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The healthcare industry is one application for data envelopment analysis (DEA) that can have significant benefits for standardizing health service delivery. This narrative review focuses on the application of DEA in emergency departments (EDs) and the management of emergency conditions such as acute ischemic stroke and acute myocardial infarction (AMI). This includes benchmarking the proportion of patients that receive treatment for these emergency conditions. The most frequent primary areas of study motivating work in DEA, EDs and management of emergency conditions including acute management of stroke are sorted into five distinct clusters in this study: (1) using basic DEA models for efficiency analysis in EDs, i.e., applying variable return to scale (VRS), or constant return to scale (CRS) to ED operations; (2) combining advanced and basic DEA approaches in EDs, i.e., applying super-efficiency with basic DEA or advanced DEA approaches such as additive model (ADD) and slack-based measurement (SBM) to clarify the dynamic aspects of ED efficiency throughout the duration of a first-aid program for AMI or heart attack; (3) applying DEA time series models in EDs like the early use of thrombolysis and percutaneous coronary intervention (PCI) in AMI treatment, and endovascular thrombectomy (EVT) in acute ischemic stroke treatment, i.e., using window analysis and Malmquist productivity index (MPI) to benchmark the performance of EDs over time; (4) integrating other approaches with DEA in EDs, i.e., combining simulations, machine learning (ML), multi-criteria decision analysis (MCDM) by DEA to reduce patient waiting times, and futile transfers; and (5) applying various DEA models for the management of acute ischemic stroke, i.e., using DEA to increase the number of eligible acute ischemic stroke patients receiving EVT and other medical ischemic stroke treatment in the form of thrombolysis (alteplase and now Tenecteplase). We thoroughly assess the methodological basis of the papers, offering detailed explanations regarding the applied models, selected inputs and outputs, and all relevant methodologies. In conclusion, we explore several ways to enhance DEA's status, transforming it from a mere technical application into a strong methodology that can be utilized by healthcare managers and decision-makers.
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