## 1 Introduction  
[PERSON] et al. (2019) [1] state that a key issue in emergency rooms is classifying patient severity based on their initial state, enabling appropriate on-site treatment, and [PERSON] et al. (2022) [2] and [PERSON] et al. (2022) [3] analyze the early identification of high-risk patients to improve survival rates. According to [PERSON] et al. (2022) [4] and [PERSON] et al. (2023) [5], this requires extensive data analysis, where the current method involves transferring data to a central data center for processing and analysis. However, centralized data analysis has drawbacks. Firstly, [PERSON] et al. (2020) [6] and [PERSON] et al. (2021) [7] state that medical data are highly sensitive and centralizing them poses privacy risks. Secondly, [PERSON] et al. (2022) [8] and [PERSON] et al. (2020) [9] propose that integrating data from multiple emergency rooms is challenging due to privacy regulations and inconsistencies in data formats among institutions. Thirdly, [PERSON] (2022) [10] explores how delays and additional costs associated with data centralization can degrade model performance and utility. According to [PERSON] et al. (2021) [11], [PERSON] et al. (2020) [12] and [PERSON] et al. (2020) [13], federated learning (FL) is a solution to these issues. FL analyzes local data in situ at each institution and transmits only the learning results to a central server, creating and sharing a global model while safeguarding data privacy and minimizing the risks and costs associated with data movement. Despite its advancements, [PERSON] et al. (2017) [14] explain that FL faces challenges with computational efficiency and prediction performance. Existing FL often randomly involves clients in the learning process, potentially negatively impacting FL performance and introducing uncertainty. Furthermore, according to [PERSON] et al. (2018) [15], disparate computational capacities among clients can increase computational load and extend training time. [PERSON] et al. (2021) [16], [PERSON] et al. (2022) [17] and [PERSON] et al. (2020) [18] state that not all clients contribute equally to FL performance; some may introduce noise or bias due to non-IID data quality and heterogeneity. To address these issues, this work proposes a new client selection algorithm designed to improve the overall efficiency and effectiveness of FL, as shown in Figure 1. This algorithm performs client selection by evaluating the client's local model (LMECS). The global model is updated by aggregating the parameters of the selected local model. The proposed LMECS utilizes a metric-based evaluation system to determine the contribution of each client's local model to the improvement of the global model's performance. Clients possessing models that meet specific performance criteria such as loss, accuracy, and area under the ROC curve (AUC) are given priority in the aggregation process for creating the global model. This not only accelerates the performance improvement of the global model but also increases resilience against data discrepancies and anomalous client updates. By proposing this LMECS, this work aims to not only comply with the stringent privacy requirements for medical data but also to present an advanced FL model that shows superior performance metrics compared to existing FL algorithms. Through this work, the goal is to extend to the rapid and accurate identification of high-risk patients in emergency rooms without data sharing, potentially improving patient outcomes and operational efficiency within the healthcare system. This work contributes in the following ways:  
* FL-based Severity Analysis of Patients: By utilizing FL technology, this work overcomes the limitations of traditional centralized data collection and analysis, enabling accurate analysis of the severity of patients in multi-institutional emergency rooms while maintaining data privacy.