A total of 606 patients were included in this study, with 360 males and 246 females. The age range of the participants was 65 to 96, with an average age of 74.1. The training cohort consisted of 424 cases, with 246 males and 178 females. The average age of this group was 73.9. The validation cohort included 182 patients, with 114 males and 68 females. The average age of this group was 74.6. There were no significant differences in various indices between the two groups (P > 0.05) (Table 1).

This study compared the all-cause mortality rates in patients with AKI between a test group and a validation group. The mortality rates were determined over a period of 28 days. In the test group, 267 cases of all-cause death occurred within 28 days, resulting in a mortality rate of 63%. Similarly, in the validation group, 112 cases of all-cause death occurred within 28 days, resulting in a mortality rate of 61.5%. Statistical analysis revealed that there was no significant difference in all-cause mortality between the two groups (p > 0.05).

This study compared the all-cause mortality rates in patients with AKI between a training cohort and a validation cohort. The mortality rates were determined over a period of 28 days. In the training cohort, 267 cases of all-cause death occurred within 28 days, resulting in a mortality rate of 63%. Similarly, in the validation cohort, 112 cases of all-cause death occurred within 28 days, resulting in a mortality rate of 61.5%. Statistical analysis revealed that there was no significant difference in all-cause mortality between the two cohorts (P > 0.05).

The initial model encompassed a large number of potential predictors, including age, sex, myocardial infarction, cerebrovascular disease, peripheral vascular disease, dementia, diabetes mellitus (DM), heart failure, hypertension, chronic obstructive pulmonary disease, K, HCO3-, P, BMI, SBP, DBP, MAP, mechanical ventilation, WBC, Hb, BUN, Cr, Alb, CRP, GFR, AKIN staging, CCI, APACHE II score, SOFA score, and cause of acute kidney injury (AKI cause). Following a comprehensive LASSO regression analysis on the training cohort, the number of potential predictors was judiciously narrowed down to eight. The table below delineates the coefficients for these eight predictors (Table 2), with their profiles visually represented in the accompanying figure (Fig. 1). The figure also incorporates a cross-validated error plot of the LASSO regression model (Fig. 2). Embracing a commitment to regularization and parsimony, the final model comprised these eight variables, with the cross-validated error falling within one standard error of the minimum. Subsequent multivariate logistic analyses were executed on distinct cohorts, and the outcomes are meticulously detailed in the subsequent table (Table 3). The ultimate logistic model, featuring 8 independent predictors (age, P, CCI, SBP, Cr, Alb, APACHE II score, and SOFA score), was crafted into a user-friendly nomogram, as elucidated in the ensuing figure (Fig. 3).

Lasso regression coefficient path plot

Lasso regression cross-validation plot

Nomogram prediction model

systolic blood pressure, SBP; creatinine, Cr; albumin, Alb; phosphorus, P; Acute Physiology and Chronic Health Evaluation II score, APACHE II score; sequential organ failure assessment score, SOFA score

The following figures illustrate the AUCs of the model in different cohorts. The AUC for the training cohort was 0.809, as shown in Fig. 4, indicating excellent predictive performance. Additionally, the model exhibited a sensitivity of 0.76, a specificity of 0.71, and an accuracy of 0.74, representing its overall correctness in classification. Similarly, in the validation cohort, the AUC was 0.799, as depicted in Fig. 4, indicating good predictive performance. The calibration curves for the training cohorts (Fig. 5) exhibited an intercept of 0.024 and a slope of 0.975, signifying strong calibration performance of the model. Furthermore, a Brier value of 0.17 was noted, indicating minimal mean squared error between the model’s probability predictions and the actual observed values. These findings underscore the reliability and stability of the model in predictive tasks. Similarly, consistent results were observed in the validation cohorts, further validating the model’s performance. As depicted in Fig. 6, the DCA showcased the nomogram’s superior overall net benefit across a wide and practical range of threshold probabilities, suggesting a high potential for clinical utility.

ROC curves of the nomogram prediction model

Calibration curve of the nomogram prediction model for the training and validation cohorts

DCA of the nomogram of the training and validation cohorts