Introduction

Abdominal aortic aneurysm (AAA) is defined as a pathological dilation of the abdominal aorta and is associated with a high mortality rate, approaching 80% upon rupture [1–3]. Currently, no effective pharmacological treatment exists to prevent the progression or rupture of AAA; therefore, surgical intervention remains the primary therapeutic strategy [1,4,5]. Surgical intervention is generally recommended for AAAs with a diameter of ≥ 5.5 cm in males and ≥ 5.0 cm in females [5–7]. The two primary surgical options are open aneurysm repair (OAR) and endovascular aneurysm repair (EVAR) [8]. Recently, EVAR has gained widespread popularity, accounting for up to 80% of AAA repair, due to its minimally invasive nature and lower early postoperative mortality compared to OAR [6,8,9]. Despite these advantages, EVAR remains associated with important long-term complications, including endoleaks and late aneurysm rupture, which are serious enough to necessitate lifelong surveillance [7,10,11].

Mortality outcomes following EVAR are influenced by numerous factors, including demographic characteristics, anthropometric measures, and comorbidities [12–15]. In addition to well-established risk factors such as advanced age, female sex, and renal disease, socioeconomic factors have also emerged as potential contributors to AAA-related mortality. Low household income, in particular, has been consistently linked to poorer AAA-related outcomes [16]. Previous research indicates that, compared to privately insured patients, those with low income have a 47% higher mortality rate following AAA surgery, and uninsured patients exhibit a 102% higher mortality rate [15]. Moreover, patients with low BMI have also been reported to have increased mortality following EVAR [13,14]. Therefore, evaluating the impact of socioeconomic and anthropometric factors on long-term survival prediction after EVAR is clinically important.

Currently, a well-established and widely accepted model for predicting long-term prognosis after EVAR is lacking, and existing models have limited clinical utility [17]. A systematic review of 13 risk prediction models for AAA treatment outcomes highlighted numerous methodological limitations, variable predictive performance across different populations, and heterogeneity in predictor variables [18]. Notably, most existing models included heterogeneous patient populations combining EVAR and OAR recipients without adequately distinguishing between the two surgical techniques [18]. Although recent studies have attempted to predict long-term outcomes specifically in EVAR populations, these have predominantly relied on conventional statistical approaches, such as Cox proportional hazards regression [9,19], While these traditional methods offer intuitive interpretations and rapid assessments, they assume proportional hazards and linear relationships among variables, thus limiting their capacity to identify complex, non-linear interactions [20]. Moreover, these methods struggle to effectively address the dynamic, time-dependent nature of risk, in which the relative contribution of prognostic factors may change throughout different phases of disease progression [21].

Recent advances in machine learning (ML) have offered new opportunities to enhance predictive accuracy by accommodating complex, nonlinear relationships and simultaneously integrating multiple patient characteristics without restrictive statistical assumptions [22,23]. Particularly, ensemble ML techniques, like stacking [24], aggregate predictions from multiple models showing superior performance by reducing prediction errors and addressing issues of bias and variance [25,26]. Additionally, ML-based survival analyses facilitate dynamic evaluation of risk over time, providing deeper insights into how prognostic factors influence patient outcomes across different stages of disease progression [27,28]. However, most prior ML-based studies of AAA have focused primarily on classification tasks, limiting the ability to evaluate temporal variations in risk and predictor importance [17,29].

Recently, our group conducted a large-scale national cohort study of patients undergoing EVAR using the Korean NHIS database; in this study, we demonstrated that insurance type was independently associated with AAA-related mortality, even after adjusting for demographic, clinical, and laboratory variables [30]. Specifically, Medical Aid patients exhibited significantly higher AAA-related mortality compared to National Health Insurance patients, as shown by Kaplan–Meier survival analyses and multivariable Cox regression models with propensity score matching [30]. These findings underscore the prognostic value of structured real-world data, even in the absence of detailed anatomical information.

Building on this finding, the present study aimed to develop a time-to-event predictive model utilizing stacking-based ensemble ML techniques within the Korean nationwide EVAR cohort. By evaluating the time-varying importance of predictive variables, we seek to identify the dynamic contributions of key risk factors to mortality and to support risk stratification and data-driven decision-making in large-scale EVAR populations.

Methods

Data source and study population

This study used data from the Korean National Health Insurance System (NHIS) database, which provides universal healthcare coverage to all South Korean residents. Data access was approved by the NHIS Institutional Review Board and can be requested by qualified researchers via the Korean National Health Insurance Sharing Service (NHISS) (https://nhiss.nhis.or.kr). The NHIS dataset used in this study was accessed for research purposes on 31 March 2025. All data provided to the research team were fully anonymized before access, and no author had access to any information that could identify individual participants during or after data extraction.

We extracted data from the Korean NHIS database for all patients newly diagnosed with aortic aneurysms from 2002 to 2019 (n = 145,672). Patients diagnosed with aneurysms other than AAA (n = 24,344) and those presenting with ruptured AAA (n = 8,357) were excluded. We further restricted the cohort to patients with AAA who underwent surgical intervention, specifically EVAR. Consequently, patients who did not undergo surgical intervention (n = 97,125), those younger than 19 years (n = 19), patients with missing or erroneous data (n = 762), and those who initially underwent open aneurysm repair (n = 2,753) were sequentially excluded. The final cohort comprised 12,312 patients who initially underwent EVAR. This cohort was randomly divided into a development set (80%; n = 9,849) and a test set (20%; n = 2,463) for subsequent analysis (Fig 1).

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Fig 1. Flowchart of the study population.

https://doi.org/10.1371/journal.pone.0349122.g001

Results

Participant characteristics

The baseline characteristics of the study patients are presented in Table 1. During the median follow-up period of 2.8 years (interquartile range: 1.1–5.4 years), a total of 740 patients (6.0%) experienced AAA-related mortality. The average age of the total patient population was 72.8 years, with 10,173 (82.6%) being male. Mean age was significantly different between the event group and censored group (75.1 vs 72.7 years; p < 0.001). The event group had significantly higher proportions of females and Medical Aid. Additionally, the event group had significantly lower weight and height compared to the censored group (p < 0.001). The proportion of patients engaging in regular exercise was also lower in the event group (p < 0.001). Among clinical variables, hypertension was the most prevalent, observed in 24.3% of total patients. Comorbidities did not show a statistically significant difference between the event and censored groups. However, systolic and diastolic blood pressure were significantly higher in the event group compared to the censored group. Regarding laboratory variables, hemoglobin levels were significantly higher in the event group compared to the censored group (13.5 vs 13.9 g/dL; p < 0.001). In terms of lipid-related parameters, no significant differences were observed between the two groups, except for triglycerides. Kidney function was significantly lower in the event group than in the censored group.

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Table 1. Baseline Characteristics of Patients who Underwent EVAR for Abdominal Aortic Aneurysm.

https://doi.org/10.1371/journal.pone.0349122.t001

Fig 2 is a Kaplan-Meier curve representing the cumulative AAA-related mortality rate. The cumulative AAA-related mortality rate increased sharply within the first 60 days after EVAR. The cumulative mortality rate was 1.6% at 1 month, 3.1% at 6 months, 3.6% at 1 year, 4.2% at 2 years, and 7.0% at 3 years.

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Fig 2. Cumulative incidence of AAA-related mortality in patients who underwent EVAR.

https://doi.org/10.1371/journal.pone.0349122.g002

Performance of the prediction model

To evaluate the performance of various survival prediction models for patients who underwent EVAR, a comparative analysis was conducted using the time-dependent C-index and the time-dependent Brier score. Fig 3a illustrates a comparative analysis of the time-dependent C-index for multiple predictive models, including the stacking-based ensemble model (Stacking), Cox Proportional Hazards (CoxPH), Gradient Boosting Survival analysis (GBSA), Random Survival Forest (RSF), and Extra Survival Trees (EXT). This evaluation was conducted at specific time points (30, 90, 180, 270, and 365 days) during the validation of the test set.

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Fig 3. Comparison of time-dependent C-index and Brier score in prediction models.

(a) Comparison of time-dependent C-index in prediction models. (b) Comparison of time-dependent Brier score in prediction models.

https://doi.org/10.1371/journal.pone.0349122.g003

Stacking consistently demonstrated superior time-dependent C-index values at each evaluated time point, beginning with the highest value of 0.759 at 30 days and declining to 0.716 at 365 days. Fig 3b presents a comparative analysis of the time-dependent Brier scores for the same predictive models. Across the evaluation period, an overall increasing trend in the time-dependent Brier scores was observed. All predictive models showed stable and consistent time-dependent Brier score values across the measured time points, with relatively minimal variation.

Variable importance

The top-ranked variable importance over time in Stacking, the model with the highest time-dependent C-index, was assessed using the permutation-based variable importance (S3 Table). At 30 days, the variable with the greatest importance was age, followed by weight, smoking, duration from diagnosis to surgery, and height (Fig 4a). At 365 days, age, weight, and smoking still remained the most important variables, while the importance of BMI, creatinine, systolic blood pressure (SBP), and diastolic blood pressure (DBP) increased (Fig 4b). In contrast, household income, GFR, and hypertension were no longer among the top 10 most important variables.

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Fig 4. Variable importance in a stacking ensemble model for AAA-related mortality.

(a) Top-ranked predictor importance for 30-day mortality in the stacking ensemble model using permutation feature importance. (b) Top-ranked predictor importance for 1-year mortality in the stacking ensemble model using permutation feature importance.

https://doi.org/10.1371/journal.pone.0349122.g004

We analyzed the influence of top-ranked variables on AAA-related mortality at 30 and 365 days. Fig 5 illustrates the relationship between these top-ranked variables and AAA-related mortality using partial dependence plots. To enhance interpretability, variables were grouped into three categories based on their temporal importance: variables important only at 30 days are shown in blue-shaded panels, those important only at 365 days in orange-shaded panels, and those important at both time points in gray-shaded panels.

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Fig 5. Partial dependence plots showing key predictors of AAA-related mortality in patients who underwent EVAR.

Predictors are color-coded by their importance for 30-day mortality (blue), 1-year mortality (orange), or both (gray).

https://doi.org/10.1371/journal.pone.0349122.g005

Specifically, age showed a sharp increase in AAA-related mortality risk in patients aged 70 years or older. Weight showed the lowest risk around 60 kg, with the risk increasing both above and slightly below this value. Smoking status showed that current smokers had the highest risk of AAA-related mortality. A longer duration from diagnosis to surgery was associated with a higher risk. Height showed an inverse relationship with mortality risk, with shorter individuals having a higher risk. Lower household income was linked to higher risk, with the highest risk observed in the Medical Aid group. GFR values below 80 mL/min/1.73 m² were associated with increased risk. AAA-related mortality risk increased progressively with creatinine levels above 0.8 mg/dL. SBP showed the lowest predicted risk around 120 mmHg. Risk increased at both lower and higher SBP levels, with a more notable increase at higher SBP.

Discussion

In the present study, we developed a stacking ensemble ML model to predict AAA-related mortality among patients undergoing EVAR, applying a time-to-event analysis framework. A key strength of this approach was the ability to evaluate how the relative importance of variables changed over different time points after EVAR, highlighting specific predictors of short-term (30-day) and long-term (365-day) AAA-related mortality. In addition, several predictors—such as age, smoking status, and the interval between diagnosis and surgery—showed consistent influence across both periods, representing persistent risk factors that were associated with outcomes regardless of time. Furthermore, our study employed partial dependence plots, which illustrated important nonlinear relationships between variables and mortality risk—relationships not typically captured by traditional statistical modeling methods. Our methodological framework provided valuable insights into both the temporal dynamics and nonlinear nature of baseline predictors, thereby supporting phase-specific and continuous risk stratification as well as data-driven clinical decision-making in EVAR-treated AAA patients. These findings extend prior evidence that socioeconomic and clinical variables derived from insurance claims data can yield clinically relevant prognostic information, even in the absence of detailed anatomical characteristics [30], highlighting the potential of real-world data to inform clinically meaningful temporal dynamics of risk evaluation.

Early postoperative mortality appeared to be more strongly associated with household income and baseline renal function as estimated by GFR. Lower household income was associated with higher 30-day AAA-related mortality, which may reflect differences in healthcare utilization, health behaviors, and broader socioeconomic circumstances [30]. For example, lower household income could be associated with variability in healthcare utilization levels [34,35], less favorable health behaviors such as smoking or inadequate weight management [36], and broader systemic barriers including limited health literacy, reduced access to continuous care, and difficulties engaging with healthcare services [37]. In the context of EVAR, these socioeconomic disparities may be associated with differences in access to care, medication adherence, and availability of recovery resources during the early postoperative period. In addition, lower estimated GFR was associated with early postoperative mortality, consistent with reduced physiological reserve. Unlike serum creatinine, which is affected by patient characteristics such as muscle mass, sex, and age, GFR provides a more direct estimate of renal filtration capacity and tends to decline earlier in the course of renal dysfunction [38]. This characteristic may account for its stronger association with early postoperative mortality observed in this study. Collectively, these findings suggest that early mortality after EVAR was more strongly associated with patient vulnerability and socioeconomic disadvantage, supporting the potential value of early identification and perioperative optimization in socially or medically high-risk groups.

At 365 days after EVAR, baseline serum creatinine and SBP were identified as two of the strongest predictors associated with long-term mortality. Creatinine showed a nonlinear association with mortality risk, remaining relatively stable within the normal range but gradually increasing at higher levels. This pattern may not directly indicate ongoing renal injury but rather reflect pre-existing mild kidney dysfunction or general health vulnerability present before EVAR [38,39]. Because serum creatinine is influenced by factors such as muscle mass, age, and overall metabolic status [38], elevated levels may serve as a proxy marker of broader systemic vulnerability rather than a direct causal factor of late mortality. Nonetheless, this finding aligns with prior studies indicating that even mild renal impairment before surgery is associated with poorer long-term outcomes after EVAR [38]. In contrast, GFR typically declines earlier in renal dysfunction, while creatinine tends to rise later [38], suggesting that these measures provide complementary but distinct clinical information about renal and overall health status at baseline.

SBP also exhibited a nonlinear relationship with mortality risk, with the lowest risk observed around 120 mmHg and increasing risk at both higher and lower SBP values. This U-shaped association suggests that sustained hypertension may contribute to vascular and graft-related stress, whereas excessive lowering of SBP may be associated with reduced organ perfusion and impaired recovery capacity. Prior evidence indicating that tight SBP control (<130 mmHg) is associated with a reduced incidence of type II endoleaks after EVAR further supports the clinical relevance of balanced hemodynamic management [40]. Collectively, these findings suggest that long-term mortality after EVAR is associated with both chronic renal vulnerability and nonlinear hemodynamic patterns, emphasizing the importance of continuous monitoring and optimization beyond the perioperative period.

Across both early and late postoperative phases, age, smoking, and the interval between diagnosis and surgery were consistently associated with AAA-related mortality. Age was identified as a key predictor, with a sharply increased risk observed beyond approximately 70 years. This pattern aligns with prior prognostic models for EVAR-treated patients, which stratified age into < 70, 70–74.9, 75–79.9, and ≥ 80 years, assigning progressively greater weights with increasing age [19]. Although age alone may not fully capture physiological heterogeneity, the consistently higher risk among older patients is consistent with a cumulative burden related to vascular aging, frailty, and comorbid burden that extends throughout the postoperative course. Smoking was also consistently associated with higher mortality, reinforcing its persistent role as a major modifiable risk factor contributing to both early and late adverse outcomes after EVAR [41].

A longer interval between AAA diagnosis and EVAR was also associated with higher AAA-related mortality. In this cohort, the mean duration from diagnosis to surgery was approximately 17 months. Although aneurysm size at diagnosis was not available, this finding may indicate that delayed surgical intervention reflects several overlapping factors rather than a single mechanism. First, some patients may have experienced rapid aneurysmal progression after diagnosis [42], particularly if their initial aneurysm was of moderate size. Second, delays in surgical referral or coordination within the healthcare system may have been associated with postponed intervention. Third, certain patients may have deferred surgery until symptom onset, leading to urgent or high-risk procedures once aneurysm expansion became clinically significant [43]. Taken together, these interpretations suggest that a prolonged diagnosis-to-surgery interval may represent a composite marker of inadequate follow-up, delayed clinical decision-making, or symptom-driven emergency repair, and was associated with worse postoperative outcomes.

A principal finding of this study is the time-varying nature of predictor importance for mortality after EVAR. The predictors of early (30-day) and late (365-day) mortality differed substantially, indicating potentially distinct clinical mechanisms [7,44]. Early mortality was more strongly associated with perioperative vulnerability—such as household income and reduced GFR— whereas late mortality showed stronger associations with chronic factors, including creatinine levels and BP control. These findings highlight that patient management after EVAR may benefit from a phase-specific approach, combining targeted perioperative care with long-term surveillance and chronic disease management.

This study applied a time-to-event stacking ensemble framework that enabled the identification of phase-specific and time-varying risk patterns for AAA-related mortality. By combining multiple base learners within a survival modeling structure, the approach allowed evaluation of how each predictor’s contribution changed over time, without relying on restrictive assumptions such as proportional hazards or linearity [27,28]. This framework also captured nonlinear relationships and interactions among predictors, providing a more flexible representation of the complex, multidimensional processes underlying post-EVAR outcomes. Similarly, previous research indicated that stacking ensemble techniques leverage the predictions of constituent models as input for a meta-learner, which can enhance predictive performance compared to other ensemble techniques [27,45]. However, as the model was not externally validated, the generalizability of these phase-specific patterns should be interpreted with caution. To enhance interpretability, permutation feature importance and partial dependence plots were used to visualize how each predictor was associated with model output [27,46]. Permutation analysis identified the variables that had the impact on prediction performance at 30 and 365 days, while partial dependence plots illustrated the nonlinear and time-dependent effects of key predictors such as household income, creatinine, and SBP. Together, these methods supported a data-driven understanding of how the relative influence of clinical and socioeconomic factors evolves across follow-up [27,46,47], representing an incremental extension over conventional survival analyses.

There are several limitations to this study. First, as a retrospective study based on nationwide Korean population data, it is subject to various biases, including selection bias. We therefore included all available data to minimize these biases. Second, identifying AAA and other risk factors solely based on diagnostic codes may have introduced inaccuracies. There is potential for outcome misclassification because AAA-related mortality was defined using cause-of-death codes without clinical adjudication, which may bias the estimated event rates. Nevertheless, most deaths were coded as I71, consistent with the definitions of AAA-related mortality commonly used in prior studies. Third, this study is subject to the inherent limitations of administrative data. Detailed anatomical and physiological information relevant to EVAR outcomes—such as aneurysm diameter, neck morphology, calcification, endoleak status, sarcopenia, cardiopulmonary fitness, or cardiac function—was unavailable, as were psychosocial factors like stress. Accordingly, our findings should be interpreted as risk predictions based on routinely collected administrative variables, rather than as substitutes for anatomical or procedure-specific risk assessments. Fourth, missing values in several clinical and laboratory predictors were addressed using simple mean imputation. For variables with substantial missingness, this method may reduce variability and affect the relative importance ranking of predictors. In our analyses, renal function markers (e.g., GFR and creatinine) were consistently identified as influential predictors despite potential variance attenuation. Future studies should consider alternative missing-data techniques such as multiple imputation to further assess the stability of predictor importance and model performance. Fifth, this study relied on internal validation using a hold-out dataset and did not include external validation with independent cohorts. Therefore, the reported discrimination and calibration may not fully represent the model’s performance across different clinical settings, time periods, or coding practices. Consequently, the model’s transportability requires further confirmation. Lastly, because the study population consisted entirely of Koreans, the model’s performance and the relative influence of predictors may vary in populations with different baseline risk profiles and healthcare systems, highlighting the need for external validation in diverse, international cohorts.

Conclusion

This study suggests the potential utility of a stacking ensemble machine learning approach for time-to-event prediction to enhance survival estimation after EVAR by identifying time-varying effects of key mortality predictors. Overall, age, smoking, and the duration between diagnosis and surgery consistently emerged as important risk factors. Household income and GFR were more strongly associated with early postoperative mortality, whereas baseline blood pressure and serum creatinine levels were key determinants of long-term outcomes. These findings indicate that ML-based approaches may support improved risk stratification and support phase-specific follow-up and management strategies for patients undergoing EVAR.

Supporting information