The Joint Institutional Review Board of Taipei Medical University (TMU-JIRB Approval No. N202103006) approved this study. For this retrospective study involving the secondary analysis of existing anonymized data, TMU-JIRB waived the requirement for informed consent. All experiments were performed in accordance with relevant named guidelines and regulations.

This study retrieved the medical records of patients who received stoke diagnoses and was treated at Taipei Medical University-Shuang Ho Hospital between January 2016 and June 2020 from the Taiwan Stroke Registry (TSR, http://taiwanstrokeregistry.org/TSR/), and retrospective analysis of the data was conducted. TSR is a multicenter database of the clinical data of patients with stroke admitted to major medical institutions in Taiwan (33).

The inclusion criteria were as follows: patients who (1) were 18 years or older, (2) received AIS diagnoses and were admitted and treated for AIS at our hospital, and (3) presented to the hospital within 10 days of AIS symptom onset (33). The exclusion criteria were as follows: patients who presented with acute intracranial hemorrhage, without a determined National Institutes of Health Stroke Scale (NIHSS) score on admission, or with incomplete registration information. All patients received non-contrast head computed tomography (CT) or brain magnetic resonance imaging (MRI) on admission. Two independent neurologists and a radiologist interpreted all CT/MRI images. Demographic data, including age, sex, and presence of cerebrovascular risk factors such as hypertension (HTN), diabetes mellitus (DM), hyperlipidemia, ischemic heart disease, atrial fibrillation (Af), and previous stroke, were collected at the presentation. Thrombolytic treatments for AIS, namely, intravenous thrombolysis (IVT) with or without endovascular thrombectomy (EVT) and non-thrombolysis, were also documented. Certified stroke specialists used the NIHSS to assess the overall severity of AIS. Blood cell counts, prothrombin time (PT), and activated partial thromboplastin time were measured at admission. Albumin, fasting glucose, glycated hemoglobin, triglyceride (TG), and low-density lipoprotein cholesterol (LDL) levels were measured within 72 h of access.

The LOS of each patient was defined as the time from admission to discharge from the hospital. Prolonged LOS was defined as the length of a hospital stay beyond the median LOS (34, 35).

All statistical analyses were conducted using Statistica version 13.3 (TIBCO Software Inc., Tulsa, Oklahoma, USA). Variables were summarized using descriptive statistics. Continuous variables are presented as medians (interquartile ranges [IQRs]), and categorical variables are expressed as counts and proportions (%).

Student's t-test was used to compare means between two groups of continuous variables. One-way ANOVA was used for comparing the means of ≥3 independent variables from the prolonged LOS and non-prolonged LOS groups. Pearson's chi-squared test was used to determine non-random associations between two categorical variables from the prolonged and non-prolonged LOS groups. All hypothesis tests were two-sided, with a p-value of 0.05 indicating significance.

The ANN applied in this study was a feedforward neural network of multilayer perceptrons with an input layer, a hidden layer, and an output layer. The ANN model used the standard backpropagation gradient estimation algorithm with a linear combination of input variables within the hidden layer that contained an intercept (bias) and the coefficient for each predictor. The neural networks were trained using the Broyden–Fletcher–Goldfarb–Shanno (BFGS) method (36). The variables used in the input layer included those associated with prolonged LOS in the study cohort (p < 0.05 by descriptive statistics, Table 1). Figure 1A shows the flow diagram for the development of the predicting models. Continuous variables included age, NIHSS score at admission, albumin level, fasting glucose level, hemoglobin level, white blood cell (WBC) count, PT, cholesterol level, and TG level. Categorical variables included initial thrombolytic treatments, Af, DM, HTN, and previous stroke. Categorical variables were inputted as neurons and converted using one-hot encoding. During the model training process, the search for optimal hyperparameters was performed with the following limits: 1 hidden layer, 1–50 neurons in the hidden layer, and the activation function was chosen to be either the exponential or the hyperbolic tangent function. The output layer contained two neurons, namely, “prolonged LOS” and “non-prolonged LOS.” The sigmoid activation function was used for the neurons in the output layer. All networks were trained using early stopping. We presented the network with an input-target pair from the training set and computed the predictions of the network for the targets. We used the cross-entropy error function to calculate the difference between the predictions of the network and the target values until all input-target pairs from the training set were presented to the network. The training algorithm was used to adjust the weights of the networks. The error of each training is compared with the error of the previous iteration. Training is continued if the error keeps decreasing; otherwise, training is stopped. All ANN models were developed using Statistica version 13.3 (TIBCO Software Inc.).

To avoid overfitting in the ANN model, we performed 5-fold cross-validation to assess the generalizability of the analysis results. The original sample was randomly partitioned into five equal-sized subsamples. In each repetition of the cross-validation process, one subsample was retained as the validation set, and the remaining four subsamples were used as the training set. The cross-validation process was repeated five times, and each of the five subsamples was used once as the validation set (Figure 1A). Model performance was evaluated based on receiver operating characteristic (ROC) curve analysis, and the area under the ROC curve (AUC) of the five training and validation sets was calculated to represent the level of discrimination. We chose the model with the highest AUC of the cross-validations for further analysis. After the models were developed, their mean accuracy, sensitivity, specificity, positive predictive value (PPV), and negative predictive value (NPV) were derived from the confusion matrix of the five validation sets (Figure 1A).

To understand the contribution of each predictor to the likelihood of extending LOS after AIS, we estimated the relative importance of each variable in the model as representative of that parameter's relative contribution to the ANN model. We performed a sensitivity analysis of each repetition of the 5-fold cross-validation and reported the mean values (37, 38).

Of the total 2,384 patients diagnosed with AIS and treated at Shuang Ho Hospital during the study period, 144 patients were excluded from baseline analyses because of incomplete registration information (142 with missing data on medical history, 1 with missing thrombolytic treatment records, and 1 without sex information). Consequently, 2,240 patients (844 women and 1,396 men) were included in the analysis (Figure 1B). The median age of the study cohort was 68 years, with an interquartile range (IQR) of 50–79 years. The median baseline NIHSS score at admission was 4 (IQR: 2–10) for the entire cohort. The median NIHSS scores at admission for patients who received non-thrombolytic treatment, IVT, and EVT were 4 (IQR: 2–8), 10 (IQR: 5–17), and 19 (IQR: 14.5–24) (p < 0.0001). The mean and median LOS of the entire cohort were 13.6 ± 11.3 and 9 days, respectively, with an IQR of 6–20 days (Table 1). Therefore, a prolonged LOS was defined as a length of stay of more than 9 days. Among patients, 1,101 (49.2%) had prolonged LOSs, with a median hospital stay of 20 days (IQR: 13–27).

Prolonged LOS was associated with different thrombolytic therapies. The median LOS of patients who received non-thrombolytic treatment, IVT, and EVT was 9 (IQR: 6–18), 13 (IQR: 7–25), and 20 (IQR: 9.5–28) days, respectively (p < 0.0001). Compared with patients without prolonged LOS, more patients with prolonged LOS were treated with IVT or EVT. Compared with patients without prolonged LOS, patients with prolonged LOS were older; had higher NIHSS scores at admission; had lower albumin, hemoglobin, serum cholesterol, and TG levels; were more likely to exhibit higher fasting glucose levels and WBC counts; and had longer PT upon hospitalization. Patients with prolonged LOS also had a higher prevalence of Af, DM, HTN, and previous stroke (Table 1).

We examined associations between prolonged LOS and neurological outcomes at discharge in patients with AIS. In the entire cohort, there were 1,368 patients (61.1%) who had unfavorable neurological outcomes, defined as a modified Rankin Scale (mRS) ≥ 2 at discharge. A higher proportion of the patients with prolonged LOS had unfavorable outcomes than did those with a shorter LOS (87.0 vs. 41.7%, odds ratio [OR] = 9.33; 95% confidence interval [CI] = 7.52–11.59; p < 0.0001). Univariable analysis showed that each day's increase in LOS was associated with a 1.2-fold increase in the risk of unfavorable AIS outcomes (95% CI = 1.18–1.22; p < 0.0001). For the AIS patients with and without a prolonged LOS, the median mRS at discharge was 4 (IQR: 3–4) and 1 (IQR: 1–2), respectively (p < 0.0001). As illustrated in Figure 2, the patients with a prolonged hospital LOS had a higher mRS score at hospital discharge than those without a prolonged LOS, indicating that a prolonged LOS is associated with less favorable outcomes in patients with AIS.

We used 14 baseline features associated with LOS (variables with a p-value of < 0.05 in Table 1) as input attributes to train the ANN models to predict prolonged LOS (Figure 3). As shown in Figures 1A, B, the 2,240 patients with AIS in the cohort were randomly partitioned into training and testing sets for 5-fold cross-validation. Table 2 shows that the baseline features remained identical across the five validation sets. Following adequate training, the models that achieved the best prediction performance after 5-fold cross-validation were the ANNs containing 5, 10, 20, 25, and 30 hidden neurons. The mean AUC was 0.808 ± 0.001 for the training set (Figure 4A) and 0.788 ± 0.007 for the validation set (Figure 4B). The confusion matrices of the five validation sets were shown in Figure 4C. The mean accuracy, sensitivity, specificity, PPV, and NPV of the five validation sets were 74.5 ± 1.1%, 74.9 ± 4.0%, 74.2 ± 2.8%, 75.2 ± 1.2%, and 73.9 ± 2.5%, respectively.

Sensitivity analysis was performed to assess the predictive value of each parameter. The ranking of predictor significance based on the mean predictive value from each repetition of 5-fold cross-validation is shown in Figure 5. The NIHSS score at admission, Af, receiving thrombolytic therapies, history of HTN, DM, and stroke history were the strongest predictors of prolonged LOS after AIS. The relative significances of predictors of each repetition during 5-fold cross-validation are reported in Supplementary Table 1.

To assess the performance and generalizability of the prediction model for different AIS treatments, we applied the developed ANN model separately for each treatment option, namely, IVT (n = 197), EVT (n = 109), and non-thrombolytic treatments (n = 1,934). As shown in Table 3, the mean AUCs for predicting prolonged LOS for the non-thrombolysis, IVT, and EVT groups were 0.805 ± 0.005, 0.776 ± 0.049, and 0.696 ± 0.054, respectively. This finding indicates that the model exhibited better predictive power for the non-thrombolytic and IVT groups than for the EVT group.

To compare the performance of the ANN model to different prediction machine learning algorithms, we included the following models to predict prolonged LOS: logistic regression, support vector machine, gradient boosting tree, and random forest. All models were trained using the 14 baseline features and validated through 5-fold cross-validation. Model performance was evaluated based on the five validation sets' mean AUC, accuracy, sensitivity, specificity, PPV, and NPV of each model. We presented the various parameters used for the models in Supplementary Table 2. The results of the comparison of the five machine learning models are reported in Table 4 and showed that ANN obtained the highest AUC, accuracy, sensitivity, PPV, and NPV when compared to the other models.

Stroke remains a leading cause of death and disability globally, and its disease and healthcare burden have increased over the past three decades (1, 2, 4). The physical and economic impacts of stroke on patients and their families have been well documented, which has increased the impact of stroke on public health (1–3). The stroke-related disability may cause prolonged LOS at hospitals and the requirement for rehabilitation, and greater LOS invariably indicates greater economic losses (7, 13). Previous studies have provided robust evidence that LOS is a major determinant of costs for patients with AIS. Prolonged hospitalization days are inevitably accompanied by an increase in medical costs, such as the consumption of beds, medications, care, and health resources. Complications associated with prolonged LOS negatively impact the prognosis and quality of life of patients with AIS and may increase the drain on medical resources and the financial burden on patients (17, 19, 20). Therefore, studies such as the present one identifying the independent predictors of LOS and developing reliable prediction methods are warranted and essential to provide data for improved decision-making related to disease management, care resource allocation, and prediction of treatment cost-effectiveness, consequently contributing positively to the individual or national healthcare management budgeting (14).

Our report showed that prolonged hospital stays are associated with worse outcomes for patients with AIS. In this study, an ANN-based model was applied to predict the risk of prolonged LOS based on the baseline characteristics of patients with AIS at admission. The ANN model achieved effective validation with an AUC of 0.788 and validation accuracy, sensitivity, specificity, PPV, and NPV of 74.5, 74.9, 74.2, 75.2, and 73.9%, respectively. These results indicate adequate discriminative power and effective prediction of the risk of prolonged LOS after AIS. Sensitivity analysis using our ANN prediction model also demonstrated that among the baseline characteristics, the NIHSS score at admission, comorbid Af, thrombolytic therapy type, HTN, DM, and history of stroke were critical predictors of prolonged LOS. These findings are consistent with a Poisson analysis-based report demonstrating that IVT and Af are significantly associated with LOS following AIS, regardless of stroke severity, age, comorbidities, or complications (39).

Evidence exists that prolonged LOS is associated with poor functional outcomes and unfavorable discharge disposition in patients with AIS (17, 40). This is in concordance with current evidence that patients with a prolonged LOS exhibited a 9.3-fold higher risk of unfavorable AIS outcomes at discharge than their non-prolonged LOS counterparts. Patients with a severe disability after AIS usually need to be hospitalized for a more extended period because they may require more treatments and rehabilitation support (41–43). Although it is challenging to accurately predict LOS because of the multifactorial nature of stroke, its prediction is of paramount clinical relevance. It is generally understood that patients with initial severe motor impairment, lower functional disability levels, and a greater stroke volume might have greater LOSs and less favorable outcomes (14, 41–44). However, these correlations are not always precise because various cofactors, including patients' medical condition, stroke subtype, prehospital and in-hospital treatment, or poststroke complications, often influence the final clinical outcomes and LOS of patients with stroke (12, 13, 18, 40, 42, 45). In addition, family support and socioeconomic status affect recovery and are also the determinants of AIS-associated LOS (41, 43). Chang et al. (13) noted that stroke severity is generally associated with prolonged LOS; however, this relationship is not absolute and linear. As concluded by Bindawas et al. (46), “a short or intermediate LOS is not necessarily associated with worse outcomes, assuming adequate care is provided.”

Stroke severity is widely used for predicting prolonged LOS after AIS (13, 18, 21, 40, 42, 47). The NIHSS is a 15-item neurological examination scale with scores ranging from 0 to 42, with higher scores indicating greater stroke severity (13, 27, 40). It has been reported that for mild to moderate AIS with an NIHSS score of ≤ 15, each 1-point increase in the NIHSS score increases LOS by ~1 day, whereas for severe stroke with NIHSS scores of >15, each 1-point increase in NIHSS score causes a decrease in LOS by ~1 day, which is attributable to the high mortality rate (13). Further significance of the NIHSS score for LOS lies in evidence from retrospective AIS treatment studies, which suggested that stroke patients who benefit most from thrombolytic therapy are those with an NIHSS score of 4 to 25 on admission, whereas patients with an NIHSS score of 5 or less are more likely to be discharged home (48, 49). Patients with scores between 6 and 13 usually require inpatient rehabilitation, potentially increasing the likelihood of prolonged LOS (27, 49). In this study, our ANN model identified the NIHSS score as the strongest predictor of prolonged LOS among all variables studied. Its importance consistently ranked first in each iteration of the 5-fold cross-validation.

Consistent with our findings, specific baseline characteristics and preexisting medical conditions, including Af, HTN, DM, and previous stroke, are significant predictors of prolonged LOS in patients with AIS (12, 13, 22, 40, 45). Most of these factors associated with prolonged LOS exhibit varying prognostic relevance, thus providing some evidence-based rationale for their application as input attributes for constructing reliable prediction models. Furthermore, our improved understanding of these factors can enable the correction of modifiable risk factors, facilitate the early detection of high-risk patients, and inform disease progression, monitoring, and treatments to improve AIS outcomes. For instance, a prolonged LOS related to Af may be due to the need for anticoagulation management or cardiac evaluation. Careful monitoring of fluid and electrolyte status to prevent arrhythmic states in patients with AIS, appropriate ECG monitoring for early detection of Af, and timely anticoagulation therapy may limit the length of hospital stay (40, 50, 51). HTN and DM are modifiable risk factors of prolonged LOS in our ANN model, suggesting that controlling these factors through preventive medicine may not only reduce the risk of ischemic stroke prevalence but also reduce LOS and improve prognosis after a stroke (51). In addition, some laboratory data at the time of admission, including patients' fasting glucose and cholesterol levels, despite their relatively modest importance in our ANN model as predictors, play a role in the predictions. Providing appropriate treatment protocols for patients with AIS to optimize these profiles may further assist in reducing LOS, thereby mitigating the economic cost of AIS to individuals and society.

IVT and EVT to restore perfusion to the ischemic areas of the brain are the standard of care for patients with AIS (48), and hospital LOS is primarily affected by therapy success (21, 52). In our cohort, patients who received IVT or EVT treatment had significantly longer LOS than those who received non-thrombolytic treatment. The prolonged LOS and the effectiveness of treatment may be related to initial stroke severity or varying indications for IVT or EVT in treated patients (48). Consistent with the findings of Kasemsap et al. (39), in our study, the thrombolytic therapy type was identified as an essential predictor in our model. It is clinically relevant that our prediction model not only provides personalized estimates of risk stratification for prolonged LOS for patients receiving different therapies but also provides information that enables vital shared decision-making by patients, their families, and healthcare professionals based on the patient's condition and informed treatment preferences.

Predicting LOS for patients with AIS is associated with some well-documented challenges or limitations (13, 21–23, 41, 42). The 8-point Stroke subtype, Oxford Community Stroke Project classification, Age, and prestroke modified Rankin (SOAR) score based on the analysis of the data from three UK stroke registers (n = 12,355 patients with stroke) exhibited poor discrimination with an AUC of 0.61 for predicting LOS (23). The AUC was slightly higher in another model based on the International Classification of Functioning, Disability, and Health (ICF) generic set from China (50 medical centers), with a barely acceptable AUC of 0.699 (42). Similarly, Koton et al.'s prolonged LOS score based on stroke severity and type, decreased level of consciousness on admission, history of congestive heart failure, and prior Af achieved an AUC of only 0.680 in the validation cohort (22). Hung et al. (21) applied four variables, namely, NIHSS score at admission, IVT, low WBC count at admission, and age, to construct classification and regression trees for LOS prediction, and the results revealed an acceptable AUC of 0.701, with a prediction accuracy of 0.674. Other LOS prediction models included the classification of AIS subtypes as an attribute but did not yield greater discrimination power (53, 54). Considering that the accurate classification of stroke subtypes usually requires a complete investigation and elucidation of stroke etiology, we excluded the stroke subtype as a predictor in this study, which was aimed at developing a prediction model that is workable at the point of hospitalization. A recent study evaluated 30 potential predicting variables to predict LOS and found the models only explained < 25% of the LOS variance (41). The survey by Kurtz et al. (55) enrolled 16,592 stroke patients admitted to the ICU using premorbid conditions, multiple organ dysfunction parameters, and acute neurological aspects as contributing variables and compared seven different types of machine learning models to predict prolonged LOS, which yielded an AUC of 0.73 by the random forest model. Although the performance of each of the aforementioned models depends on the definition of the prolonged LOS threshold and the included population, most of the models exhibited mild–moderate predictive power. This limited predictive power may be related to the complex and multifactorial nature of AIS-associated LOS, which affects the estimate accuracy in prediction models and scoring systems. Thus, it is clinically significant that our present ANN models achieved AUCs of 0.808 and 0.788, indicating excellent discrimination power between patients with prolonged LOS and non-prolonged LOS.

Adaptive computing methods in machine learning and artificial intelligence that provide enhanced data interpretation capabilities and expand the design of efficient diagnostic and predictive tools continue to be broadly applied at the frontiers of disease management, supporting clinical decision systems (25, 29, 31, 32, 56, 57). In the literature, only a few published studies have used ANN to predict LOS in stroke patients, and neural network techniques have generally yielded good predictive capabilities (58, 59). In this study, we utilized ANN-based classifiers to develop prediction models, which generated decision signals based on weighted sums of evidence (29–31). As per available data, the relationship between predictors and outcomes is complex and multidimensional; as a machine learning tool, ANNs can analyze these complex correlations to achieve the desired effectiveness (26, 27, 29–31). Our study demonstrated the feasibility of using ANNs to predict LOS in patients with AIS. ANNs identified factors associated with prolonged LOS for establishing interventions and ensuring timely management. These factors are clinically relevant, particularly in patients with identified underlying medical conditions strongly associated with prolonged LOS. As demonstrated in this study, ANN-based algorithms can analyze large-scale and non-linear data for developing new integrated methods, including different informatics features to predict LOS in patients with AIS. This enables healthcare stakeholders to use patient information obtained at admission to estimate the risk of prolonged LOS, share clinical and cost decisions, provide treatment options during hospitalization, and arrange referral pathways after discharge. For patients at high risk of prolonged LOS, hospital management can adjust strategies accordingly to improve the allocation of health resources, and insurance providers can develop reimbursement policies. This prediction model can help governments improve resource allocation, project cost-effectiveness, and contribute to individual and national health insurance budgets.

Our study has some limitations. First, this was a single-center study with a moderate sample size (n = 2,240) and without an external validation dataset. Therefore, further generalization of the developed model requires a large multicenter cohort with extensively varied characteristics that represent the disease population to be conducted, which can also validate our results. Second, this observational study may have been affected by unmeasured confounding variables. Similar to most contemporary models, this study did not consider the effects of differences related to socioeconomic status and medical service heterogeneity on LOS (41–43, 60), which may affect the model's predictive power. However, in Taiwan, the high coverage provided by the national health insurance system (61) reduces the relative inconsistency of medical care services, making our model more clinically applicable. Third, our estimates were generated at the time of admission and did not include poststroke complications or stroke subtypes that caused prolonged LOS during hospitalization (12, 18, 40), limiting model validity. Fourth, our study considered LOS in a single center during the acute phase, excluding the days a patient with stroke may have spent in rehabilitation or in a long-term care facility after stabilization of stroke. This may limit the predictive accuracy of the model.