This retrospective study was performed on the basis of the clinical data from Changsha Central Hospital. In the study, all the AP patients with records of fasting blood sugar (FBG) and triglyceride (TG) within 24 h after admission to the hospital from January 2015 to December 2022 were enrolled (n = 2,787) (Figure 1). Patients with following criteria were excluded (n = 405): (1) < 18-year-old (n = 18); (2) pregnant (n = 5); (3) tumor (n = 12); (4) liver cirrhosis (n = 1); (5) chronic obstructive pulmonary disease (COPD) (n = 18); (6) rheumatic autoimmune diseases (n = 3); (7) onset of AP > 72 h (n = 348) (Figure 1). Finally, 2,383 AP patients were included.

The definition of AP was confirmed when at least two out of three these criteria were met as follows: (1) digestive symptoms such as abdominal pain or abdominal distention; (2) the levels of serum amylase or lipase increased by three times compared with the normal levels of serum amylase or lipase; (3) ultrasonic or CT/MRI scan findings show the AP (16, 17). The etiology of hypertriglyceridemia (HTG) in AP was confirmed as follows: (1) TG ≥ 1,000 mg/dL; (2) TG ≥ 500 mg/dL with milky serum (18, 19). The definition of ARDS was based on the Berlin definition (20) and the new global definition of ARDS (2021) (21).

TyG index was defined by {ln [TG(mg/dL) × FBG(mg/dL)/2]}. The endpoint was in-hospital ARDS.

Baseline characteristics, such as age, gender, etiology (HTG, biliary), comorbidity [diabetes, hypertension, and coronary artery disease (CAD)], vital signs [heart rate (HR), systolic blood pressure (SBP), respiratory rate (RR), diastolic blood pressure (DBP)], and length of stay (LOS) in hospital were included. Lab findings within 24 h after admission in hospital were collected: TG, FBG, white blood cell (WBC), creatinine, aspartate aminotransferase (AST), platelet (PLT), total bilirubin, prothrombin time (PT), albumin, globulin, alanine aminotransferase (ALT), urea nitrogen, amylase, lipase, total cholesterol, total calcium, high-density lipoprotein (HDL), ionized calcium, and low-density lipoprotein (LDL). Scores within 24 h after admission to the hospital were collected: Ranson, bedside index of severity in acute pancreatitis (BISAP), acute physiology, and chronic health evaluation (APACHEII).

We used the Packages R¹ and EmpowerStats² software for statistical analysis. Statistically significant difference was considered with the p-value < 0.05.

First, on the basis of the tertiles of the TyG index, the study cohort was divided into three groups (T1–T3 groups). Baseline characteristics between T1 and T3 groups were analyzed. Continuous characteristics were expressed by the median with interquartile ranges (Median, Q1–Q3). Categorical characteristics were shown by the percentages (Number, %). Mann–Whitney U-test or Chi-squared test was used. Second, univariate analysis was done to discuss the relationship between different characteristics and ARDS in AP. Third, multivariate regression analysis was utilized to investigate the relationship between the TyG index and ARDS in AP. Three different models were performed as follows: Crude model (adjusted for none), Model I (adjusted for gender, age, diabetes, hypertension, CAD, HTG, biliary), Model II (adjusted for gender, age, comorbidities, etiology, vital signs, laboratory variables, scores of Ranson, BISAP, and APACHEII). Fourth, we explored whether the relationship between TyG and ARDS in AP was a linear or non-linear feature. The non-linear model was considered with the p-value less than 0.05. Moreover, the generalized additive model was used for performing the smooth fitting curve. Fifth, the receiver-operator characteristic (ROC) with accuracy, sensitivity, and specificity of the TyG index was used for predicting ARDS in AP. In addition, subgroup analysis was performed.

For dealing with missing data, the multiple imputation method Miceforest was utilized (22).

It is based on the multiple imputation of the chain equation of random forest using the process of predictive mean matching to select the value to be estimated. The Boruta algorithm in machine learning was used to rank the features according to their importance of the predictive ability of in-hospital ARDS. We use the random forest chain equation for multiple imputation and employ a predictive mean matching process to select estimated values. We use the Boruta algorithm in machine learning to assess the importance of predictive ability for ARDS in hospitalized patients and to rank features accordingly.

Then, the acceptable variables are integrated into the machine learning (ML) algorithm. The Logistic Regression (LR), eXtreme Gradient Boosting (XGBoost), K-Nearest Neighbors (KNN), Decision Tree (DT), Multinomial Naive Bayes (MultinomialNB), Random Forest (RF), Multilayer perceptron (MLP), and Gaussian Naive Bayes (GaussianNB) were used to evaluate the in-hospital ARDS risk of AP patients. The patient dataset was randomly divided into a development set and a validation set in an 8:2 ratio. A fivefold cross validation is used for internal verification. ROC curve and AUC are used to evaluate the performance of the model. The SHapley Additive exPlans (SHAP) method is used to validate the role of TyG in the model. All relevant machine learning methods and codes can be accessed for free at the following website https://github.com/philiplaw1984/TyG/.

Based on the flow chart (Figure 1), 405 patients were excluded and 2,382 AP patients were finally enrolled in this study. In the study cohort, the median age was 43 years, and men accounted for 74.06% (n = 1764) (Table 1). The number of AP patients based on the different etiologies, such as alcohol, HTG, and biliary were 509 (21.37%), 1,234 (51.81%), and 423 (17.76%), respectively. The number of patients with diabetes, hypertension, and CAD was 458 (19.23%), 436 (18.30%), and 72 (3.02%), respectively. The median TyG index was 10.58 (9.14–11.81).

In Table 1, general variables between the ARDS group (n = 137) and the non-ARDS group (n = 2,245) were compared. In the ARDS group, the ratio of HTG-AP was 71.58% (n = 98), and men accounted for 83.94% (n = 115) (both p < 0.05). The proportion of diabetes was significantly higher in the ARDS group (p = 0.017). Variables including DBP, HR, RR, TyG, TG, FBG, WBC, PT, globulin, urea nitrogen, creatinine, amylase, lipase, and total cholesterol were significantly higher in the ARDS group (all p < 0.05), while the levels of total calcium, ionized calcium, and HDL were significantly lower in the ARDS group (all p < 0.05). The LOS in hospital was longer and the scores of Ranson, BISAP, and APACHEII were higher in the ARDS group (all p < 0.001).

In Table 2, on the basis of the tertile levels of the TyG index, the AP patients were divided into three groups: T1 group (n = 794, TyG index<9.51), T2 group (n = 794, TyG index: 9.51–11.45), and T3 group (n = 794, TyG index>11.45). The incidences of ARDS in T1, T2, and T3 groups were 2.90% (n = 23), 3.40% (n = 27), and 10.96% (n = 87), respectively (p < 0.001). In the T3 group, the age was significantly lower, and the proportions of HTG, men, and diabetes were significantly higher (all p < 0.001). The median levels of TG, FBG, and TyG index in the T3 group were 2223.12 mg/dL, 198.00 mg/dL, and 12.15, respectively. The vital sign indexes, such as SBP, DBP, HR, and RR were all higher in the T3 group (all p < 0.001). Lab findings, such as WBC, PLT, PT, albumin, globulin, ALT, AST, total bilirubin, urea nitrogen, creatinine, amylase, lipase, total calcium, ionized calcium, total cholesterol, HDL, and LDL, were significantly different between the three groups.

In Table 3, variables including men (p = 0.0074), HTG (p < 0.0001), biliary (p = 0.0058), diabetes (p = 0.0182), DBP (p = 0.0248), HR (p < 0.0001), RR (p < 0.0001), TyG index (p < 0.0001), TG (p < 0.0001), FBG (p < 0.0001), WBC (p < 0.0001), PT (p < 0.0001), globulin (p = 0.0045), urea nitrogen (p = 0.0061), creatinine (p < 0.0001), amylase (p = 0.0083), lipase (p = 0.0007), total calcium (p = 0.0001), ionized calcium (p = 0.0004), total cholesterol (p < 0.0001), HDL (p = 0.0003), Ranson (p < 0.0001), BISAP (p < 0.0001), and APACHEII (p < 0.0001) were associated with ARDS in AP patients.

In Table 4, with a per-unit increment in the TyG index, the risk of ARDS in AP in the crude model, adjusted model I, and model II increased by 66% (OR = 1.66, 95%CI: 1.45–1.90, p < 0.0001), 166% (OR = 2.66, 95%CI: 2.03–3.50, p < 0.0001), and 133% (OR = 2.33, 95%CI:1.51–3.60, p < 0.0001), respectively. Compared to the T1 group, the ORs of ARDS in the T3 group in the crude model, adjusted model I, and model II were 4.13 (95%CI: 2.58–6.60, p < 0.0001), 7.30 (95%CI:2.88–18.49, p < 0.0001), and 5.64 (95%CI:1.50–21.21, p = 0.0104), respectively.

In Table 5, we compared the linear model and non-linear model, and the results showed that the non-linear relationship for indicating the association of TyG index and ARDS in AP was better [P for the log-likelihood ratio test was less than 0.05 (p = 0.010)]. When the TyG index≤11.31 (slope I), the OR was 1.40 (95%CI:0.79–2.48, p = 0.2528) (Figure 2). When the TyG index >11.31 (slope II), the OR was 4.30 (95%CI:2.26–8.19, p < 0.0001) (Figure 2). We also compared the two groups: TyG ≤ 11.31 (slope I) and TyG > 11.31 (slope II). The results showed that OR = 3.08 (95%CI: 1.31–7.25, p = 0.0100) when comparing slope II to slope I.

In Table 6, subgroup analysis is shown. In AP with men (OR = 1.87, 95%CI: 1.58–2.21, p < 0.0001), low age (OR = 3.37, 95%CI: 2.25–5.06, p < 0.0001) and HTG (OR = 3.37, 95%CI: 2.41–4.70, p < 0.0001) had a higher risk of ARDS.

In the report from Boruta algorithm, RR, LOS in hospital, TyG, total cholesterol, lipase, TG, and all the variables in the green area were defined as important factors, which demonstrate the important roles in the model. On the contrary, the variables in the yellow and red areas were tentative and rejected factors. As shown in Figure 3, TyG was one of the key factors in the impact on in-hospital ARDS, ranked by Boruta algorithm.

In Figure 4, the ROC curves of different ML prediction models are illustrated. The AUCs of RF, XGBoost, DT, MNB, GaussianNB, MLP, KNN, and LR were 0.851 ± 0.045, 0.857 ± 0.034, 0.654 ± 0.059, 0.613 ± 0.018, 0.842 ± 0.037, 0.610 ± 0.067, 0.632 ± 0.025, and 0.795 ± 0.049, respectively, which indicated that the Random Forest and XGBoost models were the best two performance models. To further evaluate the model’s performance in excluding the two components (TG and FBG) that constitute the TyG index. We retrained the XGBoost and Random Forest models, and the AUC values of these two models were 0.850 ± 0.036 and 0.843 ± 0.056, respectively. The results were shown in Supplementary Figure S1. In order to strengthen the generalizability and credibility, we conducted further experiments and generated the Precision-Recall curve, Decision curve, and Calibration curve based on the XGBoost model. The results are shown in Supplementary Figure S2. A comparative analysis revealed that the XGBoost model outperformed the BISAP scoring system in predicting ARDS with significant improvement. The results are shown in Supplementary Figure S3.

In this study, in order to verify the importance of the TyG, the SHAP method was applied to explain the ML models. In the RF model, the results showed that TyG was the second important factor (Figure 5). In addition, TyG was also one of the most important factors in the XGBoost model (Figure 6). In the SHAP method, each point represents a case. The higher the TyG is, the higher the corresponding SHAP value is, and the greater the contribution to the ARDS prediction.