Identification of Risk Factors and Prediction Models for Acute Kidney Injury in Hospitalized Elderly Patients with Heart Failure

Figure 1. This flowchart illustrates the process of patient selection for inclusion in the final analysis. A total of 7842 patients were initially screened. After the exclusion criteria were applied, 7076 patients were included in the final analysis.

Figure 2. Lasso regression for variable selection. (a) Coefficient paths of the 43 candidate predictors and the cross-validation error curve. (b) Eight predictors above the study-defined importance threshold of >20% were retained and entered into the multivariable logistic regression model.

Figure 3. Receiver operating characteristic (ROC) curves for the 13 machine learning models in the training set (a) and validation set (b). In the training set, most models achieved near-perfect AUC (>0.998), indicating good fit but with a risk of overfitting. In the validation set, logistic regression achieved the highest AUC of 0.804 (95% CI: 0.777–0.830) and was selected as the optimal model.

Figure 4. Calibration curves of the logistic regression model. (a) Calibration curve in the training set. (b) Calibration curve in the validation set. In the validation set, the Hosmer–Lemeshow test P‑value was 0.605, the calibration intercept was 0.013, the calibration slope was 0.835, and the Brier score was 0.082, indicating acceptable calibration.

Figure 5. Decision curve analysis (DCA) of the 13 machine learning models. (a) DCA in the training set. (b) DCA in the validation set. In the validation set, logistic regression showed a positive net benefit at thresholds below approximately 0.28, indicating potential clinical utility mainly in low-threshold screening scenarios; at higher thresholds, the net benefit fell below zero.

Figure 6. Nomogram for predicting AKI risk in hospitalized elderly patients with heart failure. The nomogram includes eight predictors: diuretic use, hypertension, diabetes, valvular heart disease, COPD, CKD, admission cystatin C, and LVEF. With respect to the LVEF, lower values corresponded to higher points and thus higher AKI risk, which is consistent with its protective effect in the logistic regression model.