This study employed a retrospective observational design, utilizing data extracted from the MIMIC-IV database, which contains detailed records of patients treated at Beth Israel Deaconess Medical Center from 2008 to 2019. (11) Adult patients with concurrent HF and pneumonia were identified to establish the primary study cohort for association analyses and prognostic modeling. The MIMIC-IV cohort was subsequently used for machine learning model development with internal validation. To further evaluate model generalizability, an independent cohort of patients with the same diagnoses was retrospectively enrolled from the First Affiliated Hospital of Zhengzhou University between January 2021 and December 2024.

Ethical approval for the collection of the MIMIC-IV database was obtained by the original data-collecting institutions. As the MIMIC-IV database contains exclusively de-identified patient records, the analyses conducted in this study were exempt from additional ethics committee review and the requirement for informed consent. Author Hongyu Su obtained Collaborative Institutional Training Initiative (CITI) certification (ID: 68198847) prior to authorization for database access. External validation cohort utilization was approved by the Ethics Committee of the First Affiliated Hospital of Zhengzhou University, with a waiver for informed consent (Ethical approval number: 2025-KY-0267).

For both the MIMIC-IV cohort and the external validation cohort, eligible patients were those who had concurrent diagnoses of HF and pneumonia recorded within the same hospitalization, as identified by the presence of corresponding International Classification of Diseases (ICD) codes (listed in Supplementary Table S1). Neither HF nor pneumonia was required to be the primary discharge diagnosis, and patients were included regardless of the diagnostic listing order. This inclusive definition was adopted to capture all critically ill patients affected by the coexistence of HF and pneumonia, reflecting real-world clinical practice in which diagnostic coding priority may vary according to presentation or administrative factors rather than true disease severity. Exclusion criteria included: (1) age <18 years, (2) the length of Intensive Care Unit (ICU) stay <24 h, and (3) absence of RDW and albumin results after ICU admission. The patient inclusion and exclusion process is shown in Supplementary Figure S1. The study flowchart and analytical framework are illustrated in Figure 1.

Patient data were retrieved using PostgreSQL, comprising demographic variables [age, gender, and body mass index (BMI)], comorbidities (myocardial infarction, diabetes, hypertension, hepatopathy, atrial fibrillation, kidney disease, malignant tumor, chronic pulmonary disease, as well as cerebrovascular disease), along with medication use. Medications analyzed encompassed glucocorticoids, anticoagulants, beta blockers, renin-angiotensin-aldosterone system inhibitors (RAASi, including angiotensin-converting enzyme inhibitors and angiotensin receptor blockers), diuretics, antiplatelet drugs, angiotensin receptor-neprilysin inhibitors (ARNI), sodium-glucose cotransporter 2 inhibitors (SGLT2i), together with nonsteroidal anti-inflammatory drugs (NSAIDs). At the same time, key vital signs recorded for the first time after entering the ICU were extracted, including systolic blood pressure (SBP), diastolic blood pressure (DBP), heart rate (HR), respiratory rate (RR), and oxygen saturation (SpO2). In addition, hemodynamic and clinical monitoring parameters included central venous pressure (CVP), average left ventricular ejection fraction (LVEF), and cumulative fluid balance, defined as the net fluid input minus output during the first 24 h following ICU admission.

Disease characteristics were additionally collected. The diagnosis sequence was defined according to the relative ordering of ICD codes within the same hospitalization record. A value of 1 indicated that the ICD code for HF appeared before that for pneumonia, whereas a value of 0 indicated that the ICD code for pneumonia preceded that for HF. Ischemic HF was identified based on the presence of ICD codes corresponding to coronary artery disease, prior or acute myocardial infarction, or ischemic cardiomyopathy in the MIMIC-IV database. Patients without any of these diagnoses were categorized as having non-ischemic HF.

The initial laboratory data following ICU admission were collected, including red blood cell count (RBC), platelet count (Plt), white blood cell count (WBC), hemoglobin (Hb), RDW, neutrophil percentage (Neut), lymphocyte percentage (Lymph), absolute neutrophil count (Neut abs), absolute lymphocyte count (Lymph abs), monocyte count, alanine aminotransferase (ALT), aspartate aminotransferase (AST), alkaline phosphatase (ALP), albumin, creatinine (Cr), blood urea nitrogen (BUN), international normalized ratio (INR), prothrombin time (PT), partial thromboplastin time (PTT), potassium (K⁺), sodium (Na⁺), calcium (Ca²⁺), chloride (Cl⁻), phosphorus (P), bicarbonate (HCO₃⁻), glucose (Glu), troponin T (TnT), N-terminal pro–B-type natriuretic peptide (NTproBNP), C-reactive protein (CRP), creatine kinase-MB (CKMB), and creatine kinase (CK). For repeated measurements, only the first recorded values were included. The RAR was calculated according to the following formula:RAR=RDW(%)Serumalbumin(g/dL)The primary endpoint was all-cause in-hospital mortality. Follow-up initiated at admission and terminated upon the first occurrence of: (1) death during hospitalization, (2) discharge, or (3) 31-day observation completion.

Continuous variables were described as means with standard deviation (SD) or medians with interquartile ranges, depending on their distribution. Group comparisons were made using the Mann–Whitney U-test or Student's t-test for continuous variables and Pearson's chi-square test for categorical variables.

Variables with missing rates greater than 20% were excluded from the analysis. The excluded variables are explicitly indicated in Supplementary Table S2, which also presents the proportion of missing data for each variable. To handle the remaining missing data, multiple imputation was performed using the “mice” R package with predictive mean matching. Five imputed datasets were generated, and a fixed random seed was applied to ensure reproducibility. Outliers were identified and excluded using a Z-score–based approach, with values exceeding an absolute Z-score of 3 considered as outliers. The distributions of all imputed variables before and after imputation are presented in Supplementary Table S3, indicating that the imputation did not introduce substantial systematic bias.

Associations between RAR and mortality were modeled via restricted cubic splines (RCS). Subsequently, for visualization and group-based analyses, patients were dichotomized into high- and low-RAR groups based on the median RAR value, and Kaplan–Meier (KM) analysis was then performed to compare survival probabilities between these groups.

Subsequently, univariate and multivariable Cox proportional hazards models were applied to evaluate the association between continuous or categorized RAR and in-hospital mortality. Hazard ratios (HRs) with 95% confidence intervals (CIs) were reported. Four progressively adjusted models were constructed: Model I. Unadjusted; Model II. Adjusted for demographics (age, gender), vital signs (HR, RR, SpO2), and laboratory results (RBC, Plt, WBC, Hb, Neut, Lymph, ALT, AST, ALP, Cr, BUN, INR, PT, PTT, K⁺, Na⁺, Ca²⁺, Cl⁻, P, Glu, HCO3⁻); Model III. Adjusted for disease characteristics and comorbidities including diagnosis sequence, ischemic HF, myocardial infarction, diabetes, hypertension, hepatopathy, atrial fibrillation, kidney disease, malignant tumor, chronic pulmonary disease, cerebrovascular disease, as well as concomitant medication use (glucocorticoids, anticoagulant, beta blockers, RAASi, diuretic, antiplatelet drug, and NSAIDs); Model IV: Fully adjusted model incorporating all covariates from Model II and III. ARNI and SGLT2i were not included in the multivariable analyses due to extreme imbalance in the data, which could lead to unstable estimates.

Subgroup analyses stratified by age, gender, disease characteristics, comorbidities, and medication regimens evaluated RAR's prognostic value across patient subgroups. Sensitivity analyses assessed seven medication classes (glucocorticoids, anticoagulants, antiplatelet agents, beta blockers, diuretics, RAASi, NSAIDs) for outcome associations. To further address potential confounding, we performed propensity score matching (PSM) using multivariable logistic regression with covariates spanning demographics, vital signs, laboratory parameters, and comorbidities. A 1:1 nearest-neighbor matching (caliper = 0.15 SD of logit-transformed scores) balanced baseline characteristics while minimizing data exclusion. Covariate balance after matching was assessed using standardized mean differences (SMDs), with an SMD <0.10 considered indicative of adequate balance. Cox regression was subsequently applied to assess mortality risk associations with RAR in both continuous and dichotomized forms.

The MIMIC-IV cohort was randomly partitioned into training (70%) and internal validation (30%) sets. Baseline characteristics between the training and internal validation cohorts were compared to confirm acceptable balance (Supplementary Table S5). In addition, baseline characteristics of the overall MIMIC-IV cohort and the external validation cohort were compared to assess cohort comparability and external generalizability (Supplementary Table S6). A Boruta algorithm-driven feature selection process was implemented in the training set, iteratively comparing predictor importance against permuted shadow features to retain statistically significant variables. Collinearity among selected variables was subsequently assessed, and highly correlated features were removed. Continuous variables were standardized using z-score normalization prior to model training. Eight machine learning models—Logistic Regression, Decision Tree, Random Forest, k-nearest neighbor (KNN), Support Vector Machine (SVM), Neural Network, eXtreme Gradient Boosting (XGBoost), and Light Gradient Boosting Machine (LightGBM)—were constructed on the training cohort. Hyperparameter tuning for LightGBM was conducted using 5-fold cross-validation within the training set, incorporating L1/L2 regularization and early stopping to mitigate overfitting. Hyperparameter tuning strategies for the remaining models followed similar cross-validation principles, with model-specific parameter settings detailed in the accompanying analysis code. The performance of all machine learning models was evaluated on the internal validation cohort and external validation cohort. Receiver operating characteristic (ROC) curves and decision curve analysis (DCA) were generated, with the area under the curve (AUC) serving as the primary metric for model comparison. To statistically compare AUCs in the external validation cohort, we performed pairwise DeLong's tests and applied Holm correction for multiple comparisons. In addition to discrimination, we assessed overall performance and calibration in the external validation cohort using the Brier score, calibration intercept and slope, and the Hosmer–Lemeshow test with 10 groups. To evaluate the incremental predictive value of RAR within the final predictive model, we performed a formal comparison between the optimal LightGBM model including RAR and an identical model excluding RAR (reduced model). Incremental performance was assessed using the area under the receiver AUC, integrated discrimination improvement (IDI), and net reclassification index (NRI) in both the internal and external validation cohorts. AUC was used as the primary performance metric, while IDI and NRI were used to assess incremental improvements in risk discrimination and reclassification. The optimal model underwent interpretability analysis using SHapley Additive exPlanations (SHAP) analysis to quantify feature contributions at both global and individual levels. To facilitate clinical translation, a web-based platform integrating the final model was deployed via R Shiny, enabling real-time mortality risk stratification.

Data analyses were conducted using R (v4.5.2), with statistical significance defined as a two-tailed P < 0.05.

We initially enrolled 4,618 patients from the MIMIC-IV database. After excluding patients with abnormal values, a total of 3,158 patients were included in the final analysis, comprising 2,586 survivors and 572 non-survivors. Table 1 presents the baseline characteristics of the survivor and non-survivor groups. Compared to non-survivors, survivors were markedly younger. Regarding comorbidities, the prevalence of hypertension was substantially higher in survivors, whereas non-survivors had considerably higher rates of hepatopathy, kidney disease, malignant tumor, and cerebrovascular disease. In terms of medication use, survivors showed greater utilization of glucocorticoids, beta blockers, RAASi, diuretics, antiplatelet drugs, and NSAIDs. Compared to survivors, non-survivors exhibited elevated WBC, neutrophil percentage, Cr, BUN, INR, PT, PTT, and phosphorus, alongside reduced Plt, lymphocyte percentage, and HCO₃⁻.

RCS regression analysis revealed a significant linear association between RAR and in-hospital mortality in HF patients with concomitant pneumonia (overall P < 0.001; nonlinearity P = 0.717). For visualization and comparative analysis, patients were categorized into high- and low-RAR groups based on the median RAR value (5.09, Figure 2A). KM analysis demonstrated markedly higher 31-day all-cause mortality in the high-RAR group (log-rank P < 0.001, Figure 2B).

Multivariable Cox regression revealed that elevated RAR independently predicted in-hospital mortality after full adjustment (demographics, vital signs, laboratory parameters, comorbidities). As a continuous variable, each unit elevation in RAR conferred a 13% higher mortality risk [HR: 1.13 (95% CI: 1.06–1.21); P < 0.001]. When RAR was analyzed as a categorical variable, the high RAR group demonstrated a 1.28-fold mortality hazard relative to the low RAR group [HR: 1.21 (95% CI: 1.00–1.46); P = 0.054] (Figure 2C).

Subgroup analyses revealed no significant interaction effects across demographic strata, comorbid conditions, medication regimens, or diagnosis sequence (whether heart failure diagnosis preceded pneumonia or vice versa), and no interaction between ischemic and non-ischemic HF (Supplementary Figure S2). In medication-adjusted sensitivity analyses, continuous RAR maintained a robust mortality association across all models (Supplementary Figure S3).

Following PSM to mitigate confounding, 998 matched pairs of patients were generated. Covariate balance between the low- and high-RAR groups was substantially improved after matching, with all standardized mean differences below 0.10 (Supplementary Table S4 and Supplementary Figure S4). In the matched cohort, each 1-unit increase in RAR remained associated with a 14% higher risk of all-cause mortality [HR: 1.14, 95% CI: (1.05–1.25); P = 0.002] (Supplementary Figure S5).

Despite these findings, several limitations must be considered when interpreting the results. First, the retrospective study design inherently precludes causal inference, and residual confounding from unmeasured factors, such as socioeconomic status and treatment adherence, cannot be fully excluded. Second, although external validation helps mitigate center-specific bias, the single-center recruitment strategy and limited ethnic diversity of the cohort may restrict the generalizability of the findings. Third, the lack of phenotypic stratification for HF and pneumonia limits insights into potential heterogeneity in RAR's prognostic utility across disease subtypes. Future work requires prospective multicenter validation with subtype stratification, coupled with mechanistic trials testing whether RAR-directed interventions (e.g., anti-inflammatory therapies, albumin supplementation) improve survival beyond reflecting disease severity. Additionally, the absence of biomarkers like NT-proBNP, CRP, and LVEF is a limitation due to their high missing proportions in the dataset, leading to their exclusion from the model. This highlights the advantage of RAR as an easily accessible and cost-effective biomarker, especially in settings where these specialized markers are unavailable. Finally, a potential limitation is overfitting in the machine learning model. Although the training set showed a high AUC (0.939), the AUCs for the internal (0.735) and external (0.733) validation sets were lower. However, the close similarity between the internal and external validation AUCs suggests reasonable model generalizability. We applied regularization and early stopping to mitigate overfitting, but further refinement is needed to improve model robustness across different datasets.