We conducted a multicenter, retrospective cohort study using NSICU, MIMIC-IV v3.1, and eICU-CRD v2.0. Adults (≥18 years) with a primary ICU diagnosis of ABI (ischemic stroke, hemorrhagic stroke, or TBI) were included; only the first ICU admission per hospitalization was analyzed. We excluded admissions with ICU length of stay < 24 h, missing in-hospital outcome, or fewer than two TyG measurements during the ICU stay (Figure 1). NSICU was used for model derivation with a 9:1 random split into training and internal test sets, and the pooled MIMIC-IV/eICU cohort was used exclusively for external validation. Use of de-identified data was approved for all sources; details are provided in the Ethics section. Reporting adhered to STROBE and TRIPOD recommendations for prognostic model development with external validation.

We extracted a harmonized set of ICU variables from NSICU, MIMIC-IV, and eICU to allow cross-cohort analyses (Supplementary Table 1). Baseline missingness is summarized in Supplementary Table 2, and imputation diagnostics are shown in Supplementary Figures 1–2. Variables included demographics and admission characteristics (age, sex, BMI, trauma status, ABI subtype); comorbidities [hypertension (HTN), diabetes mellitus (DM), chronic kidney disease (CKD), liver disease (LD), CCI]; acute severity scores (SOFA, APACHE III, GCS at ICU admission); physiological measurements around ICU admission [temperature, respiratory rate (RR), heart rate (HR), mean blood pressure (MBP)]; and initial ICU interventions [mechanical ventilation (MV), vasopressor use, mannitol or sedation, renal replacement therapy (RRT), and neurosurgical or endovascular procedures]. ICU laboratory data included complete blood count, coagulation tests, basic chemistries, glucose, and triglycerides. The TyG index was calculated as TyG = ln [triglycerides (mg/dL) × glucose (mg/dL)/2] after harmonizing triglyceride and glucose units to mg/dL.

Baseline characteristics were summarized as mean (SD) or median (IQR) for continuous variables and as n(%) for categorical variables. Groups defined by TyG trajectory were compared using ANOVA or Kruskal–Wallis tests for continuous variables and χ² or Fisher's exact tests for categorical variables, as appropriate. Missing baseline covariates were imputed by multiple imputation using chained equations (m = 10) under a missing-at-random assumption, and estimates were pooled using Rubin's rules.

Survival time was measured from ICU admission to in-hospital death, with patients censored at hospital discharge. Survival was described using Kaplan–Meier curves and compared with the log-rank test. Cox proportional hazards models were fitted with TyG trajectory and TBM (per 1-unit increase in the corresponding TBM) as the main exposures. The proportional hazards assumption was evaluated using Schoenfeld residuals; when a violation was detected, effects were re-estimated in a prespecified two-interval Cox model (0–7 days and >7 days), and hazard ratios (HRs) with 95% confidence intervals (CIs) were reported for each interval.

Covariates were selected a priori based on ABI literature and clinical relevance. Variables were retained if they were considered clinically essential or if they changed the exposure estimate by ≥10%. Associations were reported in three stages: Model 1 unadjusted; Model 2 adjusted for demographics and comorbidities; and Model 3 additionally adjusted for admission severity and initial ICU treatments. The same modeling strategy was applied to all prespecified TBM thresholds. Subgroup and interaction analyses were prespecified for age (< 65 vs. ≥65 years), trauma status (traumatic vs. non-traumatic ABI), HTN, craniotomy, and data source (NSICU vs. pooled MIMIC-IV/eICU). All analyses were performed in R (version 4.2.2) and the Free Statistics analysis platform (21). Two-sided P values < 0.05 were considered statistically significant.

We first defined a candidate predictor set consisting of demographics and admission characteristics, comorbidities, acute severity scores, key ICU interventions, routine laboratory variables, and the two prespecified metabolic exposures (TyG trajectory class and TBM). This full set was screened using 10 complementary feature-selection procedures [least absolute shrinkage and selection operator (LASSO), Boruta, recursive feature elimination (RFE), and seven filter/wrapper methods based on information gain, mutual information, permutation, or model performance]. Predictors that were selected by at least five of these procedures and were available in all three databases were retained as the final ICU-feasible feature set.

Using this fixed feature set, we benchmarked 14 supervised classifiers—logistic regression (Logistic), classification and regression tree (CART), k-nearest neighbors (k-NN), Naive Bayes classifier (Naive Bayes), support vector machine (SVM), multilayer perceptron neural network (Neural Network), gradient boosting machine (GBM), Adaptive Boosting (AdaBoost), Extreme Gradient Boosting (XGBoost), Light Gradient Boosting Machine (LightGBM), Categorical Boosting (CatBoost), random forest (Random Forest), Extremely Randomized Trees (ExtraTrees), and a Bayesian network (Bayes Net)—by stratified 10-fold cross-validation in the NSICU training set. Within each fold, imputation, scaling or encoding, model fitting, and hyperparameter tuning were performed inside the resampling loop to avoid information leakage. Tuned models were then evaluated on the held-out NSICU internal test set, and the classifier showing the most stable performance with the most favorable and stable overall profile in cross-validation and the internal test set. This locked model was subsequently applied, without refitting, to the pooled external validation cohort (MIMIC-IV plus eICU).

Model interpretability was assessed using SHAP to obtain global and patient-level feature attributions, and using model-agnostic permutation- and loss-based importance (DALEX/IML) to quantify the performance decrement after shuffling individual predictors.

LCGM applied to serial ICU TyG measurements in the integrated cohort identified three distinct and clinically interpretable classes (Figure 2). A three-class solution provided the best compromise between model fit (log-likelihood, AIC, BIC, SABIC), entropy, and acceptable class sizes. Models with ≥4 classes sometimes improved information criteria but generated very small or poorly separated groups and were therefore not retained. The three classes accounted for 61.8%, 23.5%, and 14.8% of patients, respectively, with reasonable posterior assignment (Supplementary Table 3). Running LCGM separately in NSICU, MIMIC-IV, and eICU yielded the same three-class structure, supporting cross-cohort stability (Supplementary Tables 4–6).

The classes were labeled according to temporal patterns: trajectory 1, low–slightly increasing (LSI); trajectory 2, moderate–increasing (MI); and trajectory 3, persistently high (PH). LSI showed low TyG with only a mild rise; MI started at an intermediate level and increased more clearly; PH began at the highest level and declined only slightly, approaching and partly overlapping with MI at later measurements, while both stayed clearly above LSI (Figure 2; Supplementary Figures 5–7), and a sensitivity analysis using 10 sequential measurements showed consistent class patterns with wider uncertainty at later measurements (Supplementary Figure 8). Because TyG came from three databases with different laboratory distributions, LCGM was performed on standardized values; class membership was then displayed on raw TyG and on its components (triglycerides and glucose), and the three patterns remained visually distinct.

Baseline characteristics showed a parallel clinical gradient across trajectories (Table 1; Supplementary Table 7). LSI had the most favorable profile, with lower BMI and the lowest prevalence of diabetes (8.6%) and hypertension (56.8%). PH concentrated adverse features, including higher BMI, more diabetes (39.1%) and hypertension (71.4%), and higher acute severity scores, while MI showed intermediate values. A similar gradient was seen in ICU interventions: MV was used in 41.5% of LSI and 66.1% of PH. These patterns indicate that TyG-based latent classes map onto clinically meaningful ICU phenotypes rather than modeling artifacts.

The proportional-hazards assumption was not met for TyG trajectories in the unstratified Cox model (Schoenfeld P < 0.001; Figure 3A), so we refitted a 7-day time-stratified Cox model, for which the test of proportional hazards was acceptable (P = 0.69; Figure 3B). This specification matched the landmark Kaplan–Meier curves: trajectories showed minimal separation during days 0–7 and then diverged in an ordered fashion after day 7, with PH having the lowest survival, LSI the highest, and MI intermediate; covariate-adjusted survival curves showed the same pattern (Figures 3C–D).

The candidate covariate set for multivariable adjustment was defined a priori and was supported by change-in-estimate screening with collinearity diagnostics (Supplementary Table 8). Time-stratified Cox estimates quantified this pattern (Table 2). During days 0–7, neither MI (adjusted HR 0.85, 95% CI 0.58–1.24) nor PH (adjusted HR 0.99, 95% CI 0.65–1.50) differed from LSI. After day 7, both higher trajectories were associated with increased in-hospital mortality: MI, HR 1.48 (95% CI 1.18–1.86); PH, HR 1.51 (95% CI 1.17–1.93). TBM showed a parallel dose–response: all prespecified TBM thresholds were positively associated with mortality, and effect sizes rose with higher thresholds. In the fully adjusted model, TBM8p7 (a prespecified threshold) gave a consistent estimate (HR 1.42, 95% CI 1.18–1.70). Sensitivity analyses were consistent, whether using 10-measurement trajectories or alternative stratification schemes, with risk concentrated after the early interval (Supplementary Tables 9–10).

Subgroup analyses showed that the excess risk of MI and PH over LSI was preserved across age, trauma status, hypertension, craniotomy, and data-source strata (all interaction P > 0.10; Figure 4). The association between TBM8p7 and mortality was likewise positive in all subgroups; the only nominal interaction (derivation vs external, P = 0.01) was small and did not alter the direction of effect (Supplementary Figure 9).

We applied 10 feature-selection procedures (LASSO, Boruta, recursive feature elimination, and seven additional filter/wrapper methods). Because individual procedures yielded partly discordant variable lists (Figure 5A), we defined a consensus as variables selected by at least 5 of the 10 methods (Figure 5B). This approach produced a compact, clinically interpretable panel consisting of sodium, age, temperature, WBC, INR, CCI, APACHE III, SOFA, GCS, mechanical ventilation, and vasopressor use. The two prespecified metabolic exposures, TyG trajectory and TBM8p7, were also retained. TBM8p7 met the consensus threshold, and TyG trajectory showed consistent co-selection with ICU severity variables in the heatmap (Figure 5C). All 13 variables were available in both the NSICU derivation cohort and the pooled external cohort (which showed slightly higher acuity; Supplementary Table 11), so this common feature set was used for subsequent benchmarking and validation. Adding TyG trajectory and TBM8p7 provided incremental predictive gain beyond baseline variables (Supplementary Figure 10).

Fourteen classifiers were benchmarked using stratified 10-fold cross-validation in the NSICU training set (Figure 6A, Supplementary Figure 11, Supplementary Table 12). Tree-based ensemble classifiers (ExtraTrees, random forest) achieved higher discrimination and more stable performance across metrics than linear, probabilistic, or margin-based learners. When the same classifiers were evaluated on the held-out NSICU internal test set and on the pooled external validation cohort, ExtraTrees showed the smallest loss of performance, suggesting superior portability across datasets (Figures 6B–C, Supplementary Tables 13–14).

ExtraTrees was therefore selected as the final model. After hyperparameter tuning (Supplementary Table 15), the AUROC was 0.79 in cross-validation, 0.83 in the internal test set, and 0.66 in external validation; the corresponding accuracies were 0.87, 0.87, and 0.74, and the specificities 0.94, 0.94, and 0.93, respectively (Table 3). Benchmarking curves across classifiers are shown in Figure 7, whereas detailed performance of the selected ExtraTrees model is shown in Figure 8 (cross-validation) and Supplementary Figures 12–13 (internal test and external validation). Sensitivity analyses using a Youden index–optimized operating threshold are reported in Supplementary Table 16.

SHAP was used to interpret the final ExtraTrees classifier, with global and patient-level explanations summarized in Figure 9. The global importance ranking highlighted MV and GCS as the dominant contributors, followed by TyG trajectory and TBM8p7 alongside SOFA and vasopressor use (Figures 9A–B). Case-level SHAP plots showed consistent directionality, with higher TyG trajectories and larger TBM8p7 values increasing predicted risk (Figures 9C–D). Complementary model-agnostic importance analyses (loss-based and permutation importance) supported a similar profile (Supplementary Figures 14, 15). The model was implemented as a web-based tool to return individualized risk estimates together with feature-level explanations (Supplementary Figure 16, https://njudrumtowernsicu.shinyapps.io/ABI_Prognosis_ModelTyG/).

As a retrospective analysis of fixed databases, our findings are observational and cannot establish causality; unmeasured heterogeneity in case mix, sampling, and treatment practices may persist despite multivariable adjustment. Because ABI in this study was operationalized as stroke and TBI, the generalizability of our findings to other ABI entities (e.g., post–cardiac arrest hypoxic–ischemic brain injury) remains uncertain. Several ABI-specific clinical details (e.g., neuroimaging and lesion characteristics) and longer-term neurological outcomes were unavailable, which restricted us to in-hospital mortality. Model discrimination also attenuated on external validation, and operating-threshold selection (including Youden optimization) may shift the sensitivity–specificity balance, indicating that the approach needs confirmation in independent, prospectively collected ABI cohorts. The web tool is intended for transparency and reproducibility, and the TyG phenotypes are hypothesis-generating rather than prescriptive. Future work should prospectively test whether patients who remain in higher TyG trajectories after day 7 benefit from targeted metabolic or infection-control strategies.