Phosphate-to-albumin ratio and 30-day mortality in critically ill acute pancreatitis: multicenter development and external validation of an interpretable machine learning model

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Abstract
Background: Despite advances in intensive care, short-term mortality in acute pancreatitis (AP) remains substantial. The phosphate-to-albumin ratio (PAR) reflects metabolic and inflammatory stress and may enable simple early risk stratification, but its prognostic value in critically ill AP is unknown. We evaluated PAR for predicting 30-day mortality and developed a PAR-integrated machine learning (ML) model. Methods: Adult intensive care unit (ICU) patients with AP were identified from multicenter databases [Medical Information Mart for Intensive Care (MIMIC)-IV, MIMIC-III, eICU)]. The primary endpoint was 30-day all-cause mortality. PAR was evaluated using Kaplan–Meier curves, restricted cubic splines, and multivariable Cox regression, and its discrimination was compared with phosphate, albumin, SOFA, and APACHE II by receiver operating characteristic analysis. Mediation analysis examined pathways through lactate and creatinine. For ML, features selected by Boruta and recursive feature elimination were used, and the best model was selected with class imbalance corrected by the adaptive synthetic minority oversampling technique. Model utility and interpretability were assessed using decision curve analysis and SHAP, and the finalized model was deployed as a web calculator. Robustness was tested with multiple imputation, E-values, propensity score methods, and inverse probability of treatment weighting. Results: High PAR independently predicted higher 30-day mortality (adjusted HR 1.94; 95% CI 1.11–3.38). PAR showed good discrimination (MIMIC-III area under the receiver operating characteristic curve (AUC) 0.78; eICU AUC 0.67), comparable to or superior to SOFA and APACHE II. Mediation analysis indicated partial effects through tissue hypoxia and renal dysfunction. Light Gradient Boosting Machine (LightGBM) achieved the best performance (MIMIC-III AUC 0.844; eICU AUC 0.841) with good calibration and net benefit, and SHAP consistently highlighted PAR among the most important predictors. Associations were stable across subgroups and sensitivity analyses. Conclusion: PAR is an accessible biomarker that independently predicts 30-day mortality in ICU patients with AP. A PAR-integrated LightGBM model provides accurate, interpretable, and clinically applicable risk stratification, with deployment via a user-friendly web tool. Graphical abstract available at: http://links.lww.com/JS9/H526

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