A retrospective observational design was conducted to obtain data from the Medical Information Mart for Intensive Care IV (MIMIC-IV) database, a large freely available database that includes high-quality medical records of more than 90,000 intensive care unit (ICU) admissions at Beth Israel Deaconess Medical Center (BIDMC) between 2008 and 2022. One author (WSJ) who had passed the tests of the Collaborative Institutional Training Initiative (CITI) gained permission to access the dataset, and was responsible for data extraction (Certification No. 56051808). The review committee of the Massachusetts Institute of Technology (MIT) and BIDMC approved the database for medical health-related research without requiring informed consent.

All patients diagnosed with sepsis met the sepsis 3.0 diagnostic criteria (14), and the Kidney Disease: Improving Global Outcomes (KDIGO) guideline was used to confirm the presence of AKI (15). AKI was defined as follows: SCr increase ≥1.5-fold than baseline within 7 days; or SCr elevation ≥0.3 mg/dL within 48 hours; or urine output <0.5 mL/kg/h for ≥6 hours. Stage III AKI was defined as follows: SCr increase ≥>3-fold than baseline; or SCr ≥4.0 mg/dL; or receipt of RRT; or urine output <0.3 mL/kg/h for ≥24 hours or anuria for ≥12 hours. Patients with pre-existing mild AKI before ICU admission who progressed to Stage III AKI were excluded. The remaining exclusion criteria were as follows: 1) age less than 18 years; 2) only the first data were extracted if multiple ICU admissions for sepsis existed; 3) AKI was diagnosed before ICU admission; 4) missing data of surrogate indices of IR within 24 hours of ICU admission; and 5) missing AKI data within 48 hours. Finally, 997 patients with sepsis were enrolled and the cohort was divided into three groups based on the tertiles of the surrogate indices of IR (Figure 1).

The basic characteristics of the patients were extracted from the MIMIC-IV database by PostgreSQL software (version 13.7.2) and Navicat Premium software (version 16) running a Structured Query Language (SQL). The primary data included: demographics, laboratory test results, comorbidities, treatment, medication, and severity of illness scores. Comorbidities were identified by the 9th and 10th revision editions of the International Classification of Diseases. All laboratory test results were extracted within the initial 24 h of ICU admission, and the serum creatinine (SCr) level and urine output were continuously monitored throughout the hospital stay. For the variables included in this study, those with missing values less than 20% were filled using multiple interpolation (MICE package), while those with missing values more than 20% were deleted. Procalcitonin, interleukin-6 (IL-6) and C-reactive protein (CRP) contained more than 20% missing value.

The surrogate indices of IR were formulated as follows:

TyG = ln [fasting TG (mg/dl) × fasting blood glucose (FBG) (mg/dL)/2] (10); METS-IR = ln[2 × TG (mg/dL) + FBG (mg/dL)] × BMI/ln HDL-C (mg/dL) (16); TG/HDL-C = TG (mg/dL)/HDL-C (mg/dL) (17).

The primary endpoint of this study was the incidence of AKI, as defined by the KDIGO guidelines (18): an increase in SCr level by ≥1.5 times the baseline level within the previous 7 days; or an increase in SCr of ≥0.3 mg/dl within 48 h; or urine volume <0.5 ml/kg/h for 6 h or more. The baseline SCr was determined as the lowest value recorded within the 7 days prior to ICU admission; in the absence of such data, the initial SCr measurement upon ICU admission was utilized. The secondary endpoint was defined as the development of stage III AKI.

The proportional hazards assumption was verified using schoenfeld residual plots, and no violation was detected (Supplementary Figure S1).

In accordance with the Events Per Variable (EPV) principle, the sample size needs to be at least 10 times the number of variables. We included a total of 45 variables, corresponding to a required sample size of 450 cases. Meanwhile, in a study on TyG and sepsis-associated AKI, the incidence of AKI in TyG quartile groups was reported as 71.1%, 75.6%, 78.4%, and 88.8% (10). We hypothesize that the AKI incidence in the tertile groups of our study was 72%, 78%, and 85%. With a two-tailed type I error rate set at 5% and statistical power maintained at 90%, the minimum sample size required for the study was determined to be 750 patients (PASS version 15.0.5, NCSS, USA). With comprehensive consideration, at least 750 patients should be enrolled.

For continuous variables, Kolmogorov-Smirnov test was performed for normality, and Mann-Whitney U test or T-test was performed for group comparison. The categorical variables were assessed by Chi-square or Fisher exact tests. The occurrence of primary and secondary endpoints was depicted by the Kaplan–Meier curve and compared by the log-rank test. Knowing that feature selection is crucial for model construction, Boruta algorithm, a supervised categorical feature selection method, was used to determine all relevant features. The Fine-Gray model was constructed to analyze the competitive risk in order to evaluate the stability of the results. Knowing that the Cox proportional risk model can better reflect the effect of time to event as compared with logistic regression, it was used to assess the correlations between the surrogate indices of IR and the study endpoint. Three models were constructed: model 1: unadjusted; model 2: adjusted for age, sex and race; and model 3: adjusted for the specific results of the Boruta algorithm. To depict the dose-response relationship between surrogate indices of IR and risk of the study endpoint, restricted cubic spline (RCS) analysis was employed, with 4 knots specified based on variable distribution and set at the 5th, 35th, 65th, and 95th percentiles. Additionally, further stratified analyses were conducted according to age, gender, hypertension, heart failure (HF), coronary heart disease (CHD), chronic kidney disease (CKD), and diabetes. The interactions were assessed with likelihood ratio tests.

All statistical analyses were performed using R 4.1.3 (R Foundation for Statistical Computing, Vienna, Austria) and STATA 17.0 (STATA corporation, Texas, United States). P < 0.05 was considered statistically significant.

A total of 997 patients with sepsis were enrolled in the study, with a median age of 66.85 [57.88, 77.93] years, including 411 (41.22%) males. The median follow-up duration was 6 days. At the end of the follow-up period, AKI occurred in 748 patients (75.03%), and 286 (28.69%) eventually progressed to stage III AKI.

The basic characteristics of the population stratified by TyG, METS-IR and TG/HDL-C were displayed in Supplementary Table S1. Numerous characteristics showed similar trends across the three indices, such that patients with higher indices tended to have higher BMI and SOFA score, higher prevalence of diabetes and septic shock, and higher usage rates of renal replacement therapy (RRT), meropenem and vancomycin. In addition, for laboratory markers, patients with higher indices tended to be associated with higher HDL, TG, SCr and glucose versus lower albumin and calcium. The incidence of AKI and stage III AKI in each group is shown as bar graphs in Figure 2. Clearly, the incidence of AKI, as well as stage III AKI, increased progressively from group Q1 to Q3 [TyG: AKI (66.07% vs 72.67% vs 86.40%, P < 0.001) and stage III AKI (25.83 vs 27.03 vs 33.23, P < 0.001); METS-IR: AKI (61.26% vs 75.68% vs 88.22%, P < 0.001) and stage III AKI (18.92% vs 25.83% vs 41.39%, P < 0.001); TG/HDL-C: AKI (65.56% vs 76.81% vs 82.63%, P < 0.001) and stage III AKI (23.26% vs 24.70% vs 38.02%, P < 0.001)].

Some inflammatory markers, such as CRP, were excluded owing to a high proportion of missing values. We therefore further compared the baseline characteristics between patients with and without CRP testing, and the results indicated no significant differences in baseline characteristics except for RRT and vancomycin (Supplementary Figure S2).

Boruta’s algorithm was used to perform feature screening of variables associated with AKI and stage III AKI (Supplementary Figure S2). In addition to the surrogate indices, the factors most strongly associated with AKI were, in order, body mass index (BMI), alanine aminotransferase (ALT), furosemide, aspartate aminotransferase (AST), age, glucose, SCr and insulin. The factors most strongly associated with stage III AKI were RRT, BMI, SCr, sequential organ failure assessment (SOFA) score, AST, blood urea nitrogen (BUN), bilirubin, hemoglobin, anion gap, hematocrit, septic shock, albumin, lymphocytes and ALT.

The occurrence of study endpoints was described by Kaplan-Meier method and compared by the log-rank test. (Figure 3). There was an overall significant difference in AKI incidence between the groups classified by TyG (log-rank χ²=6.106, P = 0.047) and METS-IR (log-rank χ²=24.709, P < 0.001), with patients in Q3 group having the highest incidence of AKI. However, when the groups were divided according to TG/HDL-C, no overall significant difference was observed (log-rank χ²=5.565, P = 0.062). Notably, for stage III AKI, an overall significant difference was observed between the groups divided by METS-IR (log-rank χ²=36.604, P < 0.001) and TG/HDL-C (log-rank χ²=15.102, P = 0.001), but not by TyG (log-rank χ²=3.188, P = 0.203).

Next, three Cox regression models were conducted to adjust for potential confounders: Model 1: unadjusted; Model 2: adjusted for age, sex and race; Model 3 (AKI): adjusted for age, sex, race, BMI, ALT, glucose, creatinine and furosemide; Model 3 (Stage III AKI): adjusted for age, sex, race, BMI, creatinine, AST, bilirubin, hemoglobin, anion gap, hematocrit, albumin, lymphocytes, RRT, septic shock and SOFA score. When METS-IR was used as a categorical variable in Models 3, the risk of AKI in the Q2 and Q3 groups was 31.3% and 52.4% higher than that in the Q1 group (P = 0.005 and P < 0.001, respectively), and the risk of stage III AKI was 40.2% and 85.5% higher (P = 0.043 and P < 0.001, respectively) (Table 1). Using TyG index as a categorical variable in Models 3, there was no overall significant difference between the groups for either AKI (P = 0.066) or stage III AKI (P = 0.855), although Q3 group showed a higher risk of AKI compared to Q1 group (P = 0.020) (Table 1). Meanwhile, there was also no significant difference between the groups for either AKI or stage III AKI for TG/HDL-C. Meanwhile, the results of the competitive risk analysis using the Fine-Gray model were similar to those of the cox regression analysis (Supplementary Table S3).

When METS-IR was used as a continuous variable, the risk of AKI and stage III AKI increased with METS-IR increasing, whether in model 1, 2, or 3 (all P < 0.001). However, similar results were not shown for TyG and TG/HDL-C (all P > 0.05) (Table 2).

Knowing that only METS-IR was independently correlated with the occurrence of AKI and stage III AKI as shown by Cox regression analysis, we further explored whether their relationship was linearly correlated by RCS curves. The results showed a gradual increase in AKI risk with METS-IR increasing in a non-linear positive manner (P for nonlinear = 0.003). A similar dose-dependent relationship was also observed between METS-IR and stage III AKI (P for nonlinear = 0.001) (Figure 4).

To examine whether the association between METS-IR and AKI persisted in specific populations, we performed stratified analyses according to age, gender, hypertension, HF, CHD, CKD and diabetes. The subgroups of age > 65 years or male sex included 553 and 411 patients, respectively. Meanwhile, the subgroups of hypertension, HF, CHD, CKD, and diabetes had 416, 67, 334, 155 and 346 patients, respectively. The results showed that METS-IR was strongly correlated with an increased risk of AKI in all populations except those with HF (P = 0.925), CKD (P = 0.284) and diabetes (P = 0.139), and there was no significant interaction between the subgroups (all P for interaction > 0.05) (Figure 5A). For stage III AKI, METS-IR was associated with an increased risk, except in patients with HF (P = 0.112) (Figure 5B).