We extracted data from MIMIC-III database version 1.4 as the training set, which is a public and free intensive care unit (ICU) database (20). Since the MIMIC-III database was approved by the Institutional Review Boards (IRB) of Beth Israel Deaconess Medical Center (Boston, MA) and the Massachusetts Institute of Technology (Cambridge, MA), IRB approval from our institution was exempted. Data of validation sets were collected from the patient data of ICU at the Second Affiliated Hospital and Yuying Children's Hospital of WMU. The Medical Ethics Committee of the Second Affiliated Hospital and Yuying Children's Hospital, WMU approved the use of the patient data of the Second Affiliated Hospital and Yuying Children's Hospital (Ethical Review Number: 2021-K-71-01).

The inclusion criteria were as follows: (1) ICU admissions age ≥ 65 years; (2) CS patients in MIMIC-III database and the Second Affiliated Hospital and Yuying Children's Hospital of WMU. Among them, patients from the MIMIC-III database were diagnosed according to the International Classification of Diseases, Ninth Revision (ICD-9) diagnostic code 785.51 or 998.01, and patients from the Second Affiliated Hospital and Yuying Children's Hospital of WMU were selected by unified diagnostic criteria: minimum systolic blood pressure (SBP) <90 mmHg, or need of vasopressors therapy or signs of hypoperfusion. Only records of the first ICU visit were selected for analysis to eliminate duplicate data. The specific process was shown in Figure 1.

We extracted the following information of patients on the first day of admission: (1) demographic information such as age, gender, ethnicity, and pathogeny; (2) vital sign data including heart rate, SBP, mean blood pressure (MBP), diastolic blood pressure (DBP), respiratory rate, temperature, and arterial oxygen saturation (SpO₂); (3) laboratory data including white blood cell (WBC) count, red cell distribution width (RDW), hemoglobin, hematocrit, platelet, activated partial thromboplastin time (APTT), international normalized ratio (INR), prothrombin time (PT), anion gap, bicarbonate, glucose, blood lactic acid, serum creatinine, serum urea nitrogen, serum sodium, and serum potassium; (4) comorbidities including congestive heart failure, atrial fibrillation, coronary heart disease, renal failure, liver disease, stroke, tumor, chronic obstructive pulmonary disease (COPD), acute respiratory distress syndrome (ARDS), and pneumonia; (5) traditional severity scores including simplified acute physiology score II (SAPSII); (6) As well as ejection fraction and the use of the vasopressor. If multiple measurements were made in the first 24 h, the vital signs and the laboratory data were based on the results of the first examination. The endpoint was 30-day mortality.

Variables with missing values ≥40% were excluded directly. We used multiple interpolations to deal with missing variables <40%. Patients with individual data missing by more than 10% or outliers [values above the mean of 3 standard deviations (SD)] were excluded. In the training set and the verification set, we carried out the above data processing respectively.

The continuous variables were expressed as mean ± SD of the normal distribution, while the non-normal continuous variables were expressed as median (interquartile range). Wilcoxon W test or Kruskal Wallis test was used to assess the differences among groups. The variance inflation factor (VIF) was calculated to verify whether multicollinearity existed.

In the model development stage, three models were established using the training set: the cox regression model, the Least Absolute Shrinkage and Selection Operator (LASSO) regression model, and the CoxBoost model. In the Cox regression model, we used the monofactor analysis to pick out targeted predictors and screened the predictors twice using multiple regression analysis. After two rounds of screening, the predictive factors were finally incorporated into the Cox regression model. The main idea of LASSO is to construct a first-order penalty function to obtain a refined model and to carry out feature screening by finally determining the coefficients of some variables to be 0. In the LASSO regression model, we determined the cutoff value based on ten-folds cross-validation to select the most useful predictive variables to form the LASSO regression model. CoxBoost (https://github.com/binderh/CoxBoost) is used to fit a Cox proportional hazards model by componentizing likelihood-based boosting, which is particularly suitable for models with a large number of predictors and allows for mandatory covariates with unpenalized parameter estimates. In contrast to gradient boosting, CoxBoost is not based on gradients of loss functions but adapts the offset-based boosting approach for estimating Cox proportional hazards models (21). According to the CoxBoost machine learning analysis of the importance of the predictors, we select targeted variables incorporated into the CoxBoost regression model.

These three models were evaluated together with the classic SAPSII score model. The area under receiver operating characteristic (ROC) curve (AUC), C index, net reclassification improvement (NRI), integrated discrimination improvement (IDI), and median improvement in risk score were used to choose the best model. In the validation set, AUC, C index, NRI, IDI, and median improvement in risk score were also used to evaluate the CoxBoost model, SAPSII score model, and the CardShock risk score model for external validation. We constructed a DynNom-based dynamic nomogram to visually display the final model. R software version 4.0.3 was used for all statistical analyses. P < 0.05 was considered statistically significant.

After excluding the patients who did not meet the inclusion criteria, a total of 919 patients were included in this study. Among them, 804 were from the training set and 115 were from the verification set. We divided these patients into two groups based on their death or survival in 30-day. Table 1 summarizes the basic distribution of all the target patients' baseline characteristics, vital signs, comorbidities, and other indicators. In the training set, the difference in age, SBP, MBP, DBP, respiratory rate, temperature, SpO₂, WBC count, RDW, INR, PT, anion gap, bicarbonate, blood lactic acid, serum creatinine, serum urea nitrogen, serum potassium, tumor, SAPSII score, and length of stay in the hospital between the two groups was statistically significant. In the validation set, the difference in temperature, PT, bicarbonate, blood lactic acid, congestive heart failure, pneumonia, SAPSII score, and length of stay in hospital between the two groups was statistically significant.

Based on the training set, we developed three models. In the traditional cox regression model, we first used the monofactor analysis to pick out 8 predictors (P < 0.05), the results are presented in Supplementary Table 1. Then, we screened the predictors twice using multiple regression analysis (Supplementary Table 2). The final Cox regression model was shown in Table 2, a total of 6 predictors including age, heart rate, temperature, WBC count, anion gap, and blood lactic acid. In the LASSO regression model, we determined the cutoff value based on the Loess smoothing function and the Youden index. In this way, 36 features were reduced to 4 potential predictors (Supplementary Table 3), including age, SBP, anion gap, and blood lactic acid (Table 3). According to the CoxBoost machine learning analysis of the importance of the predictors (Supplementary Table 4), we selected 17 predictors (P < 0.05) to construct the CoxBoost model, considering the existence of multicollinearity, we removed MBP. The final model was shown in Table 4, including age, heart rate, SBP, DBP, respiratory rate, temperature, SpO₂, WBC count, RDW, INR, PT, anion gap, bicarbonate, blood lactic acid, serum urea nitrogen, and tumor. VIF proved there was no significant multicollinearity in all three models (VIF ≤ 3).

These three models were evaluated together with the classic SAPSII score model to choose the best one. The CoxBoost model had good discrimination (AUC: 0.730) in the training set, which was better than others (Figure 2A). Besides, using the CoxBoost model as a reference, the Cox regression model, LASSO regression model, and SAPSII score model did worse in the C index (cox regression model: 0.6835; LASSO regression model: 0.6786; SAPSII: 0.6490), NRI (cox regression model: −0.0590; LASSO regression model: −0.1480; SAPSII: −0.1630), IDI (cox regression model: −0.0040; LASSO regression model: −0.0300; SAPSII: −0.0530), and median improvement in risk score (cox regression model: −0.0040; LASSO regression model:−0.0220; SAPSII: −0.0570) (Table 5). Therefore, we choose the CoxBoost model as the target model.

In the validation set, we further evaluated and validated the CoxBoost model. The CoxBoost model was well-discriminated in the external validation set (AUC: 0.770), which was greater than the SAPSII score model (AUC: 0.724) and the CardShock risk score (Supplementary Table 5) (AUC: 0.677) (Figure 2B). In the C index, the CoxBoost model has the best performance (C index: CoxBoost model 0.7713, SAPSII score model 0.7341, CardShock risk score 0.6628, Table 5). Using the CoxBoost model as a reference, the NRI of the SAPSII score model and the CardShock risk score were −0.3620 and −0.3480, the IDI of the two models were −0.1740 and −0.2490, and the median improvement in risk scores were −0.2380 and −0.1910 respectively (Table 5), all of which suggested that the CoxBoost model was better.

We constructed a DynNom-based dynamic nomogram to visually display the final model (Table 4) (https://CoxBoost-model.shinyapps.io/DynNomapp/), which could directly obtain the patient's in-hospital mortality by inputting the values of the relevant predictors. The final model formula and its regression coefficients was as follows: survival possibility in 30-day = 0.0339 ^* age + 0.0104 ^* heart rate – 0.0070 ^* SBP – 0.0127 ^* DBP + 0.0126 ^* respiratory rate – 0.1959 ^* temperature – 0.0112 ^* SpO₂ + 0.0250 ^* WBC count + 0.0422 ^* RDW + 0.0176 ^* INR + 0.0021 ^* PT + 0.0355 ^* anion gap – 0.0055 ^* bicarbonate + 0.0463 ^* blood lactic acid + 0.0026 ^* serum urea nitrogen + 0.2125 ^* (tumor = 1).