This retrospective cohort study analyzed data from the Shaanxi Provincial People's Hospital, spanning the period from January 2020 to October 2025. The study protocol, including the collection of clinical data, was approved by the Medical Research Ethics Committee of the Shaanxi Provincial People's Hospital (Approval No: 2025R082).

The patients included in this study were adult ICU patients who met both the Sepsis-3 criteria and the Berlin definition of ARDS. The diagnosis of sepsis was based on the Sepsis-3 criteria, requiring clear evidence of infection (based on clinical, microbiological, or imaging assessment), and a sequential organ failure assessment (SOFA) score increasing by ≥ 2 points compared to the baseline within 24 h of admission (1). The diagnosis of ARDS strictly follows the Berlin definition, which stipulates that patients must develop new or exacerbated respiratory symptoms within 1 week of the onset of sepsis. Chest imaging should show bilateral pulmonary infiltrates, and the oxygenation index (PaO₂/FiO₂) should meet the criteria for hypoxemia when the positive end-expiratory pressure (PEEP) is ≥ 5 cmH₂O. At the same time, exclusion of heart failure or excessive fluid load as the main cause is required (16). All diagnoses were independently reviewed by two senior critical care physicians. In case of any disagreement, a third expert would make the final decision.

This study aims to develop a prognostic prediction model for the clinical syndrome of “simultaneous sepsis and ARDS,” rather than distinguishing whether ARDS is caused by extrapulmonary sepsis or pneumonia. Therefore, the inclusion criteria do not strictly require the initial site of infection to be differentiated (either within the lungs or outside the lungs) but rather consider both as a clinical entity with common pathophysiological characteristics. Nevertheless, we still recorded all patients' suspected infection foci (as baseline variables) and explored the impact of different infection sites on the model's predictive performance in the sensitivity analysis.

The exclusion criteria were: (1) patients younger than 18 years; (2) an ICU stay of less than 24 h; (3) patients with chronic liver diseases (including liver cirrhosis, chronic hepatitis, etc.); (4) patients with bone marrow suppression, active malignancies, or those receiving chemotherapy/antiplatelet therapy, (5) patients with pregnant or lactating, and (6) incomplete key data necessary for analysis.

The following variables were collected within the first 24 h of admission to the intensive care unit (ICU): (1) Demographic and Vital Sign Data: age, gender, body temperature, heart rate, respiratory rate, and mean arterial pressure; (2) Comorbidities: hypertension, diabetes, respiratory failure, septic shock, acute kidney injury (AKI), atrial fibrillation, and chronic kidney disease; (3) Laboratory Parameters: aspartate aminotransferase, alanine aminotransferase, glucose, white blood cell count, procalcitonin, C-reactive protein, uric acid, total cholesterol, cystatin C, blood urea nitrogen, and creatinine; (4) Nine Candidate Immune-Inflammatory-Nutritional Indicators: albumin-alkaline phosphatase ratio (AAPR), albumin-bilirubin (ALBI) grade, NLR, platelet-to-lymphocyte ratio (PLR), lymphocyte-to-monocyte ratio (LMR), PNI, SII, and lactate-albumin ratio (LAR); (5) Clinical Scores: SOFA score. The formulas for the calculations are presented as follows: the AAPR is determined by dividing albumin (g/L) by alkaline phosphatase (ALP) (IU/L); the PNI is calculated by adding albumin to five times the lymphocyte count; and the SII is computed as platelet count multiplied by neutrophil count, divided by lymphocyte count. The ALBI grade is classified according to the following thresholds: ≤ −2.60 for ALBI grade 1, > −2.60 to ≤ −1.39 for ALBI grade 2, and ≥ −1.39 for ALBI grade 3, as previously established in the literature.

This study selected the 28-day all-cause mortality rate as the primary endpoint. The following considerations were taken into account: (1) It is widely accepted as a standard time point for evaluating the short-term prognosis of critical conditions (especially sepsis and ARDS), facilitating comparisons with a large number of existing studies; (2) Compared with in-hospital mortality rate, the 28-day mortality rate can more comprehensively capture early death events, avoiding bias caused by differences in discharge policies among different medical institutions; (3) It is located at the period with the highest risk of sepsis-related death, providing direct clinical guidance value for early risk stratification and intervention.

For patients who were discharged before the end of the study period (October 2025) and whose 28-day outcomes were not recorded in the hospital, we conducted outcome confirmation through the following structured process to ensure the completeness of the data: (1) Electronic medical record system query: Firstly, in the integrated electronic medical record system of the hospital, check whether the patient was readmitted within 28 days after discharge for any reason, and record the survival status of the patient during this hospitalization. (2) Telephone follow-up: For patients for whom no record of readmission was found, the research team followed a standardized follow-up procedure and attempted to contact the patient or their designated immediate family member by phone for a follow-up call. The main objective is to determine whether the patient is still alive on the 28th day after being admitted to the ICU.

Following the application of the exclusion criteria (in particular, exclusion of patients with incomplete key data), the final analytical cohort of 635 patients constituted a complete-case dataset. A systematic verification confirmed that there were no missing values for any of the demographic, clinical, laboratory, or immune-inflammatory-nutritional predictor variables listed in the Data Extraction section among these 635 patients. Consequently, no imputation methods were required or applied.

This was a retrospective, single-center study utilizing all available eligible data from the defined study period to maximize the sample size for model development. While a formal a priori sample size calculation for prediction model development is complex and depends on the anticipated outcome incidence and predictor effects, we followed established guidelines to ensure robustness. A key metric to guard against overfitting in logistic regression is the Events Per Variable (EPV). It is recommended that the EPV should be at least 10 to 20 to ensure reliable and generalizable parameter estimates (17). Our final model incorporated 7 predictors. In the training set (n = 477), we observed 226 events of 28-day mortality. This yields an EPV of 32.3 (226/7), which comfortably exceeds the recommended thresholds, indicating a very low risk of overfitting and affirming the adequacy of our sample size for the performed multivariable modeling.

The study cohort was randomly divided, using a fixed random seed (Seed = 20,231,001), into a training set (75%) for model development and an independent hold-out validation set (25%) for model evaluation. Continuous variables adhering to a normal distribution were reported as mean ± standard deviation, whereas non-normally distributed variables were presented as median (interquartile range). Categorical variables were represented as percentages. The model development process comprised three steps: (1) Univariate analysis: All potential indicators were analyzed using univariate logistic regression to identify those preliminarily associated with 28-day mortality (P < 0.05); (2) Handling of Continuous Predictors: Continuous predictors were analyzed on their original scale. The linearity assumption for each variable against the log-odds of 28-day mortality was assessed using smooth calibration plots and Martingale residual plots. Where non-linearity was evident, restricted cubic splines (RCS) were considered. However, for the selected composite indicators—which are typically interpreted monotonically—and based on our diagnostic checks, a linear form in the logit was judged appropriate to preserve simplicity and clinical interpretability. No continuous predictors were arbitrarily categorized. (3) LASSO: To mitigate overfitting and multicollinearity, the indicators significantly associated in the univariate analysis were included in a LASSO logistic regression model; (4) Nomogram construction: A multivariate logistic regression was performed using the features selected from the LASSO analysis to identify independent predictors, followed by the construction of a nomogram. The model's performance was evaluated in both the training and validation sets. Discrimination was assessed using the area under the receiver operating characteristic curve (AUC). Calibration was evaluated through the use of calibration plots incorporating a non-parametric smoothing technique. The clinical utility was quantified via decision curve analysis (DCA), which calculates the net benefit across a range of threshold probabilities.

Quantitative calibration was assessed by calculating the calibration slope and calibration intercept along with their 95% confidence intervals (obtained via bootstrapping with 1,000 replicates). A calibration slope of 1 and an intercept of 0 indicates perfect calibration. While the Hosmer-Lemeshow (H-L) goodness-of-fit test is commonly reported, it has known limitations, including sensitivity to sample size and arbitrary grouping of predicted probabilities. Therefore, we prioritized the use of the calibration slope and intercept, along with visual calibration plots, as more informative and robust measures of calibration performance.

All statistical analyses were conducted utilizing R software (version 4.1.3). A two-sided P-value of less than 0.05 was regarded as indicative of statistical significance.

The study comprised 635 eligible participants, among whom 298 individuals (46.9%) experienced 28-day mortality, as depicted in Figure 1 and detailed in Table 1. The cohort was randomly divided into a training group (75%, n = 477) and a validation group (25%, n = 158). Table 1 presents comparable demographic characteristics, vital signs, comorbidities, laboratory examinations, immune-inflammatory-nutritional indicators, and outcome data for both the training and validation groups. The median age of participants in the training group was 65 years, with a gender distribution of 269 males (59.5%) and 208 females (40.5%). Similarly, the validation group had a median age of 63 years, comprising 86 males (60.4%) and 72 females (45.6%).

All demographic and clinical data were accessible within 24 h of admission. Univariate analyses, as presented in Table 2, indicated that the levels of WBC (1.066, 95% CI: 1.036–1.096), Cystatin C (1.129, 95% CI: 1.002–1.271), ALBI (4.024, 95% CI: 2.810–5.763), NLR (1.022, 95% CI: 1.014–1.031), and SII (1.000, 95% CI: 1.000–1.000), as well as LAR (1256205.6, 95% CI: 23135.7–68208580.1), were significantly elevated in the Death group compared to the Survival group. Conversely, AAPR (0.020, 95% CI: 0.006–0.067), PLR (0.999, 95% CI: 0.999–1.000), LMR (0.987, 95% CI: 0.962–1.013), and PNI (0.902, 95% CI: 0.875–0.931) were significantly lower in the Death group.

A 10-fold cross-validation of the initial input LASSO regression method was performed to mitigate collinearity among the relevant indicators, facilitating the identification of mortality predictors (Figure 2). Ultimately, eight variables were selected as optimal based on the optimal lambda value. The model was formulated as follows: −1.125558019 + 015333867 ^* WBC - 1.487836505 ^* AAPR + 0.563129312 ^* ALBI + 0.009042757 ^* NLR - 0.000925553 ^* PLR - 0.018924139 ^* PNI + 2.38664 ^* 10^{−05 *} SII + 5.52519249 ^* LAR. A multivariate logistic regression analysis of the training set, employing these variables, revealed that AAPR, ALBI, NLR, PLR, PNI, SII, and LAR were independent risk factors for the development of 28-day mortality in sepsis patients with ARDS (Table 3). Based on these variables, a nomogram was developed to predict 28-day mortality in sepsis patients with ARDS (Figure 3).

The analysis of the ROC curve indicated that the nomogram exhibited a strong capacity to predict 28-day mortality in sepsis patients with ARDS within both the training (AUC = 0.873) and validation (AUC = 0.837) cohorts, as depicted in Figure 4. Furthermore, the simplified prediction model demonstrated superior predictive performance compared to the SOFA score in both the training (AUC = 0.689) and validation (AUC = 0.684) cohorts (Figure 4). The calibration plots demonstrated excellent agreement between predicted and observed risks (Figure 5). Quantitatively, the calibration slope was 1.01 (95% CI: 0.97–1.05) with an intercept of 0.02 (95% CI: −0.03–0.07) in the training set. In the validation set, the slope was 0.95 (95% CI: 0.90–1.00) and the intercept was −0.03 (95% CI: −0.10–0.04). These metrics indicate nearly ideal calibration in the training set and excellent calibration with only minimal shrinkage in the validation set, suggesting negligible overfitting.

DCA further quantified the clinical utility of the nomogram (Figures 5C, D). Compared to the “treat-all” or “treat-none” strategies, the use of our nomogram to guide intervention decisions provided a superior net benefit across a clinically practical range of threshold probabilities from approximately 10% to 70% in both the training and validation sets. This range encompasses the gray zone where clinical decision-making is often most uncertain. For example, at a threshold probability of 30% (meaning a clinician would consider an intervention if the patient's predicted mortality risk is ≥30%), the net benefit of using the nomogram was approximately 0.08 in the validation set, indicating that for every 100 patients, using the model would lead to 8 more beneficial interventions without increasing unnecessary interventions, compared to not using any model.