This was a multicenter, retrospective, observational cohort study that utilized admission clinical information from the electronic health record system. This study participant consisted of all elderly patients with aSAH within 24 h of onset who were admitted in the department of neurosurgery of several medical centers from April 2019 to June 2021, such as Renmin Hospital of Wuhan University, Huizhou Third People's Hospital, Affiliated Hospital of Panzhihua University, First Hospital of Shanxi Medical University, and General Hospital of Northern Theater Command. The elderly patients were defined as those aged 60 years and older. Out of all consecutive 215 patients, 153 eligible elderly patients with aSAH were eventually enrolled in our study. Figure 1 was a flowchart that showed exclusion details and the procedure of this study. Head CT, head and neck CT angiography, or intracerebral digital subtraction angiography was used for the diagnosis of aSAH.

The inclusion criteria were as follows: elderly patients aged over 60 years, admission within 24 h after onset, spontaneous SAH caused by aneurysm, head CT scan and blood laboratory tests within 24 h after admission, surgical treatment within 3 days after onset, and DCI after SAH occurred within 4–30 days.

The exclusion criteria included aSAH patients complicated with vascular malformation or intracerebral hemorrhage, postoperative state on admission, cases complicated by acute infection, permanent brain injuries or bilateral mydriasis, nonsurgical treatment, and larger missing data.

The patient clinical information that included sex, age, past medical history (hypertension, diabetes mellitus, coronary heart disease, smoking, and alcohol consumption), and admission state (World Federation of Neurosurgical Societies [WFNS], Hunt and Hess grade [HH], and modified Fisher scale [mFS]) was collected. In addition, aneurysmal details that included aneurysm location, number, length size, neck size, and surgical treatment method were recorded. Admission blood laboratory tests (D-dimer, glucose, white blood cell [WBC], neutrophil, lymphocyte, and monocyte counts) and CT value of subarachnoid clots and cerebral edema were also utilized in this study. The CT value evaluation method is provided in the Methods in the Data Supplement.

All hospitalized patients received standardized postoperative treatment based on the SAH guidelines (22), such as nimodipine to prevent vasospasms, anti-inflammatory drugs, hemostasis, and analgesic. A postoperative head CT scan was performed to determine the presence of intracranial rebleeding or cerebral infarction.

The definition of DCI is consistent with Vergouwen et al. (23). (1) No other cause could have led to the occurrence of a permanent or temporary focal neurological impairment (such as aphasia, apraxia, hemianopia, or neglect) between 4 and 14 days after aSAH; (2) the Glasgow Coma Scale score decreased by at least two points (either on one of its components [eye opening, verbal response, and motor response] or on total score); and (3) head CT scans revealed a low-density area that was not noticeable on admission or immediately after the operation, and there were no other causes except vasospasms between 4 and 30 days after aSAH.

Events per variable with a value of 10 was used to determine the effective sample size in our study (24). A total of six variables were entered into a multivariable regression model in our preliminary analysis. Hence, there should be at least 60 patients with DCI. In addition, according to the incidence rate of 30% of DCI occurrence after SAH worldwide, at least 200 patients should be enrolled in the model training cohort. Based on the limited effective sample size, the least absolute shrinkage and selection operator (LASSO) regression analysis was used to develop a conventional regression model.

A total of five elderly patients had missing data, which accounted for <5% of the patient population. Therefore, a direct deletion method was applied to process the data (25).

In this study, each patients with aSAH in the dataset was regarded as a single data point, clinical information measured at admission (demographic data, past medical history, WFNS grade, HH grade, mFS, aneurysm information, treatment methods, serum laboratory test, and image CT value) was used as feature input, and DCI occurred was used as the label of the algorithm. We randomly divided the multicentral data into the model development cohort and model validation cohort in a ratio of 70–30%. The training cohort of 111 patients was used to construct the conventional LASSO regression model and tree models, such as decision tree (DT), random forest (RF), eXtreme Gradient Boosting (XGBoost). We used grid search to find optimal parameters. Since the computational resource is limited, only some critical parameters are taken into account for each model. The searching range and steps of the chosen parameters for all investigated modes are listed below.

The LASSO regression, suitable for small sample size and high-dimensional data, was used to select the most informative prediction variables to construct the model. We used the “glmnet, corrplot, caret” packages of R and five-fold cross-validation to obtain the optimal λ and the variables selecting results.

Decision tree algorithms partition the sample data by splitting prediction features at discrete cut-points and are usually presented in the form of a tree. The DT algorithm uses the Gini index to determine each split's optimal variable and location in this study. The cost complexity parameter that penalizes more complex trees is used to control the size of the final tree. Several important parameters, such as max_depth, min_samples_split, min_samples_leaf, and max_leaf_nodes were adjusted by the 10-fold cross-validation and “rpart, partykit, caret” packages of R.

Random forest generates multiple DTs by sampling objects and variables, and then classifies the objects in turn to build a predictive model. Finally, to summarize the classification results of each DT, the mode category in all prediction categories is the category of the RF model prediction object. The important parameters, such as n-estimators, min_sample split, and min_sample_leaf, were determined using the 10-fold cross-validation and “randomForest” package.

The XGBoost is an optimized distributed gradient enhancement library whose design is efficient, flexible, and portable. An ML algorithm is implemented under the framework of gradient enhancement. XGBoost provides the promotion of parallel trees, such as gradient boosting decision trees, which can solve many data science problems quickly and accurately. The important parameters, such as gamma, subsample, nrounds, max_depth, eta, colsample_bytree, and min_child_weight were evaluated by “xgboost” package and a 10-fold cross-validation.

The area under the receiver operating characteristic (ROC) curve (AUC) with 95% CIs, a precision-recall curve, accuracy, sensitivity, and specificity were used to evaluate the model performance. Additionally, we calculated precision and recall indicators using a validation cohort. We used the optimalCutoff function to obtain the optimal threshold of the model outputs to evaluate the model performance. To better demonstrate the generalization of the above-mentioned models, we calculated those indices on both model training and validation cohorts. Furthermore, we compared the errors of the two cohorts to assess the considered models. Finally, to visualize the contribution of each clinical feature, feature importance calculated via the XGBoost method was generated to rank their relative influence on the risk of DCI development.

The Kolmogorov–Smirnov test was used to determine the distribution type of the data before formally analyzing the dataset. Continuous variables analyzed using the Mann–Whitney U-test, or independent t-test, is presented as a median with interquartile range (IQR) or mean ± SD. Categorical variables analyzed using the chi-square test, or Fisher's exact test are expressed as numbers (percentages). All statistical analyses were two-tailed, and the values of p lower than 0.05 were considered statistically significant. All statistical analyses in this study were completed using IBM SPSS Statistics for Windows, version 26.0 (IBM Corp., Armonk NY, USA) and R software (https://www.r-project.org/).

The mean age of elderly patients in the model training and validation cohorts was 67 years (IQR: 63, 71) and 66 years (IQR: 63, 69), respectively. We observed that elderly patients with aSAH were more likely to be women, and there were no significant distinctions in past medical history among the two cohorts. In addition, the admission state, aneurysmal information, admission laboratory results, CT value in subarachnoid clots, and cerebral edema had no significant differences between the two groups. The number of patients with DCI in the two groups was 31 (28%) and 11 (26%). Table 1 shows the baseline characteristics in training and validation cohorts. Moreover, we analyzed the baseline information of elderly patients with or without DCI in the training cohorts. Details are placed in Table 2.

The training process and optimal parameters of the LASSO and tree-based models are demonstrated in Figure 2. In the regression model, we used the LASSO method to select the optimal predictors. An optimal λ of 0.1356784 and log (λ) of −1.997 were adopted in LASSO, and Figure 2A demonstrates that 23 features finally decreased to two features when using the above parameters. The independent predictors were CT value in subarachnoid clots (adjusted odds ration [aOR]: 1.115, 95% CI: 1.028–1.220, p = 0.011) and aneurysm treatment method (aOR: 0.196, 95% CI: 0.067–0.522, p = 0.001) after the multivariable regression analysis. Min_samples_split, min_samples_leaf, and max_leaf_nodes were set to 2, 2, 0, respectively, and Figure 2B shows that the optimal decision nodes were CT values of subarachnoid clot and WBC count during the training process of DT. When n_estimators, min_sample_leaf, and min_sample_split indiceswere set to 63, 4, 2, respectively, and Figure 2C demonstrates that the minimum error was 0.05 corresponding to the optimal tree number of 63 during the training process of RF. Figure 2D displays the training process of XGBoost, and we can obtain the best prediction power when gamma of 0.25, subsample of 0.5, nrounds of 100, max_depth of 2, eta of 0.01, colsample_bytree of 1, and min_child_weight of 1. In addition, the optimal thresholds of LASSO, DT, RF, and XGBoost were 0.3, 0.13, 0.48, and 0.43, respectively.

When using the training cohort to evaluate the model performance, the LASSO model had a lowest AUC-ROC value of 0.793 (0.692, 0.893) than the single DT of 0.836 (95% CI: 0.747–0.926, p = 0.15), RF of 1 (95% CI: 1–1, p < 0.05), and XGBoost of 0.931 (95% CI: 0.885–0.978, p = 0.01). Moreover, the accuracy of 80.9% of the LASSO was lower than the RF of 85.7% and the XGBoost of 83.3%. However, the LASSO scored a highest AUC value of 0.894 (95% CI: 0.8–0.989) in external verification than DT of 0.764 (95% CI: 0.6–0.928, p = 0.05), RF of 0.821 (95% CI: 0.683–0.959, p = 0.27), and XGBoost of 0.865 (95% CI: 0.751–0.979, p = 0.69). Figure 3 shows the performance and evaluation of the LASSO regression model and tree ML models.

Table 3 illustrates the accuracy, specificity, sensitivity, precision, and recall indicators of the above models. As we can see, the RF model with an accuracy of 100% (100%) is higher than other models using the training cohort. However, its accuracy value decreased to 85.7% (83.7, 100%) in external validation cohort. On the contrary, the XGBoost model with an accuracy value of 87.4 and 83.3% had a stable performance in the two cohorts, and the DT model with an accuracy value of 81.1 and 78.5% performed the worst among all tree models. In the regression model, the LASSO model's accuracy improved by 3.5% from training to the external validation cohort. Moreover, the LASSO model had a higher precision and recall value of 62 and 90% than tree-based models in external validation. When evaluating the model performance using area under the precision-recall curve (AUC-PR), LASSO model scored a highest AUC-PR value of 0.681 than DT of 0.615, RF of 0.667, and XGB of 0.622 in external validation. Figure 4 shows the P–R curve and AUC value of all models.

As shown in the Supplementary Table 1, the errors of LASSO, DT, RF, and XGBoost in model training were 18.1, 20.5, 21.6, and 19.8%, respectively, while in the model validation cohort, the error percentage were 23.7, 26.9, 26.1, and 21.2%, respectively.

The feature importance was scaled so that the sum added up to 1, with a higher importance score indicating a stronger impact on the occurrence of DCI. The most important three features for DCI prediction in elderly patients were CT value pf subarachnoid clots (0.239), aneurysm therapy methods (0.184), and admission WBC counts (0.132). Figure 5 shows all admission clinical feature importance.