Parsimonious Logistic Regression Models for 90-Day Mortality Prediction in the Intensive Care Unit.

Introduction Early identification of critically ill patients is essential in intensive care units to guide triage and allocate resources. To support these decisions, prognostic scoring systems are commonly used to estimate illness severity and predict outcomes. The Acute Physiology and Chronic Health Evaluation II (APACHE II) and the Sequential Organ Failure Assessment (SOFA) are among the most widely used. While newer APACHE versions (III and IV) offer enhanced predictive power, they require extensive variables, are computationally expensive, and often rely on proprietary systems - making them less feasible for routine emergency care. In contrast, APACHE II and SOFA are simple, transparent and can be calculated using spreadsheets, clinical apps, or bedside tools. These advantages make them ideal for real-time use in busy and resource-limited settings. While each system provides valuable prognostic information individually, combining them may yield a more comprehensive and accurate prediction of mortality risk. The primary outcome in this study was 90-day mortality following ICU admission, to capture both early and delayed deaths. The objective was to develop univariate and multivariate logistic regression (LGR) models using SOFA and APACHE II scores. The study also aimed to identify optimal probability threshold values with the Youden J statistic to improve mortality risk classification in the first 24 hours of ICU admission. Method This was a retrospective single-centre study including ICU admissions at Walsall Manor Hospital between January 2024 and May 2025. SOFA and APACHE II scores calculated within 24 hours of admission were stratified into a development set (January-December 2024) and an independent test set (January-May 2025). Univariable and multivariable logistic regression models were developed using these scores as predictors. Two resampling approaches - bootstrapping and random 80/20 data splits - were applied to identify optimal probability thresholds using Youden's J statistic. Model performance was evaluated in the independent test cohort in terms of discrimination, calibration, and classification metrics at both the conventional (0.50) and optimized thresholds. Results In the independent test cohort (n = 281), all models showed low sensitivity at the conventional 0.50 probability cut-off (sensitivities: SOFA 0.29, APACHE II 0.27, Combined 0.35), misclassifying more than half of deaths as survivors. Optimized probability thresholds were substantially lower (probabilities: SOFA ~0.20, APACHE II ~0.27, Combined ~0.19) and improved sensitivity to 0.69, 0.78, and 0.88, respectively. Specificity and positive predictive values were modest (0.60 - 0.74 and 0.30 - 0.40, respectively), reflecting increased false positives. However, negative predictive values remained high (0.91 - 0.96), meaning patients classified as low risk almost always survived. Conclusion SOFA and APACHE II are well-established ICU severity scores, but reliance on the conventional 0.50 probability cut-off in logistic regression markedly reduces sensitivity and risks under-detecting patients at risk of mortality. In this study, optimising probability thresholds substantially improved sensitivity while maintaining consistently high negative predictive values. Positive predictive values remained modest, indicating that high-risk predictions should be interpreted as signals for closer clinical attention rather than definitive indicators of impending mortality.