Association between the serum glucose-to-potassium ratio and short-term mortality in critically ill patients with traumatic brain injury: a retrospective cohort study with exploratory machine-learning analysis

The serum glucose-to-potassium ratio (GPR) has emerged as a potentially informative biomarker in acute cardiovascular and cerebrovascular conditions, but its prognostic value in traumatic brain injury (TBI) remains insufficiently defined. We investigated the association between admission GPR and short-term mortality in critically ill patients with TBI and explored its incremental value in risk prediction. We conducted a retrospective cohort study using the MIMIC-IV database. Adult patients with TBI admitted to the ICU were included after predefined eligibility screening. Admission GPR was calculated from the first available serum glucose and potassium measurements obtained within 24 h of ICU admission. The primary outcome was 28-day all-cause mortality, and the secondary outcome was in-hospital mortality. Associations were assessed using Kaplan–Meier analysis, Cox proportional hazards models, and restricted cubic spline analysis. In exploratory predictive analyses, Boruta feature selection and machine-learning models were applied using a 7:3 training-validation split to assess the incremental prognostic contribution of GPR relative to glucose alone, potassium alone, and a clinical baseline model. A total of 2631 critically ill patients with TBI were included. Admission GPR showed a nonlinear association with both 28-day all-cause mortality and in-hospital mortality. Compared with the lowest quartile, patients in the highest GPR quartile had a significantly higher risk of 28-day mortality after multivariable adjustment (adjusted HR 2.232, 95% CI 1.616–3.083) and a similarly elevated risk of in-hospital mortality (adjusted HR 2.245, 95% CI 1.620–3.112). The spline analysis suggested a data-derived risk transition zone around GPR ≈ 2.96. In direct comparison, GPR showed discrimination comparable to glucose and superior to potassium. When added to a clinical baseline model, GPR yielded a statistically significant but modest increase in discrimination. In exploratory machine-learning analyses, the best-performing model was random forest for survival (AUC 0.733). Higher admission GPR was independently associated with short-term mortality in critically ill patients with TBI. GPR may serve as a simple and readily available adjunctive prognostic marker. Exploratory machine-learning analyses suggested potential incremental predictive value, although external validation and further TBI-specific modeling are required before clinical implementation.