Introduction
Acute kidney injury (AKI) is a prevalent and complex clinical complication in the intensive care unit (ICU) [1]. The incidence of AKI is increased by sepsis, and there is increasing evidence of a higher likelihood of infection or sepsis following AKI [2]. Mortality in sepsis-associated AKI (S-AKI) cannot be attributed solely to renal dysfunction. Instead, the progression of multiple organ dysfunctions—such as those affecting the heart, brain, and liver—exacerbates mortality in S-AKI [3]. Early administration of antibiotics is a highly effective intervention for reducing mortality in sepsis patients [4,5]. Despite improvements in clinical management, mortality rates for S-AKI in patients remain high, stabling at 40% to 44% due to microvascular dysfunction, systemic inflammatory response syndrome, and multiorgan failure [6–8].
Current guidance on heart rate management in the ICU is limited, and there is insufficient evidence to support specific recommendations. It is intuitive that survival outcomes may be influenced by the duration of an elevated heart rate. Tachycardia often persists for hours or days in ICU patients; however, limited data exists regarding its impact on S-AKI patients specifically. A high heart rate has been shown to correlate with poorer outcomes [9]. Among patients with sepsis, it remains unclear whether those with AKI exhibit faster heart rates than those without AKI. Furthermore, the survival prognosis of patients with prolonged elevated heart rate (pe-HR) in S-AKI is yet to be determined. It is uncertain whether treatment with β-blockers may reduce mortality in S-AKI patients with pe-HR or if a causal relationship exists.
Over the past decade, advancements in AI technology have significantly impacted healthcare, particularly in critical care big data analytics. These advancements demonstrate the potential to predict patient survival prognosis based on common laboratory tests [10,11]. The Medical Information Mart for Intensive Care (MIMIC) database facilitates the application of various algorithms to predict the occurrence and prognosis of S-AKI [12,13]. However, some technical difficulties have prevented the practical development of machine learning in this area. First, establishing feature engineering requires the involvement of medical professionals to develop and process model variables, such as the grading diagnosis of hypertension and the grading diagnosis code of acute respiratory distress syndrome. This increases the need for collaboration between physicians and computer scientists. Second, many of the variables used in these models are based on “black-box” algorithms, which are not well-suited to the medical field, where high transparency is essential. In the past, there has been limited analysis of the causal correlation between variables and outcomes, particularly in the context of machine learning models.
This study aims to explore the relationship between pe-HR and clinical prognosis in S-AKI patients. We will extract data from the MIMIC-IV database and focus on the impact of pe-HR and β-blockers on S-AKI outcomes, such as 90-day survival, hospital survival, and length of ICU/hospital stay. Specifically, the study will assess whether incorporating the pe-HR feature improves the prediction model’s performance for survival prognosis in S-AKI patients. Additionally, the inverse probability weighting method will be used to estimate the average treatment effect (ATE) of β-blocker use on prognosis in S-AKI patients with pe-HR.
Methods
Data source
This study retrospectively analyzed the MIMIC-IV database, a comprehensive repository of critical care data [14]. The MIMIC database was established in 2003 through a collaboration involving Beth Israel Deaconess Medical Center, Massachusetts Institute of Technology, National Institutes of Health, Massachusetts General Hospital, and a range of critical care professionals, including emergency and critical care physicians, computer scientists, and others. The current version of the database is an update of MIMIC-IV. The collection of patient information and creation of the research resource was reviewed by the Institutional Review Board at the Beth Israel Deaconess Medical Center, who granted a waiver of informed consent and approved the data sharing initiative (https://physionet.org/content/mimiciv/3.1/). The patients included in MIMIC-IV were admitted to the ICU between 2008 and 2019. Our research team has completed the necessary training courses and obtained the appropriate certifications prior to using the database (ID. 48389172). Since this study does not involve any clinical interventions and all sensitive health information remains anonymized, individual patient consent was not required. The research database was built using PostgreSQL (version 10.0; PostgreSQL Global Development Group), following the official MIMIC-IV tutorial.
Patients selection
All adult patients admitted to the ICU for the first time with a stay of more than 24 hours were eligible for inclusion in this study. Sepsis was defined according to the third International Consensus Definitions for Sepsis and Septic Shock (Sepsis-3) as proposed by Singer et al. [15]. Specifically, sepsis is characterized as life-threatening organ dysfunction resulting from a dysregulated host response to infection. The presence of organ dysfunction is operationalized through an increase of ≥2 points in the SOFA (Sequential Organ Failure Assessment) score. In addition, infection must be suspected or confirmed, and diagnostic codes specific to sepsis have been used to confirm the presence of infection as documented in prior studies [16]. Identification of AKI was based on the Kidney Disease: Improving Global Outcomes (KDIGO) criteria [17]. S-AKI was identified using a dual classification system, combining the Sepsis-3 definition of sepsis and the KDIGO criteria for AKI [18,19]. The median hourly heart rate was calculated using all electronically recorded heart rate measurements from the time of ICU admission to data collection. Patient data, including demographic characteristics, vital signs, laboratory results, potential causes of tachycardia, and β-blocker use, were extracted using structured query language. The duration of missing heart rate data was determined, and patients with more than 20% missing hourly measurements were excluded. The pe-HR episodes were defined as an 11-hour heart rate measurement exceeding 100 beats/min for any 12-hour interval [20,21]. The patient enrolment process for this study is shown in Fig. 1 shows a schematic diagram of heart rates in patients with and without pe-HR.
We also performed secondary analyses to evaluate the impact of different combinations of duration and heart rate thresholds, with durations ranging from 8 to 18 hours, such as from 7 hours out of the 8-hour duration to 17 hours out of the 18-hour duration. The primary endpoint of this study was survival at 90 days, with survival during hospitalization as a secondary endpoint. To provide a more comprehensive understanding of the impact of pe-HR on S-AKI prognosis, we also assessed several shorter-term outcomes and critical care parameters. These included 28-day survival, length of ICU stays, length of hospital stays, and the initiation of continuous renal replacement therapy (CRRT). A subgroup analysis was conducted to examine whether the underlying cause of tachycardia (e.g., ventricular tachycardia [VT], atrial tachycardia [AT], or sinus tachycardia [ST]) had any differential effect on 90-day survival outcomes in S-AKI patients.
Causal inference
To reduce confounding, we planned to include sex, age, race, and heart failure in the propensity score matching. We used a directed acyclic graph (DAG) to represent the assumptions underlying the causal relationship between the variables and our observed variable pe-HR, as well as the outcome variable of 90-day survival [22]. This will enable us to determine whether these variables serve as confounding or intermediate variables. We estimated propensity scores for each patient and created propensity score-matched cohorts using the nearest neighbor method with a caliper of 0.2 [23]. In this study, we used the inverse probability weighted (IPW) to make causal inferences between β-blockers and patients with S-AKI [24]. The ATE represents the effect of the variable on patient survival in both the dead and survival study groups. It is important to note that propensity score-weighted models can sometimes produce confidence intervals (CIs) that are too narrow due to the dependence on weights. To address this, robust standard error estimates were used to correct the confidence bounds, ensuring more accurate and reliable interval estimates.
Machine learning
The data set was randomly divided into a 70% training set and a 30% test set. We applied 10-fold cross-validation to the training set and selected the model that performed best on the test set. Machine learning algorithms, including logistic regression [25], support vector machines (SVM) [26], extreme gradient enhancement machines (XGBoost) [27], and light gradient boost machine (LightGBM) [28] were employed to predict 90-day survival in S-AKI patients. Initially, modeling was developed excluding the pe-HR variable. After establishing the predictive model, we incorporated pe-HR into the stacking process to assess whether including this variable improved model performance. Observing whether the area under the receiver operating characteristic curve (AUROC) is used to compare whether the pe-HR variable is included will improve the predictive performance of the model. Furthermore, the predictive performance analysis incorporated C-statistics, net reclassification improvement (NRI), and integrated discrimination improvement (IDI) measures.
Statistical analysis
Univariate Cox analysis was performed on all study variables, and multivariable Cox regression analysis was performed on variables with p-values less than 0.05 [29]. No additional variables were included in the multivariable Cox models to avoid overadjustment in the context of the propensity score-matched sample. Normally distributed continuous variables were compared using the chi-square test or Fisher exact test. Non-normally distributed continuous variables are reported as medians with interquartile range and compared using the Mann-Whitney U test [30]. The ‘CBCgrp’ package (version 2.8.2) in R (version 4.1.2; R Foundation for Statistical Computing) was used to calculate data [31]. The survival probabilities for both 90-day and in-hospital survival were estimated using the Kaplan-Meier (KM) method, with results visualized in KM curves. The log-rank test was used to compare survival differences between groups. Missing data was imputed multiple times using the ‘mice’ package (ver. 3.15.0) in R [32]. To detect differences in AUROC values between models, Delong tests were used. For sensitivity analysis, we analyzed patients with no missing data. Two-sided p-values less than 0.05 were considered statistically significant. This study is reported in accordance with the STROBE (STrengthening the Reporting of OBservational studies in Epidemiology) checklist.
Results
A total of 14,833 patients with S-AKI were included in the study, with 6,009 patients with pe-HR and 8,824 patients without pe-HR. The baseline characteristics of these two groups are presented in Table 1. Among patients with pe-HR, 2,067 (34.4%) were classified as AKI grade 3, compared to 1,999 (22.7%) in the non–pe-HR group. There was a statistically significant difference in the AKI stage between the two groups (p < 0.001). The mortality rate during hospitalization was 34.9% for patients with pe-HR and 20.7% for patients without pe-HR (p < 0.001). However, there was no statistically significant difference in the Glasgow Coma Scale score (p = 0.30). The calculation of the causal ratio of pe-HR on mortality revealed a value of 56.3, and the 95% CI ranged from 42.7 to 69.9. This indicates that S-AKI patients who developed pe-HR had a survival time of 56.3 days less than those who did not develop pe-HR (p < 0.001). Supplementary Table 1 (available online) presents a comparison of historical diseases between the two groups. To investigate whether the model is an independent prognostic factor in S-AKI patients, we conducted univariate and multivariate Cox analyses of pe-HR with clinical factors. The initial step involved the removal of insignificant variables through univariate Cox regression. In the multivariable Cox regression analyses, we found that pe-HR was significantly associated with worse outcomes (hazard ratio, 1.34; 95% CI, 1.26–1.43; p < 0.001) (Supplementary Table 2, available online).
Next, we compared the heart rates of sepsis patients with non-AKI and those with S-AKI. Non-AKI sepsis patients have lower heart rates than S-AKI patients, as shown in Supplementary Table 3 (available online). Although the difference is statistically significant (p < 0.001), the median values are normal (non-AKI sepsis patients, 85 vs. S-AKI, 87). On the other hand, the 90-day prognosis of non-sepsis AKI patients with pe-HR is better than that of S-AKI patients with pe-HR, and the difference is statistically significant (p < 0.001) (Supplementary Fig. 1, available online). The 90-day survival analysis using the univariate Cox regression model revealed the following findings: For non-AKI sepsis patients with pe-HR, the hazard ratio for 90-day survival was 1.54 (95% CI, 1.39–1.71; p < 0.001). For inpatient mortality, pe-HR was associated with a moderate but statistically significant increased risk of death (hazard ratio, 1.17; 95% CI, 1.01–1.36; p = 0.04).
Fig. 2 illustrates the KM curves for patients with and without pe-HR. Both survival curves demonstrate that patients with S-AKI and pe-HR had shorter life expectancy than those without pe-HR (Fig. 2). Specifically, Fig. 2A shows the 90-day survival curve, and Fig. 2B shows the survival curve during hospitalization. The 90-day Cox analysis indicated that pe-HR significantly increased the risk of death, with a hazard ratio of 1.62 (95% CI, 1.54–1.70; p < 0.001). Sensitivity analyses, which excluded patients with missing data, confirmed the consistency of this trend, as shown in Supplementary Fig. 2 (available online) and Supplementary Fig. 3 (available online). Further investigation of different types of tachycardia revealed that the hazard ratio for pe-HR associated with VT was 1.46 (95% CI, 1.20–1.77), with AT was 1.75 (95% CI, 1.63–1.88), and with ST was 1.29 (95% CI, 1.22–1.37) (Supplementary Table 4, available online).
We next assessed the effect of pe-HR on various shorter-term outcomes, including 28-day mortality, ICU and hospital stay durations, and the initiation of CRRT. The hazard ratio for 28-day survival was 1.34 (95% CI, 1.29–1.39), with a p < 0.001. Patients with pe-HR had significantly longer ICU stays. The rate ratio for ICU duration was 1.91 (95% CI, 1.89–1.93; p < 0.001). The rate ratio for total hospital duration was 1.45 (95% CI, 1.44–1.47; p < 0.001). The hazard ratio for CRRT initiation was 2.21 (95% CI, 2.01–2.43; p < 0.001).
To explore the relationship between pe-HR duration and survival outcomes, we constructed a hazard ratio forest plot (Fig. 3). This trend was observed in both in-hospital survival (Fig. 3A) and 90-day survival (Fig. 3B) across both groups. However, while the numerical difference in heart rate between 8 hours and 10/14/16/18 hours was observed, a weighted Cox proportional hazards model that accounted for time-dependent covariates revealed that the interaction between pe-HR occurrence and duration had a p-value of 0.91, indicating no statistically significant effect.
Fig. 4A illustrates the distribution of β-blocker use between patients with and without pe-HR. A significant statistical difference between the two groups was observed. To confirm whether β-blockers reduce patient mortality, we plotted two KM curves for S-AKI patients with pe-HR who were either taking or not taking β-blockers (Fig. 4C). Additionally, to further demonstrate the causal relationship between β-blocker use and 90-day prognosis, we calculated the ATE after propensity score matching. The DAG plot in Fig. 4B confirmed that sex, age, race, and heart failure were indeed confounders. After matching, the mean difference in survival between those using β-blockers and those not using β-blockers was estimated to be 40.2 days, with a 95% CI of 21.5 to 58.9. This suggests that S-AKI patients with pe-HR who used β-blockers may live approximately 40 days longer than their counterparts who did not. Fig. 4D displays the survival discrepancies across different AKI stages, with β-blocker usage significantly affecting survival in each stage.
We developed a predictive model for 90-day survival in S-AKI patients using four machine-learning algorithms. All models indicated that the inclusion of the pe-HR variable improved the model’s predictive performance, as evidenced by a higher AUROC (Fig. 5). The best performance was LightGBM, which achieved an AUROC of 0.76 (95% CI, 0.75–0.78) in the test set when pe-HR was included. For models without pe-HR, the AUROC was 0.67 (95% CI, 0.66–0.68), representing a 9% point increase with pe-HR inclusion (p < 0.001). The C-statistics for the models are as follows: logistic regression, 0.62; SVM, 0.61; XGBoost, 0.68; and LightGBM, 0.76. The NRI values for the models, with and without pe-HR, are as follows: logistic regression, 0.20686; SVM, 0.17219; XGBoost, 0.59198; and LightGBM, 0.68963. The IDI for models with and without pe-HR was as follows: logistic regression, 0.05424; SVM, 0.038903; XGBoost, 0.191938; and LightGBM, 0.109818 (Supplementary Table 5, available online).
Discussion
In our study of 14,833 patients with S-AKI, we found that both 90-day and in-hospital survival rates were significantly lower in patients with pe-HR compared to those without pe-HR. The use of β-blockers in S-AKI patients with pe-HR was found to improve 90-day and in-hospital survival. As this is an observational study, we utilized the propensity score matching method to minimize confounding differences between treatment groups. To further assess average treatment effects, cases were weighted according to the IPW. This approach helped determine the potential causal relationship between β-blocker treatment and 90-day prognosis among S-AKI patients with pe-HR. Our findings provide valuable insights into the understanding of S-AKI and underscore the critical need for further research in this area.
In the prediction of S-AKI prognosis by machine learning, the increase of pe-HR can bring some improvement in the prediction performance. Specifically, pe-HR improved prediction accuracy by 7% points for logistic regression and SVM algorithms, 4% points for XGBoost, and 9% points for LightGBM. This emphasizes the importance of feature engineering in developing predictive models. In the process of model building, data partitioning of variables can improve the performance of the model. The pe-HR diagnosis suggests a feature engineering approach to medical data that can be used in data subbing for a continuous increase or decrease in a variable. For example, a continuous increase in respiration, body temperature, or multiple laboratory indicators can be performed be separated as the two classification factors, and these factors can continue to increase to a certain threshold that affects the survival prognosis.
Propensity scores estimate the probability of receiving treatment based on measured baseline covariates, thereby reducing or eliminating bias due to measured confounders. The aim of using propensity scores was to maximize the similarity between the treatment and non-treatment groups and minimize non–treatment-related bias. The DAG plot was employed to identify and distinguish intermediate variables from confounders, ensuring fair comparisons between treatment groups. By calculating the ATE on the β-blocker using the IPW, confounding bias in comparisons between the β-blocker–treated and untreated groups was reduced, leading to a greater balance of detected confounders among patients with pe-HR. A sensitivity analysis also was performed to elucidate the extent to which unmeasured confounding could affect our results [33]. The sensitivity analysis performed after excluding missing values demonstrated results comparable to the primary analysis, supporting the robustness of our findings.
Furthermore, several secondary outcomes were investigated, including 28-day mortality, length of ICU stay, hospital duration, and CRRT initiation. All of these outcomes were found to be significantly associated with pe-HR. The results of this study align with those of previous studies, which have demonstrated that prolonged tachycardia in critically ill patients is associated with worse short-term outcomes, including higher mortality and prolonged hospitalizations [34]. Notably, studies have reported similar associations between tachycardia and extended ICU and hospital stays, thereby emphasizing the role of sustained elevated heart rate as a marker of increased disease severity and resource utilization. Moreover, the association between pe-HR and the initiation of CRRT underscores its potential role as an early indicator of renal dysfunction. These secondary findings underscore the broader clinical implications of a persistent elevation in heart rate, indicating that its impact extends beyond mortality. Specifically, pe-HR contributes to delayed renal recovery, longer ICU and hospital stays, and increased renal complications. Our findings support the mounting evidence that effective heart rate monitoring and management could improve outcomes and optimize healthcare resources for S-AKI patients.
Although ST has traditionally been considered a compensatory response to critical illness (e.g., hypovolemia, inflammatory storm), our findings suggest that varying degrees of duration of pe-HR confer adverse outcomes. The results were statistically significant at the 8-hour duration, indicating that clinicians should be particularly vigilant in monitoring patients with S-AKI who exhibit a continuous increase in heart rate for 7 hours out of an 8-hour period. This prolonged tachycardia may serve as an early warning sign, highlighting the need for proactive management and closer observation of these patients. This complexity highlights the need for further studies that explore not only the duration of tachycardia, but also the timing, underlying cause, and mechanisms driving this phenomenon. For example, longer durations of ventricular or AT may have more severe clinical consequences than ST, possibly due to the arrhythmia’s direct impact on the heart’s electrical and mechanical function [35]. Future studies should aim to clarify the mechanistic pathways and explore targeted interventions that could mitigate the adverse effects of tachycardia in S-AKI patients.
Heart failure is a commonly considered factor when utilizing β-blocker regimens [36]. The comorbidity between AKI and heart disease involves the activation of inflammatory cytokines and harmful hormones, such as angiotensin II, in the kidneys and circulation, which increases the risk of AKI and heart failure [37]. Several studies suggest that hypotension and reduced renal blood flow are factors in the development of AKI during cardiac surgery [38–40]. Despite the increasing incidence of AKI and the significant risks of mortality and heart failure, the U.S. Food and Drug Administration has not approved any medication for its treatment. The use of β-blockers in pe-HR patients has been shown to be cardioprotective. There is potential for β-blockers to treat and protect S-AKI patients, but the underlying mechanisms of β-blocker action in the kidneys require further investigation before their benefits for S-AKI patients can be fully assessed.
This study has several limitations. First, only measurements taken within the first 24 hours of S-AKI were used, which may not fully capture the long-term dynamics of the disease. Specifically, measurements taken throughout the ICU stay, as well as the impact of creatinine fluctuations on the prognosis of S-AKI patients, were not included. Second, this was a retrospective, single-center study, which may limit the generalizability of the findings and potentially exclude some confounding factors. Although the sample size is adequate and propensity score matching ensures low patient heterogeneity, further verification of the study results by a large, multicenter, prospective study is essential.
In conclusion, our investigation highlights the significant impact of pe-HR on survival outcomes in S-AKI patients. The inclusion of the pe-HR variable improves the performance of algorithms, particularly for predicting 90-day survival. Our data demonstrates that S-AKI patients with pe-HR have a shorter life expectancy compared to those without pe-HR. Interestingly, our study suggests that the use of β-blockers in patients with pe-HR may offer a potential survival benefit.
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