Predicting acute kidney injury in septic shock patients using inflammatory indices in the intensive care unit

Abstract

BACKGROUND

Acute kidney injury (AKI) is a prevalent and common complication in critically ill patients with septic shock, associated with increased morbidity, mortality, and healthcare resource utilization in the intensive care unit (ICU). While inflammatory indices derived from standard laboratory tests – such as the neutrophil-to-lymphocyte ratio (NLR), platelet lymphocyte ratio (PLR), monocyte-to-lymphocyte ratio (MLR), systemic immune-inflammation index (SII), systemic inflammation response index (SIRI), neutrophil percentage to albumin ratio (NPAR) and aggregate index of systemic inflammation (AISI) – have emerged as promising biomarkers for systemic immune activation in critical illness, their direct value as predictors of AKI in large ICU cohorts remains uncertain.

AIM

To evaluate the predictive value of inflammatory indices derived from standard laboratory tests as predictors of AKI in ICU patients with septic shock.

METHODS

This retrospective cohort study utilized the eICU Collaborative Research Database, including adult patients with septic shock admitted to over 200 ICUs across the United States from 2014 to 2015. Patients with pre-existing end-stage renal disease, death within 24 hours, or insufficient data for inflammatory indices were excluded. Inflammatory markers (NLR, PLR, MLR, NPAR, SII, SIRI, AISI) and clinical variables were analyzed. Multivariable logistic regression, principal component analysis, and multilayer perceptron neural network modeling were employed to identify independent predictors of AKI, defined by Kidney Disease Global Outcomes criteria.

RESULTS

Among 12660 septic shock patients, 6552 (51.7%) developed AKI during their ICU stay. Patients with AKI were older, had higher body mass index and Sequential Organ Failure Assessment scores, and a greater burden of comorbidities such as chronic kidney disease and diabetes. Univariate analysis showed significantly higher levels of NLR, MLR, SII, NPAR, SIRI, and AISI in the AKI group, suggesting an association between systemic inflammation and kidney injury. However, these indices displayed strong multicollinearity with other clinical and laboratory variables. In logistic regression, traditional predictors such as baseline serum creatinine, blood urea nitrogen, Sequential Organ Failure Assessment score, chronic kidney disease, vasopressor use, and selected comorbidities remained independently associated with AKI, while most individual inflammatory indices did not retain independent significance due to multicollinearity. To address this, principal component analysis employed, which identified three major components – an inflammatory/hematological component, a metabolic/renal/inflammatory component, and an electrolyte/age component. Incorporating these composite dimensions into predictive models significantly improved discrimination for AKI risk. Neural network models further expounded the contribution of both clinical factors and the combined inflammatory/metabolic dimension to accurate AKI prediction, capturing complex interactions and non-linear relationships not evident in traditional regression models.

CONCLUSION

In ICU patients with septic shock, composite inflammatory indices are elevated in those who develop AKI and may serve as important markers of risk. However, after accounting for multicollinearity and confounding, these markers alone offer limited incremental predictive value over traditional clinical and laboratory risk factors.

Key Words: Acute kidney injury; Septic shock; Inflammatory indices; eICU Collaborative Research Database; Principal component analysis; Machine learning; Neutrophil-to-lymphocyte ratio; Systemic immune-inflammation index; Aggregate index of systemic inflammation; Monocyte-to-lymphocyte ratio

Core Tip: Composite inflammatory markers are elevated in patients who develop acute kidney injury. However, due to heterogeneity of septic shock, multicollinearity and nonlinear relationships, these markers alone offer limited incremental predictive value. Neural network models further expounded the contribution of both clinical factors and the combined inflammatory/metabolic dimension to accurate acute kidney injury prediction, capturing complex interactions and non-linear relationships not evident in traditional regression models. Implementation of supervised and unsupervised machine learning together may offer further insights.

INTRODUCTION

Acute kidney injury (AKI) remains a frequent and common complication in critically ill patients and is associated with extended intensive care unit (ICU) stays, need for renal replacement therapy (RRT), and increased mortality[1-3]. The underlying mechanisms of AKI in this population are complex, often involving a combination of hemodynamic instability, systemic inflammation, exposure to nephrotoxic agents, and preexisting medical comorbidities[4]. Despite ongoing advances in critical care, AKI continues to be underrecognized in its early stages, and few interventions have been shown to consistently prevent its progression[5].

Timely identification of patients at risk for AKI and its severe forms – especially those who might require hemodialysis – can better inform clinical resource allocation, timely intervention, and both short-term and long-term renal outcomes[6,7]. Previously, studies have reported various clinical and laboratory risk factors, but comprehensive analyses in large, geographically diverse, high-resolution cohorts and contemporary analytic methods are limited[8].

In recent years, inflammatory indices derived from routine laboratory parameters – including the neutrophil-to-lymphocyte ratio (NLR), platelet-to-lymphocyte ratio (PLR), monocyte-to-lymphocyte ratio (MLR), neutrophil-percentage-to-albumin ratio (NPAR), systemic immune-inflammation index (SII), systemic inflammatory response index (SIRI) aggregate index of systemic inflammation (AISI), and others – have emerged as potential and readily accessible biomarkers of systemic immune activation in critically ill patients[9,10]. These indices, which integrate counts of different leukocyte subtypes and platelets (see methods for the formulae), provide a more nuanced perspective on the host inflammatory response than single laboratory measurements alone. Studies have shown that elevated NLR and SII have been associated with increased mortality and greater risk of organ dysfunction, including AKI in patients with sepsis[11-14]. Likewise, SIRI values are associated with worse outcomes in sepsis-associated AKI[9,10]. Despite all this evidence, the direct relationship between these composite indices and the development of AKI in large ICU populations with sepsis is yet to be better understood. Our study was therefore designed to systematically examine whether the above key inflammatory markers are independently associated with AKI development in critically ill septic shock patients, aiming to clarify their value in early risk stratification.

MATERIALS AND METHODS

Study design and data source

To determine the role of admission inflammatory markers obtained from routine laboratory testing, we evaluated comorbidities, demographic data, medications, and other clinical laboratory values in the development of septic shock-associated AKI. We performed a retrospective cohort study employing the eICU Collaborative Research Database. The eICU Collaborative Research Database collects de-identified patient data from over 200 ICUs across the United States between 2014 and 2015[15]. The eICU database is a rigorously curated, multicenter dataset developed by the Massachusetts Institute of Technology and Philips Healthcare. The database provides high-granularity, de-identified patient information collected for critical care research. The integrity and authenticity of the data are ensured through technical validation steps robust de-identification procedures certified to meet HIPAA safe harbor standards. The dataset undergoes updates and verification by multiple reviewers, with direct access governed by institutional data use agreements and audit trials[15].

The eICU database is publicly available after registration, users complete a training course in research with human subjects, and sign a data use agreement that mandates responsible handling of the data and collaborative research[15].

Due to its retrospective design, patient de-identification and the security schema, for which the re-identification risk was certified as meeting safe harbor standards by an independent privacy expert (Privacert, Cambridge, MA, United States) (Health Insurance Portability and Accountability Act Certification, No. 1031219-2). The use of the eICU database is exempt from institutional review board approval[15]. IBM SPSS (IBM Chicago, IL, United States) version 27 and STATA version 16 (STATACORP LLC, College Station, TX, United States) programs were used to analyze data and generate images.

Patient selection and identification

Patients admitted to the ICU with septic shock were defined on admission according to the International Classification of Diseases, 10^th Revision, Clinical Modification codes. Individuals greater than 17 years of age were included in the analysis. We excluded individuals who expired during the first 24 hours of ICU admission, those receiving chronic dialysis or end-stage renal disease, and those records lacking baseline hematologic parameters required for calculating inflammatory markers. Details of patient selection are available in Figure 1.

Figure 1 Flowchart of selection of participants. ESRD: End stage renal disease.

Study variables

Demographic variables (gender, age, ethnicity), clinical information, comorbidities, the need for RRT, requirement for mechanical ventilation, and initial laboratory parameters were extracted from electronic health records. Comorbidities included in analysis were extracted from the database were based on the International Classification of Diseases, 10^th Revision, Clinical Modification coding and included chronic kidney disease (CKD), diabetes mellitus (DM), hypertension (HTN), malignancy, congestive heart failure, cirrhosis and chronic obstructive pulmonary disease (COPD). Included in the current analysis were medications known to impact renal hemodynamics such as angiotensin converting enzyme inhibitor (ACEi), angiotensin 2 receptor antagonist (A2RB), diuretics and vasopressors/inotropic agents. Inflammatory markers easily obtained from routine laboratory studies were calculated for the analysis, NLR, PLR, MLR, NPAR, SII, SIRI, and AISI. The formulas utilized for the computation of these ratios are as follows: (1) NLR = neutrophil count (NC)/Lymphocyte count (LC); (2) PLR = platelet count (PC)/LC; (3) MLR = monocyte count (MC)/LC; (4) SII = PC × NC/LC; (5) NPAR = neutrophil percentage of total white blood cell count (%)× 100/albumin (g/dL); (6) SIRI = NC × MC/LC; and (7) AISI = NC × PC × MC/LC. Additionally, admission lab values and clinical information evaluated included alanine aminotransferase, aspartate aminotransferase, total bilirubin, serum sodium, serum potassium, serum chloride, hemoglobin, complete blood cell count, age, body mass index (BMI), prothrombin time/international normalised ratio, and Sequential Organ Failure Assessment (SOFA) score.

AKI was defined according to Kidney Disease Global Outcomes guidelines, briefly a rise in serum creatinine (SCr) of ≥ 0.3 mg/dL within 48 hours, a rise in SCr of ≥ 1.5 mg/dL above baseline within 7 days, and or the need for RRT[16]. The baseline SCr was taken as the lowest SCr obtainable within the first 7 days of admission.

Outcomes

The primary outcome of concern is the development of AKI in ICU subjects with septic shock.

Statistical analysis

In order to determine risk factors for the development of AKI, we performed univariate analysis, supervised (multivariable logistic regression), and unsupervised machine learning [principal component analysis (PCA) and neural networks]. Univariate summary statistics were computed for patients who did or did not develop AKI. The Kolmogorov-Smirnov test was employed to determine normality. Continuous variables were expressed as means with standard deviations or median with interquartile ranges and compared by the Student’s t-test or the Wilcoxon rank-sum test when indicated. Categorical variables were compared with Pearson's χ² test. Fisher’s exact test was employed when indicated. Those variables that were found to be significant by univariate analysis at P < 0.05 were candidates for multivariate analysis.

To determine risk factors that were independently associated with the outcome of AKI, we performed multivariate analysis by logistic regression with stepwise forward variable selection. We employed the Omnibus test of model coefficients to determine the statistical significance of the model as a whole, and the Goodness of fit was determined by the Hosmer-Lemeshow test. For continuous variables, the odds ratio (OR) represents the relative amount by which the OR for the outcome variable increases or decreases when the independent variable is changed by exactly one unit. ORs and their 95%CI were determined by exponentiation of the beta coefficient and its upper and lower confidence interval, respectively. Assessment of multicollinearity between predictors was performed by employing a linear regression using the previous independent variables entered into the logistic regression and calculating variance inflation factors (VIF). Problematic multicollinearity was defined as a VIF greater than 5. Additionally, multicollinearity was established if the condition index was found to be greater than 30 and the variance proportions were greater than 0.5, respectively.

A two-step approach was used to investigate the presence of non-linear relationships. The presence of non-linear relationships between continuous variables and the development of AKI was explored by creating quadratic terms of the continuous variables and entering them into the logistic model. Non-linear relationships were demonstrated if both the continuous variable and the quadratic expression were statistically significant. Predicted probability plots were generated, and restrictive cubic splines modeling was applied to selective variables[17].

As there were a large number of variables which were found to be statistically significant on univariate analysis, we next performed PCA in order to reduce the dimensionality of the data and to allow a more focused evaluation of patterns of risk factors in the development of AKI. PCA was performed using the following standardized variables obtained on admission: (1) NLR; (2) PLR; (3) MLR; (4) NPAR; (5) SII; (6) SIRI; and (7) AISI. Additionally, standardized admission lab values included blood urea nitrogen (BUN), SCr, aspartate aminotransferase, total bilirubin, serum sodium, serum potassium, serum chloride, hemoglobin, age, and prothrombin time/international normalised ratio were included in the PCA. We evaluated the scree plot break point (elbow) to select the number of important principal components. The Oblimin method was used in square rotation. The correspondence of data was calculated using the principal factors that were identified by PCA-transformed data. Kaiser-Meyer-Olkin and Bartlett’s test of Sphericity were employed to assess the adaptive validity of PCA analysis. The representative variables of principal components were chosen based on their loading factors. Variables containing PCA factor scores were created using the regression method and saved for further analysis. To reduce multicollinearity and non-linear association in our models, we next performed a stepwise forward logistic regression employing individual component factors as variables in the regression. Three models were constructed: (1) Model 1 employed all variables found to be significant on univariate analysis; (2) Model 2 included demographic variables (gender, ethnicity, and comorbidities) and component PCA score variables; and (3) Model 3 included demographic variables (gender and ethnicity, comorbidities), component PCA score variables, and SOFA score on admission. Lastly, in order to evaluate potential non-linear relationships and high-order interactions among predictor variables, we employed neural network analysis as an unsupervised machine learning tool.

To explore complex and potentially non-linear relationships among risk factors for AKI, we employed a multilayer perceptron (MLP) neural network analysis. Inputs to the network included demographic characteristics (such as ethnicity), clinical comorbidities (including diabetes, cirrhosis, heart failure, COPD, malignancy, hyperlipidemia, HTN, and immunosuppression), use of medications (vasopressors, corticosteroids, diuretics, ACEi, angiotensin receptor blockers), and PCA-derived composite scores (factors 1-3) for inflammatory and renal/metabolic and age/electrolyte dimensions, in addition to SOFA score. The dataset was randomly partitioned, with 70% of cases used for training and 30% for testing. Network architecture and the number of hidden units were optimized automatically. Model performance was assessed by classification accuracy and area under the receiver operating characteristic curve, calibration plot and quantified by the Brier score and Hosmer-Lemeshow goodness of fit[18]. The Brier score measures the performance accuracy of probabilistic predictions across decile grouping in the calibration plot[18]. In addition to employing AUC for the importance of the neural network, a decision curve analysis (DCA) was constructed comparing the advantage of the following strategies: (1) Treating all; (2) Not treating; and (3) Employing the neural network model. A performance metrics graph was constructed comparing the sensitivity, specificity, negative predictive value (NPV), positive predictive value (PPV) and accuracy.

To assess the predictive utility of the MLP neural network, a DCA was performed using the DCA in STATA. The neural network generated predictive probabilities, and the observed outcome status was analyzed employing DCA. DCA evaluated the net benefit over the range of relevant threshold probabilities, comparing the neural network-guided decision and intervention to two reference strategies: (1) Treating all subjects; and (2) Treating none.

The performance metrics of the MLP neural network were evaluated by calculating sensitivity, specificity, PPV, NPV, and accuracy across three probability thresholds: (1) 0.3; (2) 0.5; and (3) 0.7. The percentage of true positives and true negatives was calculated across the three threshold probabilities. Accuracy was determined by whether the predicted probability of each case exceeded the specified threshold. To demonstrate the changes in performance of the MLP neural network across different thresholds, performance metrics were graphically depicted for varying probability thresholds.

RESULTS

In this retrospective analysis of the eICU database, a total of 12660 patients with sepsis and septic shock were included, of whom 6552 developed AKI and 5108 did not. The demographic and clinical characteristics of the two groups revealed several significant differences. Patients who developed AKI were older, with a median age of 69 years compared to 67 years among those without AKI (P < 0.001), and had a higher BMI (27.3 vs 26.3, P < 0.001). Illness severity was greater in the AKI group, as reflected by higher SOFA scores on admission (7 vs 6, P < 0.001). Male gender was more prevalent among AKI patients (52.3% vs 49.4%, OR = 1.12, 95%CI: 1.05-1.21, P = 0.002), and African American (11.6% vs 8.5%, P < 0.001) and Hispanic (5.7% vs 5.1%, P < 0.001) ethnicities were also associated with increased risk (Tables 1 and 2).

Table 1 Univariate Analysis of Baseline Characteristics in Septic Shock Patients with and without acute kidney injury, mean (95%CI).

Variables	Without AKI (n = 5108)	With AKI (n = 6552)	P value
Age (years)	67 (55-79)	69 (58-79)	< 0.001
Body mass index (kg/m2)	26.3 (22.3-31.6)	27.3 (23.0-33.2)	< 0.001
Sequential Organ Failure Assessment on admission	6 (4-9)	7 (5-10)	< 0.001
White blood counts (× 103 cells/L)	13.0 (8.6-18.4)	14.0 (9.4-19.7)	< 0.001
Platelet count (× 103 cells/L)	220 (156-298)	211 (149-294)	< 0.001
Lymphocyte count (× 103 cells/L)	962 (557-1578)	930 (534-1560)	0.023
Neutrophil count (× 103 cells/L)	10.3 (6.3-15.1)	11.3 (7.0-16.4)	< 0.001
Monocytes (× 103 cells/L)	7.4 (4.1-11.5)	7.7 (4.3-12.1)	0.003
Neutrophil-to-lymphocyte ratio	10.1 (5.2-18.2)	11.4 (6.1-22.0)	< 0.001
Platelet-to-lymphocyte ratio	226 (132-378)	222 (130-391)	0.949
Monocyte-to-lymphocyte ratio	0.7 (0.4-1.2)	0.8 (0.4-1.3)	< 0.001
Sodium (mmol/L)	136 (133-139)	136 (132-140)	0.008
Potassium (mmol/L)	4.0 (3.7-4.5)	4.2 (3.7-4.8)	< 0.001
Magnesium (mg/dL)	1.8 (1.5-2.0)	1.8 (1.5-2.1)	< 0.001
Albumin (g/dL)	3.1 (2.6-3.6)	3.1 (2.6-3.6)	< 0.001
Initial lactate (mmol/L)	2.1 (1.3-3.4)	2.4 (1.5-3.9)	< 0.001
Initial international normalized ratio	1.2 (1.1-1.5)	1.3 (1.1-1.6)	< 0.001
Initial alanine aminotransferase (U/L)	25 (22-28)	25 (16-45)	0.751
Initial aspartate aminotransferase (U/L)	29 (19-51)	30 (20-57)	< 0.001
Bicarbonate (mmol/L)	25 (22-28)	23 (20-27)	< 0.001
Chloride (mmol/L)	101 (97-104)	100 (96-105)	< 0.001
Blood urea nitrogen (mg/dL)	20 (14-31)	34 (22-53)	< 0.001
Lactate-albumin ratio	0.7 (0.4-1.1)	0.8 (0.5-1.4)	< 0.001
Creatinine (mg/dL)	0.91 (0.70-1.30)	1.8 (1.2-3.0)	< 0.001
Total bilirubin (mg/dL)	0.6 (0.4-1.1)	0.7 (0.4-1.2)	0.004
Hemoglobin (g/dL)	11.9 (10.0-13.5)	11.5 (9.8-13.2)	< 0.001
Systemic immune-inflammation index	2185 (995-4393)	2413 (1131-4838)	< 0.001
Neutrophil-percentage-to-albumin ratio	25.5 (21.1-31.3)	26.0 (21.8-32.2)	< 0.001
Systemic inflammation response index	7072 (2760-15160)	8216 (3390-18048)	< 0.001
Aggregate index of systemic inflammation (× 109/L)	1.53 (0.50-3.83)	1.72 (0.59-4.32)	< 0.001

AKI: Acute kidney injury.

Table 2 Baseline demographic and Clinical characteristics of intensive care unit patients with septic shock, n (%).

	Without AKI	With AKI	P value	OR	95%CI for OR
Male gender	2523 (49.4)	3428 (52.3)	0.002	1.124	1.045	1.210
Ethnicity
African American	436 (8.5)	762 (11.6)	< 0.001
Asian	96 (1.9)	123 (1.9)
Caucasian	3989 (78.1)	4891 (74.6)
Hispanic	259 (5.1)	376 (5.7)
Native American	33 (0.6)	32 (0.5)
Other	294 (5.8)	368 (5.6)
Hypertension	473 (9.8)	619 (9.4)	0.730	1.022	0.902	1.159
Diabetes	88 (1.7)	203 (3.1)	< 0.001	1.824	1.416	2.349
Chronic obstructive pulmonary disease	512 (10)	586 (8.9)	0.048	0.882	0.778	0.999
Hyperlipidemia	94 (1.8)	193 (2.9)	< 0.001	1.619	1.262	2.077
Cerebrovascular disease	84 (1.6)	135 (2.1)	0.101	1.258	0.956	1.656
Malignancy	342 (6.7)	304 (4.6)	< 0.001	0.678	0.578	0.795
Chronic kidney disease	259 (5.1)	1154 (17.6)	< 0.001	4.002	3.479	4.605
Cardiomyopathy	10 (0.2)	19 (0.3)	0.311	1.483	0.689	3.191
Heart failure	460 (9.0)	679 (10.4)	0.014	1.168	1.031	1.323
Immunosuppression	315(6)	271(4)	0.0001	0.65	0.55	0.77
Cirrhosis	128 (2.6)	144 (2.2)	0.245	0.867	0.681	1.103
Corticosteroids	656 (12.8)	729 (11.1)	0.004	0.850	0.759	0.951
Ventilation	2155 (42.2)	2997 (45.7)	< 0.001	1.155	1.073	1.244
Diuretics	712 (13.9)	1185 (18.1)	< 0.001	1.363	1.232	1.508
Angiotensin converting enzyme inhibitor	345 (6.8)	602 (9.2)	< 0.001	1.397	1.217	1.603
Angiotensin 2 receptor antagonist	119 (2.3)	199 (3.0)	0.020	1.313	1.043	1.653
Vasopressors	1576 (30.9)	2975 (45.4)	< 0.001	1.864	1.726	2.013

AKI: Acute kidney injury; OR: Odds ratio.

Comorbidities were important contributors to AKI risk. CKD emerged as the strongest predictor, with an OR of 4.00 (95%CI: 3.48-4.61, P < 0.001). Diabetes (OR = 1.82, 95%CI: 1.42-2.35, P < 0.001) and hyperlipidemia (OR = 1.62, 95%CI: 1.26-2.08, P < 0.001) were also more common in the AKI group, while malignancy was less prevalent (OR = 0.68, 95%CI: 0.58-0.80, P < 0.001). Heart failure was associated with a modestly increased risk of AKI (OR = 1.17, 95%CI: 1.03-1.32, P = 0.014). Clinical interventions such as mechanical ventilation (45.7% vs 42.2%, OR = 1.16, 95%CI: 1.07-1.24, P < 0.001), diuretic use (18.1% vs 13.9%, OR = 1.36, 95%CI: 1.23-1.51, P < 0.001), and vasopressor administration (45.4% vs 30.9%, OR = 1.86, 95%CI: 1.73-2.01, P < 0.001) were significantly more frequent among those who developed AKI (Tables 1 and 2).

Laboratory findings further distinguished the AKI group. These patients had higher median white blood cell counts (14 × 10³/μL vs 13 × 10³/μL, P < 0.001), NCs (11.3 × 10³/μL vs 10.3 × 10³/μL, P < 0.001), and LCs (7.7 × 10³/μL vs 7.4 × 10³/μL, P < 0.001), but lower PCs (211 × 10³/μL vs 220 × 10³/μL, P < 0.001) and hemoglobin levels (11.5 g/dL vs 11.9 g/dL, P < 0.001). Markers of renal dysfunction, such as creatinine (1.8 mg/dL vs 0.91 mg/dL, P < 0.001) and BUN (34 mg/dL vs 20 mg/dL, P < 0.001), were markedly elevated in the AKI group. Electrolyte disturbances were also observed, with higher potassium (4.2 mmol/L vs 4.0 mmol/L, P < 0.001), lower bicarbonate (23 mmol/L vs 25 mmol/L, P < 0.001), and lower chloride (100 mmol/L vs 101 mmol/L, P < 0.001). Albumin was marginally lower in the AKI group (3.1 g/dL vs 3.1 g/dL, P < 0.001), and both initial lactate (2.4 mmol/L vs 2.1 mmol/L, P < 0.001) and international normalized ratio (1.3 vs 1.2, P < 0.001) were higher, suggesting greater metabolic and coagulopathic derangement (Tables 1 and 2).

Inflammatory indices derived from routine laboratory tests were significantly elevated in the AKI group. The NLR was higher in AKI patients (11.4 vs 10.1, P < 0.001), as were the NPAR (26.0 vs 25.5, P < 0.001), SII (2413 vs 2185, P < 0.001), SIRI (8216 vs 7072, P < 0.001), and AISI (1.72 × 10⁹ vs 1.53 × 10⁹, P < 0.001). The MLR (0.7 vs 0.8, P < 0.001) was lower in the AKI group. The PLR did not significantly differ between groups (222 vs 226, P = 0.949; Tables 1 and 2).

To identify risk factors for AKI development, we performed a stepwise logistic regression analysis with forward selection. In model 1, which included clinical and lab parameters, Higher SOFA score (OR = 1.04, 95%CI: 1.01-1.06, P = 0.005), BUN (OR = 1.01, 95%CI: 1.004-1.01, P ≤ 0.001), SCr (OR = 3.46, 95%CI: 3.00-4.00, P ≤ 0.001), use of ACEi (OR = 1.56, 95%CI: 1.16-2.08, P = 0.003) were all found to be significant predictors of AKI. Elevated total bilirubin and potassium revealed a modest protective effect. Although the omnibus test for the model was statistically significant at 0.00001, the Hosmer-Lemeshow test demonstrated a poor fit, suggesting a deviation between observed and predicted values, perhaps impacted by model complexity and nonlinear relationships. Individual VIF of several variables such as albumin (3.67), sodium (4.65), chloride (4.78), neutrophil/Lymphocyte ratio (3.10), neutrophil/Lymphocyte ratio (5.66), initial lactic acid (7.81), lactic acid/albumin ratio (8.56), SII (7.55), SIRI (6.69), and AISI (7.71). In addition, among the variables, there was a high condition index of 111.3, and multiple variables demonstrated high variance proportions. These findings suggest problematic multicollinearity.

To detect nonlinear relationships between predictor variables and the risk of AKI in model 1, we performed a multivariable logistic regression model including both linear and squared terms for continuous variables (Supplementary Table 1). The squared terms of some variables in the logistic models had coefficients that support the existence of nonlinear relationships. These variables included SCr 2 (β = -0.32, P = 0.0001), neutrophils 2 (β = -0.059, P = 0.007), BUN 2 (β = -0.16 P = 0.0001) and SOFA score 2 (β = 0.22, P = 0.0001) (Supplementary Table 1). Even though SCr 2 and SOFA scores 2 demonstrate near linear relationships, the presence and statistical significance of squared terms for the variables (SCr 2, neutrophils 2, BUN 2, and SOFA score 2, all P < 0.05) point to nonlinear (quadratic) relationships. These results emphasize that the risk associated with these variables doesn't change in a completely linear manner, suggesting the need to consider nonlinear effects in defining the risk of AKI in the setting of septic shock. Restricted cubic spline functions were evaluated for important continuous predictors, and related plots were constructed (Figure 2 and Supplementary Table 2).

Figure 2 Graph of restricted cubic splines and predictive probabilities of acute kidney injury. Graphs of restricted cubic splines marginal predicted probabilities for the development of acute kidney injury across four continuous biomarkers: (1) Sequential Organ Failure Assessment score; (2) Serum creatinine; (3) Blood urea nitrogen; and (4) Neutrophils. The fitted curves for the Sequential Organ Failure Assessment score and serum creatinine are near linear. Spline terms were kept in order to improve calibration. AKI: Acute kidney injury; Pr: Predicted probabilities; SOFA: Sequential Organ Failure Assessment.

Model 2 expanded upon the first by incorporating composite laboratory indices derived from PCA, excluding the SOFA score. Caucasian ethnicity, along with malignancy and immunosuppression, was associated with lower odds of AKI. The presence of CKD remained the strongest clinical risk factor. Vasopressor, A2RB, and ACEi use, and DM were also associated with AKI. Notably, factor 1 (inflammatory indices and hematology related factor score), OR = 1.10, 95%CI: 1.04-1.17, P < 0.001, and factor 2 (metabolic and renal function related factor score), OR = 1.10, 95%CI: 1.04-1.17, substantially improved model discrimination for AKI. The Hosmer-Lemeshow goodness of fit was 0.24. The addition of the PCA improved the fit of the model.

Model 3 included all the above variables plus the SOFA score. Here, Caucasian ethnicity shifted to confer higher odds of AKI, while malignancy and immunosuppression remained protective. CKD, use of Vasopressor, A2RB, and ACEi, along with DM, were significantly associated with increased risk. Factors 1 and 2 continued to predict AKI independently. SOFA score was associated with increased AKI risk (OR = 1.04, 95%CI: 1.01-1.05, P < 0.0001). However, the Hosmer-Lemeshow goodness of fit decreased to 0.02.

PCA

Visual analysis (elbow) of the scree plot yielded three orthogonal dimensions (Figure 3), with a Kaiser-Meyer-Olkin score of 0.6 and the Bartlett’s test of Sphericity result with a P-value of 0.0001. These together accounted for 42% of the total variance in the current septic shock cohort. Component 1 demonstrated high factor loading for inflammatory biomarkers AISI (0.83), SIRI (0.82), MLR (0.81), SII (0.87), NLR (0.77), and PLR (0.56), which accounted for 19.5% of the total variance. Component 2, accounting for approximately 13% of the total variance, demonstrated high factor loading for inflammation-metabolic and renal parameters, lactate/albumin (0.775), NPAR (0.60), lactic acid (0.6), BUN (0.5), and albumin (0.5). Component 3 accounting for 10% of the total variance revealed high factor loading for electrolytes and age variables, sodium (0.85), chloride (0.77), and age (0.37) (Figure 4 and Supplementary Table 3).

Figure 3 The scree plot. The number of components for factor analysis was determined by identifying the “elbow” of the plot.

Figure 4 Principle component analysis matrix loading by components. Graphic representation of pattern matrix of principal component analysis into three components/factors (factor 1: Inflammatory/hematological components; factor 2: Metabolic/renal/inflammatory components; factor 3: Electrolyte/age). AISI: Aggregate index of systemic inflammation; AST: Aspartate aminotransferase; BUN: Blood urea nitrogen; Hgb: Hemoglobin; INR: International normalized ratio; MLR: Monocyte-to-lymphocyte ratio; NLR: Neutrophil-to-lymphocyte ratio; NPAR: Neutrophil-percentage-to-albumin ratio; PLR: Platelet-to-lymphocyte ratio; SCr: Serum creatinine; SII: Systemic immune-inflammation index; SIRI: Systemic inflammation response index.

The scree plot displays the variance explained by each principal component in the analysis of clinical laboratory markers. The PCA identified three major factors representing distinct clinical domains. Factor 1 (inflammatory/hematologic) is characterized by strong contributions from inflammation-related indices, including the AISI, SIRI, MLR, SII, NLR, and PLR. Factor 2 (metabolic/renal/inflammatory) primarily reflects metabolic and renal parameters, highlighted by the lactate-to-albumin ratio, NPAR, initial serum lactate, BUN, and serum albumin. Factor 3 (electrolyte/age) includes key loadings from sodium, chloride, and patient age. These factors consolidate multiple individual biomarkers into interpretable dimensions, providing an integrated perspective on inflammation, metabolism, renal function, electrolytes, and age within the patient cohort.

Multivariate analysis after dimension reduction with PCA (model 2)

In an attempt to improve model fit, we performed PCA and then created a logistic model (model 2, Table 3, Supplementary Table 3), which included demographic, comorbidities, and factor components 1, 2, and 3 previously derived from the PCA. Model 2 demonstrated that Caucasian race, CKD, diabetes, ACEi, A2RB, and vasopressor use were significant predictors for the development of AKI. In contrast, a history of malignancy and immunosuppression demonstrates an inverse relationship with the development of AKI, potentially due to different baseline risks or modalities of treatment. Interestingly, factor 1, which consists mainly of markers of inflammation, and factor 2, which consists of a renal metabolic and inflammatory component, were associated with an increased risk of AKI (model 2, Table 3). Employing dimension reduction with PCA in the model markedly improved model fit (Hosmer-Lemeshow test of 0.24, Omnibus test of 0.00001). Thus, dimension reduction added the value of latent variable modeling in uncovering complex relationships between risk factors. Although in model 3, the SOFA score was strongly associated with the development of AKI, the inclusion of the SOFA score in the model (model 3) paradoxically reduced the model calibration with the Hosmer-Lemeshow, going from 0.24 to 0.00001. This may be potentially due to the redundancy of SOFA components with other predictors (vasopressor use, comorbidities) and the introduction of nonlinear interactions. Additionally, SOFA scores may have variable discriminatory abilities across subgroups[19].

Table 3 Multivariate logistic regression with forward selection of risk factors associated with acute kidney injury.

		β	SE	P value	Odds ratio	95%CI for EXP(β)
						Lower	Upper
Model 1	SOFA score	0.04	0.01	0.005	1.04	1.01	1.06
	Blood urea nitrogen	0.01	0.003	< 0.001	1.01	1.00	1.01
	Serum creatinine	1.24	0.07	< 0.001	3.46	3.00	4.00
	Neutrophils	0.001	0.0001	< 0.001	1.00	1.00	1.00
	Monocytes	0.001	0.001	0.09	1.00	1.00	1.00
	Potassium	-0.164	0.05	0.001	0.85	0.76	0.94
	Total bilirubin	-0.05	0.016	0.002	0.95	0.92	0.98
	ACEi	0.44	0.15	0.003	1.56	1.16	2.08
	Vasopressors	0.16	0.01	0.09	1.17	0.98	1.41
Model 2	Caucasian	-0.075	0.027	0.005	0.93	0.88	0.98
	Malignancy	-0.41	0.12	< 0.001	0.66	0.52	0.83
	Immunosuppression	-0.26	0.12	0.034	0.76	0.60	0.98
	CKD	1.23	0.10	< 0.001	3.40	2.82	4.19
	Vasopressors	0.44	0.06	< 0.001	1.55	1.39	1.73
	Diabetes	0.55	0.20	0.006	1.74	1.17	2.58
	ACEi	0.45	0.10	< 0.001	1.58	1.29	1.93
	A2RB	0.51	0.18	0.005	1.68	1.16	2.41
	Factor 1 (inflammatory/hematologic)	0.10	0.03	< 0.001	1.10	1.04	1.17
	Factor 2 (metabolic/renal/inflammatory)	0.26	0.03	< 0.001	1.30	1.23	1.39
Model 3	Caucasian	0.37	0.10	< 0.001	1.44	1.19	1.74
	Malignancy	-0.39	0.12	0.001	0.68	0.54	0.85
	Immunosuppression	-0.27	0.13	0.034	0.77	0.60	0.98
	CKD	1.19	0.10	< 0.001	3.29	2.70	4.01
	Vasopressors	0.30	0.07	< 0.001	1.35	1.19	1.54
	Diabetes	0.56	0.20	0.006	1.75	1.18	2.59
	ACEi	0.47	0.10	< 0.001	1.60	1.30	1.96
	A2RB	0.52	0.19	0.005	1.69	1.17	2.43
	Factor 1 (Inflammatory/hematologic)	0.12	0.03	< 0.001	1.13	1.06	1.20
	Factor 2 (metabolic/renal/inflammatory)	0.24	0.03	< 0.001	1.27	1.19	1.34
	SOFA score	0.04	0.01	< 0.001	1.04	1.01	1.05

ACEi: Angiotensin converting enzyme inhibitor; A2RB: Angiotensin 2 receptor antagonist; CKD: Chronic kidney disease; SOFA: Sequential Organ Failure Assessment.

Neural network analysis

We developed an MLP to predict AKI using demographic, clinical, and factor score inputs (Figure 5 and Supplementary Figure 1). The cases were randomly split into a training set of 70.8% and a testing set of 29.2% of the population. The final network consisted of one hidden layer with seven units, using a hyperbolic tangent activation function, and an output layer optimized with a cross-entropy error function. On the training sample, the model had 63.5% overall classification accuracy, with a correct classification rate of 80.6% for patients with AKI and 38.6% for those without AKI. Performance was consistent in the testing sample, yielding an overall accuracy of 64.9% (81.8% for AKI vs 38.9% for no AKI).

Figure 5 Simplified neural network. ACEi: Angiotensin converting enzyme inhibitor; AKI: Acute kidney injury; A2RB: Angiotensin 2 receptor antagonist; CHF: Congestive heart failure; CKD: Chronic kidney disease; COPD: Chronic obstructive pulmonary disease; SOFA: Sequential Organ Failure Assessment.

Assessment of predictor importance demonstrated that the latent factor scores and illness severity had the greatest predictive weight in the neural network. Variable-importance profiling ranked factor 1 (Inflammatory and hematological indices) as the most influential variable (normalized importance = 100%), followed by factor 2 (metabolic, renal, and inflammatory indices) of 64.9% and factor 3 (electrolytes and age) of 50.9%. Among clinical covariates SOFA score, diabetes, cirrhosis and CKD were among the strongest contributors. Other comorbidities and treatments, including ACEi/A2RB use, ethnicity, immunosuppression, heart failure, hyperlipidemia, vasopressor/corticosteroid/diuretic use, COPD, HTN and gender, had comparatively lower influence on model performance (Figure 6).

Figure 6 Normalized importance of factors contributing to acute kidney injury. Multilayer perceptron summary of the level of importance of variables contributing to the development of acute kidney injury. ACEi: Angiotensin converting enzyme inhibitor; A2RB: Angiotensin 2 receptor antagonist; COPD: Chronic obstructive pulmonary disease.

The performance of the MLP as demonstrated by the AUC of 0.67 exhibits only modest discrimination (Figure 7). Factors affecting discrimination include the biological complexity and heterogeneity of septic shock, multifactorial pathophysiology and non-inflammatory factors which influence outcomes in septic shock patients. Therefore, a calibration plot (Figure 8) was constructed to illustrate the relationship between mean deciles of predicted probabilities and the actual events provided by the MLP neural network. The calibration line points upward along the 45-degree diagonal, demonstrating accuracy across the probability spectrum. The 80%CI and 95%CI remained closely aligned along the diagonal line, showing no deviation from the predicted probabilities and actual outcome. The Brier score was 0.22 and the Hosmer-Lemeshow P-value was 0.67, demonstrating good calibration and clinically significant accuracy across all levels.

Figure 7 Receiver operating curve for multilayer perceptron. Receiver operating curve for multilayer perceptron blue line indicates no acute kidney injury, red line indicates acute kidney injury.

Figure 8 Calibration performance of the multilayer perceptron neural network. Calibration plot of the multilayer perceptron model showing the expected vs observed probabilities of the outcome. The bisector line aligns closely with the 45-degree reference, indicating good calibration. The 80%CI (light gray) and 95%CI (dark gray) remain within the bisector margins, suggesting stable model performance across risk strata. The Brier score was 0.22, and the Hosmer-Lemeshow goodness-of-fit P-value was 0.67, consistent with adequate calibration.

A DCA (Figure 9) was constructed which demonstrate that when the MLP neural network is compared to “treat all“ the following differences were noted, at a predictive threshold of 0.3-0.7, the neural network model curves remain above the treat-all curve. Thus, a treatment-based strategy is advantageous compared to a treat-all strategy across all predictive probabilities. In the context of the current study, a treatment-based strategy refers to interventions based on predicted risk, such as initiating diagnostic procedures, implementing preventative measures, and intensifying clinical monitoring.

Figure 9 Decision curve analysis of the multilayer perceptron neural network. Decision curve analysis showing net benefit vs threshold probability. The blue curve (treat-all) decreases from 0.6 at threshold 0 to 0 at 0.6. The red line (treat-none) remains at 0 across thresholds 0-0.8. The green curve (multilayer perceptron) starts near 0.6 and declines toward 0 as the threshold increases to 0.8, while maintaining higher net benefit than both reference strategies across most of the range. This indicates superior clinical utility of the multilayer perceptron model across commonly used decision thresholds.

We finally constructed a performance-based metrics graph across the probability thresholds of 0.3, 0.5, and 0.7 (Figure 10). A graphic representation demonstrates that at the lowest probability threshold of 0.3, the MLP neural network showed 100% sensitivity with almost no specificity, yielding modest PPV and NPV values of approximately 60%. This suggests the model could function well as a screening method. At mid-level threshold performance, the threshold demonstrated a sensitivity of 75% and specificity of 45%, a PPV of 68% and a NPV of 32%. At the highest threshold, the sensitivity dropped to 40% and the specificity increased to 82% with a PPV of 76% and an NPV of 48%. Thus, at the mid-level threshold of 0.5, the model can be implemented when ruling in and ruling out the condition is desired.

Figure 10  Diagnostic performance across probability thresholds threshold-dependent performance metrics for the multilayer perceptron model. At a 0.3 threshold, the model achieved high sensitivity (99.9%) but low specificity (0.2). Increasing the threshold to 0.5 balanced sensitivity (77%) and specificity (45%), while a 0.7 threshold improved specificity (82%) at the expense of sensitivity (40%). The optimal threshold (0.5) yielded the best overall accuracy (68%), representing the preferred trade-off for clinical application.

DISCUSSION

Our study confirmed that several established risk factors, such as older age, higher BMI, male sex, African American race, pre-existing CKD, diabetes, and elevated SOFA scores at admission, as well as the use of vasopressors and mechanical ventilation, were all associated with the development of AKI in patients with septic shock in univariate analysis.

The primary goal of our study was to assess whether inflammatory markers provided additional prognostic value for AKI in this high-risk setting. When comparing patients with and without AKI, univariate analysis showed that the inflammatory indices, such as the SIRI, NLR, AISI, NPAR, and the SII – are significantly elevated in patients who developed AKI. This aligns with existing evidence that inflammation is a key driver in AKI development, with neutrophil infiltration detected early in kidney injury and lymphocytes modulating the balance between injury and repair[1,20]. Previous studies have shown that higher NLR to be predictor for AKI onset, severity, and mortality in septic shock[11,13]. Such indices are particularly valuable as they are both readily available and cost-effective for clinical prognostication.

Although the role of inflammatory markers NLR, SIRI, SII, AISI, and NPAR showed statistical significance in association with AKI in univariate analyses, it did not retain significance in multivariate logistic regression. This is a common phenomenon in biomedical research and can be attributed to several critical statistical and biological factors which may be collinear[21,22]. In univariate analysis, each inflammatory marker is assessed independently for its link with AKI, without accounting for the effects of other variables. Thus, many markers appear significant due to their true relationship to AKI and their shared associations with other clinical predictors. However, in a multivariate logistic regression model, the confounding and overlap among predictors are adjusted, resulting in only variables with independent and non-redundant association with AKI. In our study, the predictive values of the inflammatory indices likely had substantially overlapped and thus were excluded from the logistic regression.

Moreover, the performance of supervised machine learning was limited by marked multicollinearity and the presence of non-linear relationships between variables. To address these limitations, we employed unsupervised machine learning strategies, including neural network analysis combined with dimension reduction via PCA. This allowed for more flexible modeling of complex and interacting risk factors, providing a deeper understanding of the underlying relationships between inflammatory markers and AKI risk when simple univariate analysis fell short.

PCA and latent-factor approaches aggregate shared variance among inflammatory biomarkers, enabling multidimensional risk phenotyping and biologically coherent patient stratification. Prior studies have shown that PCA and clustering methods applied to circulating biomarkers in sepsis and AKI can identify patient subgroups with distinct immune profiles, clinical characteristics, and outcomes, moving beyond single-marker interpretation to integrated risk models[23-26]. For example, Misset et al[23] used PCA to define biomarker patterns and clusters in sepsis, while Star et al[24] identified PCA-derived protein signatures associated with AKI development. Integrating composite scores and physiologic data bridges molecular pathophysiology and bedside prognostication, enhancing risk modeling stability and reproducibility. Latent variable modeling and machine learning approaches have shown improved predictive accuracy for AKI risk compared to traditional single-marker models[27,28]. Smith et al[26] found latent variable models outperformed linear models for AKI prediction, and Ruinelli et al[29] demonstrated that machine learning algorithms using multidimensional EHR data accurately predicted AKI and AKD. Clustering and latent-factor frameworks emphasize interconnected biological networks over individual laboratory values, paving the way for standardized composite indices that better reflect the complexity of sepsis-associated AKI. Clustering analyses based on renal and inflammatory parameters have identified biologically coherent patient groups with distinct risks for adverse kidney events, supporting the development of new risk classification systems[23,25,28,30,31]. Bhatraju et al[25] and Mascle et al[28] showed that cluster- and latent class-based sub-phenotyping can stratify patients by outcome and pathophysiology, independent of arbitrary single-index cutoffs. The use of multidimensional biomarker panels and advanced analytics is increasingly recognized as a critical step toward precision medicine in sepsis and AKI, with consensus reports and reviews advocating for combined biomarker strategies and machine learning integration to improve diagnosis, prognosis, and personalized care[32-34].

The neural network’s modest discrimination should be interpreted alongside its concordance with our regression and PCA findings. Consistent with models 2 and 3, the network assigned the greatest importance to latent factors, particularly the composite of metabolic, renal and inflammatory indices (factor 2), and to SOFA, while most stand-alone comorbidities carried smaller incremental weight. This pattern supports our dimension-reduction approach and shows that, in septic shock, acute systemic derangement and aggregated physiologic signatures outweigh traditional chronic risk factors for early AKI prediction. From a practical standpoint, models should emphasize high-signal severity composites such as factor scores and SOFA, incorporate careful calibration and threshold selection to account for asymmetric class performance. Additionally, improving discrimination will likely require incorporating granular longitudinal data rather than relying solely on baseline snapshots. In septic shock, AKI risk reflects the trajectory and intensity of illness, rising vasopressor requirements, declining urine output, evolving acid-base status, and shifts in ventilatory support. Therefore, models that contextualize physiology over clinically meaningful windows (for example, 0-6 hours, 6-12 hours, 12-24 hours) using levels, slopes, variability, and extremes, or that learn directly from sequences, generally capture more predictive signal than static list of comorbidities. Concretely, deriving trend features for dynamic change in creatinine and urine output, lactate and MAP, ventilator settings and FiO₂, cumulative nephrotoxin exposure and fluid balance can enhance early warning. Framed this way, the neural network’s findings argue for modeling how patients change over time, not just who they are at baseline, when the goal is earlier and more accurate AKI prediction.

CONCLUSION

In this large, multicenter retrospective cohort of ICU patients with septic shock, composite inflammatory indices such as SIRI, NLR, MLR, NPAR, SII, and AISI were significantly elevated in those who developed AKI. While these parameters demonstrated strong univariate associations with AKI, their independent prognostic value was diminished in multivariable models due to marked collinearity and interaction with traditional clinical factors. By applying PCA and neural network modeling, the study highlighted that multi-dimensional approaches, integrating inflammatory, metabolic, and demographic data, can enhance predictive performance for AKI risk stratification. Overall, these inflammatory indices offer insight into AKI pathophysiology in sepsis but when used in isolation, have limited incremental utility for early prediction beyond established clinical and laboratory markers. Future research should focus on prospective validation, temporal assessment of these indices, and integration into clinical decision support tools to improve outcomes for critically ill patients at risk of AKI. Future research should also focus on using machine learning models routinely especially when complex, non-linear associations are suspected.