The present retrospective study cohort comprised adult patients admitted to Karsa Husada Hospital, Batu in Indonesia between January 1, 2024 and May 31, 2025 with a primary diagnosis of HF. Data were collected from June to July 2025 after ethics approval for the study had been obtained. Karsa Husada Hospital serves as a teaching hospital affiliated with the Faculty of Medicine and Health Sciences, Maulana Malik Ibrahim Islamic State University Malang.

A total of 112 patients met the eligibility criteria and were included in the final analysis. Patients were included using a consecutive sampling approach, whereby all eligible patients meeting the inclusion criteria during the study period were enrolled sequentially to minimize bias. As the present study was a retrospective study utilizing all available data within the study period, no formal sample size calculation was performed. The inclusion criteria were: i) An age ≥18 years; ii) admission with HF as the primary diagnosis; and iii) the availability of laboratory measurements for serum urea, serum creatinine and estimated glomerular filtration rate (eGFR), along with the echocardiographic assessment of LVEF. Patients were excluded if essential clinical or laboratory data were not available, if they were discharged or transferred within 24 h of admission, or if HF was not the primary reason for hospitalization. The workflow of patient selection is depicted in (Fig. 1).

The present study was approved by the Health Research Ethics Committee of Faculty of Medicine, Maulana Malik Ibrahim Islamic State University Malang, Indonesia (Approval no. 60/01/EC/KEPK-FKIK/10/2024). Only de-identified medical records were analyzed, with a waiver of written informed consent granted due to the retrospective, anonymized data use, and non-interventional design (Letter no. 009/KEPK.FKIK/KP/XI/2025).

Demographic variables included age, sex and diabetes mellitus status (coded as 1 for presence, 0 for absence). Laboratory parameters consisted of serum urea (mg/dl), serum creatinine (mg/dl) and eGFR (ml/min/1.73 m²), calculated using the Modification of Diet in Renal Disease (MDRD) equation. Echocardiographic assessment included LVEF (%), measured using the biplane Simpson method in accordance with American Society of Echocardiography guidelines (11). LVEF was selected as the primary echocardiographic parameter as it is the most routinely available and standardized measure across all patients in clinical practice. Other echocardiographic parameters, such as right ventricular function or diastolic indices, were not included due to their inconsistent availability in the dataset. The primary outcome was hospital LOS, defined as the number of days from admission to discharge. LOS was analyzed both as a continuous variable and as a categorical variable dichotomized at the median value: ≤3 days vs. >3 days. Patients with a hospital LOS >3 days were classified as having a prolonged period of hospitalization for subsequent descriptive and inferential analyses.

Continuous variables are reported as the mean ± standard deviation (SD) or median with interquartile range (IQR), depending on the underlying distribution, while categorical variables are presented as frequencies and percentages. Normality was assessed using the Shapiro-Wilk test. Comparisons between patients with a short (≤3 days) and prolonged (>3 days) LOS were performed using the Mann-Whitney U test for continuous variables and the Chi-squared test for categorical variables. A two-tailed P-value <0.05 was considered to indicate a statistically significant difference.

For predictive modeling, three feature sets were evaluated: i) Renal biomarkers alone (serum urea, creatinine and eGFR); ii) echocardiographic variable alone (LVEF); and iii) a combined feature set incorporating renal biomarkers, LVEF, age, sex and diabetes status. Missing values were imputed using the median of each variable. Prior to modeling, the class distribution of the outcome variable (LOS ≤3 days vs. >3 days) was assessed. As the proportion of the two groups was relatively balanced, no resampling techniques, such as oversampling or undersampling were applied. Additionally, synthetic data generation methods were not used to avoid potential overfitting given the relatively small sample size. The dataset was randomly split into training (70%) and testing (30%) subsets. To enhance model robustness and reduce variability associated with a single data split, k-fold cross-validation (k=5) was performed on the training set. Logistic and linear regression models were used as baseline approaches due to their interpretability, while ensemble methods, including random forest and gradient boosting, were selected to capture non-linear associations and interactions among variables. Hyperparameter optimization for random forest and gradient boosting models was conducted using grid search within the cross-validation framework to identify optimal parameter combinations. For binary classification of prolonged LOS, logistic regression (with feature standardization) and random forest classifiers were applied. Model performance was quantified using accuracy, area under the receiver operating characteristic curve (AUC), precision, recall, and F1-score.

Continuous LOS prediction was performed using linear regression and random forest regression, with performance metrics including mean absolute error (MAE), mean squared error (MSE) and the coefficient of determination (R²). Receiver operating characteristic (ROC) curves were generated to visualize classifier performance, and feature importance values were derived from random forest models. For regression analyses, scatter plots comparing predicted vs. observed LOS were constructed to evaluate model fit. All statistical analyses and machine learning workflows were implemented in Python (pandas, scikit-learn, scipy, matplotlib). To improve reproducibility, all machine learning models were implemented with a fixed random_state. Random forest models were constructed using 100 trees (n_estimators=100) with default depth settings. Continuous variables were standardized using z-score normalization prior to logistic regression modelling. Model performance was evaluated on a held-out test set (30% of the data), while the remaining 70% was used for training. Overfitting was assessed by comparing model performance between training and testing datasets. Given the relatively small sample size, a parsimonious modelling approach was adopted to balance predictive performance and generalizability.

Baseline demographic and laboratory characteristics stratified by hospital LOS are summarized in (Table I). Patients were evenly distributed between those discharged within 3 days and those hospitalized for longer durations. Age (61.1±10.9 vs. 63.4±10.9 years; P=0.28), sex distribution (65.5 vs. 68.5% male; P=0.74) and the prevalence of diabetes (22.4 vs. 20.4%; P=0.80) were comparable between the groups. By contrast, significant differences were observed in renal function parameters. Patients with prolonged periods of hospitalization exhibited markedly higher blood urea concentrations (53.9±39.3 vs. 30.6±18.9 mg/dl; P=0.003) and serum creatinine levels (1.39±1.16 vs. 0.88±0.52 mg/dl; P=0.001), indicating greater renal dysfunction. LVEF did not differ significantly between the groups (44.3±17.0 vs. 46.1±15.3%; P=0.49), suggesting that renal dysfunction, rather than systolic cardiac performance, was more strongly associated with prolonged hospitalization.

The data for predictive model performance on the held-out test sets are presented in Table II. Using only renal biomarkers, the logistic regression demonstrated modest discrimination (accuracy, 0.56; AUC, 0.68; 95% CI, 0.58-0.78) with limited recall (0.38) and F1 score (0.44). By contrast, tree-based ensemble approaches demonstrated superior discrimination: The random forest classifier improved accuracy to 0.71 with recall (0.63) and F1 score (0.67) alongside good discrimination (AUC, 0.74; 95% CI, 0.65-0.83) outperforming both logistic regression and gradient boosting. Gradient boosting achieved a slightly higher AUC of 0.76 (95% CI, 0.67-0.85), although with lower recall (0.56) and F1 score (0.62). Models trained exclusively on LVEF features exhibited a poor predictive ability (AUC, 0.48; 95% CI, 0.38-0.58) and low classification metrics (accuracy, 0.50; F1 score, 0.32). Although random forest improved recall substantially (0.81), overall discrimination remained limited, indicating LVEF alone provides insufficient prognostic information for LOS. Incorporating additional clinical covariates, including LVEF, age, sex and diabetes, did not substantially enhance model performance. Logistic regression exhibited minimal improvement (accuracy, 0.56; AUC, 0.64; 95% CI, 0.54-0.74) while random forest delivered the most robust and consistent performance (accuracy, 0.71; AUC, 0.68; 95% CI, 0.58-0.78; F1 score, 0.67), underscoring its superior ability to leverage multimodal clinical information. From a clinical perspective, an AUC of 0.74 indicates acceptable discriminative ability, indicating that the model can correctly distinguish between patients with prolonged and non-prolonged LOS ~74% of the time. This level of performance suggests potential utility for early risk stratification in hospital settings, although it may still be insufficient as a standalone decision-making tool and should be interpreted in conjunction with clinical judgment and other patient-specific factors.

The results of regression analysis are summarized in Table III. Using the renal feature set, the linear regression model predicted LOS with an MAE of 1.16 days and explained ~10% of the variance (R²=0.10). The random forest model did not yield substantial improvement, demonstrating a slightly higher MAE of 1.30 days and a lower R² of 0.04. Models based solely on echocardiographic (LVEF) features performed poorly, with both linear and random forest regressions explaining minimal variance (R²=0.04 and 0.09, respectively) and achieving comparable MAE values (1.26-1.27 days). By contrast, incorporating additional clinical variables in the combined feature set (renal + LVEF + age + sex + diabetes) modestly enhanced predictive performance. Linear regression achieved an MAE of 1.24 days (R²=0.09; 95% CI, 0.00-0.20), whereas the random forest model improved to an MAE of 1.18 days and R² of 0.26 (95% CI, 0.11-0.41). Although the overall variance explained remained modest, the random forest model using combined features demonstrated the best balance of predictive accuracy and generalizability across all tested configurations.

The comparative performance of predictive models and their graphical summaries are presented in (Fig. 2). The ROC curve for the logistic regression model trained on the combined clinical, renal, and echocardiographic feature set (Fig. 2IA) yielded an AUC of 0.64, reflecting modest discriminative ability. The curve, which plots the true positive rate against the false positive rate across varying thresholds, lies only slightly above the diagonal reference line denoting chance-level classification. This indicates that the model captured limited but discernible signal within the data, consistent with partial discrimination between patients with prolonged versus shorter hospital stays. This implies traditional linear models using routinely collected variables may have limited utility as standalone tools for early risk stratification at admission.

Feature importance derived from the random forest classifier trained on the same combined feature set is shown in Fig. 2B. Age emerged as the most influential predictor (Gini importance >0.2), followed by serum urea concentration and LVEF. Other renal markers, including eGFR and creatinine, also contributed meaningfully, albeit with lower relative weights. These results indicate that renal biomarkers and age primarily drive model predictions, while echocardiographic indices provide comparatively limited incremental value, reinforces the clinical relevance of renal function assessment at admission

The association between the predicted and observed LOS for the linear regression model based on renal biomarkers is displayed in Fig. 2C. The red dashed line represents the line of identity, whereas the blue line denotes the model's best-fit regression line. The dispersion of points around the identity line indicates that the model captured the general direction of the association but with weak correlation, underscoring that renal parameters alone explain only a fraction of the variability in LOS among patients with HF, hence is insufficient to fully explain variability in LOS, highlighting the multifactorial nature of HF outcomes.

By contrast, the gradient boosting classifier trained exclusively on renal biomarkers demonstrated markedly enhanced discrimination (AUC, 0.76) (Fig. 2D). The ROC curve rises substantially above the diagonal reference line, indicating improved sensitivity and specificity in identifying patients at risk of prolonged hospitalization. This suggests that more advanced models capable of capturing nonlinear relationships may provide clinically meaningful improvements in identifying high-risk patients early during hospitalization. Compared with logistic regression and random forest models, Gradient boosting more effectively captured nonlinear interactions among renal variables, resulting in superior predictive accuracy. Collectively, these findings highlight the prognostic relevance of renal dysfunction and support the utility of ensemble-based learning approaches for clinical risk stratification in HF.