A Bar-Based Nomogram for Predicting Septic Shock in Patients with Acute Pancreatitis Complicated by Sepsis: Development and External Validation

Abstract

Background:

Septic shock is a common and life-threatening complication in patients with acute pancreatitis (AP) complicated by sepsis, yet rapid and accurate tools for early risk prediction remain limited in clinical practice. This study aimed to develop and externally validate a nomogram incorporating the blood urea nitrogen-to-albumin ratio (BAR) to predict the risk of progression to septic shock in this high-risk population.

Methods:

In this retrospective multicohort study, a total of 541 patients with AP complicated by sepsis were identified from the Medical Information Mart for Intensive Care IV (MIMIC-IV) database and randomly divided into a training set (n = 379) and an internal validation set (n = 162) at a 7:3 ratio. An independent cohort of 295 patients from the Second Hospital of Hebei Medical University was used for external validation. Candidate variables collected within the first 24 hours of intensive care unit admission were screened using least absolute shrinkage and selection operator regression. A multivariable logistic regression model was constructed and visualized as a nomogram. Model performance was assessed using discrimination, calibration, and decision curve analysis.

Results:

Nine variables were selected to construct the nomogram, with BAR emerging as a key predictor. The model demonstrated good discriminatory performance, with areas under the receiver operating characteristic curve of 0.777 in the training cohort, 0.707 in the internal validation cohort, and 0.832 in the external validation cohort. Calibration curves showed good agreement between predicted and observed risks, and decision curve analysis indicated favorable clinical utility across a wide range of threshold probabilities. Net reclassification improvement analysis in the external validation cohort demonstrated that the BAR-based model significantly improved risk classification compared with the model including blood urea nitrogen alone (NRI = 0.247, 95% confidence intervals 0.008–0.486, P = 0.042).

Conclusions:

We developed and externally validated a BAR-based nomogram for early and individualized prediction of septic shock in patients with AP complicated by sepsis. This clinically interpretable tool may facilitate early risk stratification and support timely clinical decision-making in the intensive care setting.

INTRODUCTION

Acute pancreatitis (AP) is a common inflammatory condition of the pancreas, with a global incidence estimated at approximately 30–40 cases per 100,000 people annually (1). Over the past two decades, both the incidence and hospitalization rates of AP have been steadily rising (2,3). The overall incidence of AP has been increasing at an annual rate of 3.07% (4), placing a growing burden on healthcare systems. Notably, a significant proportion, ranging from 40% to 70%, of AP patients progress to pancreatic or peripancreatic infections (5), which can subsequently trigger sepsis. Among these patients, a subset may further deteriorate into septic shock—a stage associated with exceedingly high mortality rates (6). Therefore, accurately identifying high-risk patients with sepsis who are likely to progress to shock during the early stages of sepsis is crucial for initiating timely and intensive interventions to improve patient outcomes.

Early identification of patients with AP who are at high risk of progressing to septic shock remains a major clinical challenge. Current severity scoring systems, such as the Sequential Organ Failure Assessment (SOFA) score (7), Acute Physiology and Chronic Health Evaluation II (APACHE II) (8), and the Modified Marshall score (9), are widely used to assess disease severity and organ dysfunction. However, these tools are primarily designed for general critical illness or established organ failure rather than for early prediction of shock progression in AP-related sepsis. Moreover, their complexity, reliance on multiple variables, and limited timeliness (10) may reduce their practicality for rapid bedside risk stratification in the early phase of intensive care unit (ICU) admission. Single laboratory biomarkers, including lactate (11), C-reactive protein (12), and procalcitonin (13), have also been investigated as predictors of disease severity and outcomes in AP and sepsis. Although these markers provide valuable information, they reflect isolated pathophysiological processes and may be influenced by transient physiological fluctuations or therapeutic interventions. As a result, no single biomarker has demonstrated sufficient robustness to reliably predict the progression to septic shock when used in isolation.

Recently, composite indices that integrate markers of metabolic stress and host reserve have gained increasing attention. The BUN-to-albumin ratio (BAR) combines two routinely available laboratory parameters: BUN, a surrogate of catabolic stress, renal perfusion (14), and neurohormonal activation; and serum albumin, a marker of nutritional status, systemic inflammation, and endothelial integrity (15). Elevated BAR has been associated with adverse outcomes in various critical illnesses, including sepsis (16), acute kidney injury (17), and cardiovascular disease (18,19). However, its prognostic value for predicting the development of septic shock in patients with AP complicated by sepsis has not been systematically explored.

In addition to biomarker-based assessment, predictive modeling approaches that integrate multiple clinical and laboratory variables offer the potential to improve individualized risk stratification. Nomograms derived from multivariable regression models provide an intuitive and interpretable framework for bedside decision-making and have been increasingly adopted in critical care research. Nevertheless, few studies have developed and externally validated prediction models specifically targeting septic shock progression in AP-related sepsis, particularly using large, real-world ICU datasets.

Therefore, using data from the Medical Information Mart for Intensive Care IV (MIMIC-IV) database and an independent external cohort, we aimed to develop and validate a clinically applicable nomogram for predicting the risk of septic shock in patients with AP complicated by sepsis. By integrating BAR with key clinical and physiological variables available within the first 24 hours of ICU admission, we sought to provide a simple, interpretable, and generalizable tool to facilitate early risk stratification and support timely clinical decision-making.

DATA AND METHODS

Data sources

We included patients from the MIMIC-IV database to construct the prediction model and perform internal validation. Patients from the Second Hospital of Hebei Medical University constituted the external validation cohort. The MIMIC-IV database contains deidentified medical data of patients admitted to the Beth Israel Deaconess Medical Center in Boston from January 2008 to December 2022, encompassing demographics, laboratory tests, medications, vital signs, diagnoses, and follow-up survival status. We obtained permission to use the database (certification number: 68429492). As all data are deidentified, this study was exempt from ethics review. Patient clinical data were extracted using SQL queries.

For the external validation cohort, clinical data were retrospectively collected from patients admitted to the ICU of the Second Hospital of Hebei Medical University between May 2022 and May 2025. Inclusion criteria comprised adult patients (≥18 years) diagnosed with AP complicated by sepsis. This study was approved by the Ethics Committee of the Second Hospital of Hebei Medical University (Approval No.: 2025-R516). As the study only involved retrospective collection of information from the electronic medical record system without participation in clinical diagnosis or treatment, and all patient data were deidentified, the requirement for informed consent was waived.

Study population

The inclusion criteria for this study were as follows: 1) patients diagnosed with AP according to the Revised Atlanta Classification and concurrently meeting the Sepsis-3.0 criteria for sepsis; 2) age ≥18 years; 3) first admission to the ICU. Exclusion criteria were as follows: 1) patients with chronic pancreatitis or status post pancreatic surgery; 2) missing data for BUN, albumin, or septic shock outcome within 24 hours of ICU admission; 3) we predicted new-onset septic shock after ICU admission within ICU stay, excluding patients with vasopressors at ICU entry. The screening process is illustrated in Figure 1.

Fig. 1.

Flowchart of patient selection and model development. BUN, blood urea nitrogen; DCA, decision curve analysis; ICU, intensive care unit; MIMIC-IV, Medical Information Mart for Intensive Care IV; ROC, receiver operating characteristic.

During data screening, a total of 863 patients in the MIMIC-IV database initially met the inclusion criteria, of which 322 (37.3%) were excluded owing to missing albumin data within the first 24 hours of ICU admission; among these, five cases had concurrent missing data for both albumin and BUN. The outcome variable (septic shock) was complete for all patients. In the external validation cohort, 429 patients were screened, of which four (0.9%) were excluded owing to missing albumin or BUN data; the outcome variable was complete for all excluded cases.

Data extraction

Using the International Classification of Diseases (ICD-10) to extract patient information from the MIMIC-IV database. For the clinical data from the Second Hospital of Hebei Medical University, extraction was conducted via the electronic medical record system by trained researchers following approval by the ethics committee. All laboratory parameters and disease severity scores were extracted from data generated within the first 24 hours after the patient’s admission to the ICU. For lactate, measurements were handled differentially based on shock status: the final value before shock onset was used for patients who developed septic shock, whereas the mean of all measurements within the first 24 hours was calculated for those who did not. For all other variables, 24-hour means were consistently applied.

The extracted variables included: 1) demographic information: age, gender, height, and weight; 2) initial vital signs upon ICU admission: heart rate, respiratory rate, ABPs, and ABPd; 3) Blood gas analysis: PO₂, PCO₂, oxygen saturation, pH, lactate (Lac), and base excess; 4) laboratory indicators: white blood cell count (WBC), neutrophil count (NE), lymphocyte count, monocyte count, eosinophil count, basophil count, red blood cell count (RBC), hemoglobin (Hb), mean corpuscular volume, hematocrit (HCT), red cell distribution width (RDW), platelet count (PLT), creatine kinase (CK), CK-MB isoenzyme, lactate dehydrogenase (LDH), alanine aminotransferase (ALT), aspartate aminotransferase (AST), alkaline phosphatase (ALP), total bilirubin (TBIL), albumin(Alb), urea nitrogen, creatinine (Cr), glucose (Glu), sodium, potassium, chloride, magnesium, calcium, anion gap, triglycerides, amylase, prothrombin time, international normalized ratio, fibrinogen (Fib), and D-dimer; 5) SOFA score; 6) comorbidities: chronic respiratory failure, arrhythmia, intracerebral hemorrhage (ICH), gallstone, hypertension (HTN), liver cirrhosis, pneumonia (PNA), stroke (CVA), chronic kidney disease, malignancy (Ca), type 2 diabetes mellitus (T2DM), type 1 diabetes mellitus (T1DM), hyperlipidemia (HLD), chronic bronchitis, heart failure, myocardial infarction, ischemic heart disease, and chronic obstructive pulmonary disease.

Treatment-related variables were not included in model development, as they act as mediators between baseline indicators and the outcome. Including mediators would interfere with variable selection and effect estimation in the prediction model and may introduce multicollinearity.

In this study, the endpoint was the occurrence of septic shock, defined as sepsis patients requiring vasopressors to maintain a mean arterial pressure ≥65 mmHg despite adequate fluid resuscitation and with a lactate level >2 mmol/L (20). The BAR was calculated using the following formula: BAR = serum urea nitrogen (mmol/L)/albumin (g/L) (19).

Statistical methods

Patients from the MIMIC-IV database were randomly allocated into a training set and an internal validation set at a 7:3 ratio. Patients from the Second Hospital of Hebei Medical University served as the external validation cohort. Variables with more than 20% missing values were excluded to mitigate potential bias. For the remaining continuous variables with missing data, multiple imputation was performed using a Random Forest algorithm.

The normality of continuous variables was assessed using the Shapiro–Wilk test. Normally distributed variables were expressed as mean ± standard deviation and compared using Student’s t test or analysis of variance (ANOVA). Non-normally distributed variables were presented as median with interquartile range, and comparisons between groups were conducted using the Mann–Whitney U test. Categorical variables were expressed as frequency and percentage [n (%)], and comparisons were made using Pearson chi-square test or Fisher exact test, as appropriate. Data analyses were performed using R and Python, and a two-tailed P < 0.05 was considered statistically significant.

Feature selection was performed using Least Absolute Shrinkage and Selection Operator (LASSO) regression. The optimal regularization parameter (λ) was determined via 10-fold cross-validation. To achieve optimal predictive performance, the λ value that minimized the cross-validation error (λ.min) was selected, and all predictors with nonzero coefficients were retained for subsequent model building.

A nomogram was constructed based on the selected variables. The variance inflation factor was calculated to assess multicollinearity among them. The discriminatory ability of the nomogram in stratifying patients with different risk levels was evaluated using the area under the receiver operating characteristic (ROC) curve (AUC). To quantify the uncertainty of the estimates, the 95% confidence intervals (CI) for the AUC values in the training, internal validation, and external validation sets were calculated using the Bootstrap resampling method with 1,000 repetitions. Calibration curves along with goodness-of-fit tests were used to evaluate the model’s accuracy. Additionally, decision curve analysis (DCA) was performed to assess the model’s clinical utility.

We further used ROC curve analysis and DeLong’s test to compare the predictive performance of BAR with its individual components (BUN and albumin) across three datasets. To evaluate whether BAR provides incremental predictive value beyond its individual components when integrated with other clinical variables, we performed net reclassification improvement (NRI) analysis in the external validation cohort. We compared the BAR-based model against alternative models containing identical baseline variables (SOFA, Ca, Hb, NE, ALP, sodium, Lac, and PO₂) but substituting BAR with BUN or albumin alone. Finally, to exclude the potential confounding effect of renal function on BAR, a sensitivity analysis was conducted in patients with relatively normal renal function based on the diagnostic threshold for acute kidney injury defined by the KDIGO guidelines (21) (serum creatinine < 133 μmol/L). Given the retrospective nature of the data, complete longitudinal creatinine measurements and accurate urine output information were not available. Although this criterion may not fully identify all patients with early-stage acute kidney injury, it allows for a preliminary assessment of the model’s robustness in a population with relatively preserved renal function based on the available data.

RESULTS

Baseline characteristics

This study included two cohorts for model development and validation. A total of 541 patients were enrolled from the MIMIC-IV database after applying the inclusion and exclusion criteria. This cohort was then randomly divided into a training set (n = 379) for model construction and an internal validation set (n = 162) for internal performance evaluation. To rigorously assess the model’s generalizability, an independent external validation cohort comprising 295 patients with AP complicated by sepsis was collected from the Second Hospital of Hebei Medical University. The proportions of patients developing septic shock in the training, internal validation, and external validation sets were 34.04%, 33.95%, and 28.14%, respectively. No significant overall differences in baseline clinical data were observed between the training and internal validation sets.

As shown in Table 1, which compares the training set with the external validation set, significant differences (P < 0.05) were noted in variables such as age, gender, SOFA score, PO₂, WBC count, NE count, Hb, ALT, and AST. These variations further underscore the importance of validating the model across diverse populations to evaluate its clinical applicability. Table 2 presents the comparison between patients who developed septic shock and those who did not. Patients with septic shock had significantly lower levels of ABPs, ABPd, PO₂, oxygen saturation, pH, base excess, RBC, Hb, HCT, sodium, chloride, and Fib upon admission. Conversely, they exhibited significantly higher levels of Lac, SOFA, WBC, NE, RDW, TBIL, BAR, Cr, potassium, anion gap, prothrombin time, and international normalized ratio. Furthermore, patients who developed septic shock were less likely to have a comorbidity of malignancy compared with those who did not.

Table 1.

Baseline characteristics between the training cohort and the external validation cohort

Variable	Total (n = 674)	Training cohort (n = 379)	External validation cohort (n = 295)	P
Age (year)	55.00 (39.0–70.00)	61.00 (48.00–74.00)	43.00 (35.00–63.00)	<0.001
Gender (%)				<0.001
Female	247.00 (36.65%)	163.00 (43.01%)	84.00 (28.47%)
Male	427.00 (63.35%)	216.00 (56.99%)	211.00 (71.53%)
Weight (kg)	80.00 (70.00–93.50)	81.50 (70.00–98.95)	80.00 (70.00–90.00)	0.037
Height (cm)	170.00 (163.00–175.00)	168.00 (163.00–173.00)	170.00 (165.00–175.00)	<0.001
HR (bpm)	101.95 (88.00–118.88)	94.34 (83.22–106.72)	116.00 (98.00–131.00)	<0.001
RR (insp/min)	22.57 (19.72–26.19)	21.48 (18.53–24.58)	25.00 (21.00–31.00)	<0.001
ABPs (mmHg)	120.09 (110.00–138.00)	114.59 (108.59–125.67)	134.00 (116.00–147.00)	<0.001
ABPd (mmHg)	65.36 (57.00–82.00)	60.64 (54.75–65.41)	82.00 (70.00–93.00)	<0.001
PO2 (mmHg)	84.40 (63.00–117.00)	93.00 (66.00–129.20)	75.00 (62.50–96.20)	<0.001
PCO2 (mmHg)	37.00 (32.13–42.00)	39.75 (34.00–44.17)	34.80 (29.30–39.20)	<0.001
Oxygen saturation (%)	93.00 (86.00–96.50)	88.00 (76.00–95.00)	94.90 (92.20–97.10)	<0.001
PH	7.36 (7.30–7.42)	7.35 (7.29–7.40)	7.39 (7.32–7.44)	<0.001
Lac (mmol/L)	1.90 (1.35–2.99)	1.90 (1.36–3.00)	2.00 (1.31–2.99)	0.694
BE	−3.39 (−7.50 to −0.10)	−3.20 (−7.00 to 0.00)	−3.40 (−8.60 to −0.20)	0.127
SOFA	7.00 (4.00–10.00)	7.00 (4.00–10.00)	5.00 (3.00–9.00)	<0.001
Shock (%)				0.102
Without shock	462.00 (68.55%)	250.00 (65.96%)	212.00 (71.86%)
Shock	212.00 (31.45%)	129.00 (34.04%)	83.00 (28.14%)
WBC (*109/L)	12.20 (8.60–16.55)	13.04 (8.80–18.60)	11.20 (8.36–14.74)	<0.001
NE (*109/L)	10.48 (6.90–14.54)	11.46 (6.84–15.39)	9.50 (7.20–12.64)	<0.001
Lymphocyte count (*109/L)	0.90 (0.57–1.29)	0.94 (0.59–1.41)	0.81 (0.53–1.17)	0.007
Monocyte count (*109/L)	0.69 (0.40–1.01)	0.78 (0.44–1.04)	0.62 (0.33–0.96)	0.006
Eosinophil count (*109/L)	0.01 (0.00–0.07)	0.01 (0.00–0.07)	0.01 (0.00–0.04)	0.421
Basophil count (*109/L)	0.02 (0.00–0.03)	0.02 (0.00–0.03)	0.01 (0.00–0.03)	0.148
RBC (*1012/L)	3.65 (3.05–4.30)	3.48 (2.95–4.01)	3.98 (3.24–4.69)	<0.001
Hb (g/L)	110.15 (94.00–132.00)	105.00 (89.00–121.50)	123.00 (100.00–144.00)	<0.001
MCV (fl)	92.40 (88.25–96.25)	92.50 (87.67–97.00)	92.20 (88.90–95.50)	0.563
HCT	33.32 (28.31–39.80)	31.47 (27.35–36.25)	37.00 (30.10–42.60)	<0.001
RDW	14.50 (13.65–15.80)	15.08 (13.97–16.90)	13.90 (13.40–14.70)	<0.001
PLT (*109/L)	169.25 (113.83–236.00)	169.67 (111.00–248.75)	169.00 (115.00–231.00)	0.680
CK (U/L)	216.50 (70.00–831.50)	283.00 (83.50–1,102.00)	156.00 (57.00–552.00)	<0.001
CK-MB (U/L)	13.67 (5.00–24.00)	6.00 (3.00–15.00)	19.40 (13.00–32.00)	<0.001
LDH (U/L)	427.88 (283.00–657.00)	395.00 (257.00–590.00)	458.00 (304.00–770.00)	<0.001
ALT (U/L)	38.17 (19.70–115.33)	59.00 (25.00–188.50)	26.60 (15.90–56.00)	<0.001
AST (U/L)	57.25 (29.40–139.50)	90.00 (39.00–213.75)	39.00 (22.90–83.80)	<0.001
ALP (U/L)	83.00 (58.00–138.00)	103.00 (68.50–180.50)	69.00 (53.10–95.10)	<0.001
TBIL (umol/L)	23.65 (12.83–54.90)	23.94 (11.97–66.69)	22.90 (14.20–44.00)	0.764
BAR	0.28 (0.16–0.49)	0.33 (0.19–0.52)	0.23 (0.14–0.44)	<0.001
Cr (umol/L)	106.08 (68.95–233.50)	110.50 (70.72–234.26)	96.00 (65.80–233.50)	0.314
Glu (mmol/L)	8.70 (6.50–11.72)	7.32 (5.89–9.64)	11.18 (8.43–13.68)	<0.001
Sodium (mmol/L)	138.33 (135.00–141.50)	138.33 (134.75–141.00)	138.50 (135.00–141.60)	0.340
Potassium (mmol/L)	4.10 (3.74–4.54)	4.10 (3.73–4.55)	4.11 (3.74–4.53)	0.837
Chloride (mmol/L)	104.00 (99.75–108.20)	104.00 (99.75–108.50)	104.20 (99.60–108.00)	0.812
Magnesium (mmol/L)	0.79 (0.71–0.88)	0.82 (0.75–0.90)	0.76 (0.66–0.84)	<0.001
Calcium (mmol/L)	1.95 (1.79–2.10)	1.98 (1.84–2.12)	1.91 (1.72–2.05)	<0.001
Anion gap (mmol/L)	14.30 (11.50–18.40)	15.00 (12.50–18.80)	13.40 (10.40–17.50)	<0.001
Triglycerides	2.16 (1.23–3.87)	2.10 (1.20–3.33)	2.35 (1.29–5.89)	0.003
Amylase	278.50 (118.00–595.50)	379.00 (170.00–633.50)	196.00 (81.00–531.00)	<0.001
PT(s)	14.40 (12.90–17.10)	15.40 (13.60–19.35)	13.40 (12.40–15.00)	<0.001
INR	1.30 (1.15–1.55)	1.40 (1.20–1.79)	1.20 (1.11–1.33)	<0.001
Fib (g/L)	4.42 (3.26–5.70)	4.30 (3.00–5.05)	4.59 (3.72–6.51)	<0.001
CRF (%)	3.00 (0.45%)	3.00 (0.79%)	0.00 (0.00%)	0.126
Arrhythmia (%)	22.00 (3.26%)	13.00 (3.43%)	9.00 (3.05%)	0.783
ICH (%)	5.00 (0.74%)	1.00 (0.26%)	4.00 (1.36%)	0.101
Gallstone (%)	99.00 (14.69%)	31.00 (8.18%)	68.00 (23.05%)	<0.001
HTN (%)	268.00 (39.76%)	160.00 (42.22%)	108.00 (36.61%)	0.140
LC (%)	70.00 (10.39%)	66.00 (17.41%)	4.00 (1.36%)	<0.001
CVA (%)	33.00 (4.90%)	18.00 (4.75%)	15.00 (5.08%)	0.841
CKD (%)	76.00 (11.28%)	72.00 (19.00%)	4.00 (1.36%)	<0.001
Ca (%)	40.00 (5.93%)	37.00 (9.76%)	3.00 (1.02%)	<0.001
T2DM (%)	177.00 (26.26%)	112.00 (29.55%)	65.00 (22.03%)	0.028
HLD (%)	155.00 (23.00%)	102.00 (26.91%)	53.00 (17.97%)	0.006
HF (%)	67.00 (9.94%)	64.00 (16.89%)	3.00 (1.02%)	<0.001
IHD (%)	111.00 (16.47%)	87.00 (22.96%)	24.00 (8.14%)	<0.001
COPD (%)	53.00 (7.86%)	48.00 (12.66%)	5.00 (1.69%)	<0.001

Data are presented as median (interquartile range) for continuous variables and number (percentage) for categorical variables.

Variables with a P < 0.05 indicate statistically significant differences between the two cohorts.

ABPd, diastolic arterial blood pressure; ABPs, systolic arterial blood pressure; ALP, alkaline phosphatase; ALT, alanine aminotransferase; AST, aspartate aminotransferase; BAR, bilirubin-to-albumin ratio; BE, base excess; Ca, malignancy; CK, creatine kinase; CKD, chronic kidney disease; CK-MB, creatine kinase-MB isoenzyme; COPD, chronic obstructive pulmonary disease.; Cr, creatinine; CRF, chronic respiratory failure; CVA, cerebrovascular accident; Fib, fibrinogen; Glu, glucose; Hb, hemoglobin; HCT, hematocrit; HF, heart failure; HLD, hyperlipidemia; HR, heart rate; HTN, hypertension; ICH, intracerebral hemorrhage; IHD, ischemic heart disease; INR, international normalized ratio; Lac, lactate; LC, liver cirrhosis; LDH, lactate dehydrogenase; MCV, mean corpuscular volume; NE, neutrophil count; PCO₂, partial pressure of carbon dioxide; PLT, platelet count; PO₂, partial pressure of oxygen; PT, prothrombin time; RBC, red blood cell count; RDW, red cell distribution width; RR, respiratory rate; T2DM, type 2 diabetes mellitus; TBIL, total bilirubin; WBC, white blood cell count.

Table 2.

Baseline characteristics of the training cohort, stratified by shock status

Variable	Total (n = 379)	Without shock (n = 250)	Shock (n = 129)	P
Age (year)	61.00 (48.00–74.00)	59.00 (46.00–74.00)	63.00 (53.00–73.00)	0.207
Gender (%)				0.739
Female	163.00 (43.01%)	106.00 (42.40%)	57.00 (44.19%)
Male	216.00 (56.99%)	144.00 (57.60%)	72.00 (55.81%)
Weight (kg)	81.50 (70.00–98.95)	79.60 (69.00–98.10)	84.00 (71.00–100.50)	0.179
Height (cm)	168.00 (163.00–173.00)	168.00 (163.00–173.00)	168.00 (163.00–175.00)	0.644
HR (bpm)	94.34 (83.22–106.72)	95.06 (83.48–106.88)	93.00 (81.11–105.50)	0.447
RR (insp/min)	21.48 (18.53–24.58)	21.42 (18.35–24.33)	21.86 (18.78–25.10)	0.065
ABPs (mmHg)	114.59 (108.59–125.67)	115.89 (109.70–126.20)	111.83 (108.04–120.09)	<0.001
ABPd (mmHg)	60.64 (54.75–65.41)	61.27 (55.50–68.00)	58.00 (54.52–63.40)	0.001
PO2 (mmHg)	93.00 (66.00–129.20)	100.46 (68.73–136.50)	87.50 (63.00–116.33)	0.029
PCO2 (mmHg)	39.75 (34.00–44.17)	39.86 (34.40–43.14)	39.25 (33.50–44.60)	0.946
Oxygen saturation (%)	88.00 (76.00–95.00)	90.00 (77.20–96.00)	85.00 (74.00–93.00)	0.003
PH	7.35 (7.29–7.40)	7.36 (7.31–7.41)	7.33 (7.26–7.38)	<0.001
Lac (mmol/L)	1.90 (1.36–3.00)	1.82 (1.30–2.70)	2.07 (1.55–4.21)	0.001
BE	−3.20 (−7.00 to 0.00)	−2.59 (−6.00 to 0.00)	−5.00 (−7.83 to −1.00)	<0.001
SOFA	7.00 (4.00–10.00)	6.00 (4.00–9.00)	10.00 (7.00–13.00)	<0.001
WBC (*109/L)	13.04 (8.80–18.60)	12.38 (8.57–16.80)	14.50 (9.90–21.33)	0.004
NE (*109/L)	11.46 (6.84–15.39)	10.48 (6.63–14.66)	13.44 (8.05–19.80)	<0.001
Lymphocyte count (*109/L)	0.94 (0.59–1.41)	0.93 (0.58–1.40)	0.98 (0.63–1.41)	0.455
Monocyte count (*109/L)	0.78 (0.44–1.04)	0.74 (0.40–1.02)	0.79 (0.49–1.14)	0.168
Eosinophil count (*109/L)	0.01 (0.00–0.07)	0.01 (0.00–0.07)	0.01 (0.00–0.07)	0.480
Basophil count (*109/L)	0.02 (0.00–0.03)	0.02 (0.00–0.03)	0.02 (0.00–0.03)	0.257
RBC (*1012/L)	3.48 (2.95–4.01)	3.53 (3.07–4.04)	3.32 (2.74–3.90)	0.006
Hb (g/L)	105.00 (89.00–121.50)	107.75 (94.50–122.30)	98.00 (83.70–117.00)	<0.001
MCV (fl)	92.50 (87.67–97.00)	92.42 (87.67–97.00)	93.00 (88.25–97.83)	0.416
HCT	31.47 (27.35–36.25)	32.51 (28.22–36.57)	30.47 (25.23–35.60)	0.007
RDW	15.08 (13.97–16.90)	14.85 (13.83–16.35)	15.65 (14.52–17.87)	<0.001
PLT (*109/L)	169.67 (111.00–248.75)	174.84 (113.67–252.00)	163.00 (111.00–230.83)	0.460
CK (U/L)	283.00 (83.50–1,102.00)	247.75 (83.00–1,158.00)	311.00 (94.00–853.00)	0.701
CK-MB (U/L)	6.00 (3.00–15.00)	6.84 (3.50–15.00)	5.00 (3.00–14.50)	0.060
LDH (U/L)	395.00 (257.00–590.00)	385.75 (258.00–571.50)	405.00 (240.00–648.00)	0.908
ALT (U/L)	59.00 (25.00–188.50)	59.75 (24.00–183.50)	59.00 (26.50–197.00)	0.690
AST (U/L)	90.00 (39.00–213.75)	84.25 (39.00–183.50)	103.67 (40.50–246.50)	0.141
ALP (U/L)	103.00 (68.50–180.50)	98.92 (67.00–162.00)	117.00 (71.00–210.50)	0.096
TBIL (umol/L)	23.94 (11.97–66.69)	20.78 (11.46–56.43)	35.91 (13.17–115.08)	0.006
BAR	0.33 (0.19–0.52)	0.28 (0.17–0.47)	0.41 (0.26–0.70)	<0.001
Cr (umol/L)	110.50 (70.72–234.26)	97.24 (64.53–189.18)	144.98 (91.05–275.81)	<0.001
Glu (mmol/L)	7.32 (5.89–9.64)	7.29 (5.72–9.69)	7.64 (6.17–9.28)	0.547
Sodium (mmol/L)	138.33 (134.75–141.00)	139.00 (135.67–141.50)	137.00 (133.00–140.00)	<0.001
Potassium (mmol/L)	4.10 (3.73–4.55)	4.03 (3.70–4.43)	4.25 (3.85–4.67)	0.004
Chloride (mmol/L)	104.00 (99.75–108.50)	104.50 (101.25–109.00)	102.33 (97.33–108.00)	0.002
Magnesium (mmol/L)	0.82 (0.75–0.90)	0.81 (0.75–0.89)	0.83 (0.75–0.90)	0.168
Calcium (mmol/L)	1.98 (1.84–2.12)	1.99 (1.84–2.12)	1.97 (1.85–2.10)	0.924
Anion gap (mmol/L)	15.00 (12.50–18.80)	14.13 (12.33–17.50)	16.67 (13.50–20.50)	<0.001
Triglycerides	2.10 (1.20–3.33)	2.08 (1.20–3.04)	2.16 (1.20–3.62)	0.445
Amylase	379.00 (170.00–633.50)	387.25 (168.00–658.00)	350.00 (171.00–531.50)	0.485
PT(s)	15.40 (13.60–19.35)	15.10 (13.40–17.63)	16.80 (14.30–22.93)	<0.001
INR	1.40 (1.20–1.79)	1.35 (1.20–1.60)	1.55 (1.30–2.10)	<0.001
Fib(g/L)	4.30 (3.00–5.05)	4.39 (3.20–5.16)	3.94 (2.39–4.79)	0.010
CRF (%)	3.00 (0.79%)	2.00 (0.80%)	1.00 (0.78%)	0.979
Arrhythmia (%)	13.00 (3.43%)	7.00 (2.80%)	6.00 (4.65%)	0.348
ICH (%)	1.00 (0.26%)	0.00 (0.00%)	1.00 (0.78%)	0.163
Gallstone (%)	31.00 (8.18%)	25.00 (10.00%)	6.00 (4.65%)	0.072
HTN (%)	160.00 (42.22%)	113.00 (45.20%)	47.00 (36.43%)	0.102
LC (%)	66.00 (17.41%)	40.00 (16.00%)	26.00 (20.16%)	0.312
PNA (%)	109.00 (28.76%)	65.00 (26.00%)	44.00 (34.11%)	0.098
CVA (%)	18.00 (4.75%)	10.00 (4.00%)	8.00 (6.20%)	0.340
CKD (%)	72.00 (19.00%)	43.00 (17.20%)	29.00 (22.48%)	0.214
Ca (%)	37.00 (9.76%)	19.00 (7.60%)	18.00 (13.95%)	0.048
T2DM (%)	112.00 (29.55%)	72.00 (28.80%)	40.00 (31.01%)	0.655
T1DM (%)	6.00 (1.58%)	5.00 (2.00%)	1.00 (0.78%)	0.365
HLD (%)	102.00 (26.91%)	65.00 (26.00%)	37.00 (28.68%)	0.577
CB (%)	19.00 (5.01%)	14.00 (5.60%)	5.00 (3.88%)	0.466
HF (%)	64.00 (16.89%)	39.00 (15.60%)	25.00 (19.38%)	0.352
MI (%)	16.00 (4.22%)	10.00 (4.00%)	6.00 (4.65%)	0.765
IHD (%)	87.00 (22.96%)	57.00 (22.80%)	30.00 (23.26%)	0.920
COPD (%)	48.00 (12.66%)	33.00 (13.20%)	15.00 (11.63%)	0.663

Data are presented as median (interquartile range) for continuous variables and number (percentage) for categorical variables.

Variables with a P < 0.05 indicate statistically significant differences between the two groups.

ABPd, diastolic arterial blood pressure; ABPs, systolic arterial blood pressure; ALP, alkaline phosphatase; ALT, alanine aminotransferase; AST, aspartate aminotransferase; BAR, bilirubin-to-albumin ratio; BE, base excess; Ca, malignancy; CB, chronic bronchitis; CK, creatine kinase; CKD, chronic kidney disease; CK-MB, creatine kinase-MB isoenzyme; COPD, chronic obstructive pulmonary disease.; Cr, creatinine; CRF, chronic respiratory failure; CVA, cerebrovascular accident; Fib, fibrinogen; Glu, glucose; Hb, hemoglobin; HCT, hematocrit; HF, heart failure; HLD, hyperlipidemia; HR, heart rate; HTN, hypertension; ICH, intracerebral hemorrhage; IHD, ischemic heart disease; INR, international normalized ratio; Lac, lactate; LC, liver cirrhosis; LDH, lactate dehydrogenase; MCV, mean corpuscular volume; MI, myocardial infarction; NE, neutrophil count; PCO2, partial pressure of carbon dioxide; PLT, platelet count; PNA, pneumonia; PO₂, partial pressure of oxygen; PT, prothrombin time; RBC, red blood cell count; RDW, red cell distribution width; RR, respiratory rate; SOFA, sequential organ failure assessment; T1DM, type 1 diabetes mellitus; T2DM, type 2 diabetes mellitus; TBIL, total bilirubin; WBC, white blood cell count.

Feature selection

In the training set, LASSO regression was used to screen for potential risk factors. A total of nine variables with nonzero coefficients were selected: SOFA score, BAR, lactate (Lac), neutrophil count (NE), hemoglobin (Hb), alkaline phosphatase (ALP), partial pressure of oxygen (PO₂), sodium, and malignancy comorbidity (Fig. 2). No significant multicollinearity was detected among these variables (Table 3).

Fig. 2.

A, Lasso coefficient profiles of the risk factors. B, Selection of the optimal lambda (λ) value in the Lasso model. The left dashed vertical line indicates the minimum mean cross-validated error (λ.min), and the right one indicates the value of λ within 1 standard error of the minimum (λ.1se). Finally, nine variables were retained as predictive features by the Lasso regression analysis in the training cohort.

Table 3.

Assessment of multicollinearity among the variables

Variable	VIF
SOFA	1.288
Ca	1.030
Hb	1.062
NE	1.119
BAR	1.101
ALP	1.093
Sodium	1.053
Lac	1.208
PO2	1.052

All VIF values are below 10, indicating no significant multicollinearity among the selected features.

ALP, alkaline phosphatase; BAR, bilirubin-to-albumin ratio; Ca, malignancy; Hb, hemoglobin; Lac, lactate; NE, neutrophil count.

Model development and validation

A prediction model was developed in the training set based on these nine predictor variables and visualized as a nomogram (Fig. 3). The discriminatory ability of the nomogram was assessed using ROC curves (Fig. 4). The model demonstrated area under the curve (AUC) values of 0.777 (95% CI 0.727–0.827), 0.707 (95% CI 0.623–0.791), and 0.832 (95% CI 0.78–0.884) in the training, internal validation, and external validation cohorts, respectively.

Fig. 3.

Nomogram for predicting progression to septic shock. Points are assigned to each predictor based on its regression coefficient, summed to a total score, and then converted to a predicted probability. ALP, alkaline phosphatase; BAR, bilirubin-to-albumin ratio; Ca, malignancy; Hb, hemoglobin; Lac, lactate; NE, neutrophil count; PO₂, partial pressure of oxygen; SOFA, Sequential Organ Failure Assessment.

Fig. 4.

ROC curves of the model in the training cohort (A), internal validation cohort (B), and external validation cohort (C). ROC, receiver operating characteristic.

Calibration curves, which depict the agreement between the predicted probabilities and the observed frequencies of events, were generated. In the training, internal validation, and external validation sets, the calibration curves closely aligned with the reference line (Fig. 5), indicating good calibration of the nomogram model. Furthermore, DCA confirmed that our nomogram provided higher clinical net benefit (Fig. 6).

Fig. 5.

Calibration curves of the model in the training cohort (A), internal validation cohort (B), and external validation cohort (C).

Fig. 6.

Decision curve analysis for the model in the training cohort (A), internal validation cohort (B), and external validation cohort (C).

To further explore the relationship between the BAR model and the SOFA score, we performed residual analysis across the three cohorts. Among patients who developed septic shock, we calculated the SOFA residual—defined as the observed outcome (shock = 1) minus the SOFA-predicted probability—to quantify the prediction error of the SOFA score, with larger values indicating greater underestimation of risk. We then analyzed the correlation between these SOFA residuals and the risk predictions from the BAR model. Strong negative correlations were observed across all cohorts (training: r = −0.728; internal validation: r = −0.761; external validation: r = −0.731; all P < 0.001; Fig. 7). Scatter plots showed that patients who developed septic shock (red points) were predominantly located in the region of low SOFA predictions but high BAR predictions, indicating that the BAR model can identify patients whose risk is underestimated by the SOFA score. These findings suggest that the BAR model provides valuable complementary information to the SOFA score by capturing early pathophysiological derangements—including metabolic stress, perfusion abnormalities, and nutritional status—that are not reflected by the SOFA score.

Fig. 7.

Added value of the BAR model to the SOFA score. Scatter plots of SOFA-predicted probability versus BAR model-predicted probability in the training (A), internal validation (B), and external validation (C) cohorts. Red points: patients with septic shock; gray points: nonshock patients; red dashed lines: linear fits for shock patients. Strong negative correlations between SOFA residuals and BAR predictions were observed in shock patients across all cohorts (P < 0.001), indicating that the BAR model identifies patients whose risk is underestimated by SOFA. BAR, bilirubin-to-albumin ratio; SOFA, Sequential Organ Failure Assessment.

When comparing the predictive performance of BAR with its individual components, BAR achieved AUCs of 0.649 and 0.693 in the training and external validation cohorts, respectively, which were significantly higher than those of albumin alone (P < 0.05). However, no significant difference was observed between BAR and BUN. In the internal validation cohort, there were no significant differences in predictive performance among the three indicators (Table 4). These findings suggest that BAR, as a composite marker integrating renal perfusion, metabolic stress, and nutritional status, demonstrates superior predictive performance compared with albumin alone in most datasets and performs comparably to, or slightly better than, BUN. This indicates that BAR may provide a more comprehensive reflection of patients’ pathophysiological status.

Table 4.

Comparison of predictive performance for septic shock among BAR, urea nitrogen, and albumin

Cohort	Indicator	AUC (95% CI)	P
Training cohort	BAR	0.649 (0.592–0.706)
	Blood urea nitrogen	0.632 (0.574–0.690)	0.06
	Albumin	0.561 (0.499–0.623)	0.0288
Internal validation cohort	BAR	0.603 (0.511–0.696)
	Blood urea nitrogen	0.587 (0.494–0.680)	0.3257
	Albumin	0.591 (0.497–0.685)	0.8182
External validation cohort	BAR	0.693 (0.627–0.759)
	Blood urea nitrogen	0.691 (0.625–0.757)	0.8502
	Albumin	0.590 (0.512–0.667)	0.0124

95% CI, 95% confidence intervals; AUC, area under the curve; BAR, bilirubin-to-albumin ratio.

Compared with the model including BUN, the BAR-based model demonstrated significant continuous NRI improvement (NRI = 0.247, P = 0.042), indicating that 24.7% of patients were correctly reclassified to more appropriate risk categories. In contrast, the comparison with the model including albumin showed negative NRI (NRI = −0.296, P = 0.019; Table 5).

Table 5.

Comparison of model performance in the external validation cohort

Model	AUC (95% CI)	Continuous NRI vs. BAR model	P
Base + BUN	0.831 (0.779–0.883)	−0.247 (−0.486 to −0.008)	0.042
Base + albumin	0.834 (0.782–0.886)	0.296 (0.049–0.543)	0.019

Base variables: SOFA, Ca, Hb, NE, ALP, Sodium, Lac, and PO₂. All analyses performed in the external validation cohort (n = 295).

BUN, blood urea nitrogen; NRI, net reclassification improvement.

Because BAR includes BUN, which is influenced by renal function, we performed a sensitivity analysis to rule out this potential confounder. According to the KDIGO guidelines, patients with serum creatinine <133 μmol/L were defined as having relatively normal renal function, and the predictive performance of the nomogram was reassessed in this subgroup.

In the training cohort, 225 patients had relatively normal renal function, among whom the incidence of septic shock was 25.78%, and the model achieved an AUC of 0.738 (95% CI 0.659–0.817). In the internal validation cohort, 83 patients met the criteria, with a septic shock incidence of 25.30% and an AUC of 0.690 (95% CI 0.562–0.817). In the external validation cohort, 183 patients had relatively normal renal function, with a septic shock incidence of 16.94% and an AUC of 0.836 (95% CI 0.750–0.921; Table 6). The ROC curves for each cohort are shown in Figure 8. These results suggest that the nomogram retains its predictive ability in patients with relatively normal renal function, implying that baseline renal function does not appear to substantially affect model performance, and the model demonstrates reasonable robustness.

Table 6.

Distribution of renal function status and septic shock incidence across cohorts

Cohort	Total (n)	Septic shock, n (%)	Renal dysfunction		Normal renal function
			Patients, n (%)	Shock, n (%)	Patients, n (%)	Shock, n (%)
Training cohort	379	129 (34.04)	154 (40.63)	71 (46.10)	225 (59.37)	58 (25.78)
Internal validation cohort	162	55 (33.95)	79 (48.77)	34 (43.04)	83 (51.23)	21 (25.30)
External validation cohort	295	83 (28.14)	112 (37.97)	52 (46.43)	183 (62.03)	31 (16.94)

Fig. 8.

ROC curves of sensitivity analysis for the model in the training cohort, internal validation cohort, and external validation cohort. ROC, receiver operating characteristic.

DISCUSSION

This study successfully developed and validated a nomogram model incorporating the BUN-to-albumin ratio to predict the risk of progression to septic shock in patients with AP complicated by sepsis. Through LASSO regression, nine key predictive variables were identified: SOFA score, BAR, lactate (Lac), neutrophil count (NE), hemoglobin (Hb), alkaline phosphatase (ALP), partial pressure of oxygen (PO₂), sodium, and history of malignancy. The nomogram model demonstrated good discriminatory ability in both the training set (AUC = 0.777) and the internal validation set (AUC = 0.707). Furthermore, it exhibited excellent predictive performance (AUC = 0.832) in an independent external validation cohort with distinct demographic and clinical characteristics, along with satisfactory calibration and clinical utility. Notably, BAR, a novel composite biomarker introduced in this study, emerged as a significant predictor within the model.

BAR (BUN-to-albumin ratio) is a composite biomarker derived from blood urea nitrogen (BUN) and albumin (22,23). It is well-established that BUN is a key indicator reflecting renal status, protein metabolism, and nutritional state (24). In AP, systemic inflammation mediates capillary leakage, leading to decreased effective circulating volume and subsequent renal hypoperfusion (25). Concurrently, necrotic tissue and a surge of inflammatory mediators drive a systemic hypermetabolic state, increasing protein breakdown and elevating BUN levels (22). The abnormal activation of pancreatic enzymes and the cytokine storm in AP cause damage to the vascular endothelial glycocalyx (26), resulting in significant protein extravasation into the interstitium and retroperitoneum. Consequently, albumin levels drop markedly within 24 hours (27). Additionally, the inflammatory response induces metabolic dysregulation and liver injury, further promoting protein catabolism and reducing albumin synthesis, thereby decreasing albumin levels (28). Thus, BAR simultaneously reflects renal perfusion, metabolic stress, and the severity of inflammation, with elevated levels indicating poorer physiological reserve and a higher risk of shock (29,30). Moreover, BAR, as an easily accessible and cost-effective composite marker, offers more comprehensive pathophysiological information compared with single biomarkers or complex scoring systems (31). By integrating it with established indicators such as the SOFA score, the model achieves enhanced predictive power.

The SOFA score serves as a tool for assessing organ function status in critically ill patients. It quantifies the degree of dysfunction across six major organ systems (respiratory, coagulation, hepatic, cardiovascular, neurological, and renal), aiding in evaluating disease severity and prognosis (32). In AP complicated by sepsis, massive fluid extravasation leads to hemoconcentration (33,34), which affects hemoglobin (Hb) concentration, exacerbating hypoxia, and microcirculatory dysfunction. This contributes to decreased PO₂ and impaired respiratory function (35). Lactate (Lac) is an indicator of tissue hypoperfusion and cellular hypoxia (36). Lactate accumulates when oxygen delivery is insufficient or when its clearance rate is lower than its production rate (37). Existing literature has established a correlation between elevated lactate levels and poor prognosis in critically ill patients. Furthermore, the lactate-to-albumin ratio has been identified as an independent risk factor for predicting 28-day all-cause mortality in patients with AP (38). During infection, neutrophils are rapidly activated and release a large number of inflammatory mediators (39,40). They further recruit other immune cells, triggering an inflammatory cascade (41). An excessive or dysregulated inflammatory response may lead to increased vascular permeability (42), tissue damage, and organ dysfunction, which are key pathophysiological processes in the development of septic shock. In septic patients, neutrophil apoptosis is often delayed, and their migratory and chemotactic abilities are impaired (43). This not only hinders the effective clearance of pathogens but also leads to abnormal accumulation at noninfected sites, exacerbating inflammation, and tissue injury. Additionally, activated neutrophils release neutrophil extracellular traps under the regulation of various signaling pathways, further aggravating tissue damage (44). Abnormal levels of alkaline phosphatase (ALP) in the blood reflect tissue injury or disturbances in normal physiological processes (45) and are associated with liver function, kidney function (46), skeletal muscle composition, and inflammatory response. Literature suggests that the ALP/Hb ratio can serve as a significant indicator for predicting clinical progression and prognosis in patients with severe AP (SAP) (47). Abnormal sodium ion concentrations indicate worsening cellular dysfunction (48) and metabolic disturbances. Sodium ions are involved in regulating the contraction and relaxation of vascular smooth muscle (49). Abnormal sodium levels may affect vascular tone and blood flow distribution, further exacerbating tissue hypoperfusion. Persistent abnormalities in sodium concentration may reflect deteriorating renal function (50) and fluid imbalance, serving as an early warning sign for shock. Malignancy-related bone marrow infiltration or the effects of chemotherapy on blood cells can lead to neutropenia (51), increasing susceptibility to bacterial or fungal infections. Additionally, neutrophils from patients with malignancies exhibit various functional defects in chemotaxis, phagocytosis, and bactericidal capacity. Consequently, septic patients with underlying malignancies tend to have a poorer prognosis (52).

In this study, the AUC value of the model on the external validation set was significantly higher than that on the training set, which may stem from population and data quality differences between the two datasets. As shown in Table 1, statistically significant differences (P < 0.05) were observed between the two datasets across multiple key indicators, including age, gender, SOFA score, PO₂, WBC, NE, Hb, ALT, and AST. Further analysis revealed that the median SOFA score was 5 in the external validation set compared with 7 in the training set, with a statistically significant difference (P < 0.05). This indicates notable heterogeneity between the patient populations from different sources in terms of disease severity and demographic characteristics. The model demonstrated efficacy not only in the development cohort with more severe illness but also exhibited good discriminatory ability in a relatively milder population still at risk of sepsis, thereby providing evidence of its generalizability to some extent. Additionally, most predictors included in the model are laboratory-based indicators, which are less susceptible to subjective judgment, likely contributing to its robustness across data from different sources.

Residual analysis in this study revealed that the BAR model can identify patients whose risk is underestimated by the SOFA score. Across the three cohorts, strong negative correlations were observed between SOFA residuals and BAR predictions in patients who developed septic shock (P < 0.001), with patients showing low SOFA predictions but ultimately developing shock receiving significantly higher risk predictions from the BAR model. While the SOFA score primarily quantifies established organ dysfunction, the BAR—a composite of BUN and albumin—reflects metabolic stress, hypoperfusion, and nutritional status, thereby capturing early risk signals not identified by SOFA. Thus, the value of the BAR model lies not in replacing SOFA, but in providing complementary information. Combined use of both tools may reduce delayed recognition of high-risk patients and enable more comprehensive early risk stratification. Future prospective studies should validate whether early intensified monitoring and intervention in patients with moderate SOFA scores and elevated BAR improve clinical outcomes, providing direct evidence for clinical application of the BAR model.

This study further supports that BAR, as a composite indicator, performs better than or at least noninferior to its individual components in predicting septic shock. In both the training and external validation cohorts, BAR achieved higher AUC values than albumin alone, with statistically significant differences (P < 0.05). Although the difference did not reach statistical significance in the internal validation cohort, this may be related to the relatively small sample size, which limited statistical power. Compared with BUN alone, BAR showed slightly higher or comparable AUC values across all cohorts, without statistically significant differences.

To further evaluate the incremental value of BAR when integrated with other clinical variables, we performed NRI analysis in the external validation cohort. The BAR-based model demonstrated significant continuous NRI improvement compared with the model including BUN alone (NRI = 0.247, P = 0.042), indicating that 24.7% of patients were correctly reclassified to more appropriate risk categories. In contrast, the comparison with the model including albumin showed negative NRI (NRI = −0.296, P = 0.019).

This seemingly paradoxical finding—positive NRI versus BUN but negative NRI versus albumin—reflects the distinct functional roles of albumin in different model structures. When albumin enters the model as an independent variable alongside baseline covariates, it synergizes with SOFA score and hemoglobin to reflect nutritional and inflammatory status. As a denominator in BAR, albumin’s predictive contribution is transformed into a calibration function for BUN rather than an independent signal. Thus, in the presence of baseline variables, the model including standalone albumin offers greater incremental value than the BAR model. However, this does not indicate inferiority of BAR; rather, it reveals BAR’s intrinsic characteristic: it optimizes BUN’s predictive capacity through nutritional calibration, at the intentional cost of sacrificing albumin’s independent contribution. Clinically, this positions BAR as a BUN-optimizing marker rather than an albumin substitute. When metabolic stress assessment is the priority, BAR outperforms BUN; when nutritional status is the primary concern, standalone albumin may be preferred. BAR’s value lies in integrating both dimensions into a single, routinely available bedside indicator.

Compared with existing clinical prediction tools, the nomogram model developed in this study demonstrates the following characteristics in terms of practicality and validation rigor: First, unlike single indicators such as lactate, this model integrates multiple key dimensions including BAR and SOFA score, providing a more comprehensive assessment of septic shock risk. Second, compared with machine learning models reliant on complex algorithms, the nomogram format is intuitive and facilitates rapid bedside calculation, aligning better with real-world clinical application scenarios. Furthermore, the model has undergone not only internal validation but also rigorous testing on an independent external cohort, supporting its reliability and generalizability across different healthcare settings.

More importantly, we conducted a sensitivity analysis to address the potential confounding effect of renal function on BUN, a core component of BAR. In the subgroup of patients with relatively normal renal function, the model demonstrated good predictive performance in both the training and external validation cohorts, with AUCs of 0.738 and 0.836, respectively, which were comparable to those observed in the overall population. The AUC in the internal validation cohort was 0.690, slightly lower than the other two cohorts, which may be attributable to the relatively small sample size (n = 83) limiting statistical power. These findings further suggest that the predictive performance of the model does not depend on renal function, and the pathophysiological status reflected by BAR retains its prognostic value even in patients with normal renal function, providing additional evidence for the clinical applicability of the model.

The exclusion rate in the MIMIC-IV database was 37.3%, all owing to missing albumin data (with five cases also missing BUN), while the outcome variable was complete. The external validation cohort had a much lower exclusion rate of 0.9%, indicating high data completeness. The final sample sizes met EPV requirements, and sensitivity analyses confirmed model stability. Therefore, missing data did not substantially affect the study conclusions.

This study has developed a clinically applicable nomogram model designed to assist clinicians in performing rapid, accurate, and individualized patient assessment during the early ICU admission of patients with AP complicated by sepsis. For patients identified as high-risk, this tool enables clinicians to initiate closer hemodynamic monitoring, more aggressive fluid resuscitation evaluation, or earlier consideration for vasopressor support, thereby shifting the intervention window forward. However, this study has several limitations. First, the model was constructed using only static data from the first 24 hours after admission and did not incorporate the dynamic evolution of clinical indicators. Future work could explore time-series models to improve the timeliness of prediction. Second, the external validation relied on retrospective data from a single center. Prospective, multicenter validation is needed to confirm the model’s robustness across diverse populations and healthcare settings. Besides, The complementary relationship between the BAR model and the SOFA score identified by residual analysis is based on retrospective data. The optimal strategy for integrating these two tools requires further validation in prospective studies. Finally, further exploration is needed in clinical practice to determine whether this model can effectively guide early, targeted interventions (such as timely initiation of vasopressor support) to ultimately improve patient outcomes.

CONCLUSION

This study successfully developed and validated a nomogram prediction model incorporating the BUN-to-albumin ratio (BAR) for early, accurate, and individualized assessment of the risk of progression to septic shock in patients with AP complicated by sepsis. The model demonstrated excellent performance in an independent external validation, indicating strong potential for clinical translation. Future research is warranted to provide evidence for its utility in guiding early interventions, such as the timely initiation of vasoactive agents, to improve patient outcomes.