The data analyzed in this study were obtained from the publicly accessible Medical Information Mart for Intensive Care IV (MIMIC-IV) database, which contains de-identified health information of patients admitted to the ICU of the Beth Israel Deaconess Medical Center in the USA from 2008 to 2019. The database comprises comprehensive data, including demographic information, clinical features, laboratory results, medication details, and vital signs. Data for analysis were extracted from the institutional electronic health record system, using the Structured Query Language (SQL). The author Yuewei Li has completed the Collaborative Institutional Training Program exam (certification number: 10007248) and the study has received institutional review board (IRB) approval. Informed consent is not necessary for the secondary utilization of this de-identified database.

Patients diagnosed with AKI within 48 h after ICU admission as per the Kidney Disease Improving Global Outcomes (KDIGO) criteria [14] were enrolled. The exclusion criteria were as follows: (i) patients with missing data of sNa for the seven consecutive days after ICU admission; (ii) patients with age younger than 18 years; (iii) patients with less than 48 h of ICU stay; (iv) patients receiving maintenance dialysis treatment. For patients hospitalized for more than 7 days, only the first 7 days of hospitalization were analyzed for sNa measurements. In patients admitted to the ICU multiple times, only the first admission was included in the analysis.

Base on the Group-Based Trajectory Modeling (GBTM), we divided the participants into three groups. In a study exploring the link between sodium level changes over a week and subsequent survival periods, the use of Group-Based Trajectory Modeling (GBTM) begins with comprehensive data collection and organization. This initial stage covers not only the tracking of sodium levels daily for a week but also observing survival times during follow-up. At this juncture, the accuracy, error checking, and management of missing or abnormal data are imperative to ensure the reliability of future analyses.

Subsequently, GBTM analyzes patient data, primarily to categorize patients based on the dynamic shifts in their sodium levels. This technique discerns typical patterns of sodium variation, essentially having patients grouped by their sodium level changes. In the implementation of GBTM, specific polynomial shapes are predetermined, exploring models ranging from two to six groups. The selection of the optimal number of groups involves an iterative process, evaluating model fitting criteria such as the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC), along with assessments of group similarities and differences.

This detailed analytical method successfully outlines various sodium level trajectories, clearly representing the diverse trends within the study population over time. Each trajectory group embodies a distinct sodium fluctuation pattern, including but not limited to stability, and gradual increases or decreases. Through delineating these unique trajectory groups, researchers can further examine the association between specific patterns of sodium changes and patient survival times, thereby offering novel insights into the effects of sodium levels on patient prognosis. The methodology outlined utilizes the R package “traj.”

Baseline data mainly included demographic information (age, gender), vital signs [systolic blood pressure (SBP), diastolic blood pressure (DBP), mean blood pressure (MBP), respiratory rate (RR), heart rate (HR) and oxygen saturation (SpO2)], glucose, white blood cell count (WBC), hemoglobin (HB), platelet, sodium, potassium, chloride, serum creatinine (SCr), anion gap (AG), blood urea nitrogen (BUN), international normalized ratio (INR), prothrombin time (PT), partial thrombin time (PTT), albumin, multimorbidity (sepsis, shock, heart failure, respiratory failure, hypertension, diabetes mellitus, chronic kidney disease (CKD) and pneumonia etc.), Risk assessment scores [simplified acute physiology score II (SAPS II), sequential organ failure assessment (SOFA) and Oxford acute severity of illness (OASIS)]. Baseline SCr was defined as the minimum value of SCr within 7 days prior to admission or, if the baseline value was unavailable, as the first SCr measurement at admission [15], The main predictor was the in-hospital sNa trajectory, which was assessed for each patient based on the sNa values during the hospital stay.

AKI was diagnosed according to KDIGO criteria [14]: (1) SCr increased by 0.3 mg/dL (or ≥ 26.5 μmol/L) within 48 h; or (2) increased by ≥ 1.5-fold from baseline within the prior 7 days; and/or (3) a decrease in urine output (UO) < 0.5 ml/kg/h for 6 h. The primary outcome was 30-day mortality and secondary outcomes was 1-year mortality.

For continuous variables, the Shapiro–Wilk test was used to determine whether the data were normally distributed, thus those normally distributed were presented as mean ± standard deviation, otherwise median (with interquartile range (IQR)). Categorical variables were presented as absolute counts (percentages). Comparisons between groups were performed using the Student’s t test for continuous variables, and chi-square test or Fisher’s exact test for categorical variables. A two-tailed p value of less than 0.05 was considered statistically significant.

SNa trajectories during the first seven days of ICU admission were created by GBTM to group longitudinal measurements intro inter-related subgroups. GBTM considers the patterns of change for measures across multiple time points and identifies distinctive trajectories, allowing for a more robust and objective classification compared to subjective criteria. The complete algorithm was fully described elsewhere. Briefly, GBTM predicts the trajectory for each group, estimates the probability of each individual of group membership, and assigns them to the group based on their highest probabilities which were summarized by a finite set of different polynomial functions of time. The model with the highest number of fitting categories was selected based on the Bayesian information criterion (BIC). Aiming to ensure that each group had a clear clinical interpretation and utility, we referred to the clinical experience of experts in the field and sought to find a proper model reflecting clinically meaningful distinctions among patient trajectories in each group. We also assessed the stability and reliability of our chosen model across different samples to ensure that the model groups were not only statistically optimal but robust and reliable in clinical practice. Hence, after thoroughly considering BIC scores, clinical experience, and the additional criteria above, sNa trajectories were categorized into three main trajectories: (i) stable group (ST), where sNa levels remained relatively stable, (ii) descending group (DS), where sNa levels declined, and (iii) ascending group (AS), where sNa levels were elevated. All trajectories are depicted in Fig. 1.

Identification of serum sodium trajectories. A The average Serum sodium level trajectories of patients in different group with acute kidney injury (AKI). B The mean serum sodium levels0 from day 1 to day 7 in each group

Kaplan–Meier survival analysis with the log-rank test were conducted to compare the 30-day mortality and 1-year mortality among distinct sNa trajectories. Furthermore, Cox proportional hazard models were performed to calculate the hazard ratios (HRs) and 95% confidence intervals (CIs) assess the association between sNa trajectories and 30-day mortality of AKI patients. Model 1 was adjusted for age, gender, BMI, BP, HR and SpO2, and model 2 was further adjusted for CKD, hypertension, diabetes, heart failure, sepsis, stroke, AKI stage, SAPSII and OASIS scores. Model 3 extended model 2 by further adjusting mean sNa and diuretics use. In the subgroup analyses, AKI patients were stratified by age, gender, hypertension, diabetes, heart failure, CKD, sepsis, vasopressors and diuretics.

GraphPad Prism 8.0 (GraphPad Software, Inc, La Jolla, CA, USA) and RStudio (version 1.0.143) were used for data analysis in the study.