2.1. Data Source and Study Participants

This study was approved by the ethics committee of the Chongqing Medical University (Approval No. 2024097), the ethics committee of the Affiliated Banan Hospital of Chongqing Medical University (Approval No. BNLLKY2023037), and the ethics committee of the First Affiliated Hospital of Zhejiang University School of Medicine (Approval No. IIT20230312B-R1). Due to the retrospective nature of the study, informed consent was waived, and the research was conducted in accordance with national regulations and institutional guidelines.

To ensure scientific rigor, internal consistency, clinical relevance, and data quality, we established the following inclusion and exclusion criteria. Inclusion criteria were (1) hospitalization(s) for T2DM and (2) data collected between 2012 and 2023. Exclusion criteria were (1) age < 65 years (n = 5142), (2) LOS < 2 days (n = 1954), (3) fewer than two admission records (n = 2586), and (4) in-hospital death (n = 327). After applying these criteria, 8800 patients were included in the study. The patient selection process is summarized in Figure 1.

Data were obtained from six tertiary hospitals affiliated with the Medical Data Science Academy of Chongqing Medical University, covering the period from January 2011 to December 2022. Patients from these hospitals were randomly divided into a training set (n = 4729) and an internal validation set (n = 2027) in a 7:3 ratio. Additionally, patients from the Affiliated Banan Hospital of Chongqing Medical University (January 2018–December 2023, n = 1244) and the First Affiliated Hospital of Zhejiang University School of Medicine (January 2020–December 2022, n = 800) were used as External Validation Set I and External Validation Set II, respectively.

2.2. Predictors and Outcomes

Clinical data were extracted from the electronic medical record (EMR) system within 48 h of admission: (1) basic information: age, sex, insurance type, past surgical history (PSH), smoking history, drinking history, age-adjusted Charlson comorbidity index (ACCI) score, and LOS; (2) diagnosis: hypertension, coronary heart disease (CHD), cerebral infarction (CI), and hyperlipidemia; (3) laboratory measurements: aspartate aminotransferase (AST), alanine aminotransferase (ALT), triglycerides (TGs), creatinine (CREA), uric acid (UA), low-density lipoprotein cholesterol (LDL-C), high-density lipoprotein cholesterol (HDL-C), albumin (ALB), estimated glomerular filtration rate (eGFR), neutrophil-to-lymphocyte ratio (NLR), platelet-to-lymphocyte ratio (PLR), lymphocyte-to-monocyte ratio (LMR), and neutrophil percentage-to-albumin ratio (NPAR); (4) vital signs: systolic blood pressure (SBP) and diastolic blood pressure (DBP); (5) medication administration: nutritional support drug use, antihypertensive drug use, antidiabetic drug use, statin drug use, antiplatelet and anticoagulant drug use, Chinese patent medicine use, analgesic drug use, antiosteoporotic drug use, antibiotic drug use, hemostatic agent drug use, and psychotropic drug use.

This study focused on two main outcomes: prolonged LOS and 30-day readmission. Prolonged LOS was defined as a binary variable, with the cutoff set at the 75th percentile of the LOS distribution among participants, which was 14 days [18–20]. Patients with a LOS of 14 days or more were coded as 1, while those with less than 14 days were coded as 0. A 30-day readmission was defined as any readmission occurring within 30 days of discharge, regardless of the reason. The time to readmission was calculated by subtracting the LOS of the initial admission from the interval between the two admissions. Only the first readmission and its corresponding initial admission were included in the final analysis.

2.3. Definition

The type of insurance selected by individuals reflects the economic burden on them and their families. In this study, insurance types were categorized as urban employee medical insurance (UEMI), urban resident medical insurance (URMI), full self-payment, and other insurance. The ACCI score was used to quantify comorbidities based on the number and severity of illnesses, serving as a prognostic evaluation tool [21]. The eGFR was calculated using the Modification of Diet in Renal Disease (MDRD) study equations [22], in line with current recommendations. Novel markers such as the NLR, PLR, LMR, and NPAR were used to assess systemic inflammation and have been linked to adverse outcomes [23–25].

2.4. Model Development

Variables identified as statistically significant in univariate logistic regression analysis were included in the least absolute shrinkage and selection operator (LASSO) regression analysis, followed by a multivariate logistic regression model. A nomogram was then constructed using the “rms” package in R. Each regression coefficient from the multivariate logistic regression model was proportionally converted into a score ranging from 0 to 100, with the highest absolute β coefficient assigned a score of 100. The total score was calculated by summing the scores of each variable, and this total score was then converted into a predicted probability.

2.5. Model Performance

To avoid overfitting and determine the optimal number of variables for the model, we iteratively identified K variables associated with prolonged LOS and 30-day readmission. We plotted the mean area under the receiver operating characteristic curve (AUROC) for different values of K to ensure a robust model. For model evaluation, we calculated the AUROC for the training set, internal validation set, and external validation sets. We also assessed sensitivity, specificity, positive predictive value (PPV), negative predictive value (NPV), and Youden’s index. Calibration plots and Brier scores were used to illustrate the relationship between predicted risk values and actual observed outcomes. Decision curve analysis (DCA) and clinical impact curve (CIC) were performed to evaluate the clinical effectiveness of the model and quantify the net benefit to patients. Subgroup analysis was conducted by categorizing patients into three age groups: under 75 years, 75–84 years, and over 84 years, to assess the model’s performance within each subgroup.

2.6. Statistical Analyses

We followed the transparent reporting of a multivariable prediction model for individual prognosis or diagnosis (TRIPOD) guidelines for reporting (Table S1) [26]. Missing data were handled using multivariate multiple imputation with chained equations to maximize statistical power and minimize bias. Discrete variables were expressed as rates and percentages, with the chi-square test used for group comparisons. Quantitative variables, which did not follow a normal distribution, were represented by the median and interquartile range [M(Q25 − Q75)], and the Mann–Whitney U test was used for group comparisons. All statistical analyses were two-sided, with statistical significance set at p < 0.05. Analyses were performed using SPSS Version 22.0 and R (Version 4.3.2, Vienna, Austria).

3.1. Patient Characteristics

A total of 8800 patients were included in the study, divided into four groups: 4729 in the training set, 2027 in the internal validation set, 1244 in External Validation Set I, and 800 in External Validation Set II. These groups were selected for predicting prolonged LOS and 30-day readmission after excluding individuals who did not meet the inclusion criteria. In the training and internal validation sets, 1902 patients (28.15%) experienced prolonged LOS, and 923 patients (13.66%) were readmitted within 30 days of discharge. Detailed patient characteristics, stratified by outcomes, are presented in Tables 1 and 2. The Mann–Whitney U test showed no significant differences in missing variables between the training and internal validation sets before and after multiple imputations (Table S2).

Patients with prolonged LOS were more likely to be male, have a history of smoking and drinking, and be diagnosed with hypertension, CHD, and CI. They also exhibited higher levels of AST, ALT, NLR, PLR, NPAR, and CREA. Conversely, they had lower levels of TGs, LMR, UA, LDL-C, HDL-C, ALB, and GFR. Patients readmitted within 30 days were younger, more likely to be male, had a longer LOS, and were more likely to have UEMI. They also had a higher prevalence of smoking, drinking, and higher ACCI scores. These patients were more frequently diagnosed with CHD, CI, and hyperlipidemia and were more likely to use nutritional support drugs, antidiabetic drugs, statins, antiplatelet and anticoagulant drugs, Chinese patent medicines, analgesics, antibiotics, hemostatic agents, and psychotropic drugs. They exhibited higher levels of NLR, PLR, NPAR, and TGs but lower SBP, TGs, LMR, LDL-C, HDL-C, and ALB.

3.2. Selection of Predictors for Prolonged LOS and 30-Day Readmission

In the univariate analysis, several factors were significantly associated with prolonged LOS, including sex, smoking history, drinking history, hypertension, CHD, CI, PSH, AST, ALT, TGs, NLR, LMR, PLR, NPAR, CREA, UA, LDL-C, HDL-C, ALB, and GFR (p < 0.05). Similarly, factors significantly associated with 30-day readmission included age, sex, LOS, smoking history, drinking history, insurance type, ACCI score, CHD, CI, hyperlipidemia, and the use of various medications (p < 0.05) (Tables 3 and 4).

For prolonged LOS, 20 variables were entered into the LASSO regression analysis, and four were identified as significant predictors: CI, AST, NPAR, and ALB (Figure 2a,b). The final multivariate logistic regression model confirmed that CI (OR: 2.273, 95% CI: 1.932–2.676, p < 0.001), AST (OR: 1.005, 95% CI: 1.003–1.007, p < 0.001), NPAR (OR: 1.100, 95% CI: 1.075–1.126, p < 0.001), and ALB (OR: 0.919, 95% CI: 0.900–0.938, p < 0.001) were independent predictors of prolonged LOS (Figure 2c). For 30-day readmission, seven predictors were identified: sex, LOS, nutritional support drug use, antiplatelet and anticoagulant drug use, analgesic drug use, antibiotic drug use, and ALB (Figure 3a,b). The multivariate logistic regression model showed that sex (OR: 1.737, 95% CI: 1.451–2.079, p < 0.001), LOS (OR: 1.011, 95% CI: 1.003–1.019, p < 0.001), nutritional support drug use (OR: 3.167, 95% CI: 2.619–3.830, p < 0.001), antiplatelet and anticoagulant drug use (OR: 0.621, 95% CI: 0.515–0.748, p < 0.001), analgesic drug use (OR: 2.201, 95% CI: 1.819–2.676, p < 0.001), antibiotic drug use (OR: 1.298, 95% CI: 1.069–1.576, p = 0.008), and ALB (OR: 0.954, 95% CI: 0.937–0.972, p < 0.001) were independent predictors of 30-day readmission (Figure 3c).

To validate the performance of the LASSO-logistic regression, we evaluated subsets of variables associated with prolonged LOS and 30-day readmission using the top K features. The addition of more variables beyond four for prolonged LOS and seven for 30-day readmission did not significantly improve the AUROC (Figure 4). This suggests that including additional variables, even if closely related to the outcomes, may not enhance the predictive performance of the models (Table S3).

3.3. Development and Validation of the Prolonged LOS Model

A static nomogram was developed to predict prolonged LOS based on a four-predictor model (Figure 5a). Figure 5b demonstrates how the nomogram can be used to estimate the probability of prolonged LOS for a patient in the training set. The total score, derived from the predictors, provides the predicted probability. Additionally, a dynamic nomogram was created and made available online, allowing clinicians to calculate the probability of prolonged LOS in elderly patients with T2DM (https://cqmuhyx.shinyapps.io/prolonged_los/).

The model showed strong predictive performance, with AUROC values of 0.720 (95% CI: 0.703–0.737) in the training set, 0.715 (95% CI: 0.688–0.742) in the internal validation set, 0.736 (95% CI: 0.696–0.777) in External Validation Set I, and 0.703 (95% CI: 0.645–0.761) in External Validation Set II (Figure 6a,b; Figure S1A, B). The optimal decision probability cutoff was 0.311. Calibration curves indicated strong agreement between predicted and actual probabilities in the training set (Brier score = 0.174, 95% CI: 0.168–0.180), internal validation set (Brier score = 0.172, 95% CI: 0.163–0.182), External Validation Set I (Brier score = 0.123, 95% CI: 0.110–0.136), and External Validation Set II (Brier score = 0.106, 95% CI: 0.090–0.121) (Figure 6c,d; Figure S1C, D). Overall, the nomogram demonstrated excellent discrimination and calibration. Detailed performance metrics for all datasets are provided in Table 5.

DCA showed favorable clinical utility. Specifically, when the threshold probability exceeded 12%, using the model to predict prolonged LOS and guide interventions provided greater net benefit than treating all or no patients (Figure S2A). The CIC further confirmed the model’s superior net benefit within the threshold probability range (Figure S2C). DCAs and CICs for the internal and external validation sets are shown in Figure S2B, S1E, F and Figure S2D, S1G, H, respectively.

3.4. Development and Validation of the 30-Day Readmission Model

A nomogram was developed to predict 30-day readmission in elderly patients with T2DM (Figure 7a). Figure 7b illustrates its application for a patient in the training set. A user-friendly web interface (https://cqmuhyx.shinyapps.io/readmission/) was also created to help clinicians calculate the 30-day readmission probability.

The model demonstrated strong predictive performance, with AUROC values of 0.766 (95% CI: 0.745–0.787) in the training set, 0.769 (95% CI: 0.736–0.801) in the internal validation set, 0.633 (95% CI: 0.594–0.673) in External Validation Set I, and 0.671 (95% CI: 0.613–0.729) in External Validation Set II (Figures 3a,b and 8a,b). The optimal decision probability cutoff was 0.148. Calibration curves for the training set (Brier score = 0.102, 95% CI: 0.096–0.108), internal validation set (Brier score = 0.100, 95% CI: 0.090–0.101), External Validation Set I (Brier score = 0.156, 95% CI: 0.143–0.169), and External Validation Set II (Brier score = 0.093, 95% CI: 0.078–0.109) confirmed the nomogram’s accuracy (Figure 8c,d; Figure S3C, D). Detailed performance metrics are provided in Table 6.

DCA (Figure S4A) and CIC (Figure S4C) confirmed the clinical utility of the nomogram. The DCA showed that the nomogram provided greater net benefit when the high-risk threshold probability exceeded 10%. The CIC, applied to a sample size of 1000, demonstrated that the predicted number of 30-day readmissions closely matched the actual number when the threshold probability was above 0.40. DCAs and CICs for the internal and external validation sets are shown in Figure S4B, S3E, F and Figure S4D, S3E, F, respectively.

3.5. Subgroup Analysis by Age

The prolonged LOS and 30-day readmission prediction models demonstrated good discrimination across all age subgroups, with AUROCs exceeding 0.60 in all groups (Table 7). Sensitivity, specificity, NPV, PPV, and Brier scores for each age subgroup are provided in Tables S4–S8. Figures S5–S12 show the ROC curves, calibration curves, decision curves, and CICs for all age subgroups. These results confirm the robustness of the models across different age groups.