This retrospective cohort study is based on health-related data obtained from the MIMIC-IV database version 3.0. The MIMIC-IV database contains comprehensive and extensive medical records of patients admitted to the intensive care unit (ICU) at Beth Israel Deaconess Medical Center (BIDMC, Boston, MA, United States) (10). The author, Yuexin Lu, completed the Collaborative Institutional Training Initiative (CITI) program (record ID: 12901560), which granted access to and permission for data extraction from the MIMIC-IV database. Given the deidentified nature of the data, the Institutional Review Board of Beth Israel Deaconess Medical Center waived the requirement for informed consent.

This retrospective study included patients diagnosed with ICH and SAH based on the International Classification of Diseases, 9th and 10th revisions. The exclusion criteria were as follows: (1) patients with multiple ICU admissions due to HS, with data extracted only from their first admission; (2) patients whose key data such as blood glucose, triglycerides, and body mass index were missing; (3) patients with an ICU stay of less than 24 h; and (4) patients under the age of 18 years at the time of first admission. Ultimately, 413 HS patients were included in this study. The inclusion flowchart is shown in Figure 1.

Data were extracted via PostgreSQL 16.4 and Navicat Premium version 17 from the database using Structured Query Language (SQL). Comprehensive data regarding each patient were collected, such as demographic variables: age, gender, race, height, and weight; clinical severity scores at admission: the Glasgow Coma Scale, Sequential Organ Failure Assessment (SOFA) score, and Acute Physiology Score III (APSIII); comorbidities: hypertension, diabetes, chronic obstructive pulmonary disease (COPD), arrhythmia, coronary artery disease (CAD), sepsis, liver disease, hyperlipemia, ventilator-associated pneumonia, Charlson comorbidity index; laboratory markers: triglyceride, glucose, red blood cells, white blood cells, platelets, hemoglobin, creatinine, chloride, albumin, blood urea nitrogen, sodium, potassium, lactate, bicarbonate, prothrombin time and international normalized ratio; treatment methods: includes vasopressors, anticoagulants, antiplatelet drugs, lipid-lowering drugs, and oxygen delivery; clinical outcomes: Length of stay (LOS) in ICU, LOS in hospital; ICU, in-hospital, 30-day; 90-day, 1-year, ICU, in-hospital mortality. All laboratory markers and severity scores were extracted from the first recorded data after ICU admission.

The primary outcome of this study was 30-day all-cause mortality. While the secondary outcomes included 90-day mortality, 1-year mortality, ICU mortality, and in-hospital mortality.

To minimize potential bias caused by missing data, variables with more than 20% missing values were excluded from the study. The results of the data integrity checks are shown in the Supplementary Table 1. Multiple imputation was performed on variables with less than 20% missing values using the “mice” package in R software.

The TyG was computed as follows: Ln [glucose (mg/dL) × triglycerides (mg/dL)/2] while BMI was calculated by dividing the body weight (kg) by the square of height (m) (kg/m²). The TyG-BMI index was calculated as TyG × BMI.

In this study, we grouped the variable TyG-BMI to explore its relationship with survival time and mortality risk. To determine the optimal cutoff point, we utilized the surv_cutpoint function from the R package “survival,” which identifies the best cutoff by maximizing the differences in survival data. After calculating the first optimal cutoff point using this method, to ensure a reasonable sample size for the intermediate group and statistically significant differences between groups, we set the second cutoff point to 1.35 times the first cutoff point. After obtaining the two cutoff points, we manually divided the data into three groups.

For continuous variables with a normal distribution, Student’s t-test and one-way ANOVA are used, and the results are presented as mean ± standard deviation (SD). For skewed or non-normally distributed continuous variables, the Kruskal-Wallis rank-sum test is used for comparison, and the results are presented as median with interquartile range (IQRs). Fisher’s exact test or chi-square test is used for analyzing categorical variables, and the results are reported as numbers and percentages. We conducted a sensitivity analysis comparing the inclusion cohort with the exclusion cohort, which was defined by missing triglyceride, glucose, and BMI data. The baseline characteristics and crude outcomes between the inclusion and exclusion cohorts are presented in Supplementary Table 2. Kaplan–Meier curves were used to visualize the incidence of endpoints in survival analysis. Univariate and multivariate cox proportional hazard models were employed to determine the impact of TyG-BMI levels on the mortality in HS patients. The multivariate models included variables related to clinical outcomes and prognosis: Model 1: unadjusted; Model 2: adjusted for age, gender, and ethnicity; Model 3: based on the results of the univariate Cox regression analysis, adjusted for age, gender, SOFA score, hypertension, arrhythmias, liver failure, urea, white blood cells, hemoglobin, chloride, vasopressors, oxygen delivery, antiplatelet, anticoagulants, and lipid-lowering drugs. The results are reported as adjusted hazard ratios (aHRs) with 95% confidence intervals. Before including covariates in the multivariate model, we assessed multicollinearity using the variance inflation factor and reported the diagnostic results. Subgroup analyses were performed to determine the robustness of the result, with the results visually described through a forest plot. Restricted cubic spline (RCS) curve analysis was performed to investigate the dose-effect relationship between TyG-BMI and mortality in HS patients. The receiver operating characteristic curve was used to evaluate the predictive efficacy of TyG-BMI.

Statistical analyses were performed using STATA 14.0, R software (version 4.4.2), and SPSS 25.0 (IBM SPSS Statistics, Armonk, NY, United States). A two-tailed p-value < 0.05 was considered statistically significant.

As shown in Table 1, this study included 413 critically ill HS patients, with a median age of 66.77 (21.21), and 58.8% were male. Participants were divided into low (n = 80), intermediate (n = 186), and high (n = 147) TyG-BMI groups. There were significant differences between the three groups in terms of age, SOFA score, diabetes, sepsis, ventilator-associated pneumonia, white blood cells, creatinine, urea, international normalized ratio, oxygen delivery, vasopressor use, and anticoagulant medication. The high TyG-BMI group had a significantly lower median age (p = 0.001) and more severe condition which has indicated by SOFA scores (p = 0.002). The prevalence of comorbidities, including diabetes (p < 0.05), sepsis (p = 0.009), and ventilator-associated pneumonia (p = 0.001), was higher in the high TyG-BMI group. In laboratory indicators, the high TyG-BMI group had higher levels of white blood cells (p = 0.019), creatinine (p < 0.001), urea (p = 0.036), and international normalized ratio (p = 0.002). The low TyG-BMI group had a lower oxygen delivery rate (p = 0.025) and anticoagulant usage rate (p = 0.002). The intermediate TyG-BMI group had a lower vasopressor usage rate (p = 0.014). Regarding clinical outcomes, the high TyG-BMI group had a longer ICU stay (p = 0.001) and longer hospital stay (p = 0.008), while the intermediate TyG-BMI group had lower 30-day mortality (p = 0.025) and ICU mortality (p = 0.025).

The results of the univariate Cox regression analysis and the Multicollinearity Diagnosis are shown in Supplementary Tables 3, 4. Multivariable Cox regression analysis was conducted to assess the effect of TyG-BMI on the mortality risk at different time points in patients with HS, which is shown in Table 2 and Supplementary Table 5. The results revealed that in both the unadjusted model (Model 1) and the model adjusted for age, gender, and race (Model 2), the low TyG-BMI group (Tertile 1) had a significantly higher risk of mortality at 30 days [Model 1: aHR = 1.863, 95% CI: 1.209–2.869, p = 0.005; Model 2: aHR = 1.842, 95% CI: 1.190–2.852, p = 0.006], 90 days, and 1 year compared to the intermediate TyG-BMI group (Tertile 2), whereas there was no significant difference between the high TyG-BMI group (Tertile 3) and the reference group (Tertile 2) (all p > 0.05). In Model 3, the low TyG-BMI group (Tertile 1) had a significantly higher risk of mortality at 30 days (HR = 1.836, 95% CI: 1.158–2.911, p = 0.010), 90 days (HR = 1.694, 95% CI: 1.104–2.601, p = 0.016), and 1 year (HR = 1.642, 95% CI: 1.107–2.437, p = 0.014) compared to the reference group. The high TyG-BMI group (Tertile 3) also had a significantly higher risk of mortality at 30 days (HR = 1.584, 95% CI: 1.024–2.453, p = 0.039), 90 days (HR = 1.571, 95% CI: 1.062–2.323, p = 0.024), and 1 year (HR = 1.484, 95% CI: 1.038–2.121, p = 0.030) compared to the reference group. These findings suggest that both the low and high TyG-BMI groups are associated with a higher mortality risk, while intermediate TyG-BMI levels have a protective effect for HS patients. Additionally, the trend test (P for trend) results across all models were not statistically significant (all p > 0.05), indicating that there may not be a linear dose–response relationship between TyG-BMI and mortality risk, but rather a U-shaped association.

The Kaplan–Meier curve was used to compare the mortality outcomes among different TyG-BMI subgroups in HS patients. The analysis revealed significant differences in survival curves between the groups at 30-day (Log-rank p = 0.017; Figure 2A) and 90-day (Log-rank p = 0.045; Figure 2B), and a marginally significant difference at 1-year (Log-rank p = 0.050; Figure 2C). Patients in the lowest TyG-BMI group had the lowest survival rate, while those in the intermediate TyG-BMI group had the highest survival rate. The difference among the three groups in terms of ICU and in-hospital mortality did not reach statistical significance, with log-rank p values of 0.42 and 0.22, respectively (Supplementary Figure 1).

Figure 3A shows the distribution of TyG-BMI. Across the 30-day (Figure 3B), 90-day (Figure 3C), or 1-year point (Figure 3D), all three RCS curves display a similarly U-shaped pattern. At lower TyG-BMI values, an increase in the index is associated with a reduction in mortality risk. However, once a certain threshold is reached, the mortality risk increases as TyG-BMI continues to rise beyond this threshold. The RCS curves for ICU and in-hospital mortality risk are shown in Supplementary Figure 2.

The predictive value of clinical TyG-BMI for mortality was assessed using receiver operating characteristic curves (Supplementary Figure 3). However, the area under the curve (AUC) values showed limited predictive ability (30-day mortality AUC: 0.529; 90-day mortality AUC: 0.513; 1-year mortality AUC: 0.523).

To further assess the relationship between TyG-BMI and mortality, we conducted subgroup analyses to evaluate the associations between age (<70 years and ≥70 years), race, hypertension, diabetes, CAD, ventilator-associated pneumonia, COPD, use of vasopressors, and anticoagulants with all-cause mortality at 30-day (Figure 4A), 90-day (Figure 4B), and 1-year (Figure 4C) in HS patients. The subgroup analysis showed that TyG-BMI was significantly associated with a lower risk of mortality at 30-day in HS patients without coronary artery disease (HR 0.77, 95% CI: 0.60–1.00, p = 0.047), and no other subgroup factors significantly influenced the relationship between TyG-BMI and all-cause mortality in HS patients. Interaction tests revealed a significant interaction between coronary artery disease and the 30-day, 90-day, and 1-year mortality risks in HS patients (all interaction p-values < 0.05). For ICU and in-hospital mortality (Supplementary Figure 4), no subgroup factors had a significant effect, and only the use of anticoagulants showed an interaction with in-hospital mortality (p for interaction = 0.007).