed grey line represents the “treat none” strategy (net benefit =0); the short-dashed coral line represents the “treat all” strategy. Both models demonstrate positive net benefit over the default strategies across a wide range of clinically relevant threshold probabilities (approximately 0.1–0.8), supporting the nomogram’s clinical utility for risk-stratified management. Net benefit curves were smoothed using the default method (3rssh). DCA, decision curve analysis.

Dialysis modality analysis

Among the 227 patients in the analytic cohort, dialysis modality was distributed as follows: hemodialysis (n=103, 45.4%), peritoneal dialysis (n=42, 18.5%), and not recorded (n=82, 36.1%). SPPH rates did not differ significantly across modalities: hemodialysis 53.4%, peritoneal dialysis 47.6%, and not-recorded 46.3% (χ²=1.01, P=0.61; Fisher’s exact P=0.62). Subgroup analysis demonstrated consistent model performance across dialysis modalities: hemodialysis (C-statistic =0.746, n=87), peritoneal dialysis (C-statistic =0.770, n=20), and not-recorded (C-statistic =0.792, n=50). Formal interaction testing confirmed that neither ALP (ALP × dialysis interaction P=0.53) nor age (age × dialysis interaction P=0.65) exhibited differential associations with SPPH across dialysis modalities. A likelihood ratio test comparing the base model with and without dialysis modality terms was non-significant (LR χ²(2)=0.27, P=0.87), and information criteria favoured the more parsimonious model without dialysis type [Akaike information criterion (AIC) 195.3 vs. 199.1; Bayesian information criterion (BIC) 210.6 vs. 220.5]. These findings indicate that the nomogram performs equivalently regardless of dialysis modality, and dialysis type does not add independent predictive value beyond the four model variables.

Risk stratification and clinical implementation

• Evidence-based risk stratification: we developed a nomogram that divides patients according to a three-tier risk stratification system based on predicted probabilities optimised to maximise clinical utility while maintaining reasonable group sizes and clear management implications (Figure 8, Table S4).
  

  Figure 8 Severe post-parathyroidectomy hypocalcemia nomogram. Each predictor axis is scaled to assign points based on its coefficient in the multivariable logistic regression model. To use: locate the patient’s value on each predictor axis, draw a vertical line to the “Points” axis to obtain the corresponding score, sum all points to obtain the “Total Points”, and read the predicted probability of SPPH from the bottom axis. Predictors: age (years), serum phosphate at 1 month (mmol/L), alkaline phosphatase at 1 month (U/L), and pre-operative parathyroid hormone at 3 months (pmol/L). Model developed on N=157 complete cases; internally validated with 200 bootstrap resamples. Generated using the nomolog package in Stata 19. PTH, parathyroid hormone; SPPH, severe post-parathyroidectomy hypocalcaemia.
• Low-risk group (predicted probability <30%):
  • Population: n=25 (15.9% of cohort);
  • Observed SPPH rate: 2/25 (8.0%);
  • Negative predictive value: 92% (23/25);
  • Management implications: Standard monitoring protocols, routine supplementation.
• Intermediate-risk group (predicted probability 30–70%):
  • Population: n=92 (58.6% of cohort);
  • Observed SPPH rate: 54/92 (58.7%);
  • Management implications: enhanced monitoring, proactive supplementation.
• High-risk group (predicted probability >70%):
  • Population: n=40 (25.5% of cohort);
  • Observed SPPH rate: 29/40 (72.5%);
  • Positive predictive value: 72.5% (29/40);
  • Management implications: intensive monitoring, prophylactic interventions.
• Clinical significance: the 9.1-fold difference in SPPH rates between low- and high-risk groups (8.0% vs. 72.5%) provides strong clinical justification for differential management strategies and demonstrates the model’s potential to improve both patient outcomes and resource allocation efficiency.

Discussion

Principal findings and clinical significance

This study developed and internally validated a nomogram for predicting SPPH in patients with sHPT undergoing total parathyroidectomy with autotransplantation. Our model, based on four readily available preoperative variables, demonstrated good discrimination (optimism-corrected c-statistic 0.739), good calibration, and positive clinical utility across a wide range of threshold probabilities.

The most significant finding is the identification of ALP as the predominant risk factor, with an odds ratio of 4.11 per 100 U/L increase—substantially higher than other predictors in our model and consistent with recent literature (58,59). These findings challenge traditional approaches that focus primarily on PTH levels and provide novel insights into the pathophysiology of post-parathyroidectomy hypocalcemia.

Pathophysiological insights and mechanistic implications

ALP as the dominant predictor

The emergence of ALP as the strongest predictor provides important biological insights that extend beyond simple statistical associations. ALP, particularly the bone-specific isoform that predominates in patients with sHPT, serves as a direct marker of osteoblastic activity and bone formation potential (60,61).

Elevated preoperative ALP levels likely indicate a skeletal system primed for rapid mineral uptake following sudden PTH withdrawal. In the chronic hyperparathyroid state, continuous PTH exposure suppresses bone formation while promoting bone resorption. When PTH levels drop precipitously following parathyroidectomy, this suppressed osteoblastic activity is suddenly released, creating a scenario where the skeleton acts as a “calcium sink”, rapidly sequestering available calcium and phosphate from the circulation (62,63).

This mechanism provides biological plausibility for our findings and suggests that the traditional focus on PTH levels alone may be insufficient for risk prediction. While PTH levels reflect the severity of hyperparathyroidism, ALP levels more directly indicate the skeleton’s capacity for mineral uptake—the primary driver of severe post-operative hypocalcemia.

Relevance to the kidney disease population

We conducted additional analyses examining the role of kidney disease-related variables. Dialysis modality (hemodialysis vs. peritoneal dialysis) did not significantly influence SPPH risk (53.4% vs. 47.6%, P=0.61), and the nomogram demonstrated consistent discrimination across modality subgroups (C-statistics 0.746–0.792). Dialysis vintage, a variable of particular interest to nephrologists, was unfortunately not available in our dataset. These findings suggest that the biochemical markers in our nomogram (phosphate, ALP, PTH) capture the clinically relevant aspects of mineral bone disease severity that are common to both hemodialysis and peritoneal dialysis patients, rather than being modality-specific.

Age-related protection

The protective effect of increasing age (OR 0.87 per year) represents another important finding with clear biological rationale. Advancing age is associated with progressive decreases in bone turnover, reduced osteoblastic activity, and diminished capacity for rapid mineral uptake (64,65). Additionally, age-related changes in vitamin D metabolism, intestinal calcium absorption, and renal function may modulate the severity of post-operative hypocalcemia through multiple pathways.

Complex PTH relationships

The unexpected protective trend associated with higher preoperative PTH levels (OR 0.87 per 10 pmol/L increase) merits careful interpretation. This finding may reflect the phenomenon of PTH resistance that develops in patients with severely elevated PTH levels, where target tissues become less responsive to PTH stimulation (66). In such cases, the skeleton may be less capable of rapid mineral uptake following PTH withdrawal, paradoxically providing some protection against severe hypocalcemia.

Clinical implementation and healthcare impact

Risk-stratified management framework

Our nomogram enables implementation of evidence-based, risk-stratified perioperative management that has the potential to significantly improve both patient outcomes and healthcare efficiency. The substantial gradient in SPPH rates across risk groups (8.0% to 72.5%) provides clear justification for differential management approaches.

For low-risk patients (15.9% of the population with 8.0% SPPH rate), standard monitoring protocols and routine supplementation may be sufficient, potentially enabling earlier discharge and reduced healthcare utilization. Intermediate-risk patients (58.6% of the population with 58.7% SPPH rate) warrant enhanced monitoring and proactive supplementation strategies. High-risk patients (25.5% of the population with 72.5% SPPH rate) require intensive perioperative management, including consideration for prophylactic high-dose supplementation, continuous monitoring, and potential intensive care unit-level observation.

Economic implications

The economic impact of implementing risk-stratified care based on our nomogram could be substantial. SPPH increases healthcare costs by $6,000–15,000 per case through prolonged hospitalization, intensive monitoring, and potential complications (67). By enabling targeted intensive interventions for high-risk patients while avoiding unnecessary interventions for low-risk patients, our nomogram could significantly improve cost-effectiveness of parathyroidectomy programs.

Quality improvement applications

Beyond individual patient care, our nomogram provides a framework for quality improvement initiatives and outcome benchmarking. Healthcare systems could use risk-adjusted outcomes to evaluate program performance, identify opportunities for improvement, and guide resource allocation decisions.

Study limitations

Protocol-specific validation

The most critical limitation of our study is that model development and validation occurred within a specific treatment protocol context. Our intensive calcium supplementation regimen may differ substantially from protocols used at other institutions, potentially limiting model generalizability. The baseline risk of severe hypocalcemia, the effectiveness of preventive interventions, and the predictive performance of our model may all vary in different treatment settings.

This limitation is not merely technical but fundamental to model interpretation and implementation. Clinicians considering adoption of our nomogram must carefully evaluate whether their institutional protocols are sufficiently similar to ours to justify model application. Significant protocol differences may require local validation studies or model recalibration before implementation.

Two-center design and population characteristics

While our two-institution design provides some diversity, the study population may not represent the broader demographic of patients undergoing parathyroidectomy for sHPT. Factors such as racial/ethnic composition, socioeconomic status, comorbidity patterns, and healthcare system characteristics may influence both baseline risk and model performance.

Mechanistic agnosticism

Our decision to focus on severe hypocalcemia as a composite outcome, while clinically practical, does not distinguish between different underlying mechanisms. Some clinicians may prefer models that attempt mechanistic differentiation, particularly for research applications or specialized clinical scenarios. However, we believe our approach better reflects clinical reality and decision-making needs.

Sample size and external validation

While our sample size exceeds statistical requirements for model development and achieved adequate EPV ratios, external validation in larger, more diverse populations remains essential. Multi-center validation studies incorporating different treatment protocols, patient populations, and healthcare systems are needed to establish broader applicability.

Missing data considerations

Our primary analysis included 157 of 227 patients (69.2%) with complete predictor data. The main source of missingness was preoperative ALP at 1 month (56/227, 24.7% missing). A sensitivity analysis using multiple imputation with 20 datasets confirmed comparable model coefficients and performance metrics, suggesting that the complete-case results are robust. Additionally, dialysis vintage—identified a priori as a candidate variable based on prior literature—was not consistently documented in the institutional databases at either centre and was entirely missing (0/234 valid values). Similarly, estimated glomerular filtration rate (eGFR) for non-dialysis-dependent patients was not available. These represent important variables for a kidney disease population and should be prospectively collected in future external validation studies. The substantial proportion of patients without recorded dialysis modality (82/227, 36.1%) is a further limitation, though subgroup analysis demonstrated consistent model performance across all modality groups.

Future research directions and clinical translation

External validation priorities

The highest priority for future research is external validation of our nomogram in independent cohorts using different treatment protocols. Such studies should assess model discrimination, calibration, and clinical utility across diverse clinical settings, with particular attention to protocol-specific factors that may influence performance.

Dynamic prediction models

Future research could explore dynamic prediction models incorporating real-time postoperative data (early calcium levels, PTH suppression, clinical symptoms) to refine risk estimates and guide adaptive management strategies. Such models could provide updated risk assessments as new information becomes available during the postoperative period.

Interventional studies

Once externally validated, our nomogram could serve as a foundation for randomized controlled trials evaluating targeted interventions for high-risk patients. Such studies could test whether intensive prophylactic strategies guided by nomogram predictions improve outcomes compared to standard care.

Implementation science

Research into optimal strategies for nomogram implementation, including decision support tools, clinician training programs, and quality improvement frameworks, will be essential for successful clinical translation.

Conclusions

We developed and internally validated a nomogram for predicting SPPH that addresses important gaps in current clinical practice. The identification of ALP as the predominant predictor provides novel pathophysiological insights and challenges traditional approaches focused primarily on PTH levels.

Our risk stratification system demonstrates substantial clinical utility, with a 9.1-fold difference in severe hypocalcemia rates between low- and high-risk groups (8.0% vs. 72.5%). This gradient supports implementation of differentiated management strategies that could improve both patient outcomes and healthcare efficiency.

However, critical limitations must be acknowledged, particularly the protocol-specific nature of our validation and the need for external validation before widespread implementation. The single-center design, while ensuring internal consistency, limits generalizability to other institutions and patient populations.

Despite these limitations, our nomogram represents a significant advancement in evidence-based perioperative management for patients with sHPT. Once externally validated, this tool has the potential to improve outcomes and optimize resource utilization for the thousands of patients who undergo parathyroidectomy annually worldwide. The mechanistically agnostic approach we employed may also provide a framework for future research in post-parathyroidectomy complications, moving beyond traditional diagnostic categories toward clinically meaningful, patient-centered outcomes.

Acknowledgments

None.

Footnote

Reporting Checklist: The authors have completed the TRIPOD reporting checklist. Available at https://gs.amegroups.com/article/view/10.21037/gs-2026-0243/rc

Data Sharing Statement: Available at https://gs.amegroups.com/article/view/10.21037/gs-2026-0243/dss

Peer Review File: Available at https://gs.amegroups.com/article/view/10.21037/gs-2026-0243/prf

Funding: None.

Conflicts of Interest: All authors have completed the ICMJE uniform disclosure form (available at https://gs.amegroups.com/article/view/10.21037/gs-2026-0243/coif). The authors have no conflicts of interest to declare.

Ethical Statement: The authors are accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved. This study was conducted in accordance with the Declaration of Helsinki and its subsequent amendments. Ethics approval was exempt from the Institutional Review Board of University of Manitoba as the data used was aggregated and anonymized (No. HS 22334 H/B 2018-436). Given the retrospective nature of this study, the requirement for written informed consent was waived.

Open Access Statement: This is an Open Access article distributed in accordance with the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International License (CC BY-NC-ND 4.0), which permits the non-commercial replication and distribution of the article with the strict proviso that no changes or edits are made and the original work is properly cited (including links to both the formal publication through the relevant DOI and the license). See: https://creativecommons.org/licenses/by-nc-nd/4.0/.

References

1. Ketteler M, Block GA, Evenepoel P, et al. Executive summary of the 2017 KDIGO Chronic Kidney Disease-Mineral and Bone Disorder (CKD-MBD) Guideline Update: what's changed and why it matters. Kidney Int 2017;92:26-36. [Crossref] [PubMed]
2. Cozzolino M, Galassi A, Conte F, et al. Treatment of secondary hyperparathyroidism: the clinical utility of etelcalcetide. Ther Clin Risk Manag 2017;13:679-89. [Crossref] [PubMed]
3. Tan ZK, Looi WL, Chen F, et al. Determinants of Severe Hypocalcemia After Parathyroidectomy in Patients with End-Stage Kidney Disease and Renal Hyperparathyroidism: A Retrospective Cohort Study. J Clin Med 2025;14:379. [Crossref] [PubMed]
4. Rodríguez-Ortiz ME, Rodríguez M. Recent advances in understanding and managing secondary hyperparathyroidism in chronic kidney disease. F1000Res 2020;9:F1000. [Crossref] [PubMed]
5. Yamamoto S, Jørgensen HS, Zhao J, et al. Alkaline Phosphatase and Parathyroid Hormone Levels: International Variation and Associations With Clinical Outcomes in the DOPPS. Kidney Int Rep 2024;9:863-76. [Crossref] [PubMed]
6. Moe S, Drüeke T, Cunningham J, et al. Definition, evaluation, and classification of renal osteodystrophy: a position statement from Kidney Disease: Improving Global Outcomes (KDIGO). Kidney Int 2006;69:1945-53. [Crossref] [PubMed]
7. Lau WL, Obi Y, Kalantar-Zadeh K. Parathyroidectomy in the Management of Secondary Hyperparathyroidism. Clin J Am Soc Nephrol 2018;13:952-61. [Crossref] [PubMed]
8. Cheng J, Lv Y, Zhang L, et al. Construction and validation of a predictive model for hypocalcemia after parathyroidectomy in patients with secondary hyperparathyroidism. Front Endocrinol (Lausanne) 2022;13:1040264. [Crossref] [PubMed]
9. Phimphilai M, Inya S, Manosroi W. A predictive risk score to diagnose hypocalcemia after parathyroidectomy in patients with secondary hyperparathyroidism: a 22-year retrospective cohort study. Sci Rep 2022;12:9548. [Crossref] [PubMed]
10. Brasier AR, Nussbaum SR. Hungry bone syndrome: clinical and biochemical predictors of its occurrence after parathyroid surgery. Am J Med 1988;84:654-60. [Crossref] [PubMed]
11. Jain N, Reilly RF. Hungry bone syndrome. Curr Opin Nephrol Hypertens 2017;26:250-5. [Crossref] [PubMed]
12. Cartwright C, Anastasopoulou C. StatPearls 2025 [cited 2025 Jul 16]. Hungry Bone Syndrome. Available online: https://www.ncbi.nlm.nih.gov/books/NBK549880/#:~:text=Multiple%20risk%20factors%20have%20been,an%20increased%20risk%20of%20HBS.&text=Common%20risk%20factors%20include:,Higher%20blood%20urea%20nitrogen%20levels
13. Witteveen JE, van Thiel S, Romijn JA, et al. Hungry bone syndrome: still a challenge in the post-operative management of primary hyperparathyroidism: a systematic review of the literature. Eur J Endocrinol 2013;168:R45-53. [Crossref] [PubMed]
14. Anwar F, Abraham J, Nakshabandi A, et al. Treatment of hypocalcemia in hungry bone syndrome: A case report. Int J Surg Case Rep 2018;51:335-9. [Crossref] [PubMed]
15. Goldfarb M, Gondek SS, Lim SM, et al. Postoperative hungry bone syndrome in patients with secondary hyperparathyroidism of renal origin. World J Surg 2012;36:1314-9. [Crossref] [PubMed]
16. Kritmetapak K, Kongpetch S, Chotmongkol W, et al. Incidence of and risk factors for post-parathyroidectomy hungry bone syndrome in patients with secondary hyperparathyroidism. Ren Fail 2020;42:1118-26. [Crossref] [PubMed]
17. Wang L, Zhang X, Hu F, et al. Impact of enhanced recovery after surgery program for hungry bone syndrome in patients on maintenance hemodialysis undergoing parathyroidectomy for secondary hyperparathyroidism. Ann Surg Treat Res 2022;103:264-70. [Crossref] [PubMed]
18. Gülen M, Emral AC, Sariyildiz GT. Importance of Alkaline Phosphatase as a Predictor of Transient Hypoparathyroidism After Parathyroidectomy. Bratisl Med J 2025;126:1923-9. [Crossref]
19. Loke SC, Tan AW, Dalan R, et al. Pre-operative serum alkaline phosphatase as a predictor for hypocalcemia post-parathyroid adenectomy. Int J Med Sci 2012;9:611-6. [Crossref] [PubMed]
20. Mu Y, Zhao Y, Zhao J, et al. Factors influencing serum calcium levels and the incidence of hypocalcemia after parathyroidectomy in primary hyperparathyroidism patients. Front Endocrinol (Lausanne) 2023;14:1276992. [Crossref] [PubMed]
21. Sun X, Zhang X, Lu Y, et al. Risk factors for severe hypocalcemia after parathyroidectomy in dialysis patients with secondary hyperparathyroidism. Sci Rep 2018;8:7743. [Crossref] [PubMed]
22. Wen P, Xu L, Zhao S, et al. Risk Factors for Severe Hypocalcemia in Patients with Secondary Hyperparathyroidism after Total Parathyroidectomy. Int J Endocrinol 2021;2021:6613659. [Crossref] [PubMed]
23. Hamouda M, Dhia NB, Aloui S, et al. Predictors of early post-operative hypocalcemia after parathyroidectomy for secondary hyperparathyroidism. Saudi J Kidney Dis Transpl 2013;24:1165-9. [Crossref] [PubMed]
24. Wang M, Chen B, Zou X, et al. A Nomogram to Predict Hungry Bone Syndrome After Parathyroidectomy in Patients With Secondary Hyperparathyroidism. J Surg Res 2020;255:33-41. [Crossref] [PubMed]
25. Gao D, Liu Y, Cui W, et al. A nomogram prediction model for hungry bone syndrome in dialysis patients with secondary hyperparathyroidism after total parathyroidectomy. Eur J Med Res 2024;29:208. [Crossref] [PubMed]
26. Zhou L, Tu Y, Qin S, et al. Development and validation of a nomogram for predicting postoperative hypocalcemia in patients undergoing surgery for differentiated thyroid cancer. Front Endocrinol (Lausanne) 2025;16:1628453. [Crossref] [PubMed]
27. Muller O, Bauvin P, Bacoeur O, et al. Machine Learning-Based Algorithm for the Early Prediction of Postoperative Hypocalcemia Risk After Thyroidectomy. Ann Surg 2024;280:835-41. [Crossref] [PubMed]
28. Peacock M, Bilezikian JP, Klassen PS, et al. Cinacalcet hydrochloride maintains long-term normocalcemia in patients with primary hyperparathyroidism. J Clin Endocrinol Metab 2005;90:135-41. [Crossref] [PubMed]
29. Block GA, Klassen PS, Lazarus JM, et al. Mineral metabolism, mortality, and morbidity in maintenance hemodialysis. J Am Soc Nephrol 2004;15:2208-18. [Crossref] [PubMed]
30. Rude RK, Singer FR, Gruber HE. Skeletal and hormonal effects of magnesium deficiency. J Am Coll Nutr 2009;28:131-41. [Crossref] [PubMed]
31. Gong W, Lin Y, Xie Y, et al. Predictors of early postoperative hypocalcemia in patients with secondary hyperparathyroidism undergoing total parathyroidectomy. J Int Med Res 2021;49:3000605211015018. [Crossref] [PubMed]
32. Ge P, Liu S, Sheng X, et al. Serum parathyroid hormone and alkaline phosphatase as predictors of calcium requirements after total parathyroidectomy for hypocalcemia in secondary hyperparathyroidism. Head Neck 2018;40:324-9. [Crossref] [PubMed]
33. Riley RD, Ensor J, Snell KIE, et al. Calculating the sample size required for developing a clinical prediction model. BMJ 2020;368:m441. [Crossref] [PubMed]
34. Quarles LD, Kendrick J. UpToDate. 2024 [cited 2025 Oct 25]. Hungry bone syndrome following parathyroidectomy in patients with end-stage kidney disease. Available online: https://www.uptodate.com/contents/hungry-bone-syndrome-following-parathyroidectomy-in-patients-with-end-stage-kidney-disease
35. Kislyy P, Parshina E, Zulkarnaev A, et al. MO812: Risk Factors of Long-Term Hypocalcemia After Parathyroidectomy in Dialysis-Dependent Patients. Nephrology Dialysis Transplantation 2022;37:gfac082. [Crossref]
36. Moons KG, Altman DG, Reitsma JB, et al. Transparent Reporting of a multivariable prediction model for Individual Prognosis or Diagnosis (TRIPOD): explanation and elaboration. Ann Intern Med 2015;162:W1-73. [Crossref] [PubMed]
37. Steyerberg EW, Moons KG, van der Windt DA, et al. Prognosis Research Strategy (PROGRESS) 3: prognostic model research. PLoS Med 2013;10:e1001381. [Crossref] [PubMed]
38. Yang M, Zhang L, Huang L, et al. Risk Factors for Elevated Preoperative Alkaline Phosphatase in Patients with Refractory Secondary Hyperparathyroidism. Am Surg 2017;83:1368-72. [Crossref] [PubMed]
39. Harrell FE. Regression Modeling Strategies: With Applications to Linear Models, Logistic and Ordinal Regression, and Survival Analysis Cham: Springer International Publishing; 2015 [cited 2025 Jul 14]. (Springer Series in Statistics). Available online: https://link.springer.com/10.1007/978-3-319-19425-7
40. Pavlou M, Ambler G, Qu C, et al. An evaluation of sample size requirements for developing risk prediction models with binary outcomes. BMC Med Res Methodol 2024;24:146. [Crossref] [PubMed]
41. Martin GP, Riley RD, Ensor J, et al. Statistical primer: sample size considerations for developing and validating clinical prediction models. Eur J Cardiothorac Surg 2025;67:ezaf142. [Crossref] [PubMed]
42. Riley RD, Snell KI, Ensor J, et al. Minimum sample size for developing a multivariable prediction model: PART II - binary and time-to-event outcomes. Stat Med 2019;38:1276-96. [Crossref] [PubMed]
43. Bujang MA, Sa'at N, Sidik TMITAB, et al. Sample Size Guidelines for Logistic Regression from Observational Studies with Large Population: Emphasis on the Accuracy Between Statistics and Parameters Based on Real Life Clinical Data. Malays J Med Sci 2018;25:122-30. [Crossref] [PubMed]
44. Guo Y, Li L, Zheng K, et al. Development and validation of a survival prediction model for patients with advanced non-small cell lung cancer based on LASSO regression. Front Immunol 2024;15:1431150. [Crossref] [PubMed]
45. Hong C, Xiong Y, Xia J, et al. LASSO-Based Identification of Risk Factors and Development of a Prediction Model for Sepsis Patients. Ther Clin Risk Manag 2024;20:47-58. [Crossref] [PubMed]
46. Luo W, Xiong L, Wang J, et al. Development and performance evaluation of a clinical prediction model for sepsis risk in burn patients. Medicine (Baltimore) 2024;103:e40709. [Crossref] [PubMed]
47. Liu Y, Xu L, Fang Y, et al. Predictive Modeling of Clinical Efficacy for (125)I Brachytherapy in Head and Neck Tumors Using Lasso-Logistic Regression. Cancer Manag Res 2025;17:1911-23. [Crossref] [PubMed]
48. Ranstam J, Cook JA. LASSO regression. British Journal of Surgery 2018;105:1348. [Crossref]
49. Musoro JZ, Zwinderman AH, Puhan MA, et al. Validation of prediction models based on lasso regression with multiply imputed data. BMC Med Res Methodol 2014;14:116. [Crossref] [PubMed]
50. Steyerberg EW, Vergouwe Y. Towards better clinical prediction models: seven steps for development and an ABCD for validation. Eur Heart J 2014;35:1925-31. [Crossref] [PubMed]
51. Austin PC, Tu JV. Bootstrap Methods for Developing Predictive Models. The American Statistician 2004;58:131-7. [Crossref]
52. Steyerberg EW, Harrell FE Jr, Borsboom GJ, et al. Internal validation of predictive models: efficiency of some procedures for logistic regression analysis. J Clin Epidemiol 2001;54:774-81. [Crossref] [PubMed]
53. Steyerberg EW, Bleeker SE, Moll HA, et al. Internal and external validation of predictive models: a simulation study of bias and precision in small samples. J Clin Epidemiol 2003;56:441-7. [Crossref] [PubMed]
54. Collins GS, Reitsma JB, Altman DG, et al. Transparent reporting of a multivariable prediction model for individual prognosis or diagnosis (TRIPOD): the TRIPOD statement. BMJ 2015;350:g7594. [Crossref] [PubMed]
55. Hosmer DW, Lemeshow S, Sturdivant RX. Applied Logistic Regression. 3rd ed. John Wiley & Sons, Inc., Hoboken, New Jersey; 2013.
56. Vickers AJ, Elkin EB. Decision curve analysis: a novel method for evaluating prediction models. Med Decis Making 2006;26:565-74. [Crossref] [PubMed]
57. Vickers AJ, Van Calster B, Steyerberg EW. Net benefit approaches to the evaluation of prediction models, molecular markers, and diagnostic tests. BMJ 2016;352:i6. [Crossref] [PubMed]
58. Longhao S, Xianghui H, Tong L. Preoperative serum alkaline phosphatase: a predictive factor for early hypocalcaemia following parathyroidectomy of primary hyperparathyroidism. Chinese Medical Journal 2014;127:3259-64. [Crossref] [PubMed]
59. He C, Zhang Y, Li L, et al. Risk Factor Analysis and Prediction of Severe Hypocalcemia after Total Parathyroidectomy without Auto-Transplantation in Patients with Secondary Hyperparathyroidism. International Journal of Endocrinology 2023. vailable online: 10.1155/2023/190169710.1155/2023/1901697
60. Garnero P, Delmas PD. Biochemical markers of bone turnover. Endocrinology and Metabolism Clinics of North America 1998;27:303-23. [Crossref] [PubMed]
61. Seibel MJ. Biochemical markers of bone turnover: part I: biochemistry and variability. Clin Biochem Rev 2005;26:97-122. [PubMed]
62. Silverberg SJ, Shane E, Jacobs TP, et al. A 10-year prospective study of primary hyperparathyroidism with or without parathyroid surgery. N Engl J Med 1999;341:1249-55. [Crossref] [PubMed]
63. Rubin MR, Bilezikian JP, McMahon DJ, et al. The natural history of primary hyperparathyroidism with or without parathyroid surgery after 15 years. J Clin Endocrinol Metab 2008;93:3462-70. [Crossref] [PubMed]
64. Riggs BL, Khosla S, Melton LJ 3rd. Sex steroids and the construction and conservation of the adult skeleton. Endocr Rev 2002;23:279-302. [Crossref] [PubMed]
65. Khosla S, Riggs BL, Atkinson EJ, et al. Effects of sex and age on bone microstructure at the ultradistal radius: a population-based noninvasive in vivo assessment. J Bone Miner Res 2006;21:124-31. [Crossref] [PubMed]
66. Dusso AS, Brown AJ, Slatopolsky E, Vitamin D. American Journal of Physiology 2005;289:F8-28. [PubMed]
67. Schneider R, Slater EP, Karakas E, et al. Initial parathyroid surgery in 606 patients with renal hyperparathyroidism. World J Surg 2012;36:318-26. [Crossref] [PubMed]