Abstract

Background:

The C-reactive protein–triglyceride glucose index (CTI) has been proposed as a novel biomarker of insulin resistance and inflammation, but its association with mortality in critically ill patients with coronary artery disease (CAD) remains unclear. This study aimed to evaluate the associations between the CTI and both short- and long-term all-cause mortality and to assess the predictive value of this index.

Methods:

Patients with CAD were identified from the MIMIC-IV database and divided into internal training and testing cohorts, while an external validation cohort was derived from the eICU-CRD and Shenzhen Regional Health Information Platform (SRHIP) database. Based on the optimal CTI cut-off values, patients were grouped into three categories. The primary outcomes were short-term (30-day) and long-term (365-day) all-cause mortality. Associations between the CTI and mortality were examined using Kaplan–Meier curves, restricted cubic spline regression, and Cox proportional hazards models. Subgroup, mediation and sensitivity analyses tested result robustness. The CTI was further compared with other single predictors, and six machine learning (ML) models were built to assess its predictive performance. Finally, the SHapley Additive exPlanations (SHAP) analysis identified feature contributions, and a user-friendly web application was developed.

Results:

The primary cohort included 1,561 patients, and two external validation cohorts included 242 and 105 patients from the eICU-CRD and SRHIP databases. High CTI values were significantly associated with increased short- and long-term mortality, demonstrating a nonlinear dose–response relationship. The CTI exhibited particularly high predictive value for short-term outcomes. The incorporation of the CTI into ML models notably improved the predictive performance, and this improvement was confirmed in the external validation cohort.

Conclusions:

The CTI was identified as an independent predictor of short- and long-term mortality in critically ill patients with CAD, with a particularly high predictive value for short-term risk stratification. Integrating the CTI into predictive models significantly increased the prognostic accuracy.

1 Introduction

Cardiovascular disease (CVD) remains the leading cause of death worldwide. CVD accounts for nearly 20 million deaths annually, representing approximately one-third of all deaths, with more than three-quarters occurring in low- and middle-income countries (1). Coronary artery disease (CAD) is the most prevalent type of CVD, with an estimated mortality rate of 108.8 per 100,000 people (2). Its incidence and mortality have greatly increased in most countries and regions (3), making it a major global health problem. Comprehensive research is therefore essential to identify key risk factors for CAD and to develop effective management and treatment strategies.

Insulin resistance (IR) is characterized by reduced sensitivity to insulin, leading to impaired glucose use and metabolic disorders. As a key pathological mechanism of metabolic syndrome and atherosclerosis, IR promotes inflammation, oxidative stress, and endothelial dysfunction, ultimately accelerating the progression of coronary atherosclerosis and increasing the risk of CAD (4–6). In epidemiological studies and clinical practice, the triglyceride–glucose (TyG) index, has been widely recognized as a reliable surrogate marker for IR due to its simplicity and strong correlations with hyperinsulinemia and insulin sensitivity, and it has been validated across diverse populations and regions (7–9). Accumulating evidence indicates that an elevated TyG index is closely associated with an increased risk of CAD, greater severity of coronary lesions, and worse clinical outcomes (10). Moreover, the role of inflammation in driving atherosclerosis and CAD progression has been well established. C-reactive protein (CRP), a nonspecific marker of systemic inflammation, not only reflects the residual inflammatory risk but is also independently associated with major adverse cardiovascular events (MACEs), cardiovascular mortality, and all-cause mortality in patients with CAD. Further studies have emphasized that both chronic inflammation and atherosclerotic dyslipidemia should be jointly assessed and managed in the primary prevention of CVD (11, 12). Therefore, the development of a composite indicator that simultaneously reflects IR and the inflammatory status to predict cardiovascular risk holds significant clinical value. In this context, Ruan et al. (13) first proposed integrating CRP levels with the TyG index to establish the C-reactive protein–triglyceride-glucose index (CTI), which is designed to comprehensively assess both inflammation and IR. This index has shown good predictive ability in various clinical settings, including in determining the cancer cachexia prognosis, cancer mortality in the general population, and the risk of developing depression (14, 15). However, the association between CTI and CAD, particularly its ability to predict short- and long-term all-cause mortality in critically ill patients with CAD, remains unclear, as existing studies have largely focused on general populations or metabolism-related cohorts. For example, a cross-sectional analysis of National Health and Nutrition Examination Survey (NHANES) data revealed that individuals in the highest CTI quartile exhibited approximately twice the risk of coronary heart disease (CHD) compared with those in the lowest quartile (16). Ou et al. used data from the China Health and Retirement Longitudinal Study (CHARLS) cohort and reported that CTI could capture cardiovascular events and all-cause mortality in individuals with stage 0–3 cardiometabolic syndrome (17). Other studies have shown that CTI is positively associated with incident CHD, particularly among individuals who are metabolically unhealthy but exhibit a normal weight, and that CTI may increase the predictive accuracy when it is combined with other inflammatory or nutritional markers (18). Nevertheless, none of these studies have focused specifically on critically ill patients with CAD, and evidence regarding the relationships between CTI and short- and long-term all-cause mortality remains limited.

In recent years, machine learning (ML) has emerged as an important approach for developing clinical prediction models. The advantage of ML lies in its ability to automatically learn patterns from high-dimensional, nonlinear, and complex interactions, often achieving superior predictive performance to traditional statistical models. For example, an ML model incorporating single-photon emission computed tomography imaging features and demographic variables predicted MACEs and all-cause mortality in CAD patients, achieving a sensitivity and specificity greater than 65% and outperforming logistic regression (19). Huang et al. (20) applied the extreme gradient boosting (XGBoost) algorithm in CAD diagnosis, and achieved an accuracy greater than 85%. In addition, Li et al. (21) developed a gradient boosting machine (GBM) model for elderly Chinese patients with CAD presenting with impaired glucose tolerance or diabetes, which showed optimal performance in predicting 1-year mortality. Although progress has been made in the application of ML to determining the CAD prognosis, research evaluating the role of CTI in the prognosis of CAD patients in the ICU is lacking, in particular, studies incorporating CTI into the ML framework to predict short- and long-term all-cause mortality in critically ill patients with CAD are lacking.

Traditional etiological statistical models provide intuitive hazard ratios (HRs) and time-to-event curves with strong clinical interpretability, but they are limited in capturing complex nonlinear relationships. In contrast, ML is well suited for handling high-dimensional features and increasing predictive accuracy. However, its “black-box” nature often limits interpretability. Therefore, this study adopted a dual validation strategy that combined traditional etiological statistical methods with ML. Conventional survival analysis methods were applied to evaluate the associations between the CTI and both short- and long-term all-cause mortality. In parallel, the CTI was integrated with key clinical features to develop and compare six ML models for more precise mortality risk stratification in critically ill patients with CAD. Although etiological analysis and predictive modeling differ in their objectives, applications, and methodological approaches, they can play complementary roles in prognostic research and together form a progressive chain of evidence (22–24). Moreover, the combined use of these two approaches in studies of clinical outcomes in critically ill patients is becoming increasingly common, supporting the feasibility and value of linking association-level evidence with application-oriented predictions (25, 26).

2 Methods2.1 Study design

The overall study design is shown in Figure 1. First, based on predefined inclusion and exclusion criteria, a total of 1,561 patients with coronary artery disease were identified from the Medical Information Mart for Intensive Care IV (MIMIC-IV) database to form the analytic cohort. The cohort was then stratified into three groups according to CTI levels. Kaplan–Meier survival analysis, restricted cubic spline (RCS) modeling, and multivariable Cox proportional hazards regression were performed to evaluate the associations between CTI and short- and long-term all-cause mortality, while subgroup and sensitivity analyses were conducted to assess the robustness of the findings. Second, to systematically evaluate the predictive value of CTI for mortality risk, its predictive performance was first compared with that of other individual biomarkers. Guided by feature selection, six ML models were subsequently developed and internally validated. Model performance was assessed using the area under the curve (AUC), F1-score, accuracy, precision, recall, net reclassification improvement (NRI), and integrated discrimination improvement (IDI). External validation was then performed using two independent cohorts: a same-region validation cohort derived from the eICU Collaborative Research Database (eICU-CRD) and a cross-region validation cohort obtained from the Shenzhen Regional Health Information Platform (SRHIP). Finally, SHapley Additive exPlanations (SHAP) was applied to interpret feature contributions in the optimal model, and a user-friendly web application was developed to enhance clinical applicability.

Flowchart of the study design process.

2.2 Data source

Data for this study were obtained from three databases: MIMIC-IV (version 3.1) (27), eICU-CRD (version 2.0) (28), and SRHIP. MIMIC-IV contains deidentified clinical data from approximately 190,000 patients and 450,000 hospital admissions at BIDMC between 2008 and 2022, including demographics, laboratory tests, vital signs, medications, diagnoses, procedures, and outcomes. The eICU-CRD contains deidentified clinical data from 139,367 patients and more than 200,000 ICU admissions across 208 hospitals in the continental United States between 2014 and 2015. There is no overlap in contributing hospitals between the MIMIC-IV and eICU-CRD. The dataset covers demographics, diagnoses, laboratory results, and treatment information. The SRHIP aggregates health records from Shenzhen, China, integrating data from 75 public hospitals, 106 private hospitals, and over 1,600 community health service centers. It functions as a comprehensive health data center, housing over 40 million electronic health archives and billions of service records. In this study, the MIMIC-IV was primarily used for original data analyses and for internal training and validation of the ML models. The eICU-CRD was used as a same-region external validation set for the ML models to evaluate generalizability, with the SRHIP serving as the cross-region external validation cohort.

In accordance with the data usage protocols for MIMIC-IV and eICU-CRD, one of the authors completed the required human subjects research training (Record ID: 71784813) and signed the Data Use Agreements (DUA). The use of these two databases was approved by the Institutional Review Boards (IRBs) of the Beth Israel Deaconess Medical Center (BIDMC) and the Philips eICU Research Institute. For the SRHIP data, this study was approved by the Ethics Committee of the Shenzhen Health Development Research and Data Management Center (registration number: 2025009). Due to the retrospective nature of the study and the use of de-identified or anonymized data, the requirement for informed consent was waived for all three databases.

The study also adhered to the Strengthening the Reporting of Observational Studies in Epidemiology (STROBE) guidelines (29) and the Declaration of Helsinki.

2.3 Study population

Patients with a first ICU admission for CAD were identified from the MIMIC-IV, eICU-CRD, and SRHIP databases using the International Classification of Diseases (ICD)-9 and ICD-10 codes. The following exclusion criteria were applied across all databases: (1) age <18 years at ICU admission; (2) ICU stay <24 h; (3) multiple ICU admissions for CAD, with only the first admission included; and (4) missing data on CRP, triglyceride, and fasting glucose. In total, 1,561 patients from MIMIC-IV, 242 from eICU-CRD, and 105 from SRHIP were included in the final analysis.

2.4 Data extraction

Clinical data were extracted using structured query language (SQL) via PostgreSQL (version 8.7.0) and Navicat Premium (version 16.3.2). Based on expert consultation and a literature review (30), clinical features were extracted across seven categories: demographics, vital signs, comorbidities, laboratory indicators, clinical treatments, scoring systems, and clinical outcomes. The extracted data included the first recorded values of all clinical variables within 24 h after the first ICU admission, including laboratory measurements such as C-reactive protein, triglyceride, and glucose. These variables were collected prior to major interventions, such as PCI or CABG, and thereby reflected the patients' baseline clinical status at ICU admission. A detailed list of these variables is presented in Table 1. Missing data were imputed using the random forest method to reduce potential bias.

ItemsCompositionDemographicsAge, gender, BMI, marriage, raceVital signsHeart rate, SBP, DBP, MBP, Resp rate, temperature, Spo2ComorbiditiesHypertension, diabetes, AHF, hyperlipidemia, obesity, CKD, AMILaboratory indicatorsCRP, hematocrit, platelet, bun, creatinine, potassium, sodium, magnesium, PT, INR, RDW, bicarbonate, eGFR, triglyceride, fasting blood glucose, WBC, RBC, ALT, ALP, hemoglobin, total bilirubin, free calcium, phosphate, chloride, lymphocytes, CTIClinical treatmentWarfarin, statin, beta blocker, NOAC, antiplatelet, metformin, insulin, vasopressin, octreotide, ventilated, RRTScoring systemAPSIII, OASIS, LODS, SOFA, GCSClinical outcomesLos Icu, Los Hospital, 30-day mortality, 90-day mortality, 180-day mortality, 365-day mortality

Extraction of information for the variables.

2.5 Definitions of CTI and study endpoint

In this study, the CTI was calculated as follows:In Equation 1, CRP represents C-reactive protein, TG represents triglyceride, and FBG represents fasting blood glucose. The primary endpoints of this study were all-cause mortality in patients with CAD at 30-day (short term) and 365-day (long term), and the secondary endpoints included all-cause mortality at 90-day and 180-day.

2.6 Statistical analysis

Continuous variables with a normal distribution are presented as the means ± standard deviations (SDs), whereas those with a nonnormal distribution are presented as the medians and interquartile ranges (IQRs). Normality was assessed using the Shapiro–Wilk test. The differences in continuous variables between groups were assessed using Student's t test or the Kruskal–Wallis test, depending on the distribution. Categorical variables are presented as counts (percentages), and differences between groups were analyzed using the chi-square test or Fisher's exact test.

X-tile software (version 3.6.1) is widely used in medical and epidemiological research to identify optimal cut-off points for continuous survival-related variables. In this study, X-tile was chosen to determine the optimal cut-off point of the CTI using 30-day mortality as the endpoint. Patients were then stratified into three groups according to the optimal cut-off points. Kaplan–Meier survival curves were created to illustrate cumulative all-cause mortality across CTI groups, and the log-rank test was applied to assess statistical significance. Multivariable Cox proportional hazards models were constructed to further examine the association between CTI levels and all-cause mortality in critically ill patients with CAD across different follow-up periods. Potential confounders were selected according to three criteria: (1) variables with variance inflation factor (VIF) <5; (2) variables with p < 0.05 in the univariate analyses; and (3) factors previously recognized in the literature or clinical practice as important prognostic variables. Three progressively adjusted models were constructed: Model 1, unadjusted; Model 2, adjusted for Hyperlipidemia, Hypertension, Diabetes, Gender, Spo2, BMI, HR, RR, Age and SBP; and Model 3, further adjusted for Beta Blocker, Statin, Antiplatelet, Metformin, Vasopressin, Warfarin, Insulin, Free Calcium, ALP, ALT, WBC, Platelet, Lymphocytes, Bicarbonate, Sodium, Phosphate, Los Hospital, OASIS, LODS, APSIII and Bun.

Subgroup analyses were performed according to age (<65 or ≥65 years), sex, race, hyperlipidemia, diabetes, acute heart failure, hypertension, obesity, chronic kidney disease, and acute myocardial infarction to assess the consistency of the predictive value of CTI across patients with different clinical characteristics. In addition, a bootstrap-based mediation analysis was conducted to investigate the potential mediating effects of five illness severity scores, namely APSIII, OASIS, LODS, SOFA, and GCS, in the association between CTI and mortality risk at each time point.

Three sensitivity analyses were conducted to assess the robustness of the findings: (1) the association between CTI, which was treated as a continuous variable, and mortality risk was examined using Cox proportional hazards models; (2) E-values were calculated for the Cox models to quantify potential bias from unmeasured confounders (31); and (3) logistic regression models were used to confirm the association between CTI and mortality risk.

Subsequently, receiver operating characteristic (ROC) curves were analyzed to evaluate the predictive performance of ten indicators (TyG, APSIII, OASIS, LODS, SOFA, GCS, CRP, triglyceride, glucose, and CTI) for mortality at 30-, 90-, 180-, and 365-day follow-up. Predictive performance was assessed on the basis of AUC, sensitivity, and specificity.

Finally, ML models were developed to predict all-cause mortality in critically ill patients with CAD and were validated using multicenter data. The analytic cohort from MIMIC-IV was randomly divided into a training set and an internal validation set at a 7:3 ratio. In the training set, feature selection was performed using Boruta, LASSO regression, and univariate Cox regression. Six ML models were developed: logistic regression (LR), k-nearest neighbor (KNN), support vector classifier (SVC), random forest (RF), eXtreme Gradient Boosting (XGBoost), and convolutional neural network (CNN). Each model was trained using either the baseline features alone or the baseline features plus CTI. Hyperparameters were optimized using fivefold cross-validation and grid search, and class imbalance in the training set was corrected using the Synthetic Minority Over-sampling Technique (SMOTE). Model performance was evaluated and compared in the internal validation set using the AUC, F1 score, accuracy, precision, recall, NRI, and IDI. The best-performing model was externally validated in the eICU-CRD and SRHIP cohorts. Its generalizability was assessed by constructing ROC curves, calibration curves, and decision curve analysis (DCA). To improve interpretability, SHAP values were calculated to quantify the contributions of individual features to model predictions. A web-based platform incorporating the optimal model was developed to support clinical application.

All the statistical analyses were performed in Python (version 3.9.7) and R (version 4.4.0), and a two-sided p value < 0.05 was considered statistically significant.

3 Results3.1 Baseline characteristics

A total of 1,561 critically ill patients who were diagnosed with critically ill CAD were included from the MIMIC-IV database. Via the use of X-tile software, the optimal CTI cut-off values were identified as 10.1 and 11.4 based on 30-day all-cause mortality after ICU admission (Figure 2). Patients were accordingly stratified into three groups: low CTI (T1, <10.1), intermediate CTI (T2, 10.1–11.4), and high CTI (T3, >11.4). The baseline characteristics of the three groups are presented in Supplementary Table S1. In the overall cohort, 1,015 patients (65.02%) were male, the median age was approximately 70 years, and 1,032 patients (66.11%) were white. During the 365-day follow-up period, 275 patients (17.62%) experienced all-cause mortality. Compared with patients in the low- and intermediate-CTI groups, patients in the high-CTI group were older, more likely to be male, and had higher BMI, heart rate, and respiratory rate. They also had higher incidences of diabetes, acute heart failure, obesity, and chronic kidney disease, as well as significantly higher APSIII and OASIS scores. In terms of laboratory indicators, patients in the high-CTI group exhibited higher levels of platelets, blood urea nitrogen, creatinine, red blood cells, white blood cells, alanine aminotransferase, and alkaline phosphatase. However, they had lower use rates of warfarin, beta-blockers, and antiplatelet agents. Moreover, higher CTI values were associated with increased all-cause mortality at 30-day (4.78% vs. 7.16% vs. 13.08%, P < 0.001), 90-day (6.78% vs. 10.60% vs. 18.22%, P < 0.001), 180-day (8.94% vs. 14.61% vs. 23.36%, P < 0.001), and 365-day (12.17% vs. 19.20% vs. 28.97%, P < 0.001). In addition, the ICU length of stay [2.00 (1.27–3.21) vs. 2.33 (1.45–4.13) vs. 3.29 (1.77–5.91), P < 0.001] and overall hospitalization duration [7.06 (4.97–10.93) vs. 8.77 (5.72–13.85) vs. 10.44 (6.65–17.13), P < 0.001] increased with increasing CTI. The baseline characteristics of the eICU-CRD and the SRHIP database were presented in Supplementary Tables S2, S3, respectively.

Chart showing the selection of the optimal cut-off point selection.

3.2 Survival analysis

A Kaplan–Meier survival analysis was performed to evaluate all-cause mortality across CTI groups at different follow-up time points (Figure 3). The log-rank test indicated significant differences in all-cause mortality among the three groups at 30, 90, 180, and 365-day (P = 0.026, 0.020, 0.012, and 0.013, respectively). Throughout follow-up, the high-CTI group (T3) consistently had the highest all-cause mortality compared with the other groups, and the survival differences became more pronounced over time.

Kaplan–meier survival curves. (A) Comparison of all-cause mortality between groups at 30-day. (B) Comparison of all-cause mortality between groups at 90-day. (C) Comparison of all-cause mortality between groups at 180-day. (D) Comparison of all-cause mortality between groups at 365-day.

To further compare the survival stratification performance of CTI with that of its individual components, additional Kaplan–Meier analyses were performed for CRP and TyG (Supplementary Figure S1). The results showed that, although CRP was associated with significant survival differences at some follow-up time points, its stratification performance was less consistent than that of CTI, whereas TyG did not demonstrate statistically significant survival separation across the follow-up periods. These findings suggest that CTI may provide more stable survival stratification than either CRP or TyG alone.

3.3 The associations between CTI and short-term and long-term all-cause mortality in critically ill patients with CAD

Three Cox proportional hazards models were established to examine the associations and independent effects of the CTI on the short-term and long-term survival of critically ill patients with CAD.

Prior to constructing the risk models, covariates were identified. Variables with a VIF >5 were excluded to avoid multicollinearity, and 54 variables were initially retained (Supplementary Table S4). Based on the univariate Cox regression analysis results (Supplementary Table S5), previous studies, and clinical expertise, 32 covariates were ultimately selected for multivariable adjustment, including Hyperlipidemia, Hypertension, Diabetes, Gender, Spo2, BMI, HR, RR, Age, SBP, Beta Blocker, Statin, Antiplatelet, Metformin, Vasopressin, Warfarin, Insulin, Free Calcium, ALP, ALT, WBC, Platelet, Lymphocytes, Bicarbonate, Sodium, Phosphate, Los Hospital, OASIS, LODS, SBP, APSIII, and Bun.

The results of the multivariable Cox regression analyses are presented in Table 2. When the low CTI group (T1) was used as a reference, the HRs for the intermediate group (T2) were not statistically significant at any time point (all P > 0.05). In contrast, the mortality risk was significantly higher in the high CTI group (T3) than in the T1 group at 30-, 90-, 180-, and 365-day. In unadjusted Model 1, the HRs for T3 were 1.97 (95% CI: 1.18–3.31, P < 0.001), 1.79 (95% CI: 1.16–2.76, P < 0.001), 1.75 (95% CI: 1.20–2.56, P = 0.003), and 1.62 (95% CI: 1.16–2.27, P = 0.004) at 30-, 90-, 180-, and 365-day, respectively. In Model 2, which was adjusted for age and sex, the HRs for T3 increased to 2.36 (95% CI: 1.36–4.09), 2.23 (95% CI: 1.40–3.54), 2.17 (95% CI: 1.45–3.26), and 1.88 (95% CI: 1.32–2.68) (all P < 0.001). In the fully adjusted Model 3, the HRs for T3 slightly decreased to 2.14, 1.84, 1.79, and 1.40 but remained statistically significant (all P < 0.001), indicating that the CTI was independently associated with increased mortality risk. Moreover, the P for trend was significant in all models at all time points (all P < 0.05), supporting a dose–response relationship between higher CTI levels and mortality risk and underscoring the potential of CTI as an independent prognostic predictor.

OutcomeModel 1 HR (95%CI)PModel 2 HR (95%CI)PModel 3 HR (95%CI)P30d T11.00 (Reference)1.00 (Reference)1.00 (Reference) T21.22 (0.77–1.92)0.3921.33 (0.84–2.10)0.2281.41 (0.88–2.25)0.148 T31.97 (1.18–3.31)0.012.36 (1.36–4.09)0.0022.14 (1.21–3.81)<.001P for trend1.40 (1.07–1.83)0.0131.59 (1.21–2.10)<.0011.46 (1.10–1.95)0.00990d T11.00 (Reference)1.00 (Reference)1.00 (Reference) T21.15 (0.79–1.68)0.4531.24 (0.85–1.81)0.271.13 (0.76–1.68)0.543 T31.79 (1.16–2.76)0.0082.23 (1.40–3.54)<.0011.84 (1.11–3.05)0.017P for trend1.33 (1.07–1.67)0.0111.52 (1.20–1.91)<.0011.34 (1.06–1.71)0.016180d T11.00 (Reference)1.00 (Reference)1.00 (Reference) T21.20 (0.87–1.66)0.2591.23 (0.89–1.71)0.2151.14 (0.81–1.60)0.441 T31.75 (1.20–2.56)0.0042.17 (1.45–3.26)<.0011.79 (1.16–2.76)0.009P for trend1.32 (1.09–1.60)0.0051.49 (1.22–1.82)<.0011.34 (1.08–1.65)0.006365d T11.00 (Reference)1.00 (Reference)1.00 (Reference) T21.14 (0.87–1.51)0.3421.10 (0.83–1.47)0.4941.00 (0.75–1.34)1 T31.62 (1.16–2.27)0.0041.88 (1.32–2.68)<.0011.49 (1.02–2.16)0.038P for trend1.27 (1.07–1.50)0.0061.40 (1.18–1.68)<.0011.25 (1.04–1.51)0.015

Multivariate Cox proportional hazards model of all-cause mortality at each time point.

RCS regression curves were generated to examine the association between CTI and all-cause mortality at multiple follow-up time points (Figure 4). Across all follow-up time points, similar patterns were observed in the association between CTI and mortality, with inflection points consistently occurring at approximately 10.34. For 30-day mortality, the unadjusted model showed an overall association that approached statistical significance (P for overall = 0.048), whereas the test for nonlinearity was not significant (P for nonlinear = 0.083). The curve suggested an approximately U-shaped association, with the HR initially decreasing as CTI increased, reaching its lowest point at a CTI of approximately 10.34, and increasing thereafter. After multivariable adjustment, both the overall association and the nonlinear association became significant (P for overall = 0.002; P for nonlinear = 0.013), and the curve appeared more stable. Similar trends were observed for 90-, 180-, and 365-day mortality, indicating a consistent nonlinear association between the CTI and mortality across both short- and long-term follow-up periods, independent of other clinical confounders.

RCS regression analysis. (A–D) RCS regression analysis of the association of the CTI with all-cause mortality at 30-day, 90-day, 180-day, and 365-day without adjusting for covariates. (E–H) RCS regression analysis of the association of the CTI with all-cause mortality at 30-day, 90-day, 180-day, and 365-day after adjusting for covariates.

3.4 Subgroup analysis

The consistency of the association between CTI and all-cause mortality across clinical subgroups was assessed in patients stratified by age, sex, race, hyperlipidemia, diabetes, acute heart failure, hypertension, obesity, chronic kidney disease, and acute myocardial infarction. The results are presented in forest plots (Figure 5). In most subgroups, higher CTI levels were consistently associated with increased all-cause mortality, indicating that the prognostic value of CTI was broadly applicable across patients with different clinical characteristics. No significant interactions were detected between CTI and most of the subgroups (all P > 0.05). An exception was observed for acute heart failure, in which modest interactions with CTI were observed at 30- and 90-day (P for interaction = 0.038 and 0.014), suggesting that the strength of the association may differ in this subgroup.

Forest plot of subgroup analyses. Forest plots of the subgroup analyses of the relationship between all-cause mortality and CTI in patients at 30-day (A), 90-day (B), 180-day (C), and 365-day (D).

3.5 Mediation analysis

To explore potential pathways linking CTI to mortality, we conducted a bootstrap-based mediation analysis using APSIII, OASIS, LODS, SOFA, and GCS as candidate illness-severity mediators of the association between CTI and mortality (Supplementary Table S6). The results showed that APSIII and LODS exhibited relatively stable partial mediating effects. The mediation proportions for APSIII were 19.12%, 17.29%, 16.39%, and 17.59% for 30-, 90-, 180-, and 365-day mortality, respectively, whereas those for LODS were 11.13%, 10.06%, 9.54%, and 10.08%, respectively. These findings suggest that the association between CTI and mortality risk may be partially mediated by overall illness severity. In contrast, the mediating effects of the other severity scores were relatively weak. However, because both CTI and the severity scores were derived from information collected during the early ICU admission window, whereas deaths occurred during hospitalization or follow-up, these mediation results should be interpreted as exploratory. They support, but do not establish, a potential pathway through which CTI may influence mortality risk by reflecting or aggravating overall illness severity.

3.6 Sensitivity analysis

Three sensitivity analyses were conducted. First, when CTI was analyzed as a continuous variable in multivariable Cox proportional hazards models, the results remained consistent with those of the categorical analyses, with no substantive changes (Supplementary Table S7). Second, E-values were calculated based on fully adjusted Model 3, with E-values of 3.71, 3.09, 2.98, and 2.34 at 30-, 90-, 180-, and 365-day, respectively. These relatively large E-values indicate the robustness of the findings, suggesting that an unmeasured confounder would need to be strongly associated with both exposure and outcome (HR ≥2.34) to fully explain the observed association between CTI and mortality. Finally, when logistic regression models were used as alternatives to Cox models, the results remained consistent and stable (Supplementary Table S8). Collectively, these sensitivity analyses support the robustness of the association between CTI and all-cause mortality in this study.

3.7 Performance of CTI in predicting the mortality risk3.7.1 Comparison of the predictive performance between CTI and individual indicators

ROC curves were used to compare the predictive performance of CTI with that of nine other indicators (TyG, APSIII, OASIS, LODS, SOFA, GCS, CRP, triglyceride, and glucose) for 30-, 90-, 180-, and 365-day all-cause mortality in critically ill patients with CAD (Figure 6). CTI consistently outperformed the other indices in predicting mortality across all time points, with AUC values of 0.79 for 30-day mortality, 0.74 for 90-day mortality, 0.70 for 180-day mortality, and 0.71 for 365-day mortality, indicating favorable predictive performance.